ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Dynamical models of the tidal disruption of Ser have been prescuted by umucrous authors., Dynamical models of the tidal disruption of Sgr have been presented by numerous authors.3 present models that seek to account for the distance to. aud radial velocity of. the M-giauts of (2003).," present models that seek to account for the distance to, and radial velocity of, the M-giants of ."4. απ include further observational constraints from the SDSS reearding the distance o the Ser leading arm., and include further observational constraints from the SDSS regarding the distance to the Sgr leading arm.5 A common feature of these studies is that while they manage to qualitatively match the features of the stream. hey do not provide a consistent model for the shape of the Milkv Wass dark matter halo.," A common feature of these studies is that while they manage to qualitatively match the features of the stream, they do not provide a consistent model for the shape of the Milky Way's dark matter halo."6 In ouwtieulu. the leading material is best matched wean oblate halo. whereas the trailing material is best matched by a prolate figure 2005).," In particular, the leading material is best matched by an oblate halo, whereas the trailing material is best matched by a prolate figure ."7. demoustrates that bv adopting a triaxial halo model. rather than the asisvinetric models assumed iu the studies above. a concordant solution is achievable.," demonstrates that by adopting a triaxial halo model, rather than the axisymetric models assumed in the studies above, a concordant solution is achievable."8 However. as point out the solution is somewhat unsatisfactory since such a configuration is expected to be dynamically uustable.," However, as point out the solution is somewhat unsatisfactory since such a configuration is expected to be dynamically unstable."9 While the above uncertainties remain in the modeling of the orbit of Ser. the portinent features for the present study are that stars are released prefercutially during perigalactic passage with an orbital period of 0.55 Cyr2005).," While the above uncertainties remain in the modelling of the orbit of Sgr, the pertinent features for the present study are that stars are released preferentially during perigalactic passage with an orbital period of $\sim0.85$ Gyr."10". Consequently, our sample at A.=66"" was ost from Ser on the preseut perigalactic passage approximately 0.5 Car ago. and the Αιξ"" saluple was lost ~1.3 Cer ago on the previous passaee of Ser2005)."," Consequently, our sample at $\Lambda_{\odot}$ $^{\circ}$ was lost from Sgr on the present perigalactic passage approximately 0.5 Gyr ago, and the $\Lambda_{\odot}$ $^{\circ}$ sample was lost $\sim1.3$ Gyr ago on the previous passage of Sgr."11. Studies of the star formation history of the nain body of Ser have revealed a complex and protracted star formation historv with three uajor phases., Studies of the star formation history of the main body of Sgr have revealed a complex and protracted star formation history with three major phases.12 These studies fiud an old (11 Cox) uetal-poor population of ΙΓΤΗ ~—1.3 dex. a dominant intermediate age population (61.5 Car. with possible bursts) with |Fe/Il] ~0.6 dex aud a young (2.3 Cxr) population of [Fe/T]| ~(.lto 0.1 dex.," These studies find an old (11 Gyr) metal-poor population of [Fe/H] $\sim -1.3$ dex, a dominant intermediate age population (6–4.5 Gyr, with possible bursts) with [Fe/H] $\sim -0.6$ dex and a young (2–3 Gyr) population of [Fe/H] $\sim -0.4$ to $-0.1 $ dex."13 If the ageanectallicity relation (AMR) of Ser was spatially uniform then we would expect our samples of Me-giauts to possess the metallicity appropriate for their relatively voung age (72 3 Car). namely OL< ο οἱ dex (as dominates the core sample).," If the age-metallicity relation (AMR) of Sgr was spatially uniform then we would expect our samples of M-giants to possess the metallicity appropriate for their relatively young age $\sim$ 2–3 Gyr), namely $-0.4 <$ [Fe/H] $< -0.1$ dex (as dominates the core sample)."14 Furthermore we would expect a ucelicible uctallicity eradieut in the debris stream., Furthermore we would expect a negligible metallicity gradient in the debris stream.15 Our observations imply that the progenitor of ie present-day Ser did not possess a spatially awitorm AMIR., Our observations imply that the progenitor of the present-day Sgr did not possess a spatially uniform AMR.16 Seen another wav. the time between verigalacticons does not allow sufficient time for themically homogeneous iu-itu clevation of the nean |Fo/TI] to the levels we observe between successive orbits.," Seen another way, the time between perigalacticons does not allow sufficient time for chemically homogeneous in-situ elevation of the mean [Fe/H] to the levels we observe between successive orbits."17 Rather. as recognised by(2007).. the abundance gradient observed nust arise due to the stripping of the outer regions of the Ser progenitor over which a metallicity eradieunt (and/or concomitant age gradient) was oyeseut.," Rather, as recognised by, the abundance gradient observed must arise due to the stripping of the outer regions of the Sgr progenitor over which a metallicity gradient (and/or concomitant age gradient) was present."18 Tudeed such population eradicuts are typically observed iu dwarf ealaxies., Indeed such population gradients are typically observed in dwarf galaxies.19 As reviewed by(2009).. dwarf irregular galaxies universally show extended envelopes dominated by old ROB stars.," As reviewed by, dwarf irregular galaxies universally show extended envelopes dominated by old RGB stars."20 Such haloes of oldintermediate age stars are seen across a range of ealaxy Iuninosity aud wader a range of tidal conditious., Such haloes of old–intermediate age stars are seen across a range of galaxy luminosity and under a range of tidal conditions.21 Stellar population eradieuts are notably less distinct amongst the local dSph galaxies., Stellar population gradients are notably less distinct amongst the local dSph galaxies.22 However. gradieuts iu the morphology of the horizoutal brauch are not nconmuuon aud are indicative of metallicity and/or age eradieuts2001).," However, gradients in the morphology of the horizontal branch are not uncommon and are indicative of metallicity and/or age gradients."23. It is plausible therefore. that the original Ser progenitor possessed an extended :id correspondinely metallicity segregated. halo consistent with our observations.," It is plausible therefore, that the original Sgr progenitor possessed an extended and correspondingly metallicity segregated, halo consistent with our observations."24 As Ser experienced strong tidal interaction with the Milky Wav. the tidal radius of," As Sgr experienced strong tidal interaction with the Milky Way, the tidal radius of"25"running through the rregion, which are replenished by material from the accretion flow.","running through the region, which are replenished by material from the accretion flow."26 The emission of this dense gas is what creates the shell., The emission of this dense gas is what creates the shell.27 Another example is shown in the lower left panel of Figure 3.., Another example is shown in the lower left panel $_2$ ) of Figure \ref{emission}.28 It shows a dense blob of gas that is externally(a2) irradiated by a massive star and creates a peak that appears to indicate the position of a second star., It shows a dense blob of gas that is externally irradiated by a massive star and creates a peak that appears to indicate the position of a second star.29" Obviously, peaks in emission maps are not an ideal guide to the coordinates of stars."," Obviously, peaks in emission maps are not an ideal guide to the coordinates of stars."30 The aforementioned shocks contribute largely to the emission seen in the maps., The aforementioned shocks contribute largely to the emission seen in the maps.31 The middle panels (b1) and (b3) in Figure 3 show an edge-on view of the rotationally flattened structure of the star cluster., The middle panels $_1$ ) and $_2$ ) in Figure \ref{emission} show an edge-on view of the rotationally flattened structure of the star cluster.32 The upper panel (bi) shows that the most massive star has created a cometary rregion., The upper panel $_1$ ) shows that the most massive star has created a cometary region.33 TheH lower panel (05) displays the same region 200 yr later.," The lower panel $_2$ ) displays the same region $200\,$ yr later."34 T'he ionizing radiation has blown away gas from the accretion flow close to the protostar., The ionizing radiation has blown away gas from the accretion flow close to the protostar.35 This shock runs away from the star and creates a filament of strong emission across the rregion., This shock runs away from the star and creates a filament of strong emission across the region.36 The right-hand plots (οι) and in Figure 3 show the same region face-on., The right-hand plots $_1$ ) and $_2$ ) in Figure \ref{emission} show the same region face-on.37" From (cg)this viewing angle, the shock shows up as shell-like structure."," From this viewing angle, the shock shows up as shell-like structure."38" This demonstrates that the shell does not trace the edge where the ionizing radiation hits the accretion disk, but rather shocks generated from inflowing gas."," This demonstrates that the shell does not trace the edge where the ionizing radiation hits the accretion disk, but rather shocks generated from inflowing gas."39 The shell-like structures around accreting protostars can be interpreted as indirect evidence for the accretion process., The shell-like structures around accreting protostars can be interpreted as indirect evidence for the accretion process.40 The origin of the shell morphology changes when accretion ceases., The origin of the shell morphology changes when accretion ceases.41 Figure 4 shows the late-stage evolution of the star cluster., Figure \ref{bubble} shows the late-stage evolution of the star cluster.42" The most massive star has stopped accreting, allowing its rregion to begin to expand quickly into the ambient gas."," The most massive star has stopped accreting, allowing its region to begin to expand quickly into the ambient gas."43 The left-hand plots and show the expanding rregion face-on in the upper panel (a1) and edge-on in the lower panel (a2)., The left-hand plots and show the expanding region face-on in the upper panel $_1$ ) and edge-on in the lower panel $_2$ ).44" Here, the strong shell-like emission clearly comes from the dense gas in the rotationally flattened structure around the protostar rather than from a shock launched by the protostar."," Here, the strong shell-like emission clearly comes from the dense gas in the rotationally flattened structure around the protostar rather than from a shock launched by the protostar."45" While the accretion onto the most massive star has stopped and cannot directly affect the structure of the growing rregion any more, it can still be influenced by other stars that interact with the gas."," While the accretion onto the most massive star has stopped and cannot directly affect the structure of the growing region any more, it can still be influenced by other stars that interact with the gas."46 Two such events occur in run B and are shown in Figure 4.., Two such events occur in run B and are shown in Figure \ref{bubble}.47 The middle panels (b;) and (05) show a time sequence of a 7.8M star approaching the rim of the shell.," The middle panels $_1$ ) and $_2$ ) show a time sequence of a $7.848M_\odot$ star approaching the rim of the shell."49 Its ionizing radiation is strong enough to create sufficient thermal pressure to blow away the rim of the shell from its direct neighborhood., Its ionizing radiation is strong enough to create sufficient thermal pressure to blow away the rim of the shell from its direct neighborhood.50" The right-hand panels (b3) and (b4) show the same star 8200 yr later, when it has already entered the compact rregion."," The right-hand panels $_3$ ) and $_4$ ) show the same star $8200\,$ yr later, when it has already entered the compact region."51 Now its ionizing radiation can freely expand., Now its ionizing radiation can freely expand.52 The gravitational attraction of the star is strong enough to pull along a dense stream of gas., The gravitational attraction of the star is strong enough to pull along a dense stream of gas.53 This stream allows the star to grow in mass although it has entered the rregion filled with underdense gas., This stream allows the star to grow in mass although it has entered the region filled with underdense gas.54 This suggests that deformed shells could be indicative of stars inside rregions., This suggests that deformed shells could be indicative of stars inside large-scale regions.55Alveady from this one sees that a spherical solution. iu eq. (3)).,"Already from this one sees that a spherical solution, in eq. \ref{eq:plus}) ),"56 must have different radial y.ructure for the immer and outer solutions (because 1ο only solutious are à=αν 2). and hence one nay expect to fud different density profiles in ie central and outer regions.," must have different radial structure for the inner and outer solutions (because the only solutions are $\alpha = 1,57-2$ ), and hence one may expect to find different density profiles in the central and outer regions."58 We poiut out that such phenomenon of simultaneous existeuce of two How patterus is rather common in hydrodyuanuics. ie sniplest may be the τας jump which is observed as a several centimetre large circular rine in any kitchen sink. when the flowing water goes roni a l/r profile to a constant. see Hausenoetal.(1997):Watanahee (2003).," We point out that such phenomenon of simultaneous existence of two flow patterns is rather common in hydrodynamics, the simplest may be the hydraulic jump which is observed as a several centimetre large circular ring in any kitchen sink, when the flowing water goes from a $1/r$ profile to a constant, see \citet{hansen97,bohr}."59. We emphasize hat a non-zero viscosity appears to be a necessary condition for the existence ofthese specific solutions. even though a fundamental uuderstaudiug of how he microscopic physics (viscosity) can deteruiue hne macroscopic propertics (the eecneral flow ραΤο) is still eeuerallv niiissing iu hivdrodyuauies.," We emphasize that a non-zero viscosity appears to be a necessary condition for the existence of these specific solutions, even though a fundamental understanding of how the microscopic physics (viscosity) can determine the macroscopic properties (the general flow pattern) is still generally missing in hydrodynamics."60 From the O-equation. we ideutified the general flow pattern. aud we noticed the possibility that one nav have different velocity-flows in the ΠΙΟ: and outer region.," From the $\Theta$ -equation, we identified the general flow pattern, and we noticed the possibility that one may have different velocity-flows in the inner and outer region."61" We will now use the ¢,-cquation to try to extract the asviuptotic radial density profiles.", We will now use the $v_r$ -equation to try to extract the asymptotic radial density profiles.62 Also the r-equation is very simple where p ds the radially depeucent density. P is the pressure. G ds the eravitational constant. and Ar) is the mass within the radius r.," Also the $r$ -equation is very simple where $\rho$ is the radially dependent density, $P$ is the pressure, $G$ is the gravitational constant, and $M(r)$ is the mass within the radius $r$ ."63" We asstuue that the pressure aud density are related through P=P,(p/p,):. where P, and p, are the πικονα pressure and density at εν"," We assume that the pressure and density are related through $P = P_\alpha\, (\rho/\rho_\alpha)^\gamma$, where $P_\alpha$ and $\rho_\alpha$ are the unknown pressure and density at $r_\alpha$."64 We assume the gas is monatomic with +=5/3., We assume the gas is monatomic with $\gamma=5/3$.65 Let us consider densities of the form such that the parameter ο) determincs the density profile., Let us consider densities of the form such that the parameter $\beta$ determines the density profile.66 I is worth cuphasisine that it is exactly this 9 which we are trvine to find., It is worth emphasising that it is exactly this $\beta$ which we are trying to find.67 Let us study he radial depenudeuce of the 3 terms in eq. (5))., Let us study the radial dependence of the 3 terms in eq. \ref{eq:vr}) ).68 Usine eo im eq. (1)), Using $v_\Theta$ in eq. \ref{eq:v}) )69" the first (kinetic). term, of eq. (5))", the first (kinetic) term of eq. \ref{eq:vr}) )70" goes likeB eg/rDior7""Pil", goes like $v_\theta^2/r \sim r^{2\alpha-1}$.71 The pressure gradient term goes like L/p-OPfar~pon Lt where we inve used à=>12/3.," The pressure gradient term goes like $1/\rho\cdot \partial P/\partial r \sim r^{\delta \beta-1}$ , where we have used $\delta = \gamma -1 = 2/3$."72 The last (eravitational) term: includiug M(7). depoeuds on the given system we are considering.," The last (gravitational) term including $M(r)$, depends on the given system we are considering."73" If the mass is dominated by a point eravitational source (6.8. a central black hole). then it goes like ALGpowr7, "," If the mass is dominated by a point gravitational source (e.g. a central black hole), then it goes like $M(r) G/r^2 \sim74r^{-2}$ ."75Tf the mass is dominated by the matter density. then i eoes like M(r)~fpteV. with dV. the volune clement.," If the mass is dominated by the matter density, then it goes like $M(r) \sim \int \rho(r) dV$, with $dV$ the volume element."76 For spherical solutions his gravitational term thus goes like 7?!t with > from eq. (6)).," For spherical solutions this gravitational term thus goes like $r^{\beta+1}$ with $\beta$ from eq. \ref{eq:rho}) ),"77 and for disk solutions it goes like re’., and for disk solutions it goes like $r^\beta$.78} This exavitational term has the correct OTi or spherical distributions (ancl point sources). mt is only an approximation for the pure disk case.," This gravitational term has the correct form for spherical distributions (and point sources), but is only an approximation for the pure disk case."79" Techuically speaking the mass is logaxithlinic divergent for spherical structures with §=3. rowever. the formula Af—6/5? holds for any 3 arbitrarily close to Ὁ, auc furthermore m a real situation there would be an outer cut-off."," Technically speaking the mass is logarithmic divergent for spherical structures with $\beta=-3$ , however, the formula $M \sim r^{\beta + 3}$ holds for any $\beta$ arbitrarily close to $-3$, and furthermore in a real situation there would be an outer cut-off."80" To be explicit. we are looking for solutions to an equation of the form. where #=3j|1.02 for spherical. cisk and BIT matter dominance respectively,"," To be explicit, we are looking for solutions to an equation of the form where $\kappa = \beta+1, \beta, -2$ for spherical, disk and BH matter dominance respectively."81 When we use the word ‘solve in the following. we are really just uxing the stancard method of divergence cancellation. in the μονο that the most divergeut ternis uust cancel with cach other.," When we use the word 'solve' in the following, we are really just using the standard method of divergence cancellation, in the sense that the most divergent terms must cancel with each other."82 The optimal case is naturally that all divergences disappear. a case which we will refer to asgood.," The optimal case is naturally that all divergences disappear, a case which we will refer to as."83 From our simple analysis the transition radius. 5a. which separates the iuner from outer region. is nof uniquely determined.," From our simple analysis the transition radius, $r_\alpha$, which separates the inner from outer region, is not uniquely determined."84" We oulv find approximate disk relatious like à,~02 αρ.", We only find approximate disk relations like $r_\alpha \sim v^2_\alpha/G \rho_\alpha$ .85 A full study includiug the coefficieu Is significantly more involved. and we will leave that for a later analysis," A full study including the coefficient is significantly more involved, and we will leave that for a later analysis."86 We want to solve eq. Γ (5)), We want to solve eq. \ref{eq:vr}) )87 for the profile paranueter 3. however. there are 1] situations to consider (the L different à from eqs. (3..1))).," for the profile parameter $\beta$, however, there are 4 situations to consider (the 4 different $\alpha$ from eqs. \ref{eq:plus}, \ref{eq:minus}) )),"88 and for each case we can choosewhich is the dominating lass contribution. either from a sphere. from a disk or from a black hole (DIT).The discussion iu sections 2.3 iud 2.1105 somewhattechnical. and thereader is encouraged to look at," and for each case we can choosewhich is the dominating mass contribution, either from a sphere, from a disk or from a black hole (BH).The discussion in sections 2.3 and 2.4 is somewhattechnical, and thereader is encouraged to look at"89results were obtained for planetesimals at a=2 AU.,results were obtained for planetesimals at $a=2$ AU.90" Because a truncated disk will have a much smaller gas density in its outer regions, it is possible that different semimajor axes will give different results."," Because a truncated disk will have a much smaller gas density in its outer regions, it is possible that different semimajor axes will give different results."91" Figure 7 shows the variation of AV for six different planetesimal pairs, as a function of the semimajor axis and for three values of ερ."," Figure \ref{fig7} shows the variation of $\Delta V$ for six different planetesimal pairs, as a function of the semimajor axis and for three values of $e_g$."92 In horizontal dashed lines we have also plotted the critical relative velocity for a catastrophic disruption Vg using the recipe developed by Stewart and Leinhardt (2009) for weak aggregates., In horizontal dashed lines we have also plotted the critical relative velocity for a catastrophic disruption $V^*_{RD}$ using the recipe developed by Stewart and Leinhardt (2009) for weak aggregates.93" As shown in this figure, AV decreases sharply in the outer parts of the disk for small planetesimals."," As shown in this figure, $\Delta V$ decreases sharply in the outer parts of the disk for small planetesimals."94" Although for collisions between very small bodies the impact velocity is still above Vi (upper leftpanel), we find that AV«Vg for planetesimals with s~2 km and semimajor axis beyond 3 AU (upper right panel)."," Although for collisions between very small bodies the impact velocity is still above $V^*_{RD}$ (upper leftpanel), we find that $\Delta V < V^*_{RD}$ for planetesimals with $s \sim 2$ km and semimajor axis beyond $3$ AU (upper right panel)."95 Collisions between larger bodies are even more favorable (middle and lower panels)., Collisions between larger bodies are even more favorable (middle and lower panels).96" In all these cases the outcome of a collision seems to be accretion, at least in a significant portion of the disk."," In all these cases the outcome of a collision seems to be accretion, at least in a significant portion of the disk."97" Even if the inner disk still appears hostile, it is possible to envision a scenario in which accretional collisions between small planetesimals occurs preferentially in the outer disk."," Even if the inner disk still appears hostile, it is possible to envision a scenario in which accretional collisions between small planetesimals occurs preferentially in the outer disk."98" Then, as these bodies grow and reach the inner regions due to orbital decay with the gas, they could continue their growth closer to the star."," Then, as these bodies grow and reach the inner regions due to orbital decay with the gas, they could continue their growth closer to the star."99 In the previous section we analyzed the relative velocity of two planetesimals after they acquired their limit cycles., In the previous section we analyzed the relative velocity of two planetesimals after they acquired their limit cycles.100" However, depending on the gas density and the radius of the object, the time required to reach the equilibrium solution may be longer than the typical collisional timescale (Paardekooper and Leinhardt 2010)."," However, depending on the gas density and the radius of the object, the time required to reach the equilibrium solution may be longer than the typical collisional timescale (Paardekooper and Leinhardt 2010)."101" During this time, the planetesimals may also undergo orbital decay."," During this time, the planetesimals may also undergo orbital decay."102" Although the interplay between dynamical and collisional evolution can only be evaluated with full numerical simulations, here we present an estimate of the characteristic timescales of the secular equilibria (Τε) and semimajor axis decay (Τα)."," Although the interplay between dynamical and collisional evolution can only be evaluated with full numerical simulations, here we present an estimate of the characteristic timescales of the secular equilibria $\tau_e$ ) and semimajor axis decay $\tau_a$ )."103" Starting with initial circular orbits and a=2 AU, we define τε as the time necessary for a planetesimal with radius s to reach the final limit cycle with a relative error less than 196."," Starting with initial circular orbits and $a=2$ AU, we define $\tau_e$ as the time necessary for a planetesimal with radius $s$ to reach the final limit cycle with a relative error less than $1 \%$."104" Since there are no equilibria in the semimajor axis, we define Τα as the time necessary for the body to decrease its semimajor axis by Aa=1 AU."," Since there are no equilibria in the semimajor axis, we define $\tau_a$ as the time necessary for the body to decrease its semimajor axis by $\Delta a = 1$ AU."105" Figure shows Te and Τα as functions of the planetesimal radius s, for different values of the disk precession rate."," Figure \ref{fig8} shows $\tau_e$ and $\tau_a$ as functions of the planetesimal radius $s$, for different values of the disk precession rate."106" The case of a non-precessing disk is identified with black lines, while color curves represent different precession rates (see figure caption for details)."," The case of a non-precessing disk is identified with black lines, while color curves represent different precession rates (see figure caption for details)."107" In the two top panels, we have assumed an almost circular gas disk (eg=0.02)."," In the two top panels, we have assumed an almost circular gas disk $e_g=0.02$ )."108" As shown here, even a slow precession rate causes a significant reduction in Te, which, for instance for a s=0.1 km planetesimal, falls from ~10° years to ~10° years."," As shown here, even a slow precession rate causes a significant reduction in $\tau_e$, which, for instance for a $s=0.1$ km planetesimal, falls from $\sim 10^5$ years to $\sim 10^3$ years."109" Hence, a precession in the disk causes a much faster evolution from the initial conditions towards the limit cycle."," Hence, a precession in the disk causes a much faster evolution from the initial conditions towards the limit cycle."110 Figure 8 also shows a comparison between T. and the timescale for orbital decay., Figure \ref{fig8} also shows a comparison between $\tau_e$ and the timescale for orbital decay.111" For a static disk Te>Ta, implying that the decay in semimajor axis occurs faster than the time necessary for the planetesimal to reach the secular solution."," For a static disk $\tau_e > \tau_a$, implying that the decay in semimajor axis occurs faster than the time necessary for the planetesimal to reach the secular solution."112" The opposite, however, occurs for a precessing disk, where now Te«Ta for all values of s."," The opposite, however, occurs for a precessing disk, where now $\tau_e < \tau_a$ for all values of $s$."113" In this case then, it is expected that the body will reach the limit cycle before suffering any significant orbital decay."," In this case then, it is expected that the body will reach the limit cycle before suffering any significant orbital decay."114 Figure 9 shows the results of two sets of N-body simulations., Figure \ref{fig9} shows the results of two sets of N-body simulations.115 Planetesimals were initially ata =2 AU with e=0 and an adopted radius of s=10 km., Planetesimals were initially at $a=2$ AU with $e=0$ and an adopted radius of $s=10$ km.116 The gas disk was assumed to have an eccentricity of e;=0.2., The gas disk was assumed to have an eccentricity of $e_g=0.2$.117 Black curves correspond to a static disk (no precession) while red curves denote a disk with (retrograde) precession period of 1000 years., Black curves correspond to a static disk (no precession) while red curves denote a disk with (retrograde) precession period of $1000$ years.118" As expected from Figure 8,, the semimajor axis of a planetesimal falls more rapidly for a precessing disk, reaching 1 AU in timescales slightly over 10? years."," As expected from Figure \ref{fig8}, the semimajor axis of a planetesimal falls more rapidly for a precessing disk, reaching $1$ AU in timescales slightly over $10^5$ years."119 The orbital decay rate increases with time due to the greater gas density near the central star (see equation (38)))., The orbital decay rate increases with time due to the greater gas density near the central star (see equation \ref{eq40}) )).120 The evolution of the eccentricity in this case shows different behaviors., The evolution of the eccentricity in this case shows different behaviors.121" While the planetesimal approaches a quasi-circular orbit in the precessing disk, the opposite occurs in the static case, reaching values close to 6ᾳ for small values of a."," While the planetesimal approaches a quasi-circular orbit in the precessing disk, the opposite occurs in the static case, reaching values close to $e_g$ for small values of $a$."122 The two bottom panels of Figure 9 show the eccentricity as a function of the semimajor axis., The two bottom panels of Figure \ref{fig9} show the eccentricity as a function of the semimajor axis.123 On the left-hand panels we have again plotted the results of the exact N-body simulations., On the left-hand panels we have again plotted the results of the exact N-body simulations.124" Due to the orbital decay, the orbital evolution occurs from the right to the left of the graph."," Due to the orbital decay, the orbital evolution occurs from the right to the left of the graph."125" On the right, we plot the values of the center of the limit cycles (continuous lines) as well as the minimum and maximum values of the eccentricity (dashed lines), each determined numerically from the averaged model (31)) for fixed values of the semimajor axis."," On the right, we plot the values of the center of the limit cycles (continuous lines) as well as the minimum and maximum values of the eccentricity (dashed lines), each determined numerically from the averaged model \ref{eq31}) ) for fixed values of the semimajor axis."126" Except for the first few tenths of AU close to the initial condition, the rest of the planetesimal’s evolution occurs very close to the instantaneous limit cycles for each value of the semimajor axis."," Except for the first few tenths of AU close to the initial condition, the rest of the planetesimal's evolution occurs very close to the instantaneous limit cycles for each value of the semimajor axis."127" In other words, even in the presence of the significant orbital decay, the secular dynamics of the planetesimals is expected to be dictated by the limit cycles in (k, h)."," In other words, even in the presence of the significant orbital decay, the secular dynamics of the planetesimals is expected to be dictated by the limit cycles in $(k,h)$ ."128" Moreover, except for the first few 10? years, it is expected that the encounter velocities of collisions between planetesimals be determined by the equilibrium solutions of the secular problem, and not by the transient evolution from the initial conditions to the limit cycles."," Moreover, except for the first few $10^3$ years, it is expected that the encounter velocities of collisions between planetesimals be determined by the equilibrium solutions of the secular problem, and not by the transient evolution from the initial conditions to the limit cycles."129PATASS All-Skv Point Source Catalog (PSC).,2MASS All-Sky Point Source Catalog (PSC).130 DIRBE has a large 0.77x square beam will a diagonal of 17., DIRBE has a large $0.7^\circ \times 0.7^\circ$ square beam with a diagonal of $1^\circ$.131 Pixel intensities in the DIRBE maps are averages of all observations made while the beam was centered in a given pixel in (he CODE Quacdiilateralized Spherical Cube (CSC) projection., Pixel intensities in the DIRBE maps are averages of all observations made while the beam was centered in a given pixel in the COBE Quadrilateralized Spherical Cube (CSC) projection.132 Due to the large beam size. bright stars outside of a particular pixel will. depending on the exact center position and position angle of the beam. occasionally affect the observed briehtness in (hat pixel.," Due to the large beam size, bright stars outside of a particular pixel will, depending on the exact center position and position angle of the beam, occasionally affect the observed brightness in that pixel."133 Thus a thick buffer ring is needed around anv studied field to keep bright stars outside the field [rom influencing the measured DIRDE intensity., Thus a thick buffer ring is needed around any studied field to keep bright stars outside the field from influencing the measured DIRBE intensity.134 The resulting inefliciency was minimized by using the clarkest possible 2° circular regions which have the largest possible area:perimeter ratio., The resulting inefficiency was minimized by using the darkest possible $2^\circ$ circular regions which have the largest possible area:perimeter ratio.135 A list of dark spots was created by smoothing the 3.5 saa DIRBE Zodiacal Subtracted Mission Average (ZSAIA) map to 1/640) it’s original resolution. reducing the 393.216 0.32°x pixels (ο 6144 pixels approximately 2.5°x using a straight average of nearest neighbor pixels ancl sorting the resulting low resolution map.," A list of dark spots was created by smoothing the 3.5 $\mu$ m DIRBE Zodiacal Subtracted Mission Average (ZSMA) map to 1/64th it's original resolution, reducing the 393,216 $0.32^\circ \times 0.32^\circ$ pixels to 6144 pixels approximately $2.5^\circ \times 2.5^\circ$ using a straight average of nearest neighbor pixels and sorting the resulting low resolution map."136 The 40 darkest regions not used in previous analyses were used., The 40 darkest regions not used in previous analyses were used.137 Ilowever. the DIRBE ZSM.A project data set only uses a fraction of the DIRBE data since extreme solar elongations were dropped.," However, the DIRBE ZSMA project data set only uses a fraction of the DIRBE data since extreme solar elongations were dropped."138" Therefore. a set of mission averaged zocliacal subtracted. DIRBE maps were created by Wright(2001) using the zodiacal light. model of Wright (1905),"," Therefore, a set of mission averaged zodiacal subtracted DIRBE maps were created by \citet{elw01} using the zodiacal light model of \citet{wr98}. ."139 The physical model is similar to the Ixelsalletal.(1998). model. with an added constraint.," The physical model is similar to the \citet{kel98} model, with an added constraint."140 The “very strong no-zodi principle.” described in Wright(1997) ancl Gorjianetal.(2000).. requires that at high Galactic latitudes. at 25 jan. the background enussion should be isotropic and adds a single pseudo-observation of zero emission to the nearly 10? observations used to fit the time variation in the weekly maps to the model brightness.," The “very strong no-zodi principle,” described in \citet{wr97} and \citet{gor00}, requires that at high Galactic latitudes, at 25 $\mu$ m, the background emission should be isotropic and adds a single pseudo-observation of zero emission to the nearly $10^5$ observations used to fit the time variation in the weekly maps to the model brightness."141 At 1.25 and 2.2 jin. no correction for interstellar dust emission is needed. while al 3.5 jin. there is a very small correction (Arendtοἱal.1998).," At 1.25 and 2.2 $\mu$ m, no correction for interstellar dust emission is needed, while at 3.5 $\mu$ m, there is a very small correction \citep{are98}."142. The i!” pixel in these maps provides the DIRBE data DZ;., The $i^{th}$ pixel in these maps provides the DIRBE data $DZ_i$.143 Using the NASA/IPAC Inlralted Science Archive (IRSA). fIuxes from all stars in each of the 40 regions brighter than [IX = 14 in the all-sky release of the ΔΙΑΣ PSC were obtained.," Using the NASA/IPAC InfraRed Science Archive (IRSA), fluxes from all stars in each of the 40 regions brighter than K = 14 in the all-sky release of the 2MASS PSC were obtained."144" Again due to the large beam size ancl effectively random distribution of the beam center and position angle. these κος were converted into intensities by smearing wilh a 0.17x0.17"" square beam with a center uniformly distributed in the DIRBE pixel and orientation uniformly distributed in position angele. to obtain the cataloged star contribution. D;. io the DIRBE intensity."," Again due to the large beam size and effectively random distribution of the beam center and position angle, these fluxes were converted into intensities by smearing with a $0.7^\circ \times 0.7^\circ$ square beam with a center uniformly distributed in the DIRBE pixel and orientation uniformly distributed in position angle, to obtain the cataloged star contribution, $B_i$, to the DIRBE intensity."145 This smearing process is described fully in Section 3.., This smearing process is described fully in Section \ref{analysis}.146 For the J-band contribution. only stars withJ and Iv less than 14 were used.," For the J-band contribution, only stars withJ and K less than 14 were used."147 This dual wavelength magnitude selection is essentially equivalent to a simple J<14 selection (Wright2001 ).., This dual wavelength magnitude selection is essentially equivalent to a simple $J <$14 selection \citep{elw01}. .148accumulated effect of still smaller scales no longer contribute significantly to the operation of the elobal dvnamo.,accumulated effect of still smaller scales no longer contribute significantly to the operation of the global dynamo.149 Magnetoconvection is expected (o cause magnetic structuring down to scales of order. mim. where (he magnetic Revnolds number becomes unity so (hat the magnetic field ceases to be frozen-in ancl decouples [rom the turbulent plasma 2009).," Magnetoconvection is expected to cause magnetic structuring down to scales of order m, where the magnetic Reynolds number becomes unity so that the magnetic field ceases to be frozen-in and decouples from the turbulent plasma \citep{stenflo-dewijn09}."150. The observational signature of the dvnamo mechanism (hat most directly represents the regeneration of the poloidal field from the toroidal one is the svstematic tilt of the bipolar magnetic regions (hat is statistically described bv Joys law., The observational signature of the dynamo mechanism that most directly represents the regeneration of the poloidal field from the toroidal one is the systematic tilt of the bipolar magnetic regions that is statistically described by Joy's law.151 Combined with Iale's polarity law this tilt deseribes how the emerging bipolar regions bring to the surlace an N-S bipolar moment that is the seed for the regeneration of the new global poloidal field οἱ reversed polarity. from which the subsequent 11 vr evele of solar activity is generated.," Combined with Hale's polarity law this tilt describes how the emerging bipolar regions bring to the surface an N-S bipolar moment that is the seed for the regeneration of the new global poloidal field of reversed polarity, from which the subsequent 11 yr cycle of solar activity is generated."152 The observed properties of the tilt angles therelore give guidance to the dynamo theories and constrain (he wavs in which the dvnamo is allowed to operate., The observed properties of the tilt angles therefore give guidance to the dynamo theories and constrain the ways in which the dynamo is allowed to operate.153 The tilt angles of sunspot pairs have been studied in many papers since the discovery by IIaleetal.(1919). of Jows law. using Witt Peak magnetograms (Wang&Sheeley 1939).. Mount Wilson magnetograms (Iloward 1991b).. and sunspot group data (IIoward1991a).. confirming the overall magnitude and crude Iatitude dependence originally found by (1919).," The tilt angles of sunspot pairs have been studied in many papers since the discovery by \citet{stenflo-haleetal19} of Joy's law, using Kitt Peak magnetograms \citep{stenflo-wangsheeley89}, , Mount Wilson magnetograms \citep{stenflo-howard91a}, , and sunspot group data \citep{stenflo-howard91b}, confirming the overall magnitude and crude latitude dependence originally found by \citet{stenflo-haleetal19}."154. In addition Wang&Sheelev(1939). found that orientations. and (hat the spread in the distribution of tilt angles increased significantly as one goes Lo smaller regions.," In addition \citet{stenflo-wangsheeley89}155 found that orientations, and that the spread in the distribution of tilt angles increased significantly as one goes to smaller regions."156 The superb quality of the SOIIO/MDI data set will allow us in (he present work to explore these properties with much better precision and in much ereater detail than has been possible before., The superb quality of the SOHO/MDI data set will allow us in the present work to explore these properties with much better precision and in much greater detail than has been possible before.157 Recently IXosovicliev&Stenflo(2008) used the set of MDI magnetograms to study the tilt changes in emerging bipolar magnetic regions., Recently \citet{stenflo-ks08} used the set of MDI magnetograms to study the tilt changes in emerging bipolar magnetic regions.158 They found that during the first few clavs after emergence the Ull angles relaxedtowards(he value expected [rom Jov's law, They found that during the first few days after emergence the tilt angles relaxedtowardsthe value expected from Joy's law159appears very faint and diffuse at a resolution of few arcseconds even at 1.4 GHz (Parma et al.,appears very faint and diffuse at a resolution of few arcseconds even at 1.4 GHz (Parma et al.160 1986)., 1986).161" The second candidate, B2 1610-29, is associated to the nearby cD central galaxy NGC 6086 in Abell 2162 and has relaxed morphology in the VLA 1.4 GHz image of Parma et al. ("," The second candidate, B2 1610+29, is associated to the nearby cD central galaxy NGC 6086 in Abell 2162 and has relaxed morphology in the VLA 1.4 GHz image of Parma et al. ("1621986).,1986).163 More recently the source has been imaged with the GMRT at 610 MHz by Giacintucci et al. (, More recently the source has been imaged with the GMRT at 610 MHz by Giacintucci et al. (164"2007), who found a very similar morphology.","2007), who found a very similar morphology."165" By using all the useful data that are available in the VLA archive since then, we studied in detail the spectral properties of these objects in order to determine if they really are dying sources or not."," By using all the useful data that are available in the VLA archive since then, we studied in detail the spectral properties of these objects in order to determine if they really are dying sources or not."166 We observed the three dying radio galaxy candidates from the WENSS minisurvey at 1.4 and 4.8 GHz with VLA in various configurations., We observed the three dying radio galaxy candidates from the WENSS minisurvey at 1.4 and 4.8 GHz with VLA in various configurations.167" A summary of this campaign of observations, including the VLA configuration, frequency date and length of observations, is reported in Tab. 2.."," A summary of this campaign of observations, including the VLA configuration, frequency date and length of observations, is reported in Tab. \ref{obssum}."168 A bandwidth of 50 MHz was used for each of the two frequencies., A bandwidth of 50 MHz was used for each of the two frequencies.169" Calibration and imaging were performed with the Astronomical Image Processing System (AIPS), following the standard procedure: Fourier-Transform, Clean and Restore."," Calibration and imaging were performed with the Astronomical Image Processing System (AIPS), following the standard procedure: Fourier-Transform, Clean and Restore."170 Self-calibration was applied to remove residual phase variations., Self-calibration was applied to remove residual phase variations.171 Data from different arrays were combined to improve uv-coverage and sensitivity., Data from different arrays were combined to improve uv-coverage and sensitivity.172" We combined the A, B and C arrays at GGHz and the C and D at GGHz."," We combined the A, B and C arrays at GHz and the C and D at GHz."173 Each combined data set was self-calibrated., Each combined data set was self-calibrated.174 The relevant image parameters are reported in Tab. 3.., The relevant image parameters are reported in Tab. \ref{imapar}.175 In order to estimate the flux density and the spectral index of the three sources the primary beam correction was applied to all the images by applying the AIPS task PBCOR., In order to estimate the flux density and the spectral index of the three sources the primary beam correction was applied to all the images by applying the AIPS task PBCOR.176" For the purposes of the spectral index imaging, we convolved the GGHz images to the slightly larger beam of the GGHz ones."," For the purposes of the spectral index imaging, we convolved the GHz images to the slightly larger beam of the GHz ones."177" However, we emphasize that the angular resolution of the final images at the two frequencies were already well matched, not just by filtering the data, but by having comparable intrinsic coverage over the relevant spatial frequencies."," However, we emphasize that the angular resolution of the final images at the two frequencies were already well matched, not just by filtering the data, but by having comparable intrinsic coverage over the relevant spatial frequencies."178" Furthermore, both data sets have nearly the same sensitivity levels."," Furthermore, both data sets have nearly the same sensitivity levels."179The extensive photometric campaigns of stars are producing important information on the values and amplitudes of the excited pulsation frequencies.,The extensive photometric campaigns of stars are producing important information on the values and amplitudes of the excited pulsation frequencies.180 However. mode identifications are required. for unique theoretical modeling.," However, mode identifications are required for unique theoretical modeling."181 These mode identifications can be obtained from spectroscopic line-profile variations. as well as from photometric color information from the light curves.," These mode identifications can be obtained from spectroscopic line-profile variations, as well as from photometric color information from the light curves."182 However. these techniques usually can only be applied to a few of the detected frequencies.," However, these techniques usually can only be applied to a few of the detected frequencies."183 Consequently. the recognition of regular frequency patterns in the power spectra becomes an important additional tool.," Consequently, the recognition of regular frequency patterns in the power spectra becomes an important additional tool."184 Statistical analyses of the frequency spacings of 6 Scuti stars show that in nany stars the photometrically observed frequencies cluster around the frequencies of the radial modes over many radial orders (Breger. Lenz Pamyatnykh 2009).," Statistical analyses of the frequency spacings of $\delta$ Scuti stars show that in many stars the photometrically observed frequencies cluster around the frequencies of the radial modes over many radial orders (Breger, Lenz Pamyatnykh 2009)."185 The observed regularities can be partly explained by modes trapped in the stellar envelope., The observed regularities can be partly explained by modes trapped in the stellar envelope.186 li particular. the low-order {= | modes have frequencies close to those of the radial modes.," In particular, the low-order $\ell$ = 1 modes have frequencies close to those of the radial modes."187 We call this the low-order spacing. which means that the nearly regular frequency patterns correspond to successive radial orders. which can then be used to infer the stellar loge values (Breger. Lenz Pamyatnykh 2005).," We call this the low-order spacing, which means that the nearly regular frequency patterns correspond to successive radial orders, which can then be used to infer the stellar $\log g$ values (Breger, Lenz Pamyatnykh 2008)."188 This contrasts with the asymptotic case. where the £ = | frequencies are found nearly halfway between successive radial orders of the radial and £ = 2 modes.," This contrasts with the asymptotic case, where the $\ell$ = 1 frequencies are found nearly halfway between successive radial orders of the radial and $\ell$ = 2 modes."189 In the asymptotic case. successive frequencies (and frequency clusters) correspond to alternating £ values.," In the asymptotic case, successive frequencies (and frequency clusters) correspond to alternating $\ell$ values."190 The observed regularities differ from the low-order situatioi by a factor of two., The observed regularities differ from the low-order situation by a factor of two.191 We note here that regular frequency spacings can also be caused by combination. modes., We note here that regular frequency spacings can also be caused by combination modes.192 In extreme cases the combination modes cover the whole frequency range from the low-order frequencies up to the asymptotic frequency range., In extreme cases the combination modes cover the whole frequency range from the low-order frequencies up to the asymptotic frequency range.193 An impressive example of such a star is KIC 97003224 (Breger et al., An impressive example of such a star is KIC 9700322 (Breger et al.194 2011) measured by the Kepler satellite., 2011) measured by the $Kepler$ satellite.195 However. close inspection of the frequency patterns can uniquely identify the combination modes.," However, close inspection of the frequency patterns can uniquely identify the combination modes."196 We do that in this paper., We do that in this paper.197 A consequence of the different behavior between the low-order and asymptotic cases is that the photometrically detectable frequency spacings differ by a factor two., A consequence of the different behavior between the low-order and asymptotic cases is that the photometrically detectable frequency spacings differ by a factor two.198" The ""wandering"" of the = | modes ts illustrated in Figure 1.. which was computed from a nonrotating ZAMS model of The corresponding diagrams using observations are not yet available because for 6 Scuti stars. € = | mode identifications are available only for low-order modes."," The `wandering' of the $\ell$ = 1 modes is illustrated in Figure \ref{intro}, which was computed from a nonrotating ZAMS model of The corresponding diagrams using observations are not yet available because for $\delta$ Scuti stars, $\ell$ = 1 mode identifications are available only for low-order modes."199 To observationally examine the progression (doubling) of the regular frequency spacings from the low-radial order to the asymptotic frequency region. it is necessary to look at stars pulsating in high orders close to the asymptotic case.," To observationally examine the progression (doubling) of the regular frequency spacings from the low-radial order to the asymptotic frequency region, it is necessary to look at stars pulsating in high orders close to the asymptotic case."200 Such stars can be found near the hot border of the 6 Scuti instability strip, Such stars can be found near the hot border of the $\delta$ Scuti instability strip201 where Oyjoce. for example. is defined as unc," where $\sigma_{T \mlogg}$, for example, is defined as The partial derivatives were calculated in Section 6.2.2."202e, Equation 1 shows that is dependent on.203rtainties in and are correlated depends on the magnitude of the error inMy., The extent to which our uncertainties in and are correlated depends on the magnitude of the error in.204. Therefore. for each star in our sample. we did a Monte Carlo experiment where we allowed and to vary based on their errors. then calculated using Equation |. then placed into Equation 5 to calculate σος.," Therefore, for each star in our sample, we did a Monte Carlo experiment where we allowed and to vary based on their errors, then calculated using Equation 1, then placed into Equation 5 to calculate $\sigma_{\rm T \mlogg}$ ."205 Other σ values were determined in the same manner., Other $\sigma$ values were determined in the same manner.206 The errors in ratios such as |[O I|/Fe] can be appreciably smaller than the addition in quadrature of [O I] error and Fe II error. because they have similar sensitivities to changes in atmospheric parameters.," The errors in ratios such as [[O I]/Fe] can be appreciably smaller than the addition in quadrature of [O I] error and Fe II error, because they have similar sensitivities to changes in atmospheric parameters."207 We used Equation A20 from MeWilliametal.(1995).. modified to include [m/H] errors. to calculate abundance ratio errors.," We used Equation A20 from \citet{m95}, modified to include [m/H] errors, to calculate abundance ratio errors."208 The error bars in Figure 10 are calculated using this formula., The error bars in Figure 10 are calculated using this formula.209 No errors were calculated for the Sun., No errors were calculated for the Sun.210 The abundance results from the Alonso and Houdashelt parameter scales are shown in Figures 9 and 10., The abundance results from the Alonso and Houdashelt parameter scales are shown in Figures 9 and 10.211 In Figure 9. neither scale results in both sets of oxygen lines giving the same abundance for all stars. although the warmer Houdashelt scale does a better job.," In Figure 9, neither scale results in both sets of oxygen lines giving the same abundance for all stars, although the warmer Houdashelt scale does a better job."212" The unweighted mean value of (=logn(O,)—logn(O;)) for the Alonso scale is 40.35£0.03 (sdom). and 40.09+0.04 (sdom) for the Houdashelt scale."," The unweighted mean value of $\equiv \log{\rm n(O_p)} - \log{\rm n(O_f)}$ ) for the Alonso scale is $+0.35 \pm 0.03$ (sdom), and $+0.09 \pm 0.04$ (sdom) for the Houdashelt scale."213 In Figure 10. is shown as a function of the stellar parameters.," In Figure 10, is shown as a function of the stellar parameters."214 The ratio is larger for the cooler. lower surface gravity giants than for the warmer. higher gravity subgiants and dwarfs.," The ratio is larger for the cooler, lower surface gravity giants than for the warmer, higher gravity subgiants and dwarfs."215 Both least-squares and Spearman rank-order tests confirm that there are highly significant anti-correlations between and these two parameters., Both least-squares and Spearman rank-order tests confirm that there are highly significant anti-correlations between and these two parameters.216 These same tests do not support a correlation between and [Fe/H]., These same tests do not support a correlation between and [Fe/H].217 This is in contrast to previous studies (see Figure 1) in which the value of increases with decreasing [Fe/H]., This is in contrast to previous studies (see Figure 1) in which the value of increases with decreasing [Fe/H].218 In these earlier studies. the forbidden oxyger abundances came from giants and the permitted abundances came from dwarfs.," In these earlier studies, the forbidden oxygen abundances came from giants and the permitted abundances came from dwarfs."219 Our result suggests that the growth of with decreasing [Fe/H] is at least partially due to comparing stars of different evolutionary status., Our result suggests that the growth of with decreasing [Fe/H] is at least partially due to comparing stars of different evolutionary status.220 In Figure 10. it appears that the distribution for the Houdashelt scale is bimodal. with some stars clustered at =40.5 and the majority around =0.0.," In Figure 10, it appears that the distribution for the Houdashelt scale is bimodal, with some stars clustered at $= +0.5$ and the majority around $= 0.0$."221 Indeed. à KMM test (Ashmanetal.1994) finds that there is a probability that two Gaussians fit the distribution better than a single Gaussian.," Indeed, a KMM test \citep{ash} finds that there is a probability that two Gaussians fit the distribution better than a single Gaussian."222 The best fit model would place 12 stars in à group with a mean of 40.51X:0.12. and the remaining 43 in à group with a mean of —0.02£0.17.," The best fit model would place 12 stars in a group with a mean of $+0.51 \pm 0.12$, and the remaining 43 in a group with a mean of $-0.02 \pm 0.17$."223 While this is only a two-sigma result. understanding why the 12 stars (all with > 40.3) are outliers may yield clues to the origin of the overall problem.," While this is only a two-sigma result, understanding why the 12 stars (all with $> +0.3$ ) are outliers may yield clues to the origin of the overall problem."224 Unfortunately. à detailed investigation into the properties these 12 stars found nothing striking about these stars except that they all have ὁ and [Fe/H] «—1.," Unfortunately, a detailed investigation into the properties these 12 stars found nothing striking about these stars except that they all have $< 3$ and [Fe/H] $< -1$."225 These 12 stars are also among the stars with the highest values when the Alonso scale is applied. so the origin of the high value may be unrelated to the Houdashelt scale.," These 12 stars are also among the stars with the highest values when the Alonso scale is applied, so the origin of the high value may be unrelated to the Houdashelt scale."226 Checks for binarity. evolutionary status. systematic errors with the photometry. EW measurements. and reddening determinations. ete.," Checks for binarity, evolutionary status, systematic errors with the photometry, EW measurements, and reddening determinations, etc."227 did not yield any noticeable pattern for the 12 stars. especially one that would lead to such a tight clustering of outliers.," did not yield any noticeable pattern for the 12 stars, especially one that would lead to such a tight clustering of outliers."228 It can be concluded here that both the Alonso and Houdashelt scales fail to totally resolve the discrepancy., It can be concluded here that both the Alonso and Houdashelt scales fail to totally resolve the discrepancy.229 While the warmer Houdashelt scale comes closer than the Alonso scale. there are still several giant stars that have large values.," While the warmer Houdashelt scale comes closer than the Alonso scale, there are still several giant stars that have large values."230 Two possible reasons for the failure are: First. there is missing input physics in the analysis and an additional correction to the abundance results is necessary. or. second. the physics of the analysis is adequate. but the input parameters for the models are incorrect.," Two possible reasons for the failure are: First, there is missing input physics in the analysis and an additional correction to the abundance results is necessary, or, second, the physics of the analysis is adequate, but the input parameters for the models are incorrect."231 Full exploration of the first option is beyond the scope of this paper. but one simple explanation is that the NLTE corrections adopted here are simply wrong.," Full exploration of the first option is beyond the scope of this paper, but one simple explanation is that the NLTE corrections adopted here are simply wrong."232 To correct the differences seen in Figure 10. NLTE corrections would have to be much larger for low-gravity stars.," To correct the differences seen in Figure 10, NLTE corrections would have to be much larger for low-gravity stars."233 The corrections of Grattonetal.(2000) are nearly identical to those of Takedaetal.(2000) (see Figure 4) for this type of star. so the choice of NLTE correction does not to affect the results.," The corrections of \citet{g00} are nearly identical to those of \citet{nlte} (see Figure 4) for this type of star, so the choice of NLTE correction does not to affect the results."234 In section 6.4. we will look at the effect of changing our choice of stellar atmospheres.," In section 6.4, we will look at the effect of changing our choice of stellar atmospheres."235 In Section 7. we will assume the second option is correct and calculate stellar parameters that reconcile the indicators.," In Section 7, we will assume the second option is correct and calculate stellar parameters that reconcile the indicators."236 As mentioned above. the analyses to this point have been done using Kurucz atmospheres.," As mentioned above, the analyses to this point have been done using Kurucz atmospheres."237 The MARCS grid of stellar atmospheres (Belletal.1976) are an independent calculation of one-dimensional. plane-parallel atmospheres.," The MARCS grid of stellar atmospheres \citep{b76} are an independent calculation of one-dimensional, plane-parallel atmospheres."238 To test whether the adopted atmosphere grid makes a significant difference. we re-analyzed the measured EW values through atmospheres using the dereddened Alonso temperature scale parameters.," To test whether the adopted atmosphere grid makes a significant difference, we re-analyzed the measured EW values through atmospheres using the dereddened Alonso temperature scale parameters."239 The comparison between the results from Kuruez and MARCS models is shown in Figure 11., The comparison between the results from Kurucz and MARCS models is shown in Figure 11.240 The abundances derived from the permitted and forbidden oxygen and Fe II lines are all slightly larger for the Kurucz models than for the MARCS models., The abundances derived from the permitted and forbidden oxygen and Fe II lines are all slightly larger for the Kurucz models than for the MARCS models.241 These tendencies are enhanced at lower metallicities., These tendencies are enhanced at lower metallicities.242 The MARCS-derived oxygen abundances show a similar discrepancy between the permitted and forbidden lines on average for MARCS compared to 0.35+0.03 for the Kuruez models)., The MARCS-derived oxygen abundances show a similar discrepancy between the permitted and forbidden lines on average $0.33 \pm 0.03$ for MARCS compared to $0.35 \pm 0.03$ for the Kurucz models).243 Therefore. the use of ΜΑΡΚΟΣ models instead of Kurucz models will not solve the problem.," Therefore, the use of MARCS models instead of Kurucz models will not solve the problem."244 However. the MARCS models show a lower discrepancy for metal-poor giant stars. while the Kurucz model results show lower discrepancies for more metal-rich. less-evolved stars.," However, the MARCS models show a lower discrepancy for metal-poor giant stars, while the Kurucz model results show lower discrepancies for more metal-rich, less-evolved stars."245 If we used the most favorable atmospheric model for a given star. the difference between the oxygen abundance indicators could be reduced byup to ~0.1 dex in some cases.," If we used the most favorable atmospheric model for a given star, the difference between the oxygen abundance indicators could be reduced byup to $\sim 0.1$ dex in some cases."246 However. there Is no justification for such a selective use of atmospheres.," However, there is no justification for such a selective use of atmospheres."247 , 248svuthesis code(Brugual&Charlot2003).,synthesis \citep{BC03}.249. This paper is organized as follows., This paper is organized as follows.250 In Section 2. we describe our cvnamical model of the spiral galaxies. including the disk. bulge aud dark halo compoucuts respectively.," In Section 2, we describe our dynamical model of the spiral galaxies, including the disk, bulge and dark halo components respectively."251 Iu Section 3. we study the stellar properties of the disks aud bulges with parameterized star formation histories.," In Section 3, we study the stellar properties of the disks and bulges with parameterized star formation histories."252 We compare our model predictions with the observational data iu Section 1., We compare our model predictions with the observational data in Section 4.253 We alse discussions on the uncertainties of our results in Section 5 aud finally eive a brief sumuuary iu Section 6., We make discussions on the uncertainties of our results in Section 5 and finally give a brief summary in Section 6.254 Our modeling of the dynamics of spiral galaxies follows and simplifies the disk formation model of MMW. but with amore attention on the bulee coutribution.," Our modeling of the dynamics of spiral galaxies follows and simplifies the disk formation model of MMW, but with more attention on the bulge contribution."255 The interested reader is referred to MM for detail., The interested reader is referred to MMW for detail.256 Tere we repeat the esseutials related to our study., Here we repeat the essentials related to our study.257 Iu this model. initially. the eas aud dark matter are uniforiulv mixed in a virialized halo.," In this model, initially, the gas and dark matter are uniformly mixed in a virialized halo."258 As a result of dissipative and radiative cooling. the gas eradually cools down aud settles iuto a disc structure due to the conservation of angular momentum.," As a result of dissipative and radiative cooling, the gas gradually cools down and settles into a disc structure due to the conservation of angular momentum."259" We define that the stellar mass of the galaxy finally formed is M. and the fraction of this mass to the initial halo mass Af, is ny.=AL/AL,.", We define that the stellar mass of the galaxy finally formed is $M_*$ and the fraction of this mass to the initial halo mass $M_h$ is $m_s\equiv M_*/M_h$.260" We express the bulge fraction of the formed galaxy being fy. so that the masses of the bulge aud disk are Mj—fü. aud AM,=(1fijAL. respectively."," We express the bulge fraction of the formed galaxy being $f_b$, so that the masses of the bulge and disk are $M_b=f_b M_*$ and $M_d=(1-f_b) M_*$ respectively."261 The rotation curve of a spiral galaxy is contributed by three dynamical components: halo. bulee aud disk.," The rotation curve of a spiral galaxy is contributed by three dynamical components: halo, bulge and disk."262 We show aud discuss our assuniptious on cach term below., We show and discuss our assumptions on each term below.263 The N-body simulations show that the collapsed aud virialized dark halos follow a universal deusitv NEW profile (Navarro.Freuk.&White 1996).. where re is a scale radius. G is the eravitational constant. Vj ds the circular velocity aud ο is the concentration parameter.," The $N$ -body simulations show that the collapsed and virialized dark halos follow a universal density NFW profile \citep*{NFW96}, , where $r_s$ is a scale radius, $G$ is the gravitational constant, $V_h$ is the circular velocity and $c$ is the concentration parameter."264 The conceutration e is defined as 6mPoppy fry. Where rogois the virial radius of the halo.," The concentration $c$ is defined as $c\equiv r_{200}/r_s$ , where $r_{200}$is the virial radius of the halo."265" For a given cosmology. the viral radius rogo. halo mass AY), ancl circular velocity Vj, ire related by where ff.) is the Unbble constaut at redshift <."," For a given cosmology, the viral radius $r_{200}$, halo mass $M_h$ and circular velocity $V_h$ are related by where $H(z)$ is the Hubble constant at redshift $z$."266" Iu this studv. we use the concordance ACDAI cosiologv model. with Z4,=T0lansHKpe|. Ου=0,3. Q4—0.7 and barvon mass deusitv Op=0.01."," In this study, we use the concordance $\Lambda$ CDM cosmology model, with $H_0=70\kms{\rm{Kpc^{-1}}}$, $\Omega_0=0.3$, $\Omega_{\Lambda}=0.7$ and baryon mass density $\Omega_B=0.04$."267 With the asseiuibliug of the baryous iuto disk aud bulec. the eravitational effect from the bulee aud disk changes the initial halo mass distribution through contraction.," With the assembling of the baryons into disk and bulge, the gravitational effect from the bulge and disk changes the initial halo mass distribution through contraction."268 We follow MM and use the adiabatic contraction assuniptiou to analysis this effect (see AIVIW for detail)., We follow MMW and use the adiabatic contraction assumption to analysis this effect (see MMW for detail).269 For a halo with given circular velocity V4. the concentration ¢ is the only parameter to be quantified.," For a halo with given circular velocity $V_h$, the concentration $c$ is the only parameter to be quantified."270 At eiven redshift :. the coucentration parameter e is mainly correlated with the mass of the halos (Navarroetal.1996:Bullocks:etal.2001).," At given redshift $z$, the concentration parameter $c$ is mainly correlated with the mass of the halos \citep{NFW96,Bullock01}."271. We adopt a simple parametrization of the concentration e at redshift zero as that in Sheuetal.(2002):: We asstune that the bulge component of spiral galaxies has a spherical mass distribution aud the mass deusity profile ο) follows ai feriquist. profile (Heruquist1990).. whose projection approximates the classical Rl! surface brightness profile of elliptical galaxies.," We adopt a simple parametrization of the concentration $c$ at redshift zero as that in \cite{Shen02}: : We assume that the bulge component of spiral galaxies has a spherical mass distribution and the mass density profile $\rho_b(r)$ follows a $Hernquist$ profile \citep{Hernquist90}, , whose projection approximates the classical $R^{1/4}$ surface brightness profile of elliptical galaxies."272" The piti) is expressed as where A, is the total bulge mass. e is the bulee scale radius. which is correlated with the effective(altlieht} radius Π in the wav Socιδδα Γι."," The $\rho_b(r)$ is expressed as where $M_b$ is the total bulge mass, $a$ is the bulge scale radius, which is correlated with the effective(half-light) radius $R_e$ in the way $R_e\approx1.82a$ [Equ."273 38 of Heruquist(19903]]., 38 of \citet{Hernquist90}] ].274" To establish the dynamics of a bulge with mass Al, we need to kuow the scale radius e or effective radius Ro."," To establish the dynamics of a bulge with mass $M_b$, we need to know the scale radius $a$ or effective radius $R_e$ ."275 We asstuue that the bulecs follow the observed mass AL) relation of elliptical galaxies (Shenet.al.2003).. The surface brightuess profile of spiral disks typically follow an exponential profile.," We assume that the bulges follow the observed $R-M$ ) relation of elliptical galaxies \citep{Shen03}, The surface brightness profile of spiral disks typically follow an exponential profile."276 Here. we assume the disk surface niass density profile is also exponential. where jy is the central surface mass density aud Ry is the scale-leugth.," Here, we assume the disk surface mass density profile is also exponential, where $\mu_0$ is the central surface mass density and $R_d$ is the scale-length."277" py and Ry are related to the total mass of the disk M, through M,=2200.", $\mu_0$ and $R_d$ are related to the total mass of the disk $M_d$ through $M_d=2\pi \mu_0 R_d^2$.278 Since the observed size of the disk in a spiral galaxy is affected by its central bulge. we do not take the observed RoAM velation of spiral galaxies as that in the model.," Since the observed size of the disk in a spiral galaxy is affected by its central bulge, we do not take the observed $R-M$ relation of spiral galaxies as that in the model."279 Following MMW. we assune that the disk size Ry is determined by its initial aneular momentum J. which can be parameterized by a spin parameter A where E is the total eunergv of the halo.," Following MMW, we assume that the disk size $R_d$ is determined by its initial angular momentum $J$, which can be parameterized by a spin parameter $\lambda$ where $E$ is the total energy of the halo."280" With reasonable asstmptions that the specific anenlar momentiun per particle of the barvous is the same as the dark matter and there is no angular momentum transfer αλλος different components. the augular ποιοτα of the diskfinally formed is therefore JJ,=ng."," With reasonable assumptions that the specific angular momentum per particle of the baryons is the same as the dark matter and there is no angular momentum transfer among different components, the angular momentum of the diskfinally formed is therefore $J_d=m_d J$."281 Hore. mq is the fraction of barvous settling iuto the disk aud is equal to m.(l— fi).The scale-leneth of the disk Ry theu equals where fis afactor coming from the halo density profile and only depeudeut on concentration e (see Equ.," Here, $m_d$ is the fraction of baryons settling into the disk and is equal to $m_s(1-f_b)$ .The scale-length of the disk $R_d$ then equals where $f_c$ is afactor coming from the halo density profile and only dependent on concentration $c$ (see Equ."282 23 of MIAIW). fig is a factor comiue from boththe halo deusity," 23 of MMW), $f_R$ is a factor coming from boththe halo density"283ealaxies.,galaxies.284" As a result. the füut-eud slope of the Iuninositv ""unctionis much. too steep."," As a result, the faint-end slope of the luminosity function is much too steep."285 It should be noted that the results for this cooliug-oulv model are sensitive to the mass resolution of the merger trees., It should be noted that the results for this cooling-only model are sensitive to the mass resolution of the merger trees.286 The cooling time or halo eas decreases with decreasiug halo mass down to ido virial temperatures around LOTS. Below this scale. cooling becomes ineffective unless molecular hwdrogen is abundant.," The cooling time for halo gas decreases with decreasing halo mass down to halo virial temperatures around $10^4$ K. Below this scale, cooling becomes ineffective unless molecular hydrogen is abundant."287" This means that for the luuinosity fiction to 0 fully converged at all galaxy Iuuinositics, we would reed to resolve halos with virial temperatures as low as 10! at all redshifts at which there is siguificaut cooling."," This means that for the luminosity function to be fully converged at all galaxy luminosities, we would need to resolve halos with virial temperatures as low as $10^4$ K at all redshifts at which there is significant cooling."288 To obtain the results shown for Model 2. we ran at the highest mass resolutiou that was computationally easible. which comes close to resolving LOTS halos at z= )," To obtain the results shown for Model 2, we ran at the highest mass resolution that was computationally feasible, which comes close to resolving $10^4$ K halos at $z=0$ ."289 We believe that our results are substantially converged. mt we cannot be certain that they would not chanee if he mass resolution were increased further.," We believe that our results are substantially converged, but we cannot be certain that they would not change if the mass resolution were increased further."290 The problem of mass resolution eucouutered in Model 2 is ctfectively removed once we include feedback processes which are effective iu low-mass halos., The problem of mass resolution encountered in Model 2 is effectively removed once we include feedback processes which are effective in low-mass halos.291 Model 3) (oue-dashed line in Fig. 1)), Model 3 (long-dashed line in Fig. \ref{fig:models_123}) )292 shows the effects of including photoionization suppression., shows the effects of including photoionization suppression.293 As described by Deusonetal. (2002).. the formation of low-mass galaxies is suppressed after the Universe is relonized and. as we noted in retsec:model.. we adopt a simplified model of this process which nevertheless is a eood approximation to a full calculation.," As described by \citet{benson02}, the formation of low-mass galaxies is suppressed after the Universe is reionized and, as we noted in \\ref{sec:model}, we adopt a simplified model of this process which nevertheless is a good approximation to a full calculation."294 The resolution of the merger trees is then sutiicicnt to follow the lowest mass halos that are able to form galaxies. resulting iu a converged solution.," The resolution of the merger trees is then sufficient to follow the lowest mass halos that are able to form galaxies, resulting in a converged solution."295 However. photoionization suppression alone is unable to xoduce a sufficicutly flat faint end im the hnuuünositv uction.," However, photoionization suppression alone is unable to produce a sufficiently flat faint end in the luminosity function."296 In addition. Model 3 also produces more bright ealaxies. since less gas has beeu locked iuto stars in he smallest halos.," In addition, Model 3 also produces more bright galaxies, since less gas has been locked into stars in the smallest halos."297 When both galaxv mereie (which was artificially switched off in Models 1 aud 2) aud photoionization are included. as in Model 1 (solid. line iu Fie. 1)).," When both galaxy merging (which was artificially switched off in Models 1 and 2) and photoionization are included, as in Model 4 (solid line in Fig. \ref{fig:models_123}) ),"298 the faint eud remains too steep and even more xieht galaxies are produced., the faint end remains too steep and even more bright galaxies are produced.299" Iu the models that follow. we investigate the effects of includiug feedback processes in addition to photoionizatiou aud πιοοιο,"," In the models that follow, we investigate the effects of including feedback processes in addition to photoionization and merging."300A solution to the £uut-eud problem is illustrated by Model 5.3 in Fie. 2..,A solution to the faint-end problem is illustrated by Model 5.3 in Fig. \ref{fig:models_4}.301 Here. feedback is included through the reheating of disk gas in star-forming ealaxies.," Here, feedback is included through the reheating of disk gas in star-forming galaxies."302" We use the standard prescription of Coleetal.(2000).. but with a lareer value of ejua0.L1 (equivalent to. VirOlas 1) which is required in order to obtain a similar faint cud slope to that in Cole et ffor the larger value of Q), asstumed in this work."," We use the standard prescription of \citet{cole00}, but with a larger value of $\erh=3030.41$ (equivalent to $V_{\rm hot}=450\kms$ ) which is required in order to obtain a similar faint end slope to that in Cole et for the larger value of $\Omega_{\rm b}$ assumed in this work."304 This form of feedback flattens the huninosity function considerably. resulting iu reasonably good agrecincut with the observed faint cud.," This form of feedback flattens the luminosity function considerably, resulting in reasonably good agreement with the observed faint end."305 While the slope is not as flat as that measured by Coleetal.(2001) or Blautonetal.(2003).. it is iu good agreement with he steeper slope reported by Iuausetal.(2002).," While the slope is not as flat as that measured by \citet{cole2mass} or \citet{blanton}, it is in good agreement with the steeper slope reported by \citet{huang02}."306".. This achievement carries a price. howeverthe overabunudauce of bright galaxies (formed through excessive cooling iu nassive halos) is exacerbated. as there is now a much eroater παν» of diff""use hot eas ΤΟΠΟ. 1u the larecr alos."," This achievement carries a price, however—the overabundance of bright galaxies (formed through excessive cooling in massive halos) is exacerbated, as there is now a much greater mass of diffuse hot gas remaining in the larger halos."307 This gas is 310icieutly deuse that the ce utralresions are able to cool: οςmsequenth-. Model 5.3 xoduces. far oo παν brieht ealaxies.," This gas is sufficiently dense that the central regions are able to cool; consequently, Model 5.3 produces far too many bright galaxies."308 This result depeids little on he choice of ay., This result depends little on the choice of $\sigma_8$.309" Acopting a,=0.7 makes he brightest ealaxies only 0.5 nuve fainter.", Adopting $\sigma_8=0.7$ makes the brightest galaxies only 0.5 mag fainter.310 This clearly «enionstrates a longstanding probeni dn οπμ nioels: previous calculations have citrer assuined low values o Qu. or have invoked rather artificial wavs to prevent the cooling which forms these overluminous objects.," This clearly demonstrates a longstanding problem in semi-analytic models: previous calculations have either assumed low values of $\Omega_{\rm b}$ , or have invoked rather artificial ways to prevent the cooling which forms these overluminous objects."311Dased on observations obtained at the Gemini Observatory (program LL) €5-2005A-C-4). which is operated. bv the Association of Universities lor Research in. Astronomy. Inc.. under a cooperative agreement with the NSE on rchall of the Geniuini partnership: the National Science Foundation (United States). the Particle hvsics and Astronomy esearch Council (United. WKinecom). the tional Research Council (Canada). CONICYT. (Chile). he Australian Research Council (Australia). €o (Brazil) and CONICET (Argentina).,"Based on observations obtained at the Gemini Observatory (program ID GS-2005A-C-4), which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Particle Physics and Astronomy Research Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), CNPq (Brazil) and CONICET (Argentina)."312" Jased on observations made with ESO ""Telescopes at the Paranal Observatories under programme LD <074.B-046 1 an", Based on observations made with ESO Telescopes at the Paranal Observatories under programme ID $<$ $>$ $<$ $>$.313d <<This research has mace use of the NASA/LPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Aeronautics and Space Acmuinistration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."314 D.C. gratefully. acknowledges financial. support. fron the Fundacignn Ances., D.C. gratefully acknowledges financial support from the Fundaciónn Andes.315 DZ acknowledges that this research was supportedin part by National Science Foundation under Grant No., DZ acknowledges that this research was supported in part by the National Science Foundation under Grant No.316 PIIY99-07949.n during his visit to ΙΤ. a Cuggenheim --generous support from the NYU Physies department and Center for Cosmology ancl Particle Physics during his sabbatical there. NASA LYSA grant NNGOSGES2CG. NSE AST-0307482.. and the David and Lucile Packard Foundation.," PHY99-07949 during his visit to KITP, a Guggenheim fellowship, generous support from the NYU Physics department and Center for Cosmology and Particle Physics during his sabbatical there, NASA LTSA grant NNG05GE82G, NSF AST-0307482, and the David and Lucile Packard Foundation."317 JBIL is funded by a Federation Fellowship from the Australian Research Council., JBH is funded by a Federation Fellowship from the Australian Research Council.318 We particularly thank the referee. Michael Pohlen. for avery careful reading of the manuscript ancl extensive and helpful comments and suggestions.," We particularly thank the referee, Michael Pohlen, for a very careful reading of the manuscript and extensive and helpful comments and suggestions."319The magnitude of the RGB bump depends upou critically upon the maximum depth of the convection zone.,The magnitude of the RGB bump depends upon critically upon the maximum depth of the convection zone.320 Iu contrast. the enhancement in the observed 1unber of stars in the bump depeucds ipou the size of the chemical discoutinuity.," In contrast, the enhancement in the observed number of stars in the bump depends upon the size of the chemical discontinuity."321 Bouoetal.(2001) introduced the joparaieter. which measures the relative number of stars iu te RGB bump.," \citet{bono} introduced the parameter, which measures the relative number of stars in the RGB bump."322 Bonoetal.(2001) ound that was a robust precdictiou of stellar evolution theory. as chauges 1 the opacity. equation of state. aud iuclear cross sectious Changed the j»redicted. value of ον a few percent.," \citet{bono} found that was a robust prediction of stellar evolution theory, as changes in the opacity, equation of state, and nuclear cross sections changed the predicted value of by a few percent."323 Their work foud fair agreement between te observed valies aud those preclietecl by staicard stellar evolution theory., Their work found fair agreement between the observed values and those predicted by standard stellar evolution theory.324 More recently sec HST data to determine iin OL Galactic globula “clusters., More recently \citet{riello} used HST data to determine in 54 Galactic globular clusters.325 TIey loud this data was in good ag‘eerment with staudard stellar evolutiou mocels., They found this data was in good agreement with standard stellar evolution models.326" This paper )reselts a compreieusive aualvsis of how uncertaiuies in the inputs into stellar evoltion theory e[Tect the predictidLs for aaudIt;,.", This paper presents a comprehensive analysis of how uncertainties in the inputs into stellar evolution theory effect the predictions for and.327. Sectio 12 p'ovides all oe‘all of the Monte Carlo approacl used in the paper. while §3 presents a detailed analysis of tlie uu‘eltaluties in standard stellar evoutiou theory.," Section \ref{method} provides an overall of the Monte Carlo approach used in the paper, while \ref{uncertain}328 presents a detailed analysis of the uncertainties in standard stellar evolution theory."329 The theoretical luminosity functions are presented iu 8L., The theoretical luminosity functions are presented in \ref{theolf}.330 Section 5 cliscusses the rresults. while the rresults are presentec in 86...," Section \ref{rgbb} discusses the results, while the results are presented in \ref{rbmp}."331 A sumimnary of the main results is eiveu lu ST., A summary of the main results is given in \ref{summ}.332" Since it is not feasible to use analytic error propagation fortiulas with the complex calculations of stellar evolution. oie lust use numerical methods to study be»w uncertainty in the parameters of stellar evolution theory propagate to the precdictious of the theo""v."," Since it is not feasible to use analytic error propagation formulas with the complex calculations of stellar evolution, one must use numerical methods to study how uncertainty in the parameters of stellar evolution theory propagate to the predictions of the theory."333 Asiuple approach is to cousider one parameter at a tiue. performing calculations with several «lifferen values of the parameter to examine how the predictions of the theory are affected (e.g.Casellani&deelIunoceuti1999).," A simple approach is to consider one parameter at a time, performing calculations with several different values of the parameter to examine how the predictions of the theory are affected \citep[e.g.][]{cast99}."334. The effects involved are generally siuall. so changes 1 the parameters procice a roughly linear respouse in results of the calculaious.," The effects involved are generally small, so changes in the parameters produce a roughly linear response in results of the calculations."335 However. tlis imethod does uot «escribe how uucertaiuties in many different parameters 1Heract to prexluce a coimibiued uncertainy in the preclictious of the theory.," However, this method does not describe how uncertainties in many different parameters interact to produce a combined uncertainty in the predictions of the theory."336 To iuvestigate this requires a larger set o ‘calculations. in wlich all of the siguificant )araineters vary simultaneously.," To investigate this requires a larger set of calculations, in which all of the significant parameters vary simultaneously."337 We use a Monte Carlo approachi to lthe problem., We use a Monte Carlo approach to the problem.338 Describiig the estimated uucertaiuy in each paraneer with a probability distrinition. wer ua laree nuuiber of inclepeucler| stellar evolutioniti calculations in which tje. value of d parameter is drawn randomly from its correspoudingi probability distribution.," Describing the estimated uncertainty in each parameter with a probability distribution, we run a large number of independent stellar evolution calculations in which the value of each parameter is drawn randomly from its corresponding probability distribution."339 For specil antitative predictious of the theory. 11en. the results of all the ruis can be combiued into histograms showing tlie mos probable value atd the distribuuO1 of uncertainty around it.," For specific quantitative predictions of the theory, then, the results of all the runs can be combined into histograms showing the most probable value and the distribution of uncertainty around it."340 This method las been used previoilv dn a series of papers exanmdiulug unce‘tainties in theoretical globular cluster ages, This method has been used previously in a series of papers examining uncertainties in theoretical globular cluster ages341latest versiou ofENIX.,latest version of.342. Here. we are interested in small differential effects so it was essential that all models be run with the code version frozen.," Here, we are interested in small differential effects so it was essential that all models be run with the code version frozen."343 The simplest effect o. inetallicity ou ie spectral formation in iis the change in he metal content of the uuburued C+O layer neglectiug changes in the density structure and deeper layes., The simplest effect of metallicity on the spectral formation in is the change in the metal content of the unburned C+O layer neglecting changes in the density structure and deeper layers.344 In this sectio we examine these ellects incdepeucdently of other effects ol progenitor met:dlicity on 91ce ongoing supernova searches are expected to discover SNe early. aud early specra probe the oiermost layers ouly. this approach is seusible aid. vields physical iusight tal is somewhat model idepeudent.," In this section we examine these effects independently of other effects of progenitor metallicity on Since ongoing supernova searches are expected to discover SNe early, and early spectra probe the outermost layers only, this approach is sensible and yields physical insight that is somewhat model independent."345" When we ook at the overall UVOIR svuthetic spectra (Figures 1.. 6.. δν, 11.. and 13)) of the inodels with variaious in the C--O layer metallicity. we see two consistent. aud siguificant. effects: shifts iu the UV pseudo-contiuuum level (expaudec view for day 7 in Figure 2)) aud. variatious in the Si H line at 6150 ((expaucded. views in Figure 5))."," When we look at the overall UVOIR synthetic spectra (Figures \ref{fig:07zall}, , \ref{fig:10zall}, , \ref{fig:15zall}, , \ref{fig:20zall}, and \ref{fig:35zall}) ) of the models with variations in the C+O layer metallicity, we see two consistent and significant effects: shifts in the UV pseudo-continuum level (expanded view for day 7 in Figure \ref{fig:07zuv}) ) and variations in the Si II line at 6150 (expanded views in Figure \ref{fig:sigrid}) )."346 The general eect in the UV is the LLcrease in the UV. pseudo-contiuuunm level with decreasing metallicity., The general effect in the UV is the increase in the UV pseudo-continuum level with decreasing metallicity.347 Simultaneous is the recdward (blueward shift of most UV [features with decreasiug (increasiug) metalicity., Simultaneous is the redward (blueward) shift of most UV features with decreasing (increasing) metallicity.348 Iu the UV. the iie-Lorming region is iu the C+O Layer.," In the UV, the line-forming region is in the C+O layer."349 As the metallicity decreases. the line forming regiou must ‘each deeper iuto the atmosphere to have the same line opacity. resulting in stualler iue velociles.," As the metallicity decreases, the line forming region must reach deeper into the atmosphere to have the same line opacity, resulting in smaller line velocities."350 Mocification of the C+O layer metal abuudauce gives a classic surface cooling effec. lower telu;»eratures for higher metallicity.," Modification of the C+O layer metal abundance gives a classic surface cooling effect, lower temperatures for higher metallicity."351 The higher temperatures of the lower imeallicity C4-O. atinosple‘es give higher thermal luxes. inoviug the UV. higlier with lower uetallicits2," The higher temperatures of the lower metallicity C+O atmospheres give higher thermal fluxes, moving the UV pseudo-continuum higher with lower metallicity."352 The surface cooling aud the resulting shifts iu UV. are evident at every epocl., The surface cooling and the resulting shifts in UV pseudo-continuum are evident at every epoch.353 There is the complemenary effect. of additional metals increasing he line blocking., There is the complementary effect of additional metals increasing the line blocking.354 We maxe 10 attempt to seyarate these two ellects in this paper., We make no attempt to separate these two effects in this paper.355 The 5i II line αἱ 6150 ((Figure 5 ) shifts blueward with itcreases in metalliciy for epochs through day 20., The Si II line at 6150 (Figure \ref{fig:sigrid}) ) shifts blueward with increases in metallicity for epochs through day 20.356 These shifts deinoustrae that solue line formation in this feature akes place in the CO layer., These shifts demonstrate that some line formation in this feature takes place in the C+O layer.357 The earlier epochs show large variations iu the otal depth of the leature which iuplies that the liue forms less in the incomplete |turbine zone with its large. uuchaieli© silicon abundance. aud more in the C+O laver where the silicon abundance ciinges.," The earlier epochs show large variations in the total depth of the feature which implies that the line forms less in the incomplete burning zone with its large, unchanging silicon abundance, and more in the C+O layer where the silicon abundance changes."358 At later epochs these conditions are reversed. resulting in sinaller changes wil1 CO layer metallicity variation.," At later epochs these conditions are reversed, resulting in smaller changes with C+O layer metallicity variation."359 These effects are discussed. further in 51., These effects are discussed further in \ref{siii}.360" The Me IL ""h4k eature at 2600 ((Figure 2)) does not move to the blue or red as the metallicity varies.", The Mg II “h+k” feature at 2600 (Figure \ref{fig:07zuv}) ) does not move to the blue or red as the metallicity varies.361 The decrease in Me II h4-k feature streneth with increasing metallicity is caused by the increasing UV line blauketiug from backerouud line opacity inthe C+Olayer., The decrease in Mg II h+k feature strength with increasing metallicity is caused by the increasing UV line blanketing from background line opacity inthe C+Olayer.362The Me II absorption occurs mostly in the deeper.,"The Mg II absorption occurs mostly in the deeper,"363"The runs of the approximate radiative transfer code are performed on a radially stretched, polar uniform, spherical, two-dimensional grid.","The runs of the approximate radiative transfer code are performed on a radially stretched, polar uniform, spherical, two-dimensional grid."364 The grid consists of 60 cells in the radial direction times 61 cells in the polar direction (plus additional cells for the storage of boundary conditions)., The grid consists of 60 cells in the radial direction times 61 cells in the polar direction (plus additional cells for the storage of boundary conditions).365 The polar range covers the full spatial setup of 180°., The polar range covers the full spatial setup of $180\degr$.366 Stretching of the radial grid dimension by an additional from one cell to the next is applied., Stretching of the radial grid dimension by an additional from one cell to the next is applied.367 The implicit diffusion Eq., The implicit diffusion Eq.368 is solved via the GMRES method (see Sect. 2.4)), is solved via the GMRES method (see Sect. \ref{sect:gmres}) )369" after parallel/global Block-Jacobian and serial/local ILU pre-conditioning in the framework of the version 2.3.3 of the open source parallel solver library PETSc (Portable, Extensible Toolkit for Scientific Computation)."," after parallel/global Block-Jacobian and serial/local ILU pre-conditioning in the framework of the version 2.3.3 of the open source parallel solver library PETSc (Portable, Extensible Toolkit for Scientific Computation)."370 More detailed information about this solver library can be found in ??..," More detailed information about this solver library can be found in \citet{petsc-web-page, petsc-user-ref}."371" The gradient of the radiation energy is zero at the inner radial and both polar boundaries (VE-0), i.e. radiative flux over these boundaries is prohibited."," The gradient of the radiation energy is zero at the inner radial and both polar boundaries $\left( \vec{\nabla} E_\mathrm{R} = 0 \right)$, i.e. radiative flux over these boundaries is prohibited."372 The radial outer boundary is defined as a constant Dirichlet boundary corresponding to To=147K (En2aT1)., The radial outer boundary is defined as a constant Dirichlet boundary corresponding to $T_0 = 14.7 \mbox{ K}$ $\left( E_\mathrm{R} = a ~ T_0^4 \right)$.373" The timestep used for the FLD solver is 10* s. The main iteration (circle of irradiation and FLD steps) is stopped when the relative change of the temperature in each cell is smaller than0.01%,, leading to 3 main iterations in the “purely absorption"" runs and more than 600 main iterations in the ""irradiation plus FLD"" runs."," The timestep used for the FLD solver is $10^4$ s. The main iteration (circle of irradiation and FLD steps) is stopped when the relative change of the temperature in each cell is smaller than, leading to 3 main iterations in the “purely absorption” runs and more than 600 main iterations in the “irradiation plus FLD” runs."374 For comparison we use the Monte-Carlo based radiation transfer code RADMC described in ? and ?.., For comparison we use the Monte-Carlo based radiation transfer code RADMC described in \citet{Dullemond:2000p2185} and \citet{Dullemond:2004p2184}. .375 The general solver method of the code is based on ?.., The general solver method of the code is based on \citet{Bjorkman:2001p2187}.376 The Monte-Carlo runs are performed on a 60 x 31 grid assuming symmetry to the disk midplane., The Monte-Carlo runs are performed on a 60 x 31 grid assuming symmetry to the disk midplane.377 The grid is stretched in both directions., The grid is stretched in both directions.378 One million photons are used., One million photons are used.379" Scattering can be handled by this code, but is simply switched off as it is neglected in the radiation transport module described here."," Scattering can be handled by this code, but is simply switched off as it is neglected in the radiation transport module described here."380 Scattering would increase the temperature in the irradiated parts (up to an optical depth of about unity) by about in the optically thin envelope up to a maximum of in the optically thick inner rim of the disks midplane due to higher extinction., Scattering would increase the temperature in the irradiated parts (up to an optical depth of about unity) by about in the optically thin envelope up to a maximum of in the optically thick inner rim of the disks midplane due to higher extinction.381 The more effectively shielded outer regions of the disk would be about cooler., The more effectively shielded outer regions of the disk would be about cooler.382" For more massive and luminous stars the effect of scattering would decrease due to stronger forward scattering, which is included in our ray-tracing routine per definition."," For more massive and luminous stars the effect of scattering would decrease due to stronger forward scattering, which is included in our ray-tracing routine per definition."383 The following comparison of the results is divided into three parts (each of the proposed components of the theoretical Sects., The following comparison of the results is divided into three parts (each of the proposed components of the theoretical Sects.384" 2.1 - 2.3 are tested independently): First, we study a pure absorption scenario without diffusion in the optically thin and thick case."," \ref{sect:fld} - \ref{sect:freqdepirradiation} are tested independently): First, we study a pure absorption scenario without diffusion in the optically thin and thick case."385 Afterwards we include diffusion effects., Afterwards we include diffusion effects.386" Therefore, we perform three different runs of the Monte-Carlo based code: a full run for the optically thin case Τ550µπι=0.1, a full run for the optically thick case Τσσοπι=100, and an additional run for the optically thick case T5sonm=100 with excluded re-emission of the photons (to achieve a pure absorption scenario for comparison with our first order ray-tracing routine), hereafter called *one-photon-limit""."," Therefore, we perform three different runs of the Monte-Carlo based code: a full run for the optically thin case $\tau_{550\mathrm{nm}} = 0.1$ , a full run for the optically thick case $\tau_{550\mathrm{nm}} = 100$, and an additional run for the optically thick case $\tau_{550\mathrm{nm}} = 100$ with excluded re-emission of the photons (to achieve a pure absorption scenario for comparison with our first order ray-tracing routine), hereafter called “one-photon-limit”."387 An overview of these three comparison runs is given in table 1.., An overview of these three comparison runs is given in table \ref{MC-runs}.388 The resulting temperature distributions of these Monte-Carlo runs are compared with the results of the approximate radiative transfer runs including different components of our module: We discuss five different configurations for the optically thin and thick setup including gray and frequency dependent irradiation plus potential diffusion., The resulting temperature distributions of these Monte-Carlo runs are compared with the results of the approximate radiative transfer runs including different components of our module: We discuss five different configurations for the optically thin and thick setup including gray and frequency dependent irradiation plus potential diffusion.389 An overview of the physics applied and the resulting deviations of these runs from the comparison data is given in table 2.., An overview of the physics applied and the resulting deviations of these runs from the comparison data is given in table \ref{run-table}.390 These results are discussed and illustrated in detail in the following subsections., These results are discussed and illustrated in detail in the following subsections.391" In the most optically thin case Tssonm=0.1, diffusion effects should be negligible."," In the most optically thin case $\tau_{550\mathrm{nm}} = 0.1$, diffusion effects should be negligible."392" Therefore, we can test the validity of the routines described in Sect."," Therefore, we can test the validity of the routines described in Sect."393 2.2. without running the diffusion routine., \ref{sect:irradiation} without running the diffusion routine.394 Compared to the full Monte-Carlo simulation from RADMC also the deviation in the most “difficult” region of the midplane (due to having the highest absorption) stays below (see Fig. 3))., Compared to the full Monte-Carlo simulation from RADMC also the deviation in the most “difficult” region of the midplane (due to having the highest absorption) stays below (see Fig. \ref{Tau0001}) ).395" In this optically thin limit, the diffusion effects are indeed negligible: An additionally performed full run of the approximate radiation transfer module with frequency dependent irradiation plus Flux Limited Diffusion shows a variation in the radial temperature slope from the pure gray irradiation run below1%."," In this optically thin limit, the diffusion effects are indeed negligible: An additionally performed full run of the approximate radiation transfer module with frequency dependent irradiation plus Flux Limited Diffusion shows a variation in the radial temperature slope from the pure gray irradiation run below."396". In the most optically thick case Tssonm=100, we test a pure absorption case to distinguish the deviations introduced by the FLD approximation in the full run from the deviations introduced by the irradiation component of our module."," In the most optically thick case $\tau_{550\mathrm{nm}} = 100$, we test a pure absorption case to distinguish the deviations introduced by the FLD approximation in the full run from the deviations introduced by the irradiation component of our module."397" Therefore, we run the Monte-Carlo code only until every initial photon is absorbed, neglecting re-emission or scattering events."," Therefore, we run the Monte-Carlo code only until every initial photon is absorbed, neglecting re-emission or scattering events."398" In this scenario, we are able to probe the absorption routines of Sects."," In this scenario, we are able to probe the absorption routines of Sects."399 2.2 and 2.3 in detail and determine the improvement by considering the frequency dependence of the stellar irradiation., \ref{sect:irradiation} and \ref{sect:freqdepirradiation} in detail and determine the improvement by considering the frequency dependence of the stellar irradiation.400 The resulting temperature profiles through the midplane for the case of gray and frequency dependent irradiation as well as the corresponding deviations from the Monte-Carlo comparison run are shown in Fig. 4.., The resulting temperature profiles through the midplane for the case of gray and frequency dependent irradiation as well as the corresponding deviations from the Monte-Carlo comparison run are shown in Fig. \ref{Tau1000ab}.401" Indeed, we found that in order to limit the deviation in the absorption part of the radiation module to less than it is essential to account for thefrequency dependence of the stellar irradiation."," Indeed, we found that in order to limit the deviation in the absorption part of the radiation module to less than it is essential to account for thefrequency dependence of the stellar irradiation."402 That is, That is403the presence. of metallicity. gradients. within the dSph's was included.,the presence of metallicity gradients within the dSph's was included.404 Tamura. Hirashita Takeuchi (2001) moclel the enrichment of svstems like the local dwarf spheroidals. and conclude that internal metallicity eracdicnts arc to he expected. a dillerence between the global mean metallicity and local values. corresponding perhaps to the small regions studied. by. direct. spectroscopic samples. would. not. be surprising.," Tamura, Hirashita Takeuchi (2001) model the enrichment of systems like the local dwarf spheroidals, and conclude that internal metallicity gradients are to be expected, a difference between the global mean metallicity and local values, corresponding perhaps to the small regions studied by direct spectroscopic samples, would not be surprising."405 Still. Shetrone et al. (," Still, Shetrone et al. ("4062001b) find no evidence of any stars more metal rich than Fe/1]—-1.45 in the region of Ursa Minor which they study.,2001b) find no evidence of any stars more metal rich than [Fe/H]=-1.45 in the region of Ursa Minor which they study.407 Although this does not prove no stars more metal rich than the above limit exist in Ursa Minor. it does make our result of the average present clay metallicity for this system of. Fe/1I]—-1.2 appear unlikely.," Although this does not prove no stars more metal rich than the above limit exist in Ursa Minor, it does make our result of the average present day metallicity for this system of [Fe/H]=-1.2 appear unlikely."408 The most probable explanation being the selective expulsion of metals discussed. previously. and not directly modeled in our stucly.," The most probable explanation being the selective expulsion of metals discussed previously, and not directly modeled in our study."409 ‘This first test gives us some confidence on the validity ofour assumptions. as a prediction below the observed range would have invalidated the moclel.," This first test gives us some confidence on the validity of our assumptions, as a prediction below the observed range would have invalidated the model."410 lt is intuitive that (fpi—1)lslewm1. if we wanted o calibrate 5. from the currently available metallicities at 5=0.5. we would therefore end up with fpi=1.5. an interesting possibility.," It is intuitive that $(f_{DM}-1) + \gamma + \nu \approx 1$, if we wanted to calibrate $\gamma$ from the currently available metallicities at $\gamma =0.5$, we would therefore end up with $f_{DM}=1.5$, an interesting possibility."411" Ehe above makes sense if this value Or 7, is thought of as a geometric form factor allowing for a clisk-like structure for the gas in our systems. which permits a fraction of the heated gas to escape before interacting with he totality of the galaxies ΙΛ."," The above makes sense if this value for $\gamma$ is thought of as a geometric form factor allowing for a disk-like structure for the gas in our systems, which permits a fraction of the heated gas to escape before interacting with the totality of the galaxies ISM."412 Panel (ο) gives the time evolution of the gravitational and thermal energies of the eas. the first. growing due to the acerction of gas. and the second. due to the heating produced. by SNea.," Panel (c) gives the time evolution of the gravitational and thermal energies of the gas, the first growing due to the accretion of gas, and the second due to the heating produced by SNea."413 Phe crossing point of the two curves defines the onset of the galactic wind. ancl the cessation of star formation.," The crossing point of the two curves defines the onset of the galactic wind, and the cessation of star formation."414 Ln panel (d) we show the time evolution of the dillerent SNae rates. with type HE and type Ib rates ending once star formation has finished. and tvpe la rates continuing bevond. rellecting the extended evolution of low mass binary systems.," In panel (d) we show the time evolution of the different SNae rates, with type II and type Ib rates ending once star formation has finished, and type Ia rates continuing beyond, reflecting the extended evolution of low mass binary systems."415 In panel (ο) we give the evolution of he gas. stellar and total barvonic masses. with the gas mass going rapidly to zero with the onset of the galactic wind. and the stellar mass remaining essentially constant after this »»int.," In panel (e) we give the evolution of the gas, stellar and total baryonic masses, with the gas mass going rapidly to zero with the onset of the galactic wind, and the stellar mass remaining essentially constant after this point."416 Finally. panel (£) gives the details of the infall. used ancl outllows obtained.," Finally, panel (f) gives the details of the infall used and outflows obtained."417 The model is largely. insensitive to re details of the former. as the latter are a solid consequence X having formed as many stars as are visible today. within 1e inferred dark haloes of the observed. systems.," The model is largely insensitive to the details of the former, as the latter are a solid consequence of having formed as many stars as are visible today, within the inferred dark haloes of the observed systems."418 The second. set of. models. in Table. 1 gives the corresponding moclels for Ursa Minor. all analogous to those escribed for Leo LL.," The second set of models in Table 1 gives the corresponding models for Ursa Minor, all analogous to those described for Leo II."419 For this galaxy it is well known that star ormation ended more than 10 Gyr ago (e.g. Mateo 1908). s is rellected in its S£Igea which shows a strong pulse M star formation in the remote past. and nothing since.," For this galaxy it is well known that star formation ended more than 10 Gyr ago (e.g. Mateo 1998), this is reflected in its $SFR_{HGV}$ which shows a strong pulse of star formation in the remote past, and nothing since."420 In us case. the discrepancy. in the first. model compared. to four=1.0 being 1.32.," In this case, the discrepancy in the first model compared to $f_{DM}=1.0$ being 1.32."421 This vields a higher j£=0.31 in the second model. a lower +=0.74 in the third and a slightly. ower initial luminous to dark matter ratio of 0.24 in the ourth model.," This yields a higher $\nu =0.31$ in the second model, a lower $\gamma=0.74$ in the third and a slightly lower initial luminous to dark matter ratio of 0.24 in the fourth model."422 This numbers remain unacceptably extreme.," This numbers remain unacceptably extreme,"423The Airy integral is (Abramowitz&Stegun1965) £0. where in the second form. terms of a Macdonald. function. follows from hystt).,"The Airy integral is \citep{AS65}424 ) ), where in the second form, terms of a Macdonald function, follows from ),."425 For a test particle. using (2.3)). one needs to add subscripts d lo a—at. b— bin (3.1)). and to z.€ in (3.1)).," For a test particle, using \ref{phase0}) ), one needs to add subscripts $\pm$ to $a\to a_\pm$, $b\to b_\pm$ in \ref{Airy1}) ), and to $z,\xi$ in \ref{Airy2}) )."426 One has, One has427One of the tightest correlations in extragalactic astronomy is that between the FIR luminosity. as calculated from the IRAS flux densities at 60 and 100 jim (for example combined in the above-mentioned relation Fyg—js9 by Helou et al.,"One of the tightest correlations in extragalactic astronomy is that between the FIR luminosity, as calculated from the IRAS flux densities at 60 and 100 $\mu$ m (for example combined in the above-mentioned relation $F_{40-120}$ by Helou et al."428 1988). and the differential radio continuum luminosity in the GHz range for late-type galaxies.," 1988), and the differential radio continuum luminosity in the GHz range for late-type galaxies."429 It was originally found by de Jong et al. (, It was originally found by de Jong et al. (4301985). Helou et al. (,"1985), Helou et al. ("4311985) and Wunderlich et al. (,1985) and Wunderlich et al. (4321987). and holds for the spatially integrated emissions of objects whose luminosity is dominated by star formation and not by an active nucleus.,"1987), and holds for the spatially integrated emissions of objects whose luminosity is dominated by star formation and not by an active nucleus."433 This radio-FIR correlation can be theoretically explained. since the Interstellar Medium im such galaxies acts as a global calorimeter for the relativistic electrons and. in large part. for the UV photons. both of which are generated by the stars (VOIIK 1989).," This radio-FIR correlation can be theoretically explained, since the Interstellar Medium in such galaxies acts as a global calorimeter for the relativistic electrons and, in large part, for the UV photons, both of which are generated by the stars (Völlk 1989)."434 Usually the correlation is found to be somewhat steeper than unity. the radio luminosity increasing faster than linearly with the FIR luminosity.," Usually the correlation is found to be somewhat steeper than unity, the radio luminosity increasing faster than linearly with the FIR luminosity."435 Restricting the FIR to the IRAS 60 jm luminosity. Yun et al. (," Restricting the FIR to the IRAS 60 $\mu$ m luminosity, Yun et al. ("4362001) have recently obtained a nearly linear correlation. based on a very large sample of 1809 galaxies from the local Universe. which Bell (2003) considers as à matter of conspiracy of different conflicting effects.,"2001) have recently obtained a nearly linear correlation, based on a very large sample of 1809 galaxies from the local Universe, which Bell (2003) considers as a matter of conspiracy of different conflicting effects."437 Our present work allows us to investigate whether such a correlation also exists for the typically sub-kpe size galactic substructures such as the star-forming regions in M33., Our present work allows us to investigate whether such a correlation also exists for the typically sub-kpc size galactic substructures such as the star-forming regions in M33.438 For this purpose we made use of the 6.3cem radio map of Buezilowski Beck (1987). which has a spatial resolution of2.," For this purpose we made use of the cm radio map of Buczilowski Beck (1987), which has a spatial resolution of."4394/.. Since this resolution is considerably lower than the resolution of our 60 and 1004/m maps we smoothed the FIR maps to a comparable spatial resolution. before rederiving the photometry for the knots in M33.," Since this resolution is considerably lower than the resolution of our 60 and $\mu$ m maps we smoothed the FIR maps to a comparable spatial resolution, before rederiving the photometry for the knots in M33."440 For the estimate of the FIR fluxes we used the relation given by Helou et al. (, For the estimate of the FIR fluxes we used the relation given by Helou et al. (4411988) to allow a comparison with IRAS data.,1988) to allow a comparison with IRAS data.442 Fig., Fig.443 9 shows the radio flux plotted versus the FIR flux., 9 shows the radio flux plotted versus the FIR flux.444 There appears to be indeed a correlation., There appears to be indeed a correlation.445 Even taking into account the difficulties inherent i1 the data reduction. the slope of this correlation is smaller tha1 unity. of the order of 0.9.," Even taking into account the difficulties inherent in the data reduction, the slope of this correlation is smaller than unity, of the order of 0.9."446 We can ask ourselves why we should expect such a “local” correlation., We can ask ourselves why we should expect such a “local” correlation.447 A priori this is not obvious., A priori this is not obvious.448 The absorption of the norionizing stellar UV photons depends strongly on the dust column density through the star-forming regions., The absorption of the non-ionizing stellar UV photons depends strongly on the dust column density through the star-forming regions.449 And even for NGC 604 about 60 percent of the UV light escapes the dust sphere of the region. as mentioned above.," And even for NGC 604 about 60 percent of the UV light escapes the dust sphere of the region, as mentioned above."450 For smaller regions this fraction 1s expected to be higher., For smaller regions this fraction is expected to be higher.451 The rest goes into the diffuse dust in the galactie disk., The rest goes into the diffuse dust in the galactic disk.452" This is the dominant FIR. part in the standard global radio-FIR correlation. but it can be neglected in the ""local"" correlation. unless the surface filling factor of the ensemble of regions becomes a significant fraction. say more than 10 percent of the disk area."," This is the dominant FIR part in the standard global radio-FIR correlation, but it can be neglected in the “local” correlation, unless the surface filling factor of the ensemble of regions becomes a significant fraction, say more than 10 percent of the disk area."453 Nevertheless. the fact that we did not include the jim in the FIR luminosity of Fig.," Nevertheless, the fact that we did not include the $\mu$ m in the FIR luminosity of Fig."454 9 emphasizes the shorter wavelengths. and we noted earlier that a large fraction (about 80%)) of the emission at m comes from the localized component.," 9 emphasizes the shorter wavelengths, and we noted earlier that a large fraction (about ) of the emission at $\mu$ m comes from the localized component."455 Thus. some fraction. say30%.. of the spatially integrated IRAS FIR lummosity may come from individual star-forming regions and will be proportional to their respective star formation rates.," Thus, some fraction, say, of the spatially integrated IRAS FIR luminosity may come from individual star-forming regions and will be proportional to their respective star formation rates."456 In fact. a higher star formation rate will probably imply a higher dust column density and thus a strorger than linear dependence of the FIR Juminosity on the local star formation rate.," In fact, a higher star formation rate will probably imply a higher dust column density and thus a stronger than linear dependence of the FIR luminosity on the local star formation rate."457 Let us next consider the radio emission. from individual regions., Let us next consider the radio emission from individual regions.458 If we assume that the sources of the radio emitting relativistic electrons are mainly the remnants of core collapse supernovae. then their progenitor stars will have remained in the star-forming region during their evolution.," If we assume that the sources of the radio emitting relativistic electrons are mainly the remnants of core collapse supernovae, then their progenitor stars will have remained in the star-forming region during their evolution."459" In addition to this non-thermal radiation. the progenitor stars will give rise to loeal thermal (free-free) radio emission,"," In addition to this non-thermal radiation, the progenitor stars will give rise to local thermal (free-free) radio emission."460 Therefore the necessary condition for a “local” correlation is satisfied. because the sources for both emissions are localized in the star-forming region.," Therefore the necessary condition for a “local” correlation is satisfied, because the sources for both emissions are localized in the star-forming region."461 Also. for a face-on galaxy. the star-forming regions are detected along the direction perpendicular to the disk.," Also, for a face-on galaxy, the star-forming regions are detected along the direction perpendicular to the disk."462 Along that direction we see the integrated emission. and the electrons confined to this column will have lost their energy by Inverse Compton and synchrotron emission. and thus their luminosity can be proportional to the local star formation rate.," Along that direction we see the integrated emission, and the electrons confined to this column will have lost their energy by Inverse Compton and synchrotron emission, and thus their luminosity can be proportional to the local star formation rate."463 Much more important is the following effect: the supernova remnants which accelerate the electrons. confine them during the active remnant life time of ~10° yr. during which time they radiate with a very hard energy spectrum.," Much more important is the following effect: the supernova remnants which accelerate the electrons, confine them during the active remnant life time of $\sim 10^5$ yr, during which time they radiate with a very hard energy spectrum."464 Acceleration automatically implies confinement. because the particles are convected in the downstream direction.," Acceleration automatically implies confinement, because the particles are convected in the downstream direction."465 During their confinement the electrons radiate in the interior effective magnetic field which can be expected to be several times. say 5 times higher than in the average interstellar medium (Bell Lucek 2001; Berezhko et al.," During their confinement the electrons radiate in the interior effective magnetic field which can be expected to be several times, say 5 times higher than in the average interstellar medium (Bell Lucek 2001; Berezhko et al."466 2002)., 2002).467 In agreement, In agreement468We now wish to compare the amount of detected sub-mm flux to the predictions of an obscured AGN model which also fits the X-ray background (XRB).,We now wish to compare the amount of detected sub-mm flux to the predictions of an obscured AGN model which also fits the X-ray background (XRB).469" The model will also allow us to estimate the amount of sub-mm flux which is predicted to arise in Compton-thick AGN which will not be detected as X-ray sources but whose hosts may be detected as individual galaxies, for instance the z>0.5 red galaxy population we have also found to be a significant contributor to the sub-mm background."," The model will also allow us to estimate the amount of sub-mm flux which is predicted to arise in Compton-thick AGN which will not be detected as X-ray sources but whose hosts may be detected as individual galaxies, for instance the $z>0.5$ red galaxy population we have also found to be a significant contributor to the sub-mm background."470" The model we employ is that of Gunn Shanks (1999), which is known to match the observed hard X-ray background."," The model we employ is that of Gunn Shanks (1999), which is known to match the observed hard X-ray background."471" It assumes that AGN are drawn from an intrinsically flat distribution of seven absorbing columns between Ng=10135 cm (essentially unobscured) and 10255 cm""? (heavily Compton-thick).", It assumes that AGN are drawn from an intrinsically flat distribution of seven absorbing columns between $N_{\rm{H}}=10^{19.5}$ $^{-2}$ (essentially unobscured) and $10^{25.5}$ $^{-2}$ (heavily Compton-thick).472"? The model as presented by Gunn Shanks (1999; see also Gunn, 1999) is non-unified: it assumes that the observed column density is directly a measure of the intrinsic amount of gas, not a result of viewing angle."," The model as presented by Gunn Shanks (1999; see also Gunn, 1999) is non-unified: it assumes that the observed column density is directly a measure of the intrinsic amount of gas, not a result of viewing angle."473" This assumption has no bearing on the model’s success in fitting the XRB, but is significant in the sub-mm since dust masses in the model are calculated from a gas-to-dust ratio, so more heavily absorbed sources will have greater dust masses and therefore make a greater contribution in the sub-mm."," This assumption has no bearing on the model's success in fitting the XRB, but is significant in the sub-mm since dust masses in the model are calculated from a gas-to-dust ratio, so more heavily absorbed sources will have greater dust masses and therefore make a greater contribution in the sub-mm."474" We make use of the model within this non-unified paradigm, but also later adapt it in order to explore the unified AGN scenario, in which different column densities arise due to orientation effects and do not reflect any intrinsic difference between AGN populations."," We make use of the model within this non-unified paradigm, but also later adapt it in order to explore the unified AGN scenario, in which different column densities arise due to orientation effects and do not reflect any intrinsic difference between AGN populations."475" In both cases we assume a dust temperature of 30K, consistent with observations of sub-mm sources (Coppin et al,"," In both cases we assume a dust temperature of 30K, consistent with observations of sub-mm sources (Coppin et al.,"476" 2008b; Elbaz et al,"," 2008b; Elbaz et al.,"477" 2010) and an emissivity index of B—1.5 (Dunne Eales, 2001)."," 2010) and an emissivity index of $\beta=1.5$ (Dunne Eales, 2001)."478" In reff-850cnts we show the prediction of the non-unified model, which gives an excellent fit to the sub-mm source counts at Sasso>0.5 mJy."," In \\ref{f-850cnts} we show the prediction of the non-unified model, which gives an excellent fit to the sub-mm source counts at $S_{850}>0.5$ mJy."479" At fainter ffluxes, the AGN model begins to underpredict the counts,"," At fainter fluxes, the AGN model begins to underpredict the counts,"480In 1933. Becklin Zuckerman announced the discovery of the coolest dwarl star vet seen.,"In 1988, Becklin Zuckerman announced the discovery of the coolest dwarf star yet seen."481 Imaged with the first generation of infrared. cameras. (his companion to the white dwarf GD165 went without proper classification lor several vears.," Imaged with the first generation of infrared cameras, this companion to the white dwarf GD165 went without proper classification for several years."482 The L clwarl prototwpe.," The L dwarf prototype,"483driven by turbulence from supernovac.,driven by turbulence from supernovae.484 They fouud correlation between SFR aud DILAR oulv for sources with Ap>0401 AL. ὃν and they predict that the SER/DIIAR ratio should iucrease with ACN Iuuinosity. reaching a maxima ratio ~2.," They found a correlation between SFR and BHAR only for sources with $\dot{M}_{BH}>0.01$ $_{\odot}$ $^{-1}$, and they predict that the SFR/BHAR ratio should increase with AGN luminosity, reaching a maximum ratio $\sim2$."485 This model predicts less cicunmnnuclear star formation thin we observe iu l kpe apertures. and can oulv be reconciled with our observations if there is 10« more star formation on 100 pecrz1 kpe scales than ou r<100 pc scales.," This model predicts less circumnuclear star formation than we observe in $r=1$ kpc apertures, and can only be reconciled with our observations if there is $10\times$ more star formation on 100 $<r<1$ kpc scales than on $r<100$ pc scales."486 went a step further iux uade predictions for the relationship between SER iux BITAR as a function of radius;, went a step further and made predictions for the relationship between SFR and BHAR as a function of radius.487 They used results front arge-scale (100. kpe to LOO pc) simulations of ealaxy uereers and barred galaxy disks. and then re-smuulatec he ceutral kpc (1 kpc to 10 pe} aud the central 10 pc (10 pe to 0.1 pe) at higher spatial resolution.," They used results from large-scale (100 kpc to 100 pc) simulations of galaxy mergers and barred galaxy disks, and then re-simulated the central kpc (1 kpc to 10 pc) and the central 10 pc (10 pc to 0.1 pc) at higher spatial resolution."488 They fine SER/DBILAR ratios ranging from ~LO for R«100 pe ο 30 for R<1 kpe. and ~300 for the whole galaxy. which is consistent with our results for unclear aud tota SFRs.," They find SFR/BHAR ratios ranging from $\sim10$ for $R<100$ pc to $\sim30$ for $R<1$ kpc, and $\sim300$ for the whole galaxy, which is consistent with our results for nuclear and total SFRs."489 They also find SFRxMp on the smallest scales GR10 pe) and SFRκ on larger scales. which is in eeneral agreement with the ADscalines we fiud for nuclear star formation.," They also find $SFR\propto\dot{M}_{BH}$ on the smallest scales $R<10$ pc) and $SFR\propto\dot{M}_{BH}^{0.7}$ on larger scales, which is in general agreement with the scalings we find for nuclear star formation."490 Tt is wortlwhile to consider our measurements of nuclear SFRs aud BITARs in terms of the observed scaling between galaxy bulge aud black hole masses2001)., It is worthwhile to consider our measurements of nuclear SFRs and BHARs in terms of the observed scaling between galaxy bulge and black hole masses.491. analyzed a sample of bulec-domunated ealaxies frou the Sloan Digital Sky Survey aud found iat the integrated black hole erowth (from galaxies josting Ανν) and star formation (fom all galaxies) corresponded to SFR/BITAR ~10°. cousistent with 1ο observed bulge/black hole mass ratio.," analyzed a sample of bulge-dominated galaxies from the Sloan Digital Sky Survey and found that the integrated black hole growth (from galaxies hosting AGNs) and star formation (from all galaxies) corresponded to SFR/BHAR $\sim10^3$, consistent with the observed bulge/black hole mass ratio."492 performed similar exercise for a sample of 1nuinous infrared ealaxies aud found similar results for ιο iuteerated population., performed a similar exercise for a sample of luminous infrared galaxies and found similar results for the integrated population.493 For our sample. we find nedian SFR/BUAR =36 ou scales of +=1 kpe (the (miteerated total corresponds to SFR/BIAR = 23). which is factor of ~20 below the median bulge/black hole mass ratio2001).," For our sample, we find a median SFR/BHAR $=36$ on scales of $r=1$ kpc (the integrated total corresponds to SFR/BHAR $=23$ ), which is factor of $\sim20$ below the median bulge/black hole mass ratio."494. This implies an ACN duty evele of ~ which is within a factor of two of the Sevfert fraction in the RSA galaxy. sample1997a).," This implies an AGN duty cycle of $\sim5\%$, which is within a factor of two of the Seyfert fraction in the RSA galaxy sample."495. There are several caveats associated with the above estimate. inchiding the fact we excluded the most star-formation dominated Sevferts (see Section ??)) aud that the our nuclear apertures have not been customized to match the bulee of each galaxy.," There are several caveats associated with the above estimate, including the fact we excluded the most star-formation dominated Seyferts (see Section \ref{sec:data}) ) and that the our nuclear apertures have not been customized to match the bulge of each galaxy."496 A svstematic bulee/disk decomposition is bevoud the scope of this work. but r=1 kpe corresponds roughly to the effective radius of a 1017.AL. Indee2008).. meaniug that our uuclear apertures euconipass half the ποτ of sucha bulge (and less light for more massive bulges).," A systematic bulge/disk decomposition is beyond the scope of this work, but $r=1$ kpc corresponds roughly to the effective radius of a $10^{10}~M_{\Sun}$ bulge, meaning that our nuclear apertures encompass half the light of such a bulge (and less light for more massive bulges)."497 Accounting for these effects; as well as poteutial bulee erowth through dynamical process that relax the orbits of pre-existing stars. would tend to increase our estimate of the AGN dutv cvele.," Accounting for these effects, as well as potential bulge growth through dynamical process that relax the orbits of pre-existing stars, would tend to increase our estimate of the AGN duty cycle."498 We lave also assumed that local Seyfert ealaxies obey the black holebulge scaling relations defined primarily bv earbv-tvpe galaxies with classical bulges. which may or may not be the case2011).," We have also assumed that local Seyfert galaxies obey the black hole–bulge scaling relations defined primarily by early-type galaxies with classical bulges, which may or may not be the case."499. We now consider our results iu the context of ACN cling miechiuisiis., We now consider our results in the context of AGN fueling mechanisms.500 A nmuuber of morphological studies of ACN host galaxies at 2<L have argued that the cling for most systems is not merecr driven2011)., A number of morphological studies of AGN host galaxies at $z<1$ have argued that the fueling for most systems is not merger driven.501 While large-scale bars can also provide the necessary gravitational torques ο drive gas down to ~LOO pc. there is uot strong evidence that Sevfert ealaxies exhibit a huger bar raction than do star-forming galaxies1999).," While large-scale bars can also provide the necessary gravitational torques to drive gas down to $\sim100$ pc, there is not strong evidence that Seyfert galaxies exhibit a larger bar fraction than do star-forming galaxies."502. ILowever. both Sevfert aud star-foruüug activity appear ο be associated with a higher meileuce of bars than coud in quiescent galaxies2009).," However, both Seyfert and star-forming activity appear to be associated with a higher incidence of bars than found in quiescent galaxies."503. We have demonstrated that the DITAR is correlated with the amount of eas ou sub-kpe scalessassumptionoftheScehinidt 1998). butmonmentun such eas still needs to shed most ofnic its augular to reach the black hole.," We have demonstrated that the BHAR is correlated with the amount of gas on sub-kpc scales assumption of the Schmidt-Kennicutt , but such gas still needs to shed most of its angular momentum to reach the black hole."504 Future studies with ALMA of the spatial distribution aud kinenmiaties of molecular gas down to ~pec scales in local Sevfert ealaxies will probe the nature of this fucling more directly., Future studies with ALMA of the spatial distribution and kinematics of molecular gas down to $\sim$ pc scales in local Seyfert galaxies will probe the nature of this fueling more directly.505 We note that and presented evidence for a time delay. between he onset of star formation and ACN activity. which cau ο explained if the black hole is being fed by outflows roni intermeciate-age stars.," We note that and presented evidence for a time delay between the onset of star formation and AGN activity, which can be explained if the black hole is being fed by outflows from intermediate-age stars."506 Our observations are nof sensitive to detecting such a 100 Myr time delay )ecause the aromatic features will continue to be excited w UV photous from longer-lived. B stars2010)., Our observations are not sensitive to detecting such a $\sim$ 100 Myr time delay because the aromatic features will continue to be excited by UV photons from longer-lived B stars.507 The ‘required oss of angular momentum could also be explained ly dynamical instabilitics im selteravitating disks20100., The required loss of angular momentum could also be explained by dynamical instabilities in self-gravitating disks.508 There have been suggestions from theoretical and observational work that star formation is eulianuced in obscured(i.c.. standardtype 2) AGNs.," There have been suggestions from theoretical and observational work that star formation is enhanced in obscured (i.e., type 2) AGNs."509 This would be inconsistent with the unified model where differences between obscured aud uniobseured ACNs are attributed to our viewing augle towards a central obscuring torus. and would sugeest that the obscuring material in type 2 AGNsis related to star-formation activity iu the Lost ealaxy.," This would be inconsistent with the standard unified model where differences between obscured and unobscured AGNs are attributed to our viewing angle towards a central obscuring torus, and would suggest that the obscuring material in type 2 AGNs is related to star-formation activity in the host galaxy."510 However. we flud that the distiibutious of nuclear SFRs. extended SFRs. total SFRs. aud SFR/BITAR ratios for our sample do not exhibit auv statistically sienificaut differences between type 1 and type 2 Sevterts.," However, we find that the distributions of nuclear SFRs, extended SFRs, total SFRs, and SFR/BHAR ratios for our sample do not exhibit any statistically significant differences between type 1 and type 2 Seyferts."511 While this result does not definitively rule out any differcuce between the star-forming properties of type 1 and type 2 Αννα. it does imply that such differences are not dranatic.," While this result does not definitively rule out any difference between the star-forming properties of type 1 and type 2 AGNs, it does imply that such differences are not dramatic."512 We note that results on starformation activity as a function of Sevtert type likely depend om sample selection and the method used to measure the SER., We note that results on star-formation activity as a function of Seyfert type likely depend on sample selection and the method used to measure the SFR.513 A comprehensive analysis of these factors is bevoud, A comprehensive analysis of these factors is beyond514contribute about 2 per cent of unresolved CXB and the volume filling factor of the lobes is ~0.03-0.02 at 2=2-3.,contribute about $2$ per cent of unresolved CXB and the volume filling factor of the lobes is $\sim0.03$ $0.02$ at $z=2$ $3$.515 The jet lifetime is an important parameter that affects the predicted distribution of the sources., The jet lifetime is an important parameter that affects the predicted distribution of the sources.516 A larger jet lifetime means that sources will grow longer while there are also fewer predicted sources with jets turned off during the quasar era., A larger jet lifetime means that sources will grow longer while there are also fewer predicted sources with jets turned off during the quasar era.517" The predicted volume filling factor exceeds 0.25 at redshifts of the quasar era for an increased jet lifetime of 5x10°yr, while the volume filling factor decreases toς<0.01 for a decreased jet life time of 5x107yr."," The predicted volume filling factor exceeds $0.25$ at redshifts of the quasar era for an increased jet lifetime of $5\times 10^8~{\rm yr}$, while the volume filling factor decreases to$\zeta\leq 0.01$ for a decreased jet life time of $5\times 10^7~{\rm yr}$."518 Evidence that a significant fraction of sources have long jet lifetimes on the order of 5x108yr will mean that double- sources can account for 20 per cent of the unresolved CXB and 60 per cent of the extended sources in the CDFN survey., Evidence that a significant fraction of sources have long jet lifetimes on the order of $5\times 10^8~{\rm yr}$ will mean that double-lobed sources can account for $20$ per cent of the unresolved CXB and $60$ per cent of the extended sources in the CDFN survey.519 Increasing the injection index to p=3 has the effect of reducing the radio luminosities and consequently sources are more likely to be below the radio flux limit and hence a larger number of total sources in the underlying distribution are predicted., Increasing the injection index to $p=3$ has the effect of reducing the radio luminosities and consequently sources are more likely to be below the radio flux limit and hence a larger number of total sources in the underlying distribution are predicted.520" Consequently, the predicted volume filling factor of sources at redshift z are significantly higher, surpassing unity in the quasar era and even at z—1."," Consequently, the predicted volume filling factor of sources at redshift $z$ are significantly higher, surpassing unity in the quasar era and even at $z=1$."521 The contribution of lobes to the unresolved CXB is 60 per cent (Figure 13))., The contribution of lobes to the unresolved CXB is $60$ per cent (Figure \ref{fig:bgxf}) ).522" Despite the large volume fraction, the sources are less bright in the X-ray compared with [A] and the number of sources observed per square degree is 9 at the flux density limit of the CDFN survey."," Despite the large volume fraction, the sources are less bright in the X-ray compared with [A] and the number of sources observed per square degree is $9$ at the flux density limit of the CDFN survey."523" The minimum electron injection energy determined by ymin, when increased to —2000, leads to higher X-ray and radio luminosities than our original case, meaning there are fewer sources predicted to go undetected and hence a smaller number of total sources in the underlying distribution and volume filling factor."," The minimum electron injection energy determined by $\gamma_{\rm min}$, when increased to $\gamma=2000$, leads to higher X-ray and radio luminosities than our original case, meaning there are fewer sources predicted to go undetected and hence a smaller number of total sources in the underlying distribution and volume filling factor."524 The volume filling factor is still as high as 0.017 during the quasar era., The volume filling factor is still as high as $0.017$ during the quasar era.525" Additionally, setting ymin=2000 results in the X-ray luminosity falling less steeply for the majority of the time the source is an IC ghost, meaning that it is above the flux limit for a longer period of time and hence more observable."," Additionally, setting $\gamma_{\rm min}=2000$ results in the X-ray luminosity falling less steeply for the majority of the time the source is an IC ghost, meaning that it is above the flux limit for a longer period of time and hence more observable."526" The ratio of observable IC ghosts to all observable sources for mi,= 2000, at the flux limit of the CDEN survey is 30 per cent versus 13 per cent for ymin= 1."," The ratio of observable IC ghosts to all observable sources for $\gamma_{\rm min}=2000$ , at the flux limit of the CDFN survey is $30$ per cent versus $13$ per cent for $\gamma_{\rm min}=1$ ."52734.<Ms€10M. ).,$3 M_\odot \la M_2 \la 10 M_\odot$ ).528 We attribute the slow outflow of ~50—75kms.! that probably contains most of the mass to the extveme-AGB star. as il is about equal to its escape speed (assuming a radius of Ry75AU).," We attribute the slow outflow of $\sim 50-75 \kms$ that probably contains most of the mass to the extreme-AGB star, as it is about equal to its escape speed (assuming a radius of $R_1 \simeq 5 \AU$ )."529 The faster outflow of up to ~600kms.! fits better the escape velocity [rom the AIS companion., The faster outflow of up to $\sim 600 \kms$ fits better the escape velocity from the MS companion.530 Our scenario starts with some kind of instability in the extreme-AGD star that causes a nass of xO.1A/. to be lost from the star at a slow velocity., Our scenario starts with some kind of instability in the extreme-AGB star that causes a mass of $\times 0.1 M_\odot$ to be lost from the star at a slow velocity.531 Ia our model the instability is not the source of the extra energy., In our model the instability is not the source of the extra energy.532 Therefore. we can assume that the instability does not increase much. or even reduces. (he primary luminosity.," Therefore, we can assume that the instability does not increase much, or even reduces, the primary luminosity."533 We do not specilv the source of the instability. but it might be. for example. a strong magnetic eruption.," We do not specify the source of the instability, but it might be, for example, a strong magnetic eruption."534 AGB stars are known to iive extensive convective region with strong convection (the convective cells have a relative vigh velocity and long mixing length)., AGB stars are known to have extensive convective region with strong convection (the convective cells have a relative high velocity and long mixing length).535 If the star has a non-negligible rotation due to its tidal interaction. with the companion. then a strong magnetic aclivily night be expected2001).," If the star has a non-negligible rotation due to its tidal interaction with the companion, then a strong magnetic activity might be expected."536 The magnetic eruption causes (he primary to overfill its Roche lobe. resulting in both mass loss from Che system and mass transfer to the companion.," The magnetic eruption causes the primary to overfill its Roche lobe, resulting in both mass loss from the system and mass transfer to the companion."537 According to Dond et al. (, According to Bond et al. (5382009). the transient at maximum light exhibited a spectrum of an F superigant.,"2009), the transient at maximum light exhibited a spectrum of an F superigant."539 The underlviug radiation sourceduring the event could be even hotter. if the observed spectrum was produced in an optically thick wind.," The underlying radiation source the event could be even hotter, if the observed spectrum was produced in an optically thick wind."540 However. this cannot be used {ο constrain the spectral type of the progenitor the event.," However, this cannot be used to constrain the spectral type of the progenitor the event."541 We take the most conservative approach. and take the star (o have (he lowest temperature possible for iis mass at this evolutionary stage (extreme-AGD). ~3500IX.," We take the most conservative approach, and take the star to have the lowest temperature possible for its mass at this evolutionary stage (extreme-AGB), $\sim 3500 \K$."542 For an extreme AGB effective temperature ol ~3500IX the radius of the progenitor of NGC 300 OT was Ay~3AU., For an extreme AGB effective temperature of $\sim 3500 \K$ the radius of the progenitor of NGC 300 OT was $R_1 \sim 3 \AU$.543 The dvnamical {ime scale for à mass of M4=15M. is ~5 months., The dynamical time scale for a mass of $M_1=15 M_\odot$ is $\sim 5~$ months.544 The outburst duration of 80days can be understood as cdvnamical time scale., The outburst duration of $80 \days$ can be understood as dynamical time scale.545 Namely. in our model a dynamical instability lead to hieh mass (ransler episode.," Namely, in our model a dynamical instability lead to high mass transfer episode."546 The super-Exldington Iuminositv. of the accreting secondary might have helped in terminating the high mass transfer rate., The super-Eddington luminosity of the accreting secondary might have helped in terminating the high mass transfer rate.547 For an efficient accretion the companion in our model of NGC 300 OT has to be very close to the primary. ~2/4.," For an efficient accretion the companion in our model of NGC 300 OT has to be very close to the primary, $\sim 2 R_1$."548" We note that if (he orbit is highly eccentric. sav e=0.9 as in jj Car. and periastron passage is ab a,=21406AU. then the orbital period is ~100vr."," We note that if the orbit is highly eccentric, say $e=0.9$ as in $\eta$ Car, and periastron passage is at $a_p=2R_1 \simeq 6 \AU$, then the orbital period is $\sim 100 \yr$."549 Furthermore. if the outburst was caused by the periastron passage. then some high mass loss episode could have occurred. 100 vears ago. but not necessarily as strong.," Furthermore, if the outburst was caused by the periastron passage, then some high mass loss episode could have occurred 100 years ago, but not necessarily as strong."550 Assuming a velocity of τὸkins| (as observed Lor the present bipolar outflow) these ejecta are al a distance of ~1500AU., Assuming a velocity of $75 \km \s^{-1}$ (as observed for the present bipolar outflow) these ejecta are at a distance of $\sim 1500 AU$.551 If the progenitor was indeed an Fstar. its hisher temperature would imply a smaller radius. and hence a shorter dvnanmical timescale of about half a month for an effective temperature of 7500Ex.," If the progenitor was indeed an F, its higher temperature would imply a smaller radius, and hence a shorter dynamical timescale of about half a month for an effective temperature of $ 7500 \K$."552 This will considerably ease the constraints on our model. as the ou€burst in our model is limited [rom below by the dvnamical time scale.," This will considerably ease the constraints on our model, as the outburst in our model is limited from below by the dynamical time scale."553 In our scenario most of the outburst energy comes from accretion onto the companion., In our scenario most of the outburst energy comes from accretion onto the companion.554be determined as the respective colin deusities are uot known.,be determined as the respective column densities are not known.555 The mean molecular fraction along the line of seh is f=1.7<10°, The mean molecular fraction along the line of sight is $f=1.7\times 10^{-3}$.556 The kinetic temperate in IL- bearing clouds can be approxima to a first ΟΥ:erbvt 1e exclation temperature Zyj measured between t aud llevels, The kinetic temperature in $_2$ -bearing clouds can be approximated to a first order by the excitation temperature $T_{01}$ measured between the $J=0$ and 1 levels.557 We fud Z4=7647. 81+29 and OF+ la Labs1.96168. 1.96211 aud 1.96221 res)octive," We find $T_{01}=76\pm 7$, $81\pm 29$ and $97\pm 40$ K at $z_{\rm abs}=1.96168$, 1.96214 and 1.96221 respectively."558 These values are typical of what is measured in the ilo of our Galaxy aud along lines osieht tfwoueh the LAIC aud SAIC (Shull ο al., These values are typical of what is measured in the halo of our Galaxy and along lines of sight through the LMC and SMC (Shull et al.559 2000. Tiuuliusou et al.," 2000, Tumlinson et al."560 2002) and are simular to wha is derived in different coumponcuts at tabs=2.31 toward | 082 and ταν1.97 toward 004 Παπάς et al., 2002) and are similar to what is derived in different components at $z_{\rm abs}=2.34$ toward $+$ 082 and $z_{\rm abs}=1.97$ toward $-$ 004 (Srianand et al.561 2000. Petitjean et al.," 2000, Petitjean et al."562 2002)., 2002).563 Excitation temperatures for hiever J levels are also elven i Table , Excitation temperatures for higher $J$ levels are also given in Table \ref{tabmol}.564Iu the case of he components at. respectively. tans1.96165 aud 1.906221 toward 366. the high J level poplatious cal dC explained by a single excitalon temiperature within lncasurement uncertainties (respectively Ta~--270 and 35 VIN).," In the case of the components at, respectively, $z_{\rm abs}=1.96168$ and 1.96221 toward $-$ 366, the high $J$ level populations can be explained by a single excitation temperature within measurement uncertainties (respectively $T_{\rm ex}\approx 270$ and 350 K)."565 These values are larger than the neasured dLOTIC teuperatures., These values are larger than the measured kinetic temperatures.566 This suggests that. in addition to collisions. otier processes like UV. pumping aud formation ptmpi18o are at play to poplate hese levels.," This suggests that, in addition to collisions, other processes like UV pumping and formation pumping are at play to populate these levels."567" In the case of the tabs=1.96211 com»»nent. line αιιο, uncertaiu vin the position of tlic zero level aud. possible saturation of the low J lines actually result in large errors in the column density iieasurenmen. alc asinele excitation tempcraure. Tis8B80 Ts. is also consisteut with the observed uel J level populations."," In the case of the $z_{\rm abs}=1.96214$ component, line blending, uncertainty in the position of the zero level and possible saturation of the low $J$ lines actually result in large errors in the column density measurement, and a single excitation temperature, $T_{\rm ex}\approx 380$ K, is also consistent with the observed high $J$ level populations."568 Iucideitallv. simular population ratios are observed aloug lines of sieht through the Alagelanc stremu (Sembach et al.," Incidentally, similar population ratios are observed along lines of sight through the Magellanic stream (Sembach et al."569 2OL. Richter et al.," 2001, Richter et al."570 2001)., 2001).571 Cousidering the cosmüc microwave background radiatiou (CAMDBR) to be the oulv source of excitation (e.g. Sriunand et al., Considering the cosmic microwave background radiation (CMBR) to be the only source of excitation (e.g. Srianand et al.572 2000). we cau derive upper lits on the CBR temperature from the column deusities ofCL. παπα “that we measure in different compoucuts of f DLA system toward 366 (see Table 5)).," 2000), we can derive upper limits on the CMBR temperature from the column densities of, $^\star$ and $^{\star\star }$ that we measure in different components of the DLA system toward $-$ 366 (see Table \ref{tabphy}) )."573 In t colponcuts where Ty is detected. the values are fouud ve mach larecr than what is predicted from stanclare Die-Bang cosinology (io. aout. 8 Wj.," In the components where $_2$ is detected, the values are found to be much larger than what is predicted from standard Big-Bang cosmology (i.e. about 8 K)."574 Under he conditio oxevadlius in these clouds. fiuorescence is uceleible iu o»pulatiug the excited levels of (see Fig.," Under the conditions prevailing in these clouds, fluorescence is negligible in populating the excited levels of (see Fig."575 2 of Silva Vicmioas 2002)., 2 of Silva Viegas 2002).576 This meaus that excitation x collisiols is imuportaut and. therefore. that the iuflueice. of local plivsical couditious (both deusifv aud teniperature) substantial iu those clouds.," This means that excitation by collisions is important and, therefore, that the influence of local physical conditions (both density and temperature) is substantial in those clouds."577" Ccsuverscly, assundus t CXIBR temperature to be 8 1 ane the kinetic teniperature cine approximated by the excitation tempcrature of t J=l rotational level. we can estimate the hydrogen density from the relative popuations of t10 fine-structure levels."," Conversely, assuming the CMBR temperature to be 8 K and the kinetic temperature being approximated by the excitation temperature of the $J=1$ rotational level, we can estimate the hydrogen density from the relative populations of the fine-structure levels."578" For the compoucuts where I. is nof detected. we assume Zig,=LOO I. As cau be seen from Talde 5.. it is apparent that the densities are larger in the eas where I» is detected."," For the components where $_2$ is not detected, we assume $T_{\rm kin}=100$ K. As can be seen from Table \ref{tabphy}, it is apparent that the densities are larger in the gas where $_2$ is detected."579 Therefore. the nou«etection of II» iu components haviug of heavy. clenents ds ac 4sequence of lower densities and possibly higher cluperatures.," Therefore, the non-detection of $_2$ in components having of heavy elements is a consequence of lower densities and possibly higher temperatures."580 This is in Lue with the conchsious of Petitjean et al. (, This is in line with the conclusions of Petitjean et al. (5812000).,2000).582 The allowed range in pressure p/h ueasured in the three Ty components are res)ectivelv 13770. 20280 and S550 cur? I. Such uch ο aye seen oulv in < of the eas of our Galaxy CJeukius Tripp 2001) butare consistent with the uch pressures :uso derived iu the case of," The allowed range in pressure $p/k$ measured in the three $_2$ components are respectively $-$ 13770, $-$ 20280 and $-$ 8550 $^{-3}$ K. Such high pressures are seen only in $\le 3$ of the gas of our Galaxy (Jenkins Tripp 2001) butare consistent with the high pressures also derived in the case of"583 to the typical Galactic values., to the typical Galactic values.584 This places a constraint on the cosmic ray diffusion., This places a constraint on the cosmic ray diffusion.585 The enhancement of scattering corresponding to a reduction (110%) of the CR diffusion coefficient compared to Galactic mean has been suggested by a few earlier models to match the observations (Fujita et al., The enhancement of scattering corresponding to a reduction $1-10\%$ ) of the CR diffusion coefficient compared to Galactic mean has been suggested by a few earlier models to match the observations (Fujita et al.586 2009. Ohira et al.," 2009, Ohira et al."587 2011. Li Chen 2010).," 2011, Li Chen 2010)."588 No physical justification on how and why the scattering 1s boosted has been provided. however.," No physical justification on how and why the scattering is boosted has been provided, however."589 In addition. earlier studies made a few serious assumptions including the Bohm diffusion. and a phenomenological power law evolution of the maximum energy accelerated at a certain epoch.," In addition, earlier studies made a few serious assumptions including the Bohm diffusion and a phenomenological power law evolution of the maximum energy accelerated at a certain epoch."590 We shall reinvestigate this problem by incorporating a proper physical deseription of the relevant processes. re. the shock acceleration 1n the presence of the streaming instability and nonlinear damping processes by background turbulence.," We shall reinvestigate this problem by incorporating a proper physical description of the relevant processes, i.e. the shock acceleration in the presence of the streaming instability and nonlinear damping processes by background turbulence."591 The slower diffusion implies enhanced wave perturbations. which may arise from streaming instability (see. e.g.. Longair 2002).," The slower diffusion implies enhanced wave perturbations, which may arise from streaming instability (see, e.g., Longair 2002)."592 Earlier work has shown that streaming instability is limited by background turbulence (Yan Lazarian 2002: Farmer Goldreich 2004; Beresnyak Lazarian 2008)., Earlier work has shown that streaming instability is limited by background turbulence (Yan Lazarian 2002; Farmer Goldreich 2004; Beresnyak Lazarian 2008).593 This could be the determinative factor for the maximum energy attainable at the shock front as suggested by Ptuskin Zirakashvili (2005)., This could be the determinative factor for the maximum energy attainable at the shock front as suggested by Ptuskin Zirakashvili (2005).594 However. the isotropic Kolmogorov scaling for the turbulence. adopted by Ptuskin Zirakashvilt (2005). is not applicable to MHD turbulence.," However, the isotropic Kolmogorov scaling for the turbulence, adopted by Ptuskin Zirakashvili (2005), is not applicable to MHD turbulence."595 Moreover. if the enhanced scattering in. the vicinity of SNRs as indicated by the observations are due to the increased flux of cosmic rays there. we need to examine whether the flux of accelerated particles is sufficient to induce high enough growth rates of the streaming instability to overcome the nonlinear damping by background turbulence.," Moreover, if the enhanced scattering in the vicinity of SNRs as indicated by the observations are due to the increased flux of cosmic rays there, we need to examine whether the flux of accelerated particles is sufficient to induce high enough growth rates of the streaming instability to overcome the nonlinear damping by background turbulence."596 In this paper. we apply our present day understanding of the interaction between the streaming instability and the background turbulence to the modeling of the gamma ray emission from molecular clouds near SNRs.," In this paper, we apply our present day understanding of the interaction between the streaming instability and the background turbulence to the modeling of the gamma ray emission from molecular clouds near SNRs."597 We shall treat the problem in a self-consistent way by comparing the streaming level that is allowed by the preexisting turbulence and the, We shall treat the problem in a self-consistent way by comparing the streaming level that is allowed by the preexisting turbulence and the598wwest of north for the major axis of the ellipse.,west of north for the major axis of the ellipse.599 If this elliptical lobe of emission traced in the linecore is tracing a rotating cloud core. then it could be used to constrain the position angle of the outflow. as the outflow would be expected to be orthogonal to the orientation of the cloud core.," If this elliptical lobe of emission traced in the linecore is tracing a rotating cloud core, then it could be used to constrain the position angle of the outflow, as the outflow would be expected to be orthogonal to the orientation of the cloud core."600 The approximately northeast-to-southliwest. direction implied by the blueshifted outflow lobe is more consistent with the orientation of the e¢loud core. than a north-south outflow implied by the redshilted lobe of the outflow. (see Figure 3)).," The approximately northeast-to-southwest direction implied by the blueshifted outflow lobe is more consistent with the orientation of the cloud core, than a north-south outflow implied by the redshifted lobe of the outflow (see Figure \ref{intco}) )."601" Our numerical modeling of the inlall region (see relinfall-model below) is also more consistent with a 45"" position angle than a orientation for the rotational axis.", Our numerical modeling of the infall region (see \\ref{infall-model} below) is also more consistent with a $\sim 45$ position angle than a north-south orientation for the rotational axis.602 A rotating tvpe of structure was also seen in the case of the protobinary IAS 16293. where submillimeter linecore and linewing emission of CS and showed evidence for a rotating. cireumbinary structure (Naravananetal.1993).," A rotating type of structure was also seen in the case of the protobinary IRAS 16293, where submillimeter linecore and linewing emission of CS and showed evidence for a rotating, circumbinary structure \citep{nwb98}."603. The maps seen in the rightmost panel of Figure 4 also show a similar result., The maps seen in the rightmost panel of Figure \ref{inthco} also show a similar result.604 Here too. the lincore emission is elongated orthogonal to the outflow. and the linewings seem 1o trace rotation in the cloud core.," Here too, the lincore emission is elongated orthogonal to the outflow, and the linewings seem to trace rotation in the cloud core."605 The orthogonality of the lnewing emission fromthe EIIV linewine emission of CO (see Figure 3)) is even more pronounced., The orthogonality of the linewing emission fromthe EHV linewing emission of CO (see Figure \ref{intco}) ) is even more pronounced.606 It is also seen Chat the peaks of redshiltecl and blieshiltec enussion of this next higher transition are located closer to the center of SMMA compared to the lobes. probably due to the enhanced excitation conditions closer to the center of the object.," It is also seen that the peaks of redshifted and blueshifted emission of this next higher transition are located closer to the center of SMM4 compared to the lobes, probably due to the enhanced excitation conditions closer to the center of the object."607 In summary. the linewing emission of bbeconmes progressively less associated with outflow as we eo up the rotational ladder.," In summary, the linewing emission of becomes progressively less associated with outflow as we go up the rotational ladder."608 The linecore emission of (he and (transitions of are likely not impacted by the outflow. while the ]linecore emission might5 be tracing5 both the embedded cloud core as well as dense shells of ihe molecular outflow.," The linecore emission of the and transitions of are likely not impacted by the outflow, while the linecore emission might be tracing both the embedded cloud core as well as dense shells of the molecular outflow."609 The centroid velocity of a line prolile is that velocity at which the integrated intensity (ihe area under (he line profiles) is equal on either side., The centroid velocity of a line profile is that velocity at which the integrated intensity (the area under the line profiles) is equal on either side.610 Centroid velocity maps have been shown to be a better tool in the detailed study of complicated velocity fields Chan integrated intensity maps (Adelson&Leung1988;Naravananetal. 1993)..," Centroid velocity maps have been shown to be a better tool in the detailed study of complicated velocity fields than integrated intensity maps \citep{ade88,nwb98}. ."611 Centroid velocity maps of CS and, Centroid velocity maps of CS and612The model described above requires emerging bipolar magnetic region areas. locations. and (ill angles as input.,"The model described above requires emerging bipolar magnetic region areas, locations, and tilt angles as input."613 We have these data lor the period between 1913 and 1986., We have these data for the period between 1913 and 1986.614 The [lux (ransport model gives as output the radial component of the magnetic field on the solar surface., The flux transport model gives as output the radial component of the magnetic field on the solar surface.615 Throughout most of the period covered by (he simulations. observational maegnetogranm data are unavailable for comparing against (he results of the simulations.," Throughout most of the period covered by the simulations, observational magnetogram data are unavailable for comparing against the results of the simulations."616 We therefore consider the Sun's open flux.£554... Which has been inferred from the aa-index of geomagnetic variations (and its extensions) from 1842 onwards (77)..," We therefore consider the Sun's open flux, which has been inferred from the $aa$ -index of geomagnetic variations (and its extensions) from 1842 onwards \citep{Lockwood99, Lockwood03}."617 To obtain Ifrom the simulation. we take the surface distribution of D and use the current sheet source surface model (227). lo extrapolate the solar surface field out into the heliosphere (see??)..," To obtain from the simulation, we take the surface distribution of $B$ and use the current sheet source surface model \citep{Zhao95b, Zhao95, Zhao02} to extrapolate the solar surface field out into the heliosphere \citep[see][]{Schuessler06, Jiang10}."618 The results of the extrapolation are dependent on the assumed. value of the ‘cusp radius. [Hosp Which is the radial distance bevond which all the field lines are open.," The results of the extrapolation are dependent on the assumed value of the `cusp radius', $R_{\mathrm{cusp}}$, which is the radial distance beyond which all the field lines are open."619 We also compare the simulation results against (he (timing of the polar field reversals. which have been inferred by ? [vom polar filament observations from 1870 to 2001.," We also compare the simulation results against the timing of the polar field reversals, which have been inferred by \cite{Makarov03} from polar filament observations from 1870 to 2001."620" We here give the results for the parameter set jjj=250 knigs. tg =0.7. By=—10.2 G. jj,=0 and Hu=τοΠω."," We here give the results for the parameter set $\eta_{H}=250$ $^2$ $^{-1}$, $g=0.7$, $B_0=-10.2$ G, $\eta_r=0$ and $R_{\mathrm{cusp}}=1.55 \rsun$."621" The value D,,4;=374 G was found by matching to the total observed unsigned magnetic flix from the Mount. Wilson and Wilcox Solar Observatories (see Figure 4)).", The value $B_{\mathrm{max}}=374$ G was found by matching to the total observed unsigned magnetic flux from the Mount Wilson and Wilcox Solar Observatories (see Figure \ref{fig:calib_Bmax}) ).622 With these parameters. the model reproduces well the open flux inferred by ? as shown in Fieure 5..," With these parameters, the model reproduces well the open flux inferred by \cite{Lockwood03} as shown in Figure \ref{fig:ref}."623 This applies to the phases as well as the amplitudes of both (he maxima and minima of the inlerred open flux., This applies to the phases as well as the amplitudes of both the maxima and minima of the inferred open flux.624 The corresponding evolution of the polar [lield (defined as the average field above 475° latitude) ancl axial dipole moment are shown in (he upper panel of Figure 6.., The corresponding evolution of the polar field (defined as the average field above $\pm 75^{\circ}$ latitude) and axial dipole moment are shown in the upper panel of Figure \ref{fig:ref_pol}.625 The polar field closely follows the axial dipole moment. with a delav of several vears.," The polar field closely follows the axial dipole moment, with a delay of several years."626 This is understandable as the dipole moment reacts more quickly to [lux transport across the equator. which then takes several additional vears to reach the polar latitudes (> 75°).," This is understandable as the dipole moment reacts more quickly to flux transport across the equator, which then takes several additional years to reach the polar latitudes $>75^{\circ}$ )."627 The simulated. polar fields reverse for all eveles., The simulated polar fields reverse for all cycles.628 Without (the variations of the tilt. angle the weak evele 20 would have been unable to offset the polar field alter evele 19., Without the cycle-dependent variations of the tilt angle the weak cycle 20 would have been unable to offset the polar field after cycle 19.629 It was this tvpe of problem which led 7. and? to introduce a decay term., It was this type of problem which led \cite{Schrijver02} and \cite{Baumann06} to introduce a decay term.630 Here we achieve a good agreement with the observations even without such a term because of the anti-correlation in the observed tilt angles and evele strengths (?).., Here we achieve a good agreement with the observations even without such a term because of the anti-correlation in the observed tilt angles and cycle strengths \citep{Dasi-Espuig10}.631 The asterisks in (he upper panel of Figure 6 indicate the (imines of the polar reversals as derived bv? from Ilo polar filament data., The asterisks in the upper panel of Figure 6 indicate the timings of the polar reversals as derived by \cite{Makarov03} from $\alpha$ polar filament data.632 The reversal times are reasonably well reproduced. except for the first reversal which is still affected by arbitrary form of the initial condition.," The reversal times are reasonably well reproduced, except for the first reversal which is still affected by arbitrary form of the initial condition."633Our result is directly applicable to xotoplanetauv disks (PPDs). where the ionization frac‘tion resultiug YOU Major jonizatio1 sonrces such as Nnws and cosnic ravs is generally οτίcrs of magnitude heow unity. aud it decreases frou surface to the midplane because of he ateuuation of ionizing particles (Came1996).,"Our result is directly applicable to protoplanetary disks (PPDs), where the ionization fraction resulting from major ionization sources such as X-rays and cosmic rays is generally orders of magnitude below unity, and it decreases from surface to the midplane because of the attenuation of ionizing particles \citep{Gammie96}."634. Nou-dcval MIID effects are closely reevant to the Hageorotational mstabilitv (MBI. Balns&Tawlev 1991)). whose linear dispersion relation as well as the 1on-linear saturatioi propertics are stronglv aflected (Wardle1999:Balbus2009).. aud whether the AMIRI is responsible for driving rapid accretion with Al~10StMo in PPDs (Παπιάταetal.1995) has been a long-standing problem.," Non-ideal MHD effects are closely relevant to the magnetorotational instability (MRI, \citealp{BH91}) ), whose linear dispersion relation as well as the non-linear saturation properties are strongly affected \citep{Wardle99,Balbus09}, and whether the MRI is responsible for driving rapid accretion with $\dot{M}\sim10^{-8\pm1}M_{\bigodot}$ $^{-1}$ in PPDs \citep{Hartmann_etal98} has been a long-standing problem."635 Mos studies lave focused on the role of the Olunic resistivity (6.8.itTurner etal.2007:Bai&Goodman 2009)). while was not uutil recerilv have AD Όσοιtaken iuto accoltiur to estimate the effectiveness of the MRI (Chiang&MurlTaV-Clav.2007τιPerezDecker&Cliang 2011a).," Most studies have focused on the role of the Ohmic resistivity (e.g., \citealp{Turner_etal07,BaiGoodman09}) ), while it was not until recently have AD beentaken into account to estimate the effectiveness of the MRI \citep{CMC07,PerezBeckerChiang11}."636. Codiinue the most recent results from ποΊσα. simulations of the MRI with AD (Bai&Stone2011).. Bai(2011) showed hat while the MRI cau always operate in PPDs. AD cau be a main limiting facor for tl1ο MBRI«riven. accretion (besides Oluuic yoslsivitv).," Combining the most recent results from numerical simulations of the MRI with AD \citep{BaiStone11a}, \citet{Bai11a} showed that while the MRI can always operate in PPDs, AD can be a main limiting factor for the MRI-driven accretion (besides Ohmic resistivity)."637 The redction of AD cofheieut bv tiny eyadus (e.g. PATI). while counterintuitive. helps eulance the accrotlon rate. as we will demoustrate iu this paper.," The reduction of AD coefficient by tiny grains (e.g., PAHs), while counterintuitive, helps enhance the accretion rate, as we will demonstrate in this paper."638" Although observational data slow stroug evidence of eran erowth to nuücron size or larger 1in PPDs (οον, D'Alessioctal.2001:vanBoekelet 20033). PAII enudsson has also|jen detected in majoritv of IIerbie Aec/Doe stars (Acke&vandenAncker2001).. as well as a small fraction of T-Tauw stars (CeersOjvenactal. 2010)."," Although observational data show strong evidence of grain growth to micron size or larger in PPDs (e.g., \citealp{DAlessio_etal01,vanBoekel_etal03}) ), PAH emission has also been detected in majority of Herbig Ae/Be stars \citep{AckeAncker04}, as well as a small fraction of T-Tauri stars \citep{Geers_etal06,Oliveira_etal10}."639. As aveued in Perez-Decker&Chi-aug(2011: |. PATIs nav be equally abundant in T- disks but they fluoresce less hunuinouslv due to faiuter ultraviolet radiation field of their host stars.," As argued in \citet{PerezBeckerChiang11}, PAHs may be equally abundant in T-Tauri disks but they fluoresce less luminously due to fainter ultraviolet radiation field of their host stars."640 Tje existence of PATIs also suggests a continuous size distribution of eyalus to the inallest cud of a few A as a result of erain coagulation and fragnentation., The existence of PAHs also suggests a continuous size distribution of grains to the smallest end of a few ${\rm \AA}$ as a result of grain coagulation and fragmentation.641" Tiroughout this paper. we use the phrases ""tinv eran and PAIT interchaugeably. which refer to eai1 with size a (01a. Tiny grains may dominate larcor eras in =abundance while coutrvibute a noeglieile yaction of the total eraiu mass,"," Throughout this paper, we use the phrases “tiny grain"" and PAH interchangeably, which refer to grain with size $a\lesssim0.01\mu$ m. Tiny grains may dominate larger grains in abundance while contribute a negligible fraction of the total grain mass."642" Talking the C»eraiu deusv to be 3 o cniὉand the eas mean C»molecular weight Hy, to be 2.35] atomic mass (ax appropriate for PPDs). tιο relation between eram nass fraction (f£) aud grain abudance per II» molecule (ev) reads where e ds erain size."," Taking the grain density to be 3 g $^{-3}$and the gas mean molecular weight $\mu_n$ to be $2.34$ atomic mass (as appropriate for PPDs), the relation between grain mass fraction $f$ ) and grain abundance per $_2$ molecule $x$ ) reads where $a$ is grain size."643" The abuudauce of eraius with aS O.0lpim may easily reach large abundance of 10‘9 or higher. while the abundance of α=θ, μι graius would be at most about 1012."," The abundance of grains with $a\lesssim0.01\mu$ m may easily reach large abundance of $10^{-9}$ or higher, while the abundance of $a\gtrsim0.1\mu$ m grains would be at most about $10^{-12}$."644 The significanceOo of this abundance cut Ce=10 ?) will be addressed iu this paper., The significance of this abundance cut $x=10^{-9}$ ) will be addressed in this paper.645 Iu Section ?? we describe a generalized. model for uon-ideal MIID diffusion cocfficieuts with the inchision of chareed erains., In Section \ref{sec:grain} we describe a generalized model for non-ideal MHD diffusion coefficients with the inclusion of charged grains.646 The model is applied to interpret the the results in Section ?7.. where we study the role of tiny eraius iu PPDs following the methodology of Dai(2011)..," The model is applied to interpret the the results in Section \ref{sec:ppd}, where we study the role of tiny grains in PPDs following the methodology of \citet{Bai11a}."647 Suuuuary and discussion follow iu Section ?7.., Summary and discussion follow in Section \ref{sec:conclusion}.648 The Ohuvs Law derives from the motion of charged particles. which is characterized by the Wall parameter. the ratio between the evrofrequeney aud the moments exchange rate (Wardle2007).," The Ohm's Law derives from the motion of charged particles, which is characterized by the Hall parameter, the ratio between the gyrofrequency and the momentum exchange rate \citep{Wardle07}."649".. For species j with mass my aud charge Z;c. the Tall parameter reads where μμdoanj) with (re); being the rate coefficient>; forcoe) moment transfer between charged species j with the ueutrals aud yi, is the mean molecular weight of the neutrals."," For species $j$ with mass $m_j$ and charge $Z_je$, the Hall parameter reads where $\gamma_j\equiv\langle\sigma v\rangle_j/(\mu_n+m_j)$ with $\langle\sigma v\rangle_j$ being the rate coefficient for momentum transfer between charged species $j$ with the neutrals and $\mu_n$ is the mean molecular weight of the neutrals."650 Charged species j ds stronely coupled to the neutrals if [|«1. and is strongly tied to magnetic ficlds when |./j1.," Charged species $j$ is strongly coupled to the neutrals if $|\beta_j|\ll1$, and is strongly tied to magnetic fields when $|\beta_j|\gg1$."651" Tn weakly ionized sas with a nuuber of different charged species. the general expressions for the Olunic. Tall and ambipolar diffusion coefficients are eiven bv (Wardle2007:Bai2011) where σι—Voy,m=|5 aud the Olunic.. Πα aud Pedersen couductivities areop respectively, where the sunuuatiou goes over all charged species."," In weakly ionized gas with a number of different charged species, the general expressions for the Ohmic, Hall and ambipolar diffusion coefficients are given by \citep{Wardle07,Bai11a}652 where $\sigma_\perp\equiv\sqrt{\sigma_H^2+\sigma_P^2}$ and the Ohmic, Hall and Pedersen conductivities are respectively, where the summation goes over all charged species."653 Note that the Wall conductivity depends ou the sign of while o0 aud ap depend ouly on |Z].," Note that the Hall conductivity depends on the sign of $Z_j$, while $\sigma_O$ and $\sigma_P$ depend only on $|Z_j|$."654 The simple Z;.expressions for the magnetic diffusion cocfiicicuts (2)) can be obtained by asstuuine electrous and ious are the only two charged species., The simple expressions for the magnetic diffusion coefficients \ref{eq:diff0}) ) can be obtained by assuming electrons and ions are the only two charged species.655 Below we eeneralize it to include tiny erains., Below we generalize it to include tiny grains.656 considerBesides the reason mentioned iu the iutroduction. we tiny eraius because they are unlikely to possess multiple charges due to higher poteutial barrier (Perez-Decker&Chi- 2011a).. which simplifics the algebra cousiderablv.," Besides the reason mentioned in the introduction, we consider tiny grains because they are unlikely to possess multiple charges due to higher potential barrier \citep{PerezBeckerChiang11}, , which simplifies the algebra considerably."657" Du addition. the mean free path for tiny eraius is sufficieutlv πια so that they can be treated as Πα,"," In addition, the mean free path for tiny grains is sufficiently small so that they can be treated as fluid."658 The momentum trausfer rate coefficieuts for clectrous. ious and eras can be found in equations (11) - (16) of Dai (2011)..," The momentum transfer rate coefficients for electrons, ions and grains can be found in equations (14) - (16) of \citet{Bai11a}. ."659 Converting to the Mall parameter. we have," Converting to the Hall parameter, we have"660reftable:dates)).,).661 The NTT data used a dithered pattern of 3 and 9 exposures per final image in the optical and nIR respectively., The NTT data used a dithered pattern of 3 and 9 exposures per final image in the optical and nIR respectively.662 Data were reduced using the package wherein crosstalk correction. flatfielding. sky subtraction. bias-subtraction and frame addition were carried. out as necessary.," Data were reduced using the package wherein crosstalk correction, flatfielding, sky subtraction, bias-subtraction and frame addition were carried out as necessary."663 The 3.9'x3.9' images were astrometrically calibrated against 2MASS (Skrutskieetal..2006) or USNO-B1.0 (Monetetal..2003) within the GAIA package and given positional errors include a 22MASS systematic uncertainty reftable:positions))., The $3.9\arcmin \times 3.9\arcmin$ images were astrometrically calibrated against 2MASS \citep{Skrutskie2006:AJ.131} or USNO-B1.0 \citep{Monet2003:AJ125} within the GAIA package and given positional errors include a 2MASS systematic uncertainty \\ref{table:positions}) ).664 PSF photometry was carried out on the final images using the package (Stetson.1987) withinIRAF., PSF photometry was carried out on the final images using the package \citep{stetson1987:PASP99} within.665 The magnitude of the source of interest in each field was calculated relative to a number of comparison stars in. the field. including the seatter as a measure of error.," The magnitude of the source of interest in each field was calculated relative to a number of comparison stars in the field, including the scatter as a measure of error."666 The comparison stars were calibrated against Perssonetal.(1998) or Landolt(1992) photometric standards (though in. the case ofJ17379-3747.. no suitable optical standards were observed so magnitudes were calibrated against USNO-BI.0 sources).," The comparison stars were calibrated against \cite{Persson1998:AJ116} or \cite{Landolt1992:AJ.104} photometric standards (though in the case of, no suitable optical standards were observed so magnitudes were calibrated against USNO-B1.0 sources)."667 If a field was observed on more than one night we tested for variability. using only the error associated with the relative magnitude.," If a field was observed on more than one night we tested for variability, using only the error associated with the relative magnitude."668 As no variability was found. the tabulated magnitudes are calculated from the weighted average relative magnitudes and. since the exposures being compared were equal. the quoted exposures are of a single image only.," As no variability was found, the tabulated magnitudes are calculated from the weighted average relative magnitudes and, since the exposures being compared were equal, the quoted exposures are of a single image only."669 The equation. /—7=(0.24740.003R—D) Jordietal..2006)... was used to transform the cataloged / magnitudes of the standard stars into 7 magnitudes with which to calibrate the images.," The equation, $i-I = (0.247 \pm 0.003) (R-I)$ \citep{Jordi2006A&A.460}, was used to transform the cataloged $I$ magnitudes of the standard stars into $i$ magnitudes with which to calibrate the images."670 It was again used to transform the observed i band magnitude of the object into appropriate 7 magnitudes., It was again used to transform the observed $i$ band magnitude of the object into appropriate $I$ magnitudes.671 Upper limits are approximated from the dimmest observable object in the region of interest., Upper limits are approximated from the dimmest observable object in the region of interest.672 To supplement our own observations. we utilise data from the Telescopes (Werneretal...2004) Galactic Legacy Infrared Mid-Plane Survey Extraordinaire(GLIMPSE:: Benjaminetal 2003). when available.," To supplement our own observations, we utilise data from the 's \citep{Werner2004:ApJS154} Galactic Legacy Infrared Mid-Plane Survey Extraordinaire; \citealt{Benjamin2003:PASP115}) ), when available."673" was carried out by the IRAC instrument (Fazioetal..2004) aboardSpitzer.. spans eeither side of the Galactic center up to 42-4"" un latitude and includes mosaic images and catalog entries at 3.6. 4.5. 5.8 and 8.0 μπι. The observed infrared magnitudes reftable:mags)) were first converted to flux densities. F,. at frequency v. then to flux per filter. ων in units of tonscem2 ss!."," was carried out by the IRAC instrument \citep{Fazio2004:ApJS154} aboard, spans either side of the Galactic center up to $\pm$ in latitude and includes mosaic images and catalog entries at 3.6, 4.5, 5.8 and 8.0 $\mu$ m. The observed infrared magnitudes \\ref{table:mags}) ) were first converted to flux densities, $F_{\nu}$, at frequency $\nu$, then to flux per filter, $F_{filter}$ in units of $^{-2}$ $^{-1}$."674" This is done via Friern=1509.18896F, (ALLY where to and. Al are. the effective wavelength and full width at half maximum of the filter in question.", This is done via $F_{filter} = 1509.18896 F_{\nu}$ $( \Delta\lambda/\lambda )$ where $\lambda$ and $\Delta\lambda$ are the effective wavelength and full width at half maximum of the filter in question.675 compatible files. for Spectral Energy Distribution (SED) fitting. are then produced from the flux per filter value using the FTOOL.," compatible files, for Spectral Energy Distribution (SED) fitting, are then produced from the flux per filter value using the ,."676£1x2xsp. The transient X-ray source.XTEJI637—498.. was first detected by the (RXTE) at à 2-l10kkeV flux of 2-4 mCrab: an outburst) which lasted approximately from August 25 to September 5 2008 (Markwardtetal..2008a)..," 	 The transient X-ray source, was first detected by the (RXTE) at a keV flux of 2-4 mCrab; an outburst which lasted approximately from August 25 to September 5 2008 \citep{Markwardt2008ATel.1699}."677 Follow up observations by the XX-ray Telescope (XRT) allowed the position to be refined reftable:positions:: Starlingetal. 2008))., Follow up observations by the X-ray Telescope (XRT) allowed the position to be refined \\ref{table:positions}; \citealt{Starling2008ATel.1704}) ).678 Based on a power law fit (photon index 1.5+ 0.4) of the XRT spectrum. Wijnandsetal.(2008) suggested that the source was anLMXB.. though they cautioned that another system type (1.e.. high mass X-ray binary) could not be excluded.," Based on a power law fit (photon index $1.5 \pm 0.4$ ) of the XRT spectrum, \cite{Wijnands2008ATel.1700} suggested that the source was an, though they cautioned that another system type (i.e., high mass X-ray binary) could not be excluded."679 Starlingetal. also noted that an optical source. consistent with 2MASS object J16370267-4951401. was detected in the v band by the UUltraviolet Optical Telescope (UVOT). within the XRT," \citeauthor{Starling2008ATel.1704} also noted that an optical source, consistent with 2MASS object $-$4951401, was detected in the $v$ band by the Ultraviolet Optical Telescope (UVOT), within the XRT"680lower. making the line intensities more sensitive to the OPR value.,"lower, making the line intensities more sensitive to the OPR value."681 The observed para-water lines are consistent with an OPR value of 3:1 (40.4)., The observed para-water lines are consistent with an OPR value of 3:1 $\pm0.4$ ).682 The lowest energy level of H:O is ~34KK below that of ortho-H:O. When water forms in the gas phase via exothermic reactions the energy released is much greater than this energy difference and the OPR reflects the high-temperature (-50 KK) thermodynamic 3:1 ratio of the statistical weights between the species., The lowest energy level of $_2$O is $\sim$ K below that of $_2$ O. When water forms in the gas phase via exothermic reactions the energy released is much greater than this energy difference and the OPR reflects the high-temperature $\sim$ K) thermodynamic 3:1 ratio of the statistical weights between the species.683 The derived OPR value of 3:1 confirms that water in IK Tau is formed in warm and dense regions of the envelope where the chemistry ts in thermodynamical equilibrium., The derived OPR value of 3:1 confirms that water in IK Tau is formed in warm and dense regions of the envelope where the chemistry is in thermodynamical equilibrium.684 Assuming the same photodissociation radius as for the main tsotopolog. the isotopic ratios we derive for IK Tau are HIO/H!'Oz2600 and H!9O/H!502200(430).. hence well below the solar values (10/!70-2632 anc 150/150-.499:3).," Assuming the same photodissociation radius as for the main isotopolog, the isotopic ratios we derive for IK Tau are $_2^{16}$ $_2^{17}$ O=600 and $_2^{16}$ $_2^{18}$ , hence well below the solar values \citep[$^{16}$ $^{17}$ $\sim$ 2632 and $^{16}$ $^{18}$ $\sim$."685 Interpreting the derived isotopic ratios ii terms of nucleosynthesis and subsequent dredge-ups or extra mixing processes is quite complex (e.g.???).. ," Interpreting the derived isotopic ratios in terms of nucleosynthesis and subsequent dredge-ups or extra mixing processes is quite complex \citep[e.g.][]{Harris1985ApJ...292..620H, Harris1987ApJ...316..294H, Karakas2010ApJ...713..374K}."686In stars that are sufficiently massive to undergo. CNO-cycle. hydroger burning. the low initial Ο abundance (assumed to be solar) is enhanced.," In stars that are sufficiently massive to undergo CNO-cycle hydrogen burning, the low initial $^{17}$ O abundance (assumed to be solar) is enhanced."687 When helium burning begins inside the hydrogen- shell. '’O is expected to be completely destroyed in the region where maximum hydrogen burning occurs.," When helium burning begins inside the hydrogen-burning shell, $^{17}$ O is expected to be completely destroyed in the region where maximum hydrogen burning occurs."688 The isotope 50. on the other hand. is expected to be destroyed during hydrogen burning. so that it virtually disappears from. the hydrogen-burning zone and from the hydrogen-exhausted CNO equilibrium zone within it.," The isotope $^{18}$ O, on the other hand, is expected to be destroyed during hydrogen burning, so that it virtually disappears from the hydrogen-burning zone and from the hydrogen-exhausted CNO equilibrium zone within it."689 When helium burning starts. the 5Ο abundance might slightly increase.," When helium burning starts, the $^{18}$ O abundance might slightly increase."690 A succession of convective mixings brings to the surface material that is affected by these nuclear transformations., A succession of convective mixings brings to the surface material that is affected by these nuclear transformations.691" Calculations by ? show that in every star that becomes a red giant star (M20.8 Msun)). the initial '*O/""O ratio decreases to ~440 during the first dredge-up. while the '°O/'*O slightly increases."," Calculations by \citet{Harris1985ApJ...292..620H} show that in every star that becomes a red giant star $\ga$ ), the initial $^{16}$ $^{17}$ O ratio decreases to $\sim$ 440 during the first dredge-up, while the $^{16}$ $^{18}$ O slightly increases."692 The second dredge-up occurs at the end of core helium burning only for the most massive intermediate-mass stars (M24.5 Msun))., The second dredge-up occurs at the end of core helium burning only for the most massive intermediate-mass stars $\ga$ ).693 The estimated !*O/'7O ratio ranges between 150 and 500. while the '°O/'SO ratio slightly increases.," The estimated $^{16}$ $^{17}$ O ratio ranges between 150 and 500, while the $^{16}$ $^{18}$ O ratio slightly increases."694 The third dredge-up occurs in the subsequent helium shell-burning phasefor stars 22Msun.. and is expected to yield isotopic ratios of ΙΟο <200.," The third dredge-up occurs in the subsequent helium shell-burning phasefor stars $\ge$, and is expected to yield isotopic ratios of $^{16}$ $^{17}$ O $\le200$."695 If hot bottom burning occurs (for stars above Msun)). the /*O/!'O ratio will be of the order of 20-50.," If hot bottom burning occurs (for stars above ), the $^{16}$ $^{17}$ O ratio will be of the order of 20–50."696" That the !*0/""O ratio is around 600. implies that the first but no subsequent dredge-ups occurred and constrains the initial mass of IK Tau to be withinMsun."," That the $^{16}$ $^{17}$ O ratio is around 600, implies that the first but no subsequent dredge-ups occurred and constrains the initial mass of IK Tau to be within."697". Alternatively. if the star is more massive than 2 M. and the third dredge-up has occurred (but has not turned the star into a carbon-rich star). transferred material from a third dredge-up envelope must have had a !'*O/""O ratio <200."," Alternatively, if the star is more massive than 2 $M_\odot$ and the third dredge-up has occurred (but has not turned the star into a carbon-rich star), transferred material from a post-third dredge-up envelope must have had a $^{16}$ $^{17}$ O ratio $\leq 200$."698 This implies that in stars with '*O/'*O ~600 the transferred material has been heavily diluted by material from the star's own envelope with much higher !*O/'O ratios., This implies that in stars with $^{16}$ $^{17}$ O $\sim 600$ the transferred material has been heavily diluted by material from the star's own envelope with much higher $^{16}$ $^{17}$ O ratios.699 From Fig., From Fig.700 5 of ?.. 1t is estimated that IK Tau has a low s-process neutron exposure. το <0.1. implying a low absolute enhancement of the s-process elements and only a few third dredge-up events. consistent with IK Tau still being an oxygen-rich AGB star.," 5 of \citet{Harris1987ApJ...316..294H}, it is estimated that IK Tau has a low s-process neutron exposure, $\tau_0$ $\le 0.1$, implying a low absolute enhancement of the s-process elements and only a few third dredge-up events, consistent with IK Tau still being an oxygen-rich AGB star."701 Hitherto. the lower than solar '°O/'SO ratios cannot be explained by any stellar evolution model in the literature.," Hitherto, the lower than solar $^{16}$ $^{18}$ O ratios cannot be explained by any stellar evolution model in the literature."702 However. IK Tau is not the only Galactic star with a low 150/130 ratio (seeFig.3in2): some barium stars analyzed by ? also have a low '°O/'SO value.," However, IK Tau is not the only Galactic star with a low $^{16}$ $^{18}$ O ratio \citep[see Fig.\ 3 in][]{Karakas2010ApJ...713..374K}; some barium stars analyzed by \citet{Harris1985ApJ...292..620H} also have a low $^{16}$ $^{18}$ O value."703 It is anticipated that the observations of other evolved stars in the framework of the HIFISTARS programme BBujarrabal) will add new information to this discussion., It is anticipated that the observations of other evolved stars in the framework of the HIFISTARS programme Bujarrabal) will add new information to this discussion.704 Being a simple diatomic molecule with a well understood energy diagram. CO has been successfully used to study the structure of the CSEs around evolved stars (e.g..??).. Di," Being a simple diatomic molecule with a well understood energy diagram, CO has been successfully used to study the structure of the CSEs around evolved stars \citep[e.g.,][]{Schoier2002A&A...391..577S, Decin2006A&A...456..549D}."705fferent transitions can be used to investigate different regions of the envelope. probing the density. the temperature. and the velocity of the CSE.," Different transitions can be used to investigate different regions of the envelope, probing the density, the temperature, and the velocity of the CSE."706 ? used the 'CO J21-0 to J=7-6 lines to determine the thermophysical structure of the CSE of IK Tau beyond ~100Rstar.. based on a non-local thermodynamic equilibrium (norLTE) radiative transfer analysis of the available transitions.," \citet{Decin2010} used the $^{12}$ CO J=1–0 to J=7–6 lines to determine the thermophysical structure of the CSE of IK Tau beyond $\sim$, based on a non-local thermodynamic equilibrium (non-LTE) radiative transfer analysis of the available transitions."707 In the first instance. the kinetic temperature and velocity structure of the envelope were calculated by solving the equations of motion of gas and dust and the energy balance simultaneously.," In the first instance, the kinetic temperature and velocity structure of the envelope were calculated by solving the equations of motion of gas and dust and the energy balance simultaneously."708" To get insight into the structure in the inner wind region. the HCN J23-2 and J=4—3 transitions were used. since observational evidence exists that HCN ts formed close to the star (£3.85"",?).."," To get insight into the structure in the inner wind region, the HCN J=3–2 and J=4–3 transitions were used, since observational evidence exists that HCN is formed close to the star \citep[$\la$3.85\arcsec,][]{Marvel2005AJ....130..261M}."709 The Gaussian HCN line profiles indeed point toward line formation partially in the inner wind where the stellar wind has not yet reached its full terminal velocity (?).., The Gaussian HCN line profiles indeed point toward line formation partially in the inner wind where the stellar wind has not yet reached its full terminal velocity \citep{Bujarrabal1991A&A...251..536B}.710 The results of ? infer a wind acceleration that is lower than derived from solving the momentum equation., The results of \citet{Decin2010} infer a wind acceleration that is lower than derived from solving the momentum equation.711 Adopting the thermodynamic structure derived in ? (and reproduced in Fig., Adopting the thermodynamic structure derived in \citet{Decin2010} (and reproduced in Fig.712 4. of the online Appendix). the theoretical line profiles for the | 00 J=10-9 and J=16-15 are calculated (see Fig. 2))," \ref{fig:structure_IKTau} of the online Appendix), the theoretical line profiles for the $^{12}$ CO J=10–9 and J=16–15 are calculated (see Fig. \ref{Fig:2}) )"713 using the non-LTE radiative transfer code GASTRoNOoM (??).. ," using the non-LTE radiative transfer code GASTRoNOoM \citep{Decin2006A&A...456..549D, Decin2010}. ."714"The ""CO J=10-9 line is very well reproduced. while theJ=16-15 line exhibits slightly larger deviations."," The $^{12}$ CO J=10–9 line is very well reproduced, while theJ=16–15 line exhibits slightly larger deviations."715 The latter most likely reflects the very difficult calibration of this frequency setting (forwhichstandingwavesheavilyperturbedthebaseline.see ?)..," The latter most likely reflects the very difficult calibration of this frequency setting \citep[for which standing waves heavily perturbed the baseline, see][]{Bujarrabal2010}. ."716 This result is consistent with the temperature structure in the region between 20 and dderived by ?.., This result is consistent with the temperature structure in the region between 20 and derived by \citet{Decin2010}.717 To constrain the wind acceleration in the CSE. all molecular emission lines as shown in Figs. 1-," To constrain the wind acceleration in the CSE, all molecular emission lines as shown in Figs. \ref{Fig:1}-"718—2. were modelled (see the online Appendix Appendix B:))., \ref{Fig:2} were modelled (see the online Appendix \ref{modelling}) ).719 The line formation region of, The line formation region of720according to whether we do or do not apply the unbinding and reassignment procedures.,according to whether we do or do not apply the unbinding and reassignment procedures.721" In the former case we refer to all other structures as (self-bound)subhaloes, whereas in the latter case we refer to them assubstructures."," In the former case we refer to all other structures as (self-bound), whereas in the latter case we refer to them as."722" A subhalo is thus always part of a substructure, but a substructure does not necessarily contain a subhalo."," A subhalo is thus always part of a substructure, but a substructure does not necessarily contain a subhalo."723 We study the phase-space structure of Milky Way-sized DM haloes using the high-resolution simulations of the Aquarius Project (Springeletal.2008)., We study the phase-space structure of Milky Way-sized DM haloes using the high-resolution simulations of the Aquarius Project \citep{Springel2008}.724". The cosmological parameters for these simulations are (2,,=0.25,Q,0.75,080.9 and Ho=73km s!Mpc!."," The cosmological parameters for these simulations are $\Omega_m=0.25, \Omega_\Lambda = 0.75 ,\sigma_8=0.9$ and $H_0=73 \rm{km}$ ${\rm s}^{-1}\rm{Mpc}^{-1}$."725 For this project six Galaxy-mass haloes (Aq-A to Aq-F) were selected from a lower resolution version of the Millennium-II Simulation (Boylan-Kolchinetal.2009) and resimulated with progressively higher particle number and smaller softening length.," For this project six Galaxy-mass haloes (Aq-A to Aq-F) were selected from a lower resolution version of the Millennium-II Simulation \citep{Boylan2009}726 and resimulated with progressively higher particle number and smaller softening length."727 The haloes were selected to have no close massive companion at z=0., The haloes were selected to have no close massive companion at $z=0$.728" When studying differences in phase-space structure between these haloes, we use the second resolution level (the highest for which results are available for all six objects)."," When studying differences in phase-space structure between these haloes, we use the second resolution level (the highest for which results are available for all six objects)."729" At this resolution all haloes have more than 1.6x105 particles inside rso, corresponding to a particle mass ~10*Mo."," At this resolution all haloes have more than $1.6\times10^8$ particles inside $r_{50}$, corresponding to a particle mass $\sim10^4{\rm M}_{\sun}$."730" In addition, we use resimulations of the Aq-A halo at four different resolution levels to check the numerical convergence of our results."," In addition, we use resimulations of the Aq-A halo at four different resolution levels to check the numerical convergence of our results."731" In the final section of this paper we investigate phase-space structure in the inner halo, defined as r«Tinner—35 kpc."," In the final section of this paper we investigate phase-space structure in the inner halo, defined as $r<r_{\rm inner}=35$ kpc."732 For this purpose we usethree resolution levels of the Aq-A halo with the largest one (Aq-A-1) having almost 1.5x10? particles inside r59 and more than 2x108 particles inside rinner., For this purpose we usethree resolution levels of the Aq-A halo with the largest one (Aq-A-1) having almost $1.5\times10^9$ particles inside $r_{50}$ and more than $2\times10^8$ particles inside $r_{\rm inner}$.733" Together with the ability of HSF to analyse the full 6D particle distribution, this simulation set allows the first robust and fully general quantification of the various phase-space components predicted by the ACDM model at r~8 kpc where direct detection takes place."," Together with the ability of HSF to analyse the full 6D particle distribution, this simulation set allows the first robust and fully general quantification of the various phase-space components predicted by the $\Lambda$ CDM model at $r\sim 8$ kpc where direct detection takes place."734 We begin by analysing the mass functions of substructures and of self-bound subhaloes in the Aq-A halo and their dependence on resolution., We begin by analysing the mass functions of substructures and of self-bound subhaloes in the Aq-A halo and their dependence on resolution.735" To be consistent with earlier work we define the edge of the halo at rgo=433 kpc and we count all objects within this radius, but we note that this is a large radius and, as a result, the counts are dominated by objects beyond 100 kpc, more than an order of magnitude further from the Galactic Centre than the Sun."," To be consistent with earlier work we define the edge of the halo at $r_{50}=433$ kpc and we count all objects within this radius, but we note that this is a large radius and, as a result, the counts are dominated by objects beyond 100 kpc, more than an order of magnitude further from the Galactic Centre than the Sun."736 In the upper panel of Fig., In the upper panel of Fig.737 1 we compare the differential mass functions of substructures (solid curves) and of self-bound subhaloes (dashed curves) at four different resolutions., \ref{mass_res} we compare the differential mass functions of substructures (solid curves) and of self-bound subhaloes (dashed curves) at four different resolutions.738 The lower panel shows the corresponding cumulative mass functions., The lower panel shows the corresponding cumulative mass functions.739 In both cases the mass functions agree quite well between the simulations above their respective resolution limits., In both cases the mass functions agree quite well between the simulations above their respective resolution limits.740" For the self-bound subhaloes, the slope of the differential mass function is close to —1.9, as found earlier in the SUBFIND analysis of Springeletal.(2008)."," For the self-bound subhaloes, the slope of the differential mass function is close to $-1.9$, as found earlier in the SUBFIND analysis of \cite{Springel2008}."741". At lower resolution the distribution is better approximated, particularly in the low mass bins, by a slope close to —1.8."," At lower resolution the distribution is better approximated, particularly in the low mass bins, by a slope close to $-1.8$ ."742" For the Aq-A-2 halo, we find that 1496 of the halo mass is in self-bound subhaloes, which is"," For the Aq-A-2 halo, we find that $14\%$ of the halo mass is in self-bound subhaloes, which is"743These equations are similar (o those used by Pipin&Seehaler(2009) and Pipin (2009).,These equations are similar to those used by \cite{pip-see09} and \cite{see-pip09}.744. We use the same notations for the Functions and. parameters as in the paper of Pipin(2008) (hereafter. POS).," We use the same notations for the functions and parameters as in the paper of \cite{pip08} (hereafter, P08)."745" Here. G=OQ,logp is the density stratification scale."," Here, $G=\partial_{r}\log\rho$ is the density stratification scale."746" Functions /15,, depend on the Coriolis number Q*=27,04: functions v, describe magnetic quenching and depend on 3j=Ενqiupui?."," Functions $f_{1,2,3,10}^{(a,d)}$ depend on the Coriolis number $\Omega^{*}=2\tau_{c}\Omega_{0}$; functions $\psi_{\eta,\alpha}$ describe magnetic quenching and depend on $\beta=B/\sqrt{\mu_{0}\rho\bar{u^{2}}}$."747 For reference. these functions are given in Appendix.," For reference, these functions are given in Appendix."748" The parameter C5, controls the strength of the a-elfect.", The parameter $C_{\alpha}$ controls the strength of the $\alpha$ -effect.749 In the presented mocel the a-ellect is clistributed in the bulk of the convection zone., In the presented model the $\alpha$ -effect is distributed in the bulk of the convection zone.750 For a more clear demonstration of the boundary condition impact. we confine (he o-affect in a low-latitude region where the racial gradient of the angular velocity is positive in the most part of the solar convection zone.," For a more clear demonstration of the boundary condition impact, we confine the $\alpha$ -affect in a low-latitude region where the radial gradient of the angular velocity is positive in the most part of the solar convection zone."751 Similarly to Dikpatietal.(2004) we specify the confinement function: In the radial direction the a-elfect depends on the density. stratification. G. and function of the Coriolis number ty(Q*).," Similarly to \citet{dikp:04} we specify the confinement function: In the radial direction the $\alpha$ -effect depends on the density stratification, $G$, and function of the Coriolis number $f^{(a)}_{10}\left(\Omega^*\right)$."752" We introduce parameter C5, to control the turbulent diffusion coefficient. gp=Cup. where DE—7.2/3."," We introduce parameter $C_{\eta}$ to control the turbulent diffusion coefficient, $\eta_{T}=C_{\eta}\eta_{T}^{(0)}$, where $\eta_{T}^{(0)}=\tau_{c}\bar{u^{2}}/3$."753 The internal parameters of the solar convection zone are given by Stix(2002)..., The internal parameters of the solar convection zone are given by \citet{stix}.754 At the top of the solar convection zone the stratification is strongly deviates from acdiabatic. and also the turbulence parameters varv sharply.," At the top of the solar convection zone the stratification is strongly deviates from adiabatic, and also the turbulence parameters vary sharply."755 For this reason we confine the integration domain between 0.7142. ancl HR. in radius. and it extends Irom the pole to pole in latitude.," For this reason we confine the integration domain between $R_{\odot}$ and $R_{\odot}$ in radius, and it extends from the pole to pole in latitude."756 The differential rotation profile. Q=OgfoCe.ji) (shown in Fig.laa) is a slightly modified version of the analytical," The differential rotation profile, $\Omega=\Omega_{0}f_{\Omega}\left(x,\mu\right)$ (shown in \ref{fig:fig0-1-1}a a) is a slightly modified version of the analytical"757Minimizing the magnetic energy in the transition laver 2y«orHf implies that B is a potential field in that region.,Minimizing the magnetic energy in the transition layer $R_1<r<R_2$ implies that $\mathbf{B}$ is a potential field in that region.758 To find the miuimum energy Πο] satisfying these requirements. we represent the magnetic field through scalar potentials S aud T: Both the vertical field aud the inclined dipole field do not have a toroidal part T. thus we set T—0 everywhere.," To find the minimum energy field satisfying these requirements, we represent the magnetic field through scalar potentials $S$ and $T$: Both the vertical field and the inclined dipole field do not have a toroidal part $T$, thus we set $T=0$ everywhere."759" For the poloidal scalar potential ο. we make the ausatz where YY""QU.) are the spherical harmonics of order 1 and degree η."," For the poloidal scalar potential $S$, we make the ansatz where $Y_1^m(\vartheta,\varphi)$ are the spherical harmonics of order $1$ and degree $m$."760 Equation (B2)) is compatible with both the inner aud the outer field: auy spherical harmonics of higher order would ouly increase the total euergy. so we do not iuclude then.," Equation \ref{Eq-S-spher-harm}) ) is compatible with both the inner and the outer field; any spherical harmonics of higher order would only increase the total energy, so we do not include them."761 Minimizing the sum of the energy CÀ3)) [with &= Ry] and the energy of the potential field for Ry«rBs. we liud the following coeflicieuts for 9 after a straight-forward. but somewhat teclious calculation: where aud," Minimizing the sum of the energy \ref{Eq-E-inner}) ) [with $R=R_1$ ] and the energy of the potential field for $R_1<r<R_2$, we find the following coefficients for $S$ after a straight-forward, but somewhat tedious calculation: where and"762Patat. 22006. ATel. 454.,"Patat, 2006, ATel, 454."763 Chandra. P... Chavalier. Patat. 22008. ATel. 1393.," Chandra, P., Chavalier, Patat, 2008, ATel, 1393."764 Chugai. 22008. Astron.," Chugai, 2008, Astron."765Let..,"Let.,"766 in press (arXNiv:0801.4463)., in press (arXiv:0801.4468).767 Cyotis. 22008. in preparation.," Crotts, 2008, in preparation."768 Crotts. 22007. HST proposal H11Y1 (httpz//www.stsci.edu/observing/phase2-public/ 11171.pro).," Crotts, 2007, $HST$ proposal 11171 (http://www.stsci.edu/observing/phase2-public/ 11171.pro)."769 Crotts. Sugerman. 22006. //ST proposal 10991 (http://wwvw.stsci.edu/observing/ phase2-public/10991.pro).," Crotts, Sugerman, 2006, $HST$ proposal 10991 (http://www.stsci.edu/observing/ phase2-public/10991.pro)."770 Crotts. A.D.S.. et 22008. in preparation.," Crotts, A.P.S., et 2008, in preparation."771 Crutcher. 11985. ApJ. 288. 604.," Crutcher, 1985, ApJ, 288, 604."772 Della Valle. M.. Panagia. N.. Padovani. P.. Cappellaro. E.. Mannucd. Turatto. 22005. ApJ. 629. 150.," Della Valle, M., Panagia, N., Padovani, P., Cappellaro, E., Mannucci, Turatto, 2005, ApJ, 629, 750."773" Foley. R.J.. et 22007. ApJ. submitted (preprint at arXiv:0710.2338),"," Foley, R.J., et 2007, ApJ, submitted (preprint at arXiv:0710.2338)."774 Freedman. W.L.. et 22001. ApJ. 553. 47.," Freedman, W.L., et 2001, ApJ, 553, 47."775 Gerardy. C.. et 22004. ApJ. GO7. 391.," Gerardy, C., et 2004, ApJ, 607, 391."776 Ilamuy. AL. et 11996. AJ. 112. 2348.," Hamuy, M., et 1996, AJ, 112, 2348."777 Tamuy. AL. et 22000. AJ. 120. 1479 (Erratum. 122. 3506).," Hamuy, M., et 2000, AJ, 120, 1479 (Erratum, 122, 3506)."778" Παιν, AL. et 22003. Nature. 424. 651."," Hamuy, M., et 2003, Nature, 424, 651."779 Immler. S.I. et 22006.," Immler, S.I., et 2006."780 ApJ. 648. L119.," ApJ, 648, L119."781 Kolb. 22005. report of Dark Energy. Task Force to the NSF-NASA-DOE Astronomy," Kolb, 2005, report of Dark Energy Task Force to the NSF-NASA-DOE Astronomy"782"period is £24,=0.108d:0.006 davs. which coincides with the superhump period derived by Rolfe et ((2000).","period is $P_{\mathrm{sh}}=0.108 \pm 0.006$ days, which coincides with the superhump period derived by Rolfe et (2000)."783 The length of our database is not enough to perform a consistent period analysis. since the short. variability could »e due to Dickering.," The length of our database is not enough to perform a consistent period analysis, since the short variability could be due to flickering."784 Consequently. a large database is then needed to reveal the nature of the oscillation.," Consequently, a large database is then needed to reveal the nature of the oscillation."785 periodicity of ~15 min is suggested. by eve. although a detailed »eriod. analvsis with a long database would. be required or confirmation.," A periodicity of $\sim 15$ min is suggested by eye, although a detailed period analysis with a long database would be required for confirmation."786 The finding of coherent. of semi-coherent (QPOs) oscillations would strengthen the idea of V348 Pup »neg an IP., The finding of coherent of semi-coherent (QPOs) oscillations would strengthen the idea of V348 Pup being an IP.787 From the evidences presented. along this paper we can conclude that V348 Pup belongs to the family of the SW Sex stars., From the evidences presented along this paper we can conclude that V348 Pup belongs to the family of the SW Sex stars.788 Actually. it satisfies all the conditions stated for a system to belong to this family (see 1: see also Thorstensen et al.," Actually, it satisfies all the conditions stated for a system to belong to this family (see 1; see also Thorstensen et al."789 1991. where these conditions are established. auc nez-Pais et al.," 1991, where these conditions are established, and nez-Pais et al."790 1999. where they are revised). namely: We have shown that V348 Pup is an SW Sex star.," 1999, where they are revised), namely: We have shown that V348 Pup is an SW Sex star."791 Among all these svstems. it has the shortest orbital period. which lies in the period gap.," Among all these systems, it has the shortest orbital period, which lies in the period gap."792 The other SW Sex system in the eap is V795 Ler. which has an slighth longer orbital period. of 2.6 h. The main dillerence between them is the orbital inclination.," The other SW Sex system in the gap is V795 Her, which has an slightly longer orbital period of 2.6 h. The main difference between them is the orbital inclination."793" While V348 Pup is an eclipsing (high-inclination) svstem (72 SO""). V795 Ler is non-eclipsing (has lower inclination)."," While V348 Pup is an eclipsing (high-inclination) system $i\simeq80\degr$ ), V795 Her is non-eclipsing (has lower inclination)."794 From geometrical considerations we can sav that the inclination of V795 is 7<70°., From geometrical considerations we can say that the inclination of V795 is $i\la70\degr$.795 The similarity between the orbital periods makes it very interesting to compare the spectroscopic behaviour of both We have used the results of the spectroscopic study performed by Casares et al. (, The similarity between the orbital periods makes it very interesting to compare the spectroscopic behaviour of both We have used the results of the spectroscopic study performed by Casares et al. (7961996) to derive the inclination of V795 Ler.,1996) to derive the inclination of V795 Her.797 The racial velocity curve of A4686 has a senii-amplitude of 85 kni s.+. which they consider as the dvy-velocity. of the svstem.," The radial velocity curve of $\lambda$ 4686 has a semi-amplitude of 85 km $^{-1}$, which they consider as the $K_1$ -velocity of the system."798 On the other hand. V795 Ler also exhibits superhumps (Patterson Skillman 1994).," On the other hand, V795 Her also exhibits superhumps (Patterson Skillman 1994)."799 The fractional superhump excess. which only depends on q. is z—0.07.," The fractional superhump excess, which only depends on $q$, is $\varepsilon=0.07$."800" Using the relation (Patterson 1998). to caleulate the mass ratio. we obtain gyro,=0.33."," Using the relation (Patterson 1998), to calculate the mass ratio, we obtain $q_{\mathrm{V795}}=0.33$."801" ""his value is almost identical to our estimated. mass ratio of V348 Pup (¢ysixs=0.31).", This value is almost identical to our estimated mass ratio of V348 Pup $q_{\mathrm{V348}}=0.31$ ).802 We can derive the mass of the secondary from equation (1)). which gives M32(V795)=0.22 AL...," We can derive the mass of the secondary from equation \ref{eq1}) ), which gives $M_2({\mathrm{V795}})=0.22$ $_{\sun}$."803 Entering A4. q and Mo in equation (2)) and solving. we ect an orbital inclination of 7253 for VT95 Ler (Casares et al.," Entering $K_1$, $q$ and $M_2$ in equation \ref{eq2}) ) and solving, we get an orbital inclination of $i\simeq53\degr$ for V795 Her (Casares et al."804 1996 estimated /2256). We have seen that the svstem parameters of V348 Pup and V795 Ler are almost identical. with the exception of 7. so the main cdillerences between both svstems are very likely to be clue to inclination elfects.," 1996 estimated $i\simeq56\degr$ We have seen that the system parameters of V348 Pup and V795 Her are almost identical, with the exception of $i$, so the main differences between both systems are very likely to be due to inclination effects."805 Phe most remarkable dillerence is that the lines blueward of A4471 in V795 Her are fully in absorption., The most remarkable difference is that the lines blueward of $\lambda4471$ in V795 Her are fully in absorption.806" This may suggest, that the absorption component is stronger at lower orbitaln inclination.", This may suggest that the absorption component is stronger at lower orbital inclination.807 This is also observed in the non-eclipsing system. LS Peg (see e.g. nez-Pais et al., This is also observed in the non-eclipsing system LS Peg (see e.g. nez-Pais et al.808 1999)., 1999).809 On the other hand. the A4686 line in V348 Pup is much stronger than in V795 Her.," On the other hand, the $\lambda$ 4686 line in V348 Pup is much stronger than in V795 Her."810 This can be due to enhanced. emission located. above the disc. as we have already suggested.," This can be due to enhanced emission located above the disc, as we have already suggested."811 Now. we are going to compare the FLAWAL and. EW of the Balmer lines I12. Hs and H9 in both systems.," Now, we are going to compare the FHWM and EW of the Balmer lines $\beta$, $\gamma$ and $\delta$ in both systems."812 The JNLEMs are a factor 2 larger in V348 Pup., The FWHMs are a factor $\sim 2$ larger in V348 Pup.813 This is a clear elfect ofits higher inclination. because the projected velocity of the disc material is larger.," This is a clear effect of its higher inclination, because the projected velocity of the disc material is larger."814 Phe same elfect can be seen in the and lines., The same effect can be seen in the and lines.815 Phe same inclination effect applies to the EWs., The same inclination effect applies to the EWs.816 They are larger in V348 Pup because the disc is scen at a higher inclination. so the projected surface is smaller and the continuum emission from the disc lower.," They are larger in V348 Pup because the disc is seen at a higher inclination, so the projected surface is smaller and the continuum emission from the disc lower."817 As we described in 3.1. the Balmer and emission is allected by an absorption component at phases 0.350.55.," As we described in 3.1, the Balmer and emission is affected by an absorption component at phases 0.35–0.55."818 This is one of the defining features of the SW. Sex class of CVs., This is one of the defining features of the SW Sex class of CVs.819 In a recent study. Groot. Rutten van Paraclijs (2001) found SW Sex itself in low state.," In a recent study, Groot, Rutten van Paradijs (2001) found SW Sex itself in low state."820 During the phases O75««4 ας Balmer lines changed. from emission to absorption up to 1., During the phases $0.75 < \varphi <0.85$ the bluer Balmer lines changed from emission to absorption up to H14.821 The spectrum closely resembles that of a B-type star. (earlier than B2)., The spectrum closely resembles that of a B-type star (earlier than B2).822 The absorption in SW Sex is also present in phases around 0.5. as we can see in the trailec spectra of Balmer (especially 119) and lines in Groot’s study.," The absorption in SW Sex is also present in phases around 0.5, as we can see in the trailed spectra of Balmer (especially $\delta$ ) and lines in Groot's study."823 Having this in mind. we tried to obtain the spectrum of the absorption component at orbital phases 0.850.55 in V348 Pup.," Having this in mind, we tried to obtain the spectrum of the absorption component at orbital phases 0.35–0.55 in V348 Pup."824 We assume that the, We assume that the825results which included the Bigiel et al. (,results which included the Bigiel et al. (826"2008) data at low X, and up to the starburst regime data of Ix&ennicutt (1998).",2008) data at low $\Sigma_{g}$ and up to the starburst regime data of Kennicutt (1998).827 In this work we propose that the fraction of dense molecular gas that is converted into stars per unit (ime is mainly determined by metallicity dependent feedback in protocluster forming regions which are themselves embedded in larger GMCS., In this work we propose that the fraction of dense molecular gas that is converted into stars per unit time is mainly determined by metallicity dependent feedback in protocluster forming regions which are themselves embedded in larger GMCs.828 We explore the effects of this metallicity dependent prescription on the star formation laws from low surface density regions up to the starburst regime ancl [ind an excellent agreement with the observations., We explore the effects of this metallicity dependent prescription on the star formation laws from low surface density regions up to the starburst regime and find an excellent agreement with the observations.829" In the IKMTO09 model. the surface density of star formation Mgy-y is given bv: where X, is the total gas surface density. and SFEr, is the dimensionless star formation efficiency and which corresponds to the mass fraction of the molecular gas Chat is converted into stars per free-fall Gime /jj of the GAICs in which stars form."," In the KMT09 model, the surface density of star formation $\Sigma_{SFR}$ is given by: where $\Sigma_{g}$ is the total gas surface density, and $SFE_{ff}$ is the dimensionless star formation efficiency and which corresponds to the mass fraction of the molecular gas that is converted into stars per free-fall time $t_{ff}$ of the GMCs in which stars form."830 The SFEr; that is used in IKAITO9 is the one derived bv I&rumholz Mekee (2005) based on a model which describes (he egravo-turbulent regulation of star formation in GMCSs., The $SFE_{ff}$ that is used in KMT09 is the one derived by Krumholz Mckee (2005) based on a model which describes the gravo-turbulent regulation of star formation in GMCs.831" The quantity /j, is the mass fraction of the total gas that is in molecular form.", The quantity $f_{H_{2}}$ is the mass fraction of the total gas that is in molecular form.832 Krumbholz et al. (, Krumholz et al. (833"2009b) have shown that a good approximation of fj, in a given atomic-molecular complex is given by: where s=In(1+0.6N)/(0.049,4.pe.2)Zi) x=O.7TURBA Z9), 0.675) 2%. and Z is the metallicity in units of the solar value.","2009b) have shown that a good approximation of $f_{H_{2}}$ in a given atomic-molecular complex is given by: where $s={\rm ln} (1+0.6~\chi)/(0.04\Sigma_{comp} ({\rm M_{\odot} pc^{-2}})~Z^{'})$, $\chi=0.77 (1+3.1~Z^{'0.365}$ ), $\delta=0.0712~(0.1~s^{-1}+0.675)^{-2.8}$ , and $Z^{'}$ is the metallicity in units of the solar value."834" As pointed out bv KMTO09. ορ relers to the surface density of atomic-molecular complexes of twpical scales of ~100 pe whereas the (wpical current spatial resolution on which X, is measured is several hundred pc or larger."," As pointed out by KMT09, $\Sigma_{comp}$ refers to the surface density of atomic-molecular complexes of typical scales of $\sim 100$ pc whereas the typical current spatial resolution on which $\Sigma_{g}$ is measured is several hundred pc or larger."835" Thus. it is appropriate to consider (hat yon)=cM, where e> Lis a chunping [actor which approaches unitw as the spatial resolution of the observations approaches 100 pc."," Thus, it is appropriate to consider that $\Sigma_{comp}= c~\Sigma_{g}$ where $c \geq 1$ is a clumping factor which approaches unity as the spatial resolution of the observations approaches 100 pc."836 The only dependence of το on metallicity in their model is through the term fy., The only dependence of $\Sigma_{SFR}$ on metallicity in their model is through the term $f_{H_{2}}$.837 Their model also assumes that stars form in a distributed way in GAICS with an efficiency per unit lime that depends only on their dynamical properties (their virial parameter anc, Their model also assumes that stars form in a distributed way in GMCs with an efficiency per unit time that depends only on their dynamical properties (their virial parameter and838 Their model also assumes that stars form in a distributed way in GAICS with an efficiency per unit lime that depends only on their dynamical properties (their virial parameter ancl, Their model also assumes that stars form in a distributed way in GMCs with an efficiency per unit time that depends only on their dynamical properties (their virial parameter and839 210Myr! (P210° diffuse (D—104 K) ionized gas20049)., $>10\sfr$ $>5\sfr$ $T\geq 10^6$ diffuse $T\sim 10^4$ K) ionized gas.840. The fate of the ejected iuultiiphase eas is likely to depend on the galaxy mass as well as cuvirouuent., The fate of the ejected multi-phase gas is likely to depend on the galaxy mass as well as environment.841 For exanrple. massive. isolated galaxies are able to retain their hot. N-rav ciuitting gas reservoirs wlile low-mass ealaxies are not2010).," For example, massive, isolated galaxies are able to retain their hot, X-ray emitting gas reservoirs while low-mass galaxies are not."842. Wot eas winds from ealaxics iu eroups aud clusters may be confined by the dense intergalactic eas in these svstenis οἱ stripped away bv it2006)., Hot gas winds from galaxies in groups and clusters may be confined by the dense intergalactic gas in these systems or stripped away by it.843. Cas which is stripped will curich the intergalactic medium with metals and eutropy1999)., Gas which is stripped will enrich the intergalactic medium with metals and entropy.844 Alost galaxies iu the local universe are in eroups and eroups are the building blocks of ealaxy clusters2009)., Most galaxies in the local universe are in groups and groups are the building blocks of galaxy clusters.845. As outflows are common among star-forming galaxies. we expect to see many in eroup aud field cuvirouments whose star-foruiug galaxy populations are comparable at θ<20.552011)..," As outflows are common among star-forming galaxies, we expect to see many in group and field environments whose star-forming galaxy populations are comparable at $0.3 < z < 0.55$."846 We search for outflows frou galaxies using integral field unit (IFT) spectroscopic observations of SC1120-1202 (hereafter SCL120). a svstein of four N-ray bright ealaxy eroups that will merece to form a cluster comparable in mass to Coma2005).," We search for outflows from galaxies using integral field unit (IFU) spectroscopic observations of SG1120-1202 (hereafter SG1120), a system of four X-ray bright galaxy groups that will merge to form a cluster comparable in mass to Coma."847". We asune a Πατ cosinoloeyv with ΊανPMpe 1. Og,=027. seteQ4,=0.73."," We assume a flat cosmology with $H=71 \kmsmpc$ , $\Omega_M=0.27$, $\Omega_{vac}=0.73$."848 We used FLAMES/CURAFFE ou the VLT (PID: 052.D-0765) to take IFU spectroscopy of 60SCAL20 imienibers in February 2009., We used FLAMES/GIRAFFE on the VLT (PID: 082.B-0765) to take IFU spectroscopy of 60SG1120 members in February 2009.849 The instruueut, The instrument850ith. of the sky). which are statistically peculiar.,"path of the sky), which are statistically peculiar."851 Some of the abovementioned sources of the C(7) anisotropics are frequencydepeudent. thus their coutributious to the naps at different frequency chauucls of the are different.," Some of the above–mentioned sources of the $C(l)$ anisotropies are frequency–dependent, thus their contributions to the maps at different frequency channels of the are different."852 For example. the foregrounds such as dust enüssion. svuchrotrou. freefree. as well as bright and aint point sources. have differeut frequency dependencics and intensities at 33 aud 857 GIIz range. which definitely can manifest as some sources of errors m the pixel window function aud iu he corresponding correlation πιοΊο of the signals.," For example, the foregrounds such as dust emission, synchrotron, free–free, as well as bright and faint point sources, have different frequency dependencies and intensities at 33 and 857 GHz range, which definitely can manifest as some sources of errors in the pixel–pixel window function and in the corresponding correlation function of the signals."853 The influence of the low αιItipole nodes (point (1v)) on the possible anisotropies of the maps oei the flat sky approximation can be detected directly roni the corresponding Ck) amplitudes of the power PA)octruni., The influence of the low multipole modes (point (iv)) on the possible anisotropies of the maps in the flat sky approximation can be detected directly from the corresponding $C({\bf k})$ amplitudes of the power spectrum.854 This paper ids inaiulv devoted. to illustration of jo idea about nuanifestatiou aud estimation of the asvuuuetre (elliptical or more imregular) beam shapes incorporated iu the pixelized data. using both analysis of the two-dimensional spectruni and of phases of the nap (Nasclskyetal. 2000(2))).," This paper is mainly devoted to illustration of the idea about manifestation and estimation of the asymmetric (elliptical or more irregular) beam shapes incorporated in the pixelized data, using both analysis of the two-dimensional spectrum and of phases of the map \cite{naselsky}) )."855" We concentrate ou bei asviuuetrx estimation using simulated CMD map. which reflects directly the specific of the scan strateey, nap naling and noise level."," We concentrate on beam asymmetry estimation using simulated CMB map, which reflects directly the specific of the scan strategy, map making and noise level."856 There are some important issues related to the beam xofiles of the autenna for the Low Frequency Tustrmucut (LEFT) aud Tiel Frequency Tustrmment (IIET) requeney channels (Mandolesietal. 0001)., There are some important issues related to the beam profiles of the antenna for the Low Frequency Instrument (LFI) and High Frequency Instrument (HFI) frequency channels \cite{mandolesi}) ).857 For instance. down to the level -10 dB at LEL the auteuua shapes have approximately elliptical forms aud peculiarities will ouly je included. at ier niultipoles if the level decreases down to -20 dD or OSSss. according to the desigu of he Focal Plane Unit (FPU).," For instance, down to the level -10 dB at LFI, the antenna shapes have approximately elliptical forms and peculiarities will only be included at higher multipoles if the level decreases down to -20 dB or less, according to the design of the Focal Plane Unit (FPU)."858 Thus. roughly spealine. deceutralization ofthe eed horis in the FPU produces the optical distortions of the beam shapes from the circular Gaussian shapes(Buriganaetal. 1998)].," Thus, roughly speaking, decentralization of the feed horns in the FPU produces the optical distortions of the beam shapes from the circular Gaussian \cite{burigana}) )."859 Bean shape influcuce ou he accuracy of the CMD anisotropy C(/) extracion from the observational data is related to the scanning strategv aud pixclization of the πας from the time-ordered TOD)(Wuetal. 2001))., Beam shape influence on the accuracy of the CMB anisotropy $C(l)$ extraction from the observational data is related to the scanning strategy and pixelization of the maps from the time-ordered \cite{wu}) ).860 During scanning of the CMD sky the anteuna beam moves across the sky. meaniug that antenna beam is a function of time.," During scanning of the CMB sky the antenna beam moves across the sky, meaning that antenna beam is a function of time."861 After pixelizatiou of the TOD he position of cach pixel iu the CAB map is related directly with sole points in the time streaun for which we need to obtain the information of the orieutation of the beam location of the beam center relative to each pixel., After pixelization of the TOD the position of each pixel in the CMB map is related directly with some points in the time stream for which we need to obtain the information of the orientation of the beam and location of the beam center relative to each pixel.862 Iu principle. given the scamming strateev( which for the wission is under discussion) aud the beam shapes or each frequency channel. we would be able o model ie eeonietrical properties of the pixel beam shapes aud ier manifestation in the pixel window functions oeicorporated in the CMD power spectrum C().," In principle, given the scanning strategy( which for the mission is under discussion) and the beam shapes for each frequency channel, we would be able to model the geometrical properties of the pixel beam shapes and their manifestation in the pixel–pixel window functions incorporated in the CMB power spectrum $C(l)$."863 However. i6 computational cost would increase dramatically ue to the complicated character of the pixel yea (λαοetal. 19993).," However, the computational cost would increase dramatically due to the complicated character of the pixel–pixel beam \cite{maino}) )."864 Moreover. the scanning strategv and the iustrumental noise combined with the systematic effects could transform the actual beam shape ching the time of observation.," Moreover, the scanning strategy and the instrumental noise combined with the systematic effects could transform the actual beam shape during the time of observation."865 We then should fine BOLIC peculiarities of the complicated beam shape iuflueuce on the CAIB signal., We then should find some peculiarities of the complicated beam shape influence on the CMB signal.866 If the response of au auteuua ou the measured signal is lincar and the CAIB signal aud the iustruneuta nolse are Gaussian and uot correlated. then the information about the beam anisotropy obtaimime bv both methods (power spectrum analysis aud phase analysis) ds the same.," If the response of an antenna on the measured signal is linear and the CMB signal and the instrumental noise are Gaussian and not correlated, then the information about the beam anisotropy obtaining by both methods (power spectrum analysis and phase analysis) is the same."867 However in the ecucral case the sets of eucoded information obtaiuecc by both methods are different., However in the general case the sets of encoded information obtained by both methods are different.868 Thus musing both methods is desirable., Thus using both methods is desirable.869 The plan of this paper is as follows., The plan of this paper is as follows.870 In Section 2 we eive some definitions of CMD signals aud discuss the basic model of the sky map., In Section 2 we give some definitions of CMB signals and discuss the basic model of the sky map.871 In Section 3 we introduce a eeneral power spectrum and phase analysis of CMD signal and the concept of beamshape extraction., In Section 3 we introduce a general power spectrum and phase analysis of CMB signal and the concept of beam–shape extraction.872 In Section. 1 we describe the main idea and its analytical approach., In Section 4 we describe the main idea and its analytical approach.873 The umumerical results are preseuted in Section 5 aud the conclusion in Section 6., The numerical results are presented in Section 5 and the conclusion in Section 6.874 Let us iutroduce the standard model of CMD experiment where TOD contain the information about the signal (and noise ) from a large uunubers of the circular scans., Let us introduce the standard model of CMB experiment where TOD contain the information about the signal (and noise ) from a large numbers of the circular scans.875" We suppose for simplicity that all systematic errors are reinoved after a preliminary ""cleaning of the SCALIS.", We suppose for simplicity that all systematic errors are removed after a preliminary “cleaning” of the scans.876" Iu the temporal domain the observed sigual m is the colmbination of the CMB | foreground signal d; and random iustrumoental noise n5. where with [ει beie the multipole expansion of the stream beam D;(2,)."," In the temporal domain the observed signal ${m}_t$ is the combination of the CMB + foreground signal ${d}_t$ and random instrumental noise $n_t$, where with $B_{t,lm} $ being the multipole expansion of the time--stream beam $B_t(\vec{x}_t)$."877 In Eq. (2)), In Eq. \ref{eq:eq2}) )878" ej, is the correspouding iultipole cocfhicicut of the CAIB |. foreground. signal expansion on the sphere and 5, is the spherical harmonics.", $a_{lm}$ is the corresponding multipole coefficient of the CMB + foreground signal expansion on the sphere and $Y_{lm}$ is the spherical harmonics.879 Following Teemark (1996) we will assume that apmaking algorithm is linear., Following Tegmark (1996) we will assume that map–making algorithm is linear.880" The signal im each pixel s, is then where Mz, is the corresponding poiutiug matrix and s, represeuts the CMD plus foregrounds signals frou the sky convolved by the pixel beam By an."," The signal in each pixel $s_p$ is then where $M_{t,p}$ is the corresponding pointing matrix and $s_p$ represents the CMB plus foregrounds signals from the sky convolved by the pixel beam $B_{p,lm}$ ,"881resulting photometry.,resulting photometry.882" For the HAWKI photometric data, we estimated the effective observed stellar spectrum by multiplying the baseline theoretical stellar spectrum by a theoretical model for the transmission of Earth’s atmosphere and by the transmission curve of the utilized filter."," For the HAWKI photometric data, we estimated the effective observed stellar spectrum by multiplying the baseline theoretical stellar spectrum by a theoretical model for the transmission of Earth's atmosphere and by the transmission curve of the utilized filter."883 The theoretical model for the transmission of Earth’s atmosphere was calculated for the line of sight through atmosphere above the observatory on the night of the observations using the method described by ?.., The theoretical model for the transmission of Earth's atmosphere was calculated for the line of sight through atmosphere above the observatory on the night of the observations using the method described by \citet{seifahrt10}.884" After integrating over the effective bandpasses, we fit a quadratic function to the intensities to determine the limb darkening coefficients."," After integrating over the effective bandpasses, we fit a quadratic function to the intensities to determine the limb darkening coefficients."885" We limited our fits to the range ju,=cos@< 0.1, where 0 is the angle between the emergent intensity and the line of sight."," We limited our fits to the range $\mu\,\equiv\,cos\,\theta\,<\,0.1$ , where $\theta$ is the angle between the emergent intensity and the line of sight."886" We allowed the limb darkening coefficients to be free parameters in the light curve modeling, and we used the estimated theoretical values as priors."," We allowed the limb darkening coefficients to be free parameters in the light curve modeling, and we used the estimated theoretical values as priors."887" That is, the differences between the coefficients used for the light-curve modeling and the coefficients calculated from the PHOENIX models were included in the tabulation of the goodness-of-fit metric (see below)."," That is, the differences between the coefficients used for the light-curve modeling and the coefficients calculated from the PHOENIX models were included in the tabulation of the goodness-of-fit metric (see below)."888 The adopted uncertainties for the priors were set by the spread in the values for the coefficients at the three different temperatures considered for GJ11214., The adopted uncertainties for the priors were set by the spread in the values for the coefficients at the three different temperatures considered for 1214.889 We also tested the effects of using the ? non-linear limb darkening law., We also tested the effects of using the \citet{claret00} non-linear limb darkening law.890" While this functional form yielded better fits at µ<0.1 for the MMIRS data, it did not yield better light curve fits and the final determined transmision spectrum values for the planet are not significantly affected by using it instead of the quadratic law."," While this functional form yielded better fits at $\mu\,<\,0.1$ for the MMIRS data, it did not yield better light curve fits and the final determined transmision spectrum values for the planet are not significantly affected by using it instead of the quadratic law."891 The best-fit limb darkening coefficients were in all cases within of the theoretical values estimated from the Tes = 3026KK model atmosphere., The best-fit limb darkening coefficients were in all cases within $\sigma$ of the theoretical values estimated from the $T_{eff}$ = K model atmosphere.892" We first analyzed the broadband light curves (MMIRS J, H, and K; FORS blue and red; and HAWKI) to determine values for all the transit parameters."," We first analyzed the broadband light curves (MMIRS $J$, $H$, and $K$; FORS blue and red; and HAWKI) to determine values for all the transit parameters."893" We analyzed the MMIRS, FORS, and HAWKI data separately."," We analyzed the MMIRS, FORS, and HAWKI data separately."894" We assumed thesystem scale, inclination, and transit time are the same for the J-, H-, and K-band MMIRS data because they were obtained simultaneously for the same transit."," We assumed thesystem scale, inclination, and transit time are the same for the $J$ -, $H$ -, and $K$ -band MMIRS data because they were obtained simultaneously for the same transit."895 Each of the MMIRS bands were allowed to have a unique transit depth., Each of the MMIRS bands were allowed to have a unique transit depth.896" We used a linear least-squares algorithm toidentify the best-fit parameters, and a residual (?)permutation bootstrap algorithm to asses the uncertainties on the parameters."," We used a non-linear least-squares algorithm \citep{markwardt09} toidentify the best-fit parameters, and a residual permutation bootstrap algorithm to asses the uncertainties on the parameters."897 The standard x? metric was used throughout to asses the quality of themodel fits., The standard $\chi^{2}$ metric was used throughout to asses the quality of themodel fits.898 The determined transit times from analysis of the broadband data with all parameters free are given in Table 2.., 				 The determined transit times from analysis of the broadband data with all parameters free are given in Table \ref{tab:times}.899" Combining these timeswith the previously reported times from ?, 7, and ?,, we can calculate a revised period P +11.2E-7dd, and reference transit"," Combining these timeswith the previously reported times from \citet{desert11}, , \citet{carter11}, , and \citet{berta11}, , we can calculate a revised period $P$ $\pm$ d, and reference transit"900that it is possible for haloes to find their nearest neighbour among their own galaxy. population.,that it is possible for haloes to find their nearest neighbour among their own galaxy population.901 Only a fraction of the least massive haloes be homogencously cistributed with respect to the spirals. but in the top left. panel of Fig. 6..," Only a fraction of the least massive haloes be homogeneously distributed with respect to the spirals, but in the top left panel of Fig. \ref{fig:CNN_All_1_6_Fig},"902 the dash-dotted line of the cumulative fraction of D; for the sample after randomization of the positions is above the dashed. line., the dash-dotted line of the cumulative fraction of $D_{to}$ for the sample after randomization of the positions is above the dashed line.903 Less than a third of the low mass haloes are homogencously distributed., Less than a third of the low mass haloes are homogeneously distributed.904 Phe dillerence. between the dash-dotted and dashed. line is much lareer for the haloes in the right) panel. because they are more clustered. and. the randomization thus has a proportionally greater οσοι.," The difference between the dash-dotted and dashed line is much larger for the haloes in the right panel, because they are more clustered, and the randomization thus has a proportionally greater effect."905 The trend goes in the same direction. but is weaker. for the samples of galaxies selected by. Iuminosities.," The trend goes in the same direction, but is weaker, for the samples of galaxies selected by luminosities."906 There is only limited difference in the distribution of these samples of galaxies with respect to the reference spirals., There is only limited difference in the distribution of these samples of galaxies with respect to the reference spirals.907 Position randomization acts in the same way as for the haloes. but the cumulative fraction of the partly randomized test objects is always the highest.," Position randomization acts in the same way as for the haloes, but the cumulative fraction of the partly randomized test objects is always the highest."908 Less than a third of even the faintest galaxies is homogencously distributed., Less than a third of even the faintest galaxies is homogeneously distributed.909 The colour-selected. blue sample. would. be the best candidate for a population filling the voids between spirals.," The colour-selected, blue sample would be the best candidate for a population filling the voids between spirals."910 However. after partly. reclistributing its population. the istance to the nearest spiral at a given. fraction. of the objects is still higher than for the initial sample.," However, after partly redistributing its population, the distance to the nearest spiral at a given fraction of the objects is still higher than for the initial sample."911 Although the difference between true. and. randomized samples is somewhat weaker than in the previous cases. the conclusion for a homogeneous population is negative.," Although the difference between true and randomized samples is somewhat weaker than in the previous cases, the conclusion for a homogeneous population is negative."912" Note that galaxies in also have the highest average SER per stellar mass (among all colour selected. samples). aud may be termed ""active galaxies”."," Note that galaxies in also have the highest average SFR per stellar mass (among all colour selected samples), and may be termed “active galaxies”."913 Conversely. the reddest sample has nearest spiral neighhours clearly closer than have the spirals themselves. consistent with the above results for massive clusters. and the fact that very red galaxies are mostly satellite galaxies of such systems.," Conversely, the reddest sample has nearest spiral neighbours clearly closer than have the spirals themselves, consistent with the above results for massive clusters, and the fact that very red galaxies are mostly satellite galaxies of such systems."914 The trends in nearest neighbour statistics for the morphologically selected samples (CrAl;)) are similar to the results obtained for colour selection. but with a somewhat lower amplitude.," The trends in nearest neighbour statistics for the morphologically selected samples ) are similar to the results obtained for colour selection, but with a somewhat lower amplitude."915 A detailed comparison with the observational results presented in >POL is dillicult both because the analysis there is carried out in redshift space and. more importantly. because the definition and completeness of the observational samples are dilflicult to quantify.," A detailed comparison with the observational results presented in P01 is difficult both because the analysis there is carried out in redshift space and, more importantly, because the definition and completeness of the observational samples are difficult to quantify."916 The qualitative agreement is. however. quite good.," The qualitative agreement is, however, quite good."917 The most. broadly distributed subsamples in our simulation (e.g.GC). or )) have nearest neighbour distributions which relate to those of the reference spirals in much the same way as POL finds for his observed. samples of chwarl ancl LSB galaxies.," The most broadly distributed subsamples in our simulation (e.g., or ) have nearest neighbour distributions which relate to those of the reference spirals in much the same way as P01 finds for his observed samples of dwarf and LSB galaxies."918 In. addition. the change in the distributions caused by randomizing the positions of a third. of the test. galaxies. are similar in the simulated. ancl observed samples.," In addition, the change in the distributions caused by randomizing the positions of a third of the test galaxies, are similar in the simulated and observed samples."919 We conclude that the nearest neighbour statistics suggest that the behaviour of the observed. ancl simulated: populations with respect to voids are quite similar., We conclude that the nearest neighbour statistics suggest that the behaviour of the observed and simulated populations with respect to voids are quite similar.920 We have looked for signatures of voids in the simulation of MOI. which miniues the dark matter and galaxy cüstribution of the Local Universe up to SOOO The simulation can resolve the morphology of an LAIC-type galaxy and the luminosity of a cwarl elliptical.," We have looked for signatures of voids in the simulation of M01, which mimics the dark matter and galaxy distribution of the Local Universe up to 8000 The simulation can resolve the morphology of an LMC-type galaxy and the luminosity of a dwarf elliptical."921 We have aclelressedl the question. raised by POL. of whether numerica simulations of galaxy formation in the current stanclare picture predict objects in the observationallv empty spaces defined by normal. ἐν spirals.," We have addressed the question, raised by P01, of whether numerical simulations of galaxy formation in the current standard picture predict objects in the observationally empty spaces defined by normal, $L_{*}$ spirals."922 We showed first that regions of size ~10h.1Mpe exis in the simulation which are devoid of even the smallest. D haloes we can resolve., We showed first that regions of size $\sim10\:\hMpc$ exist in the simulation which are devoid of even the smallest DM haloes we can resolve.923 We studied the distribution of galaxies as à function. of luminosity. colour and. morphology. ane the halo distribution as a function of mass.," We studied the distribution of galaxies as a function of luminosity, colour and morphology, and the halo distribution as a function of mass."924 We found tha of our samples fills in underdense DAL environments., We found that of our samples fills in underdense DM environments.925" ‘The faint-end slope of the ""equal-mass Luminosity functions computed. in regions of different densities. shows some steepening as one goes to less dense regions: dwarls are relatively more abundant than L, galaxies in comparison with high density regions. but the overall variation of the shape of the LE is limited."," The faint-end slope of the “equal-mass” luminosity functions computed in regions of different densities shows some steepening as one goes to less dense regions: dwarfs are relatively more abundant than $L_{*}$ galaxies in comparison with high density regions, but the overall variation of the shape of the LF is limited."926" Nearest. neighbour statistics sugeest that none of our simulated populations can be considered. to fill in the voids defined by £, spirals.", Nearest neighbour statistics suggest that none of our simulated populations can be considered to fill in the voids defined by $L_{*}$ spirals.927 This contrasts with the discussion of POL. who states that at z=0 there is still a significant fraction of the matter in regions between clusters and filaments in simulations of a flat. low-density universe.," This contrasts with the discussion of P01, who states that at z=0 there is still a significant fraction of the matter in regions between clusters and filaments in simulations of a flat, low-density universe."928 Down to its resolution limit. our scheme of galaxy formation. qualitatively reproduces the observed galaxy populations around. voids.," Down to its resolution limit, our scheme of galaxy formation qualitatively reproduces the observed galaxy populations around voids."929 The present simple study can be expanded in two wavs., The present simple study can be expanded in two ways.930 First. one might derive a more quantitative. comparison based. for instance. on the distribution of the sizes of the voids. which could be compared to the observations of etal.(2000) or to the analvtical model of Eriedmann&Piran (2001).," First, one might derive a more quantitative comparison based, for instance, on the distribution of the sizes of the voids, which could be compared to the observations of \citet{Mu00} or to the analytical model of \citet{Fr00}."931. Second. one can go to higher resolution.," Second, one can go to higher resolution."932 l]lowever. with current computer capacities. simulations of the size of the one exploited. here are already costly.," However, with current computer capacities, simulations of the size of the one exploited here are already costly."933 Furthermore. a comprehensive reevaluation of the relative importance of the physical processes would be needed.," Furthermore, a comprehensive reevaluation of the relative importance of the physical processes would be needed."934 For example. nearby ionizing sources at z3 or the general UV background. may inhibit the formation of galaxies like the Fornax dwarf in a spatially modulated way.," For example, nearby ionizing sources at $z\sim3$ or the general UV background may inhibit the formation of galaxies like the Fornax dwarf in a spatially modulated way."935 The simulations presented in this paper were carried. out on the PSE supercomputer at the Computing Center of the Alax-Planek-Society in Garching. Germany.," The simulations presented in this paper were carried out on the T3E supercomputer at the Computing Center of the Max-Planck-Society in Garching, Germany."936 Simulated galaxy populations analysecl here are publically available at httpz//www.mpa-garching.mpe.cde/NumCos/ClI, Simulated galaxy populations analysed here are publically available at http://www.mpa-garching.mpg.de/NumCos/CR/937 Simulated galaxy populations analysecl here are publically available at httpz//www.mpa-garching.mpe.cde/NumCos/ClIt, Simulated galaxy populations analysed here are publically available at http://www.mpa-garching.mpg.de/NumCos/CR/938Since the maximum polarization percentage observed i sitbauilliietre polarization maps is rarely ereater than 1054. equation 3lL sugeestsgs that 0.1 is a reasonalle choice for (nj.,"Since the maximum polarization percentage observed in sub-millimetre polarization maps is rarely greater than $10\%$, equation \ref{eq:pmax} suggests that $0.1$ is a reasonable choice for $\meanalpha$."939" Using this choice. our approach predicts the magnitude of the polarization peorceutage obtained from our models. which is eoncrally less than p,,,,."," Using this choice, our approach predicts the magnitude of the polarization percentage obtained from our models, which is generally less than $p_{max}$."940 This is i coutrast to WIS90 who worswith normalized quantities., This is in contrast to WK90 who work with normalized quantities.941 We caution the reader that £0? could. iu principle. vary from region to regiou. which would affect the magnitude of the polarization percentage that we predict.," We caution the reader that $\meanalpha$ could, in principle, vary from region to region, which would affect the magnitude of the polarization percentage that we predict."942 It would also slightly affect the shapes of the polarization profiles. since (0) apppears in the deuoninuator of equation 3.1. aud cauwot be factored out.," It would also slightly affect the shapes of the polarization profiles, since $\meanalpha$ apppears in the denominator of equation \ref{eq:p} and cannot be factored out."943 Polariuetry only maps the component of the magnetic fickL parallel to the plane of the ska., Polarimetry only maps the component of the magnetic field parallel to the plane of the sky.944 Suppose hat the magnetic field hreading the integra-shaped filament in Orion A contains only this planc-ofsky compoucut., Suppose that the magnetic field threading the integral-shaped filament in Orion A contains only this plane-of-sky component.945 If this were truc. the Matthews :uid. Wilso1 (2000) nap. as well as the smaller scale map by Schleuning (1998). svoukL suecooest that we are seciug eiher a filament or au cdge-on sheet beiie mipaled wea well-ordered feld tat is perpendicular o the filanent axis or the midplane of the sheet.," If this were true, the Matthews and Wilson (2000) map, as well as the smaller scale map by Schleuning (1998), would suggest that we are seeing either a filament or an edge-on sheet being impaled by a well-ordered field that is perpendicular to the filament axis or the midplane of the sheet."946 While this wieht explain the overall seuse of the polarizatio1 vectors. it cannot easily account for the deplarization of hese maps seen toward the ceutre of the putative slice or filament.," While this might explain the overall sense of the polarization vectors, it cannot easily account for the depolarization of these maps seen toward the centre of the putative sheet or filament."947 For such a transverse fiek model. it is easv to verity from equations 6.. 7.. and 3.1. that p would be coustant over the eutire flument. since ¢=0 everywhere aud ce=const.," For such a transverse field model, it is easy to verify from equations \ref{eq:q}, \ref{eq:u}, and \ref{eq:p} that $p$ would be constant over the entire filament, since $\zeta=0$ everywhere and $\psi=const$."948 The analysis of Section 3.1 would 1t predict the observed depolarization aloug he axis of the flament or the midplane of the sheet.," The analysis of Section \ref{sec:analysis}949 would not predict the observed depolarization along the axis of the filament or the midplane of the sheet."950 It could. hiowever. be accomplished if the polarization were due to eraius that are preferentially more spherical or poorlv aligned in dense regions.," It could, however, be accomplished if the polarization were due to grains that are preferentially more spherical or poorly aligned in dense regions."951 We show in Section 12. that helical fields tweacding a filamentary cloud can result iu depolarization toward the filament axis. otherwise similar in aypearance to wliat would be expected from the above transverse field scenario.," We show in Section \ref{sec:patterns} that helical fields threading a filamentary cloud can result in depolarization toward the filament axis, otherwise similar in appearance to what would be expected from the above transverse field scenario."952 However. the depoarization is due to fhe 3-dimensional structure of the field iu this case aud does not depend on the erain shapes or their aliguinent.," However, the depolarization is due to the 3-dimensional structure of the field in this case and does not depend on the grain shapes or their alignment."953 We present polarization maps of our helically magnetized models of flamentary clouds using the method discussed in Section 3.1..., We present polarization maps of our helically magnetized models of filamentary clouds using the method discussed in Section \ref{sec:analysis}.954 We first restrict our parameter space by only showing results for filaneuts whose axes lie in the plane of the sla., We first restrict our parameter space by only showing results for filaments whose axes lie in the plane of the sky.955 Tn Section LL. we show maps for a filament at several inclination angles ou the sky.," In Section \ref{sec:inc}, we show maps for a filament at several inclination angles on the sky."956 Figure d shows tfree represeutative models to illustrate the eeneral tvpes of behaviour tlat we find iu our maps., Figure \ref{fig:types} shows three representative models to illustrate the general types of behaviour that we find in our maps.957 We refer to these qualitative patterus as types 1 to 3 for simplicity. although we cuphasize that the underlying models represent a continu in parameter spacὉ (sce FPL).," We refer to these qualitative patterns as types 1 to 3 for simplicity, although we emphasize that the underlying models represent a continuum in parameter space (see FP1)."958 In panel a) we siow. a nodol (type 1) where the polarization vectors are everywhere parallel to the flament., In panel a) we show a model (type 1) where the polarization vectors are everywhere parallel to the filament.959 The most striking feature of the map is the ¢epolarization aloug the axis., The most striking feature of the map is the depolarization along the axis.960 Qualitativelv. this ulap shares some features with he Mathews and Wilson (200) nap of the Orion filament. specifically the ovγα oricutation of the polarization vectors and the depolar‘ization toward the οσοιήτα. regions.," Qualitatively, this map shares some features with the Matthews and Wilson (2000) map of the Orion filament, specifically the overall orientation of the polarization vectors and the depolarization toward the central regions."961 Panel b) «Ixavs a model (type 2) whose polarization vectors are oriented opposite to the type 1l model in panel a)., Panel b) shows a model (type 2) whose polarization vectors are oriented opposite to the type 1 model in panel a).962 If such a patteru were observed. it could be uusiuterpreted as the result of a pirely poloidal Seld.," If such a pattern were observed, it could be misinterpreted as the result of a purely poloidal field."963 These models have two depolarized regious. with," These models have two depolarized regions, with"964Space Astrophysics Grant NACAV-2596 and S'TSCL/NASA Grant. CO-5903.,Space Astrophysics Grant NAGW-2596 and STScI/NASA Grant GO-5903.965 Phe financial support. by the (ASL) is. gratefully acknowledged., The financial support by the (ASI) is gratefully acknowledged.966 An anonvmous referee provided verv detailed anc helpful comments., An anonymous referee provided very detailed and helpful comments.967 ΓΗ. acknowledges. useful. conversations with Craig Sarazin. ancl we especially thank him for assistance with the aarchival cata.," RTR acknowledges useful conversations with Craig Sarazin, and we especially thank him for assistance with the archival data."968reftab3)) are very similar and agree well within 1o.,) are very similar and agree well within $\sigma$.969 On other hand. dSSct stars are typically fast-rotating objects. and the rotation cllects on the structure ancl evolution might moclily the estimates of global parameters of the stars al. 2006).," On other hand, $\delta$ Sct stars are typically fast-rotating objects, and the rotation effects on the structure and evolution might modify the estimates of global parameters of the stars \citep[see e.g. ][]{goupil05, suarez05, fox06}."970. To verify if this elfect is important in our case. we considered. a typical case for a star with mass 1.7-1.8AL.," To verify if this effect is important in our case, we considered a typical case for a star with mass 1.7-1.8."971 According to Suárezctal. (2005).. even in case of vsini~ 150-200 kms. the clleet on the mass estimate from the HI diagram is of few%.. well within the uncertainty due to the errors on the empirical estimates of luminosity and elfective temperature (see table 3)).," According to \citet{suarez05}, , even in case of $\sin$ $\sim$ 150-200 km/s, the effect on the mass estimate from the HR diagram is of few, well within the uncertainty due to the errors on the empirical estimates of luminosity and effective temperature (see table \ref{tab3}) )."972 We used the parallaxes measured. by the LIPPATRCOS satellite (Perrvmanetal.1997). to verify the [Iuminosities derived. ini the present work., We used the parallaxes measured by the HIPPARCOS satellite \citep{perryman97} to verify the luminosities derived in the present work.973 We also estimated independently the luminosity of cluster stars by adopting the distances found in the literature obtained. through e.g. isochrone fitting., We also estimated independently the luminosity of cluster stars by adopting the distances found in the literature obtained through e.g. isochrone fitting.974 Only four stars in our sample are sullicicntly bright [or inclusion in the LEPPATC'OS parallax catalogue., Only four stars in our sample are sufficiently bright for inclusion in the HIPPARCOS parallax catalogue.975 Phese are Isloc in reftab4 together with the parallaxes from the vanLecuwen(2007) revised catalogue., These are listed in \\ref{tab4} together with the parallaxes from the \citet{leeuwen} revised catalogue.976 To derive the luminosity we used he V and £(2V) values listed in reflabl as well as the bolometric correction as a function of spectral ἵνρο from Pickles(1998)..., To derive the luminosity we used the $V$ and $E(B-V)$ values listed in \\ref{tab1} as well as the bolometric correction as a function of spectral type from \citet{pickles}.977 The resulting uminosities and errors are listed in reftab4d where our spectroscopic results are also shown for comparison purposes., The resulting luminosities and errors are listed in \\ref{tab4} where our spectroscopic results are also shown for comparison purposes.978 An inspection of the table reveals hat there is agreement within the CrLors., An inspection of the table reveals that there is agreement within the errors.979 The only obvious discrepancy is found. for the star 003429637 1178875)., The only obvious discrepancy is found for the star 03429637 178875).980 The clilferenee in luminosity is lo. and. deserves Sonic cliscussion.," The difference in luminosity is $> 1\,\sigma$, and deserves some discussion."981 We clic not [ind any significant cdillerence between the spectroscopic and the photometric estimates of Zir for this star., We did not find any significant difference between the spectroscopic and the photometric estimates of $T_{\rm eff}$ for this star.982 Furthermore. the IHIPPABRCOS parallax (vanLeeuwen:2007) is very small relative to the parallax estimated. from. its spectral tvpe and apparent magnitude.," Furthermore, the HIPPARCOS parallax \citep{leeuwen} is very small relative to the parallax estimated from its spectral type and apparent magnitude."983 In our opinion. 003420637 1178875) is very likely a double star. (DommanectNvs1994).," In our opinion, 03429637 178875) is very likely a double star \citep{dommanget94}."984. The binary nature can significantly alfect the estimated: parallax. colour. ancl Yigg.," The binary nature can significantly affect the estimated parallax, colour, and $T_{\rm eff}$."985 As mentioned. in Section 3.. our spectroscopic determination of Tir ds in agreement with that derived by Abt(1984)..," As mentioned in Section \ref{parameter}, our spectroscopic determination of $T_{\rm eff}$ is in agreement with that derived by \citet{abt}."986 As for cluster stars. we have to estimate the distances o the host clusters NGC 6866 and NGC 6811 first.," As for cluster stars, we have to estimate the distances to the host clusters NGC 6866 and NGC 6811 first."987 lm as reported by Molenda-Zalowicz(2009).. both the distance. modulus. and ECD-V) vary significantly from author to author.," 1mm as reported by \citet{molenda}, both the distance modulus and E(B-V) vary significantly from author to author."988 Here. we decided: to assume a distance D=1200£120 pc as in Molenda-Zakowiez(2000) (no error on clistance is available in the literature. we assumed conservatively an uncertainty of 1054).," Here we decided to assume a distance $\pm$ 120 pc as in \citet{molenda} (no error on distance is available in the literature, we assumed conservatively an uncertainty of )."989 As for the reddening we adopted (D.V)=0.12£0.02. according to Dutra&Biea(2000) who mace a study of the foreground au background. dust in the direction of the cluster.," As for the reddening we adopted $E(B-V)=0.12\pm0.02$, according to \citet{dutra} who made a study of the foreground and background dust in the direction of the cluster."990 The resulting luminosities for the three variables in NCC 6866 are shown in Table 4 in comparison with our estimates., The resulting luminosities for the three variables in NGC 6866 are shown in Table \ref{tab4} in comparison with our estimates.991 The agreement is good. within the errors., The agreement is good within the errors.992 diam distance modulus. and ο.12 of this cluster were measured by Glushkovactal.(1999) and Luoetal.(2009)., 1mm distance modulus and $E(B-V)$ of this cluster were measured by \citet{Glushkova} and \citet{luo}.993. Thev found PAL=1042cx 0.03. E(D V)=0.12+0.02. and DAL=10.5940.09. £(B V)-0.12x0.05. respectively.," They found $DM=10.42\pm0.03$ , $E(B-V)$ $\pm$ 0.02, and $DM=10.59\pm0.09$, $E(B-V)$ $\pm$ 0.05, respectively."994 To estimate the distance. we made a weighted. mean of these results. obtaining D=1030£50 pc.," To estimate the distance, we made a weighted mean of these results, obtaining $\pm$ 50 pc."995 Then. we calculated the luminosity for the star 009655114 (NGCGSII-III35) which is reported in the last row of Fable 4..," Then, we calculated the luminosity for the star 09655114 (NGC6811-RH35) which is reported in the last row of Table \ref{tab4}."996 Again. we note the good agreement within the errors with the spectroscopic result.," Again, we note the good agreement within the errors with the spectroscopic result."997 Information on observations for the stars studied here is given in reftab:kepler.., Information on observations for the stars studied here is given in \\ref{tab:kepler}.998 For 15 out of 19 stars short cadence observations are available., For 15 out of 19 stars short cadence observations are available.999 From these cata we calculated he periodograms (bv using L. Balona’s custom. software. xwed on a combination of EET and normal periodogram) shown in Fig. 5..," From these data we calculated the periodograms (by using L. Balona's custom software, based on a combination of FFT and normal periodogram) shown in Fig. \ref{fig:per1}."1000 We note that. practically all stars show »aks in both the low-frequency (5 DDor: mmode) and ueh-[requeney. (0 8Sct: pmmocde) regions., We note that practically all stars show peaks in both the low-frequency $\gamma$ Dor; mode) and high-frequency $\delta$ Sct; mode) regions.1001 In. this sense. wactically all 0 SSet stars observed byNepler are hybrids.," In this sense, practically all $\delta$ Sct stars observed by are hybrids."1002 This is a surprising finding which has been discussed in CGrigahceneetal.(2010)., This is a surprising finding which has been discussed in \citet{griga10}.1003.. Po make a distinction. we followed he classification scheme proposed by latter author.," To make a distinction, we followed the classification scheme proposed by latter author."1004 We visually classified the stars as 0 SSct if most of the peaks are in the 0 SSct region and as ASSct 5 DDor if most of he peaks are in the ὁ οσο regionbut. with a significant contribution from the + DDor region., We visually classified the stars as $\delta$ Sct if most of the peaks are in the $\delta$ Sct region and as $\delta$ Sct – $\gamma$ Dor if most of the peaks are in the $\delta$ Sct regionbut with a significant contribution from the $\gamma$ Dor region.1005 The frequency 5ccfd was taken as the boundary between the two regions., The frequency c/d was taken as the boundary between the two regions.1006 Following similar arguments. we classify a star as  DDor or ~ DDor OSSet.," Following similar arguments, we classify a star as $\gamma$ Dor or $\gamma$ Dor – $\delta$ Sct."1007 There appears to be physical significance to such a scheme. as discussed by Crigahceneetal. (2010)..," There appears to be physical significance to such a scheme, as discussed by \citet{griga10}. ."1008 We applied. these classification criteria to the stars of this, We applied these classification criteria to the stars of this1009shedding region.,shedding region.1010 Increasing the degree of differential rotatio by reducing the value of the Ao parameter. the two familiesPA join again in the parameter space.," Increasing the degree of differential rotation by reducing the value of the $R_0$ parameter, the two families join again in the parameter space."1011 The area of the regio separating the two topologically different families depends o the Pg. of the configuration. becoming smaller as the latter is Increasing.," The area of the region separating the two topologically different families depends on the $\rho_{max}$ of the configuration, becoming smaller as the latter is increasing."1012 Stated differently. starting from the Newtonia limit and going to the more general relativistic case. it becomes more and more complicated to find a value of Ro for which the solution can reach the toroidal family. in fact the separatio increases between the two types of solutions.," Stated differently, starting from the Newtonian limit and going to the more general relativistic case, it becomes more and more complicated to find a value of $R_0$ for which the solution can reach the toroidal family, in fact the separation increases between the two types of solutions."1013 We have studiec the parameter space of the solutions for the three different rotation laws analyzed here. and will collect the results along with the dependency hidden in the EOS in the followup paper.," We have studied the parameter space of the solutions for the three different rotation laws analyzed here, and will collect the results along with the dependency hidden in the EOS in the followup paper."1014 To visualize our results. we plot gravitational mass of stellar models in the parameter space.," To visualize our results, we plot gravitational mass of stellar models in the parameter space."1015 Figure 1. shows the surfaces of equilibrium models embedded in the RoοM/Mgun space. where M is the gravitational mass in units of solar masses. for three different values of the parameter a: a=—1 (top panel). a=—2 (middle panel) and α=—4 (bottom panel).," Figure \ref{fig:Mass surface plot} shows the surfaces of equilibrium models embedded in the $R_0-\rho_{max}-M/M_{sun}$ space, where $M$ is the gravitational mass in units of solar masses, for three different values of the parameter $\alpha$: $\alpha=-1$ (top panel), $\alpha=-2$ (middle panel) and $\alpha=-4$ (bottom panel)."1016" In order to have the same degree of differential rotation for all the models with a constant Ro. following the prescription of ?.. we define: where &,. is the circumferential radius."," In order to have the same degree of differential rotation for all the models with a constant $R_0$, following the prescription of \citet{Shapiro2000}, we define: where $R_c$ is the circumferential radius."1017 On the bases of these plots. we marked each parameter pair (mas.Ro) with different symbols to indicate how the equilibrium sequence ends.," On the bases of these plots, we marked each parameter pair $(\rho_{\rm max}, \hat R_0)$ with different symbols to indicate how the equilibrium sequence ends."1018 The triangles correspond to the parameters for which 7/|W| of the model reaches 0.14 (and the computations are stopped there)., The triangles correspond to the parameters for which $T/|W|$ of the model reaches $0.14$ (and the computations are stopped there).1019 The dots correspond to the parameter pairs for which the sequence terminates at the mass-shedding limit., The dots correspond to the parameter pairs for which the sequence terminates at the mass-shedding limit.1020 The solid lines are for the parameters for which the sequence of spheroids ends with a topological change., The solid lines are for the parameters for which the sequence of spheroids ends with a topological change.1021 As mentioned in Section 3.4.. our sequences terminate at the three different criteria.," As mentioned in Section \ref{subsec: numerical sequence}, our sequences terminate at the three different criteria."1022 Therefore one needs to be careful in reading these figures., Therefore one needs to be careful in reading these figures.1023 It is important to stress that for the sequences terminating at 7/|W|=0.14 and at the topological change. the value of mass plotted here is the maximum mass of the sequence.," It is important to stress that for the sequences terminating at $T/|W|=0.14$ and at the topological change, the value of mass plotted here is the maximum mass of the sequence."1024 The solutions of the toroidal class do not possess a value for the maximum mass. instead this quantity can arbitrarily increase as the torus becomes thinner and thinner along the sequence of equilibrium figures (see. ?)).," The solutions of the toroidal class do not possess a value for the maximum mass, instead this quantity can arbitrarily increase as the torus becomes thinner and thinner along the sequence of equilibrium figures (see. \citet{Ansorg2003}) )."1025 It is seen from Eq.(9)) that the angular velocity profile becomes uniform as Rp—cv., It is seen from \ref{eq: functional form of g}) ) that the angular velocity profile becomes uniform as $\hat R_0\to\infty$.1026 In this rigid rotation limit. the sequence of N=| polytropes is known to terminate with mass-shedding state before reaching 7/|W|=0.14.," In this rigid rotation limit, the sequence of $N=1$ polytropes is known to terminate with mass-shedding state before reaching $T/|W|=0.14$."1027 The degree of differential rotation depends both on the power-law exponent a and on the radius Ro., The degree of differential rotation depends both on the power-law exponent $\alpha$ and on the radius $R_0$.1028 We may regard it as when the profile is close to uniform rotation (Le. Ry—co and/or a— -οο)., We may regard it as when the profile is close to uniform rotation (i.e. $R_0 \to \infty$ and/or $\alpha \to -\infty$ ).1029 As in the case of uniform rotation. for stars with weak differential rotation the centrifugal force at the equator on the surface reaches a value at which the star sheds mass before its 7/|W] value reaches 0.14.," As in the case of uniform rotation, for stars with weak differential rotation the centrifugal force at the equator on the surface reaches a value at which the star sheds mass before its $T/|W|$ value reaches $0.14$."1030 In this case all the sequences terminate at mass-shedding limit before reaching 7/|W|=O.14 or the point of topology change., In this case all the sequences terminate at mass-shedding limit before reaching $T/|W|=0.14$ or the point of topology change.1031 However a star with sufficiently strong differential rotation can store large rotational energy deep inside the star and allow the surface angular frequency to be smaller than that of the mass-shedding limit., However a star with sufficiently strong differential rotation can store large rotational energy deep inside the star and allow the surface angular frequency to be smaller than that of the mass-shedding limit.1032 Therefore a star with e=—1 or —2 reaches the critical point T/|W|=0.14 before encountering mass-shedding or topology change. provided that Ro is small enough (that is a smaller core region of nearly uniform rotation).," Therefore a star with $\alpha=-1$ or $-2$ reaches the critical point $T/|W|=0.14$ before encountering mass-shedding or topology change, provided that $\hat R_0$ is small enough (that is a smaller core region of nearly uniform rotation)."1033 For these choices of a and sufficiently small Ro. we also see the appearance of topological change the critical 7/|W|=0.14 is reached (represented as the triangles in Fig.1)).," For these choices of $\alpha$ and sufficiently small $\hat R_0$, we also see the appearance of topological change the critical $T/|W|=0.14$ is reached (represented as the triangles in \ref{fig:Mass surface plot}) )."1034 Indeed. the sequences which we terminate at 7/|W|=0.14 will eventually see the topology chage If extended to faster rotation.," Indeed, the sequences which we terminate at $T/|W|=0.14$ will eventually see the topology change if extended to faster rotation."1035 An important observation here is that for a=—4 none of the models reach 7/|W|=0.14 before mass shedding occurs. and fora =—1I. and —2 we need to set Rp sufficiently small (.e.. enabling high degree of differential rotation) to have the critical 7/|W]| before topology change or mass shedding occurs.," An important observation here is that for $\alpha=-4$ none of the models reach $T/|W|=0.14$ before mass shedding occurs, and for $\alpha=-1,$ and $-2$ we need to set $\hat R_0$ sufficiently small (i.e., enabling high degree of differential rotation) to have the critical $T/|W|$ before topology change or mass shedding occurs."1036 We have introduced a new rotation profile to study equilibrium sequences of differentially rotating relativistic stars., We have introduced a new rotation profile to study equilibrium sequences of differentially rotating relativistic stars.1037 Compared with the previous studies. which assume only one type of rotation profile. we are now able to investigate a broader class of rotating stars.," Compared with the previous studies, which assume only one type of rotation profile, we are now able to investigate a broader class of rotating stars."1038 As a first step towardssystematic studies. we focus on the simplest neutron star model with a polytropic EOS with index N=1. (5). Eq.(9)). (?).. Eq.(9)) 222222)). (??)). (e.g.2:: 2))," As a first step towardssystematic studies, we focus on the simplest neutron star model with a polytropic EOS with index $N=1$ \ref{hydrostatic eq}) \ref{eq: functional form of g}) \citep{EriguchiMueller1985}. \ref{eq: functional form of g}) \citet{Centrella_etal2001, Shibata_etal2002, Watts_etal2003, SaijoYoshida2006, OuTohline2006, Baiotti2008}) \citet{Watts2005,Corvino2010}) \citet{ShibataUryu2002}; \citet{Baiotti2008})"1039K on the main sequence. the effects of diffusion are expected to be essentially confined to the atmosphere. and non-magnetic evolution models by ?. show that no specific accumulation or depletion of carbon 1s expected in the interior of these stars that could appear at their surface as they will evolve up the giant The evolutionary models for Ap/Bp stars are not yet available since the effects of magnetic fields and how to take them into account is still a matter of debate.,"K on the main sequence, the effects of diffusion are expected to be essentially confined to the atmosphere, and non-magnetic evolution models by \citet{turcotte2003}1040 show that no specific accumulation or depletion of carbon is expected in the interior of these stars that could appear at their surface as they will evolve up the giant The evolutionary models for Ap/Bp stars are not yet available since the effects of magnetic fields and how to take them into account is still a matter of debate."1041 Still. ? suggested that magnetic Ap stars give rise to the very few RGB stars that present light elements abundances He.’Li. C. N) complying to the predictions of standard and rotating models.," Still, \citet{charbon2007b} suggested that magnetic Ap stars give rise to the very few RGB stars that present light elements abundances $^3{\rm He},1042^7{\rm Li}$, C, N) complying to the predictions of standard and rotating models."1043 Strong magnetic fields are actually invoked as à mean to inhibit the thermohaline mixing that is thought to be responsible for the light elements abundance variations seen at the surface of RGB stars that have evolved past the bump., Strong magnetic fields are actually invoked as a mean to inhibit the thermohaline mixing that is thought to be responsible for the light elements abundance variations seen at the surface of RGB stars that have evolved past the bump.1044 Following this work and considering that for intermediate mass. stars. thermohaline mixing is inefficient unless maybe during the TP-AGB phase. that is at a more advanced evolutionary stage than that attributed to WGB stars. magnetic fields are not expected at all to favour carbon depletion of any sort. and the scenario proposed by ? is lass transfer (or mass accretion) appears as one of the very few options left to try and understand the WGB phenomenon.," Following this work and considering that for intermediate mass stars, thermohaline mixing is inefficient unless maybe during the TP-AGB phase, that is at a more advanced evolutionary stage than that attributed to WGB stars, magnetic fields are not expected at all to favour carbon depletion of any sort, and the scenario proposed by \citet{lambert1984} is Mass transfer (or mass accretion) appears as one of the very few options left to try and understand the WGB phenomenon."1045 Fromthe HST UV spectra ? find evidence for the presence of a white dwarf companion to the weak G-band star HD165634.," Fromthe HST UV spectra \citet{bohm2000}1046 find evidence for the presence of a white dwarf companion to the weak G-band star HD165634."1047 On the other hand ? searched for binarity in a sample of 7 WGB stars of the northern hemisphere. finding a binarity rate of. that is not very different from that expected for normal K giants.," On the other hand \citet{tomkin1984} searched for binarity in a sample of 7 WGB stars of the northern hemisphere, finding a binarity rate of, that is not very different from that expected for normal K giants."1048 This result is however questionable since the number of targets selected was rather small and these observers did not exhibit the persistence that 1s really needed for an investigation of radial velocity variability because they stopped their observations after only two years (seeargumentsalsogivenby?).., This result is however questionable since the number of targets selected was rather small and these observers did not exhibit the persistence that is really needed for an investigation of radial velocity variability because they stopped their observations after only two years \citep[see arguments also given by][]{griffin1992}.1049 For the binary scenario to work. the secondary of the system should also be a star from which the accreted matter would be carbon depleted (and possibly sometimes lithium enriched).," For the binary scenario to work, the secondary of the system should also be a star from which the accreted matter would be carbon depleted (and possibly sometimes lithium enriched)."1050 According to ? (see their Table 8). stars in the mass range 5-6 at solar metallicity are expected to produce yields baring such a chemical imprint.," According to \citet{forestini1997} (see their Table 8), stars in the mass range 5-6 at solar metallicity are expected to produce yields baring such a chemical imprint."1051" In their models. due to the operation of efficient Hot Bottom Burning. they predict that the yields of ""Li are positive and more interestingly. that the net yields of 'C are negative with values up to -1.21 1077.."," In their models, due to the operation of efficient Hot Bottom Burning, they predict that the yields of $^7{\rm Li}$ are positive and more interestingly, that the net yields of $^{12}{\rm C}$ are negative with values up to -1.21 $10^{-2}$."1052 ? do not give any expected decrease of C at the surface of the secondary., \citet{forestini1997} do not give any expected decrease of C at the surface of the secondary.1053 They find lifetimes of 111 Myrs and 65.8 Myrs for their 5 and 6 respectively at solar metallicity. to be compared with the 473 Myrs and 210 Myrs for their and 4 respectively.," They find lifetimes of 111 Myrs and 65.8 Myrs for their 5 and 6 respectively at solar metallicity, to be compared with the 473 Myrs and 210 Myrs for their and 4 respectively."1054 These numbers imply that the mass aceretion from the more massive shorter lived primary onto the secondary would occur during the early main sequence evolution of the latter., These numbers imply that the mass accretion from the more massive shorter lived primary onto the secondary would occur during the early main sequence evolution of the latter.1055 As main sequence stars in the mass range 3 to 4.5 have a radiative envelope. it 15 likely that the material that would be accreted would remain at the surface and possibly slowly diffuse inwards.," As main sequence stars in the mass range 3 to 4.5 have a radiative envelope, it is likely that the material that would be accreted would remain at the surface and possibly slowly diffuse inwards."1056 If WGB stars are intermediate-mass stars undergoing core helium burning. they have already evolved through the first dredge-up. one of the main signatures of which is the decrease of surface abundances of carbon and lithium. and the increase of nitrogen abundance.," If WGB stars are intermediate-mass stars undergoing core helium burning, they have already evolved through the first dredge-up, one of the main signatures of which is the decrease of surface abundances of carbon and lithium, and the increase of nitrogen abundance."1057 The dredge-up of carbon depleted. lithium enhanced material could exacerbate the carbon depletion at the end of the dredge-up (but this need to be actually computed and check before drawing any conclusion) but will certainly not affect the lithium abundance decrease since the point i5 that the base of the convective envelope enters regions where lithium i5 destroyed by proton captures.," The dredge-up of carbon depleted, lithium enhanced material could exacerbate the carbon depletion at the end of the dredge-up (but this need to be actually computed and check before drawing any conclusion) but will certainly not affect the lithium abundance decrease since the point is that the base of the convective envelope enters regions where lithium is destroyed by proton captures."1058 Another uncertainty of the binary scenario is that of the yields. of intermediate-mass stars., Another uncertainty of the binary scenario is that of the yields of intermediate-mass stars.1059 They indeed vary greatly from one source to another (seeforinstance?).. making any conclusion illusive.," They indeed vary greatly from one source to another \citep[see for1060instance][]{karakas2007}, making any conclusion illusive."1061 Contrary to the Li-poor WGB stars. that are very seemingly rotating core He buming stars with anomalous carbon depletion. it is much more difficult to actually assess the evolutionary status of those that exhibit a lithium abundance larger than that expected after the completion of the first dredge-up.," Contrary to the Li-poor WGB stars, that are very seemingly rotating core He burning stars with anomalous carbon depletion, it is much more difficult to actually assess the evolutionary status of those that exhibit a lithium abundance larger than that expected after the completion of the first dredge-up."1062 In fact. if no postulate is made concerning à common evolutionary. status for all the stars populating the weak G-band subclass. then a strong ambiguity arises.," In fact, if no postulate is made concerning a common evolutionary status for all the stars populating the weak G-band subclass, then a strong ambiguity arises."1063" From the sole position in the HR diagram and the comparison with the stellar evolution predictions for lithium abundance (and marginally nitrogen). we can not rule out the possibility that the so-called ""Li-rich. WGB stars could tum out to be just ""normal"" stars as far as lithium is concerned. meaning with lithium abundances consistent with nodels predictions. according to their evolutionary status and their rotational Indeed. from Fig."," From the sole position in the HR diagram and the comparison with the stellar evolution predictions for lithium abundance (and marginally nitrogen), we can not rule out the possibility that the so-called ” WGB stars could turn out to be just ” stars as far as lithium is concerned, meaning with lithium abundances consistent with models predictions, according to their evolutionary status and their rotational Indeed, from Fig."1064 3. we see that the stars with large lithium abundance are well fitted by the standard tracks of intermediate mass stars that are undergoing the first dredge-up., \ref{fig2} we see that the stars with large lithium abundance are well fitted by the standard tracks of intermediate mass stars that are undergoing the first dredge-up.1065 According to these tracks. they should thus not be considered as since the first dredge-up episode is not We may argue that the WGB stars should have experienced some rotational mixing being the progeny of B-type stars.," According to these tracks, they should thus not be considered as since the first dredge-up episode is not We may argue that the WGB stars should have experienced some rotational mixing being the progeny of B-type stars."1066 The initial rotation spread observed in main sequence B-type stars in the mass range 2 to 4 M. as show by ? is actually very large. and it might well be that WGB stars are also the descendants of slow rotating late-B type stars.," The initial rotation spread observed in main sequence B-type stars in the mass range 2 to 4 $_\odot$ as shown by \cite{HGMcS2010} is actually very large, and it might well be that WGB stars are also the descendants of slow rotating late-B type stars."1067 In order to investigate the effect of a slower rotation velocity of the progenitors of the WGB stars on the ZAMS. we have computed 3 models (with initial masses of 3.0 3.5 and 4.5 )) for which we adopted vz3aig=50," In order to investigate the effect of a slower rotation velocity of the progenitors of the WGB stars on the ZAMS, we have computed 3 models (with initial masses of 3.0 3.5 and 4.5 ) for which we adopted $\upsilon_{\rm ZAMS} = 50$ ."1068 The domain covered by these slow rotators is represented, The domain covered by these slow rotators is represented1069elements.,elements.1070" The perturbation equations have the form Time average of any quantity g during one orbital period T' can be computed using where the second (,/up = r?df/dt) and the third (Απλα) = μΤ2) Kepler’s laws were used.", The perturbation equations have the form Time average of any quantity $g$ during one orbital period $T$ can be computed using where the second $\sqrt{\mu p}$ $=$ $r^{2} df/dt$ ) and the third $4 \pi^{2} a^{3}$ $=$ $\mu T^{2}$ ) Kepler's laws were used.1071 From Eqs. (17)-(21), From Eqs. (17)-(21)1072" we finally obtain for the secular time derivatives of the Keplerian orbital elements where the quantities are values of A= vy-er, B=vy-er and C = vq-en at perihelion of particle’s orbit (f = 0), respectively."," we finally obtain for the secular time derivatives of the Keplerian orbital elements where the quantities are values of $A$ $=$ $\vec{v}_{H} \cdot \vec{e}_{R}$, $B$ $=$ $\vec{v}_{H} \cdot \vec{e}_{T}$ and $C$ $=$ $\vec{v}_{H} \cdot \vec{e}_{N}$ at perihelion of particle's orbit $f$ $=$ 0), respectively."1073 The value of C is a constant on a given oscular orbit., The value of $C$ is a constant on a given oscular orbit.1074" The values of S, I and C are depicted in Fig."," The values of $S$ , $I$ and $C$ are depicted in Fig."1075 2., 2.1076" One can use also the relations Vector ep, is directed from the Sun to the ascending node.", One can use also the relations Vector $\vec{e}_{PA}$ is directed from the Sun to the ascending node.1077 «ρα: vg = Scosw — Isinw is magnitude of vg component parallel with the line of nodes., $\vec{e}_{PA}$ $\cdot$ $\vec{v}_{H}$ $=$ $S \cos \omega$ $-$ $I \sin \omega$ is magnitude of $\vec{v}_{H}$ component parallel with the line of nodes.1078 The orbital plane is defined by its normal unit vector ey., The orbital plane is defined by its normal unit vector $\vec{e}_{N}$.1079 ey X EPA — epg., $\vec{e}_{N}$ $\times$ $\vec{e}_{PA}$ $=$ $\vec{e}_{PE}$ .1080 epp : Ug = Ssinw + Icosw is magnitude of vg component perpendicular to the line of nodes and lying in the orbital plane., $\vec{e}_{PE}$ $\cdot$ $\vec{v}_{H}$ $=$ $S \sin \omega$ $+$ $I \cos \omega$ is magnitude of $\vec{v}_{H}$ component perpendicular to the line of nodes and lying in the orbital plane.1081 Eqs. (, Eqs. (108222)-(26) enable to deduce some properties of secular evolution of the dust particle under the action of the flow of interstellar gas.,22)-(26) enable to deduce some properties of secular evolution of the dust particle under the action of the flow of interstellar gas.1083 C — 0 for a special case when the velocityof hydrogen gas vg lies in the orbital plane of the particle., $C$ $=$ 0 for a special case when the velocityof hydrogen gas $\vec{v}_{H}$ lies in the orbital plane of the particle.1084 In this case we getthat the inclination, In this case we getthat the inclination1085largely cancelled out in the integrated flux. whieh we would expect to be either perpendicular to the major axis of the ellipse or along the major axis.,"largely cancelled out in the integrated flux, which we would expect to be either perpendicular to the major axis of the ellipse or along the major axis."1086" Lhe apparent rotation brought about by weak lensing would not usually be more than a few tens of degrees. and thus the determination of the direction of integrated polarization modulo"" 90 degrees would be sullicicnt to provide pretty unambiguous information about the orientation of the source galaxy."," The apparent rotation brought about by weak lensing would not usually be more than a few tens of degrees, and thus the determination of the direction of integrated polarization 'modulo' 90 degrees would be sufficient to provide pretty unambiguous information about the orientation of the source galaxy."1087 In the case of spiral galaxies. one would. expect optical polarization to arise as a result. of Phomson. Ravicigh and dust scattering of starlight primarily in the galactic disc of the spiral galaxy. with minor contributions from the halo.," In the case of spiral galaxies, one would expect optical polarization to arise as a result of Thomson, Rayleigh and dust scattering of starlight primarily in the galactic disc of the spiral galaxy, with minor contributions from the halo."1088 For Thomson and Itavleigh scattering. light scattered through 90 degrees will be entirely. polarized in a direction. perpendicular to the scattering. plane. (," For Thomson and Rayleigh scattering, light scattered through 90 degrees will be entirely polarized in a direction perpendicular to the scattering plane. ("1089For other scattering mechanisms we would expect the polarization to be either in the plane or perpendicular.),For other scattering mechanisms we would expect the polarization to be either in the plane or perpendicular.)1090 Thus if Phomson or Ravieigh scattering were dominant. à galaxy inclined to the line of sight should clisplay polarization. and one would expect in the case of a rotationally svmimetric dise that the direction of polarization to be along the minor axis of the ellipse (Bianchietal.1996).. although in exceptional circumstances it could be along the major axis.," Thus if Thomson or Rayleigh scattering were dominant, a galaxy inclined to the line of sight should display polarization, and one would expect in the case of a rotationally symmetric disc that the direction of polarization to be along the minor axis of the ellipse \cite{Bianchi96}, although in exceptional circumstances it could be along the major axis."1091 One can show that under fairly general assumptions the degree of polarization produced by Thomson or Ravleigh scattering. in the single scattering regime depends on sin?7 and the total number of scattering particles (Simmons&Audit1998).," One can show that under fairly general assumptions the degree of polarization produced by Thomson or Rayleigh scattering, in the single scattering regime depends on $\sin ^2 i$ and the total number of scattering particles \cite{SA97}."1092 Ln this section we shall give a very simplified derivation of this result to obtain an order of magnitude for the galactic polarization., In this section we shall give a very simplified derivation of this result to obtain an order of magnitude for the galactic polarization.1093 Consider a completely flat galactie disc with the light source at the centre (see Fig., Consider a completely flat galactic disc with the light source at the centre (see Fig.1094 1)., \ref{model_simple} ).1095 Take the surface density of electrons in the disc to be AY and the luminositw of the galaxy to be £., Take the surface density of electrons in the disc to be ${\cal N}_e$ and the luminosity of the galaxy to be $L$.1096 Phe axis of svmmetry of the galaxy. which we have taken to be the z-axis. is at inclination / to the line of sight.," The axis of symmetry of the galaxy, which we have taken to be the z-axis, is at inclination $i$ to the line of sight."1097 We take the x-axis to be in the plane of symmetry., We take the x-axis to be in the plane of symmetry.1098 The Dux arriving at the scattering element at ais given by L/4xa7., The flux arriving at the scattering element at ${\bf a}$ is given by $L/4\pi a^2$.1099 Thus the energy scattered. per steradian per unit time into the line of sight hy this element is simply where 8 is the angle between a and the x-axis. \ is the scattering angle and e the total scattering cross section.," Thus the energy scattered per steradian per unit time into the line of sight by this element is simply where $\theta $ is the angle between ${\bf a}$ and the x-axis, $\chi$ is the scattering angle and $\sigma$ the total scattering cross section."1100 We obtain similar expressions for the polarized flux., We obtain similar expressions for the polarized flux.1101 In terms of the Stokes parameters referred to the scattering plane we have and, In terms of the Stokes parameters referred to the scattering plane we have and1102have selected 8 caucidates withdifferent masses and mcreine histories and added 5 sunaller clustersfervoups for wmuerical load balance.,have selected 8 candidates with different masses and merging histories and added 5 smaller clusters/groups for numerical load balance.1103 We then re-mulated the clusters with higher mass resolution., We then re-simulated the clusters with higher mass resolution.1104 With particle masses of L6«105AL. a typical cluster and its environment contains more than oue million particles.," With particle masses of $4.6 \times 110510^{8}\UnitMsun$ a typical cluster and its environment contains more than one million particles."1106 The highest force resolution with 9 refinement levels was 0.9kpc., The highest force resolution with 9 refinement levels was $0.9 \Unitkpc$.1107 Sublalos with masses above 1.6«1079AL. are well resolved., Subhalos with masses above $4.6 \times 10^{10}\UnitMsun$ are well resolved.1108 A typical cluster coutains more than 150 such subhalos., A typical cluster contains more than 150 such subhalos.1109 The simulations were done using an MPI version ft the ART code where cach of eight nodes followed the evolution of one or two clusters., The simulations were done using an MPI version of the ART code where each of eight nodes followed the evolution of one or two clusters.1110 Another simulation within a box of 36\Ipe box leneth contains a galaxv-sized halo., Another simulation within a box of $36 \UnitMpc$ box length contains a galaxy-sized halo.1111 The regiou coutaimine this halo was sinnlated with an effective resolution of 10951) particles. Le. with a mass resolution of 1.7«109AL...," The region containing this halo was simulated with an effective resolution of $1024^3$ particles, i.e. with a mass resolution of $1.7 \times 10^6 \UnitMsun$."1112 The highest force resolution with 10 refinement levels was 0.1pe., The highest force resolution with 10 refinement levels was $0.1 \Unitkpc$.1113 Iu addition. we investigate the properties of a cluster-sized halo obtained bv a high-resolution simulation with uuiform mass for all particles.," In addition, we investigate the properties of a cluster-sized halo obtained by a high-resolution simulation with uniform mass for all particles."1114 This halo is resolved by more than one million particles since a huge entire nunuber of particles aud a comparatively siall simulation box was used. naunely 300° particles aud a box size of 30Mpc.," This halo is resolved by more than one million particles since a huge entire number of particles and a comparatively small simulation box was used, namely $300^3$ particles and a box size of $30 \UnitMpc$."1115" The initial conditions were set up according to the cosmological model: 5=0.65. Oy,=0.3, aud O4=0.7."," The initial conditions were set up according to the cosmological model: $h=0.65$, $\Omega_{\rm M}=0.3$, and $\Omega_{\Lambda}=0.7$."1116 The simulation has been performed using the public ADGET-codo (?).., The simulation has been performed using the public -code \citep{springel:01}.1117 For comparison we consider another simulation. performed with the GCAbGeEtT-code. with the same initial conditions as the cluster-sized halo C16 simulated with ART.," For comparison we consider another simulation, performed with the -code, with the same initial conditions as the cluster-sized halo Cl6 simulated with ART."1118 See Tab., See Tab.1119 for a compilation of the halo properties., \ref{table-halos} for a compilation of the halo properties.1120 We have determined the radial deuzitv profiles for all considered objects at redshift +=0., We have determined the radial density profiles for all considered objects at redshift $z = 0$.1121 In Fig., In Fig.1122 1 the density profiles of a chister-sized and a ealaxy-sized halos are shown., \ref{fig-profiles} the density profiles of a cluster-sized and a galaxy-sized halos are shown.1123 Both profiles can be fitted reasonably well by a ecucralizec NEW-profile with a free parameter » for the iuncr slope , Both profiles can be fitted reasonably well by a generalized NFW-profile with a free parameter $n$ for the inner slope _0 	 = _c 	.1124"The parameters p. ὃς, and r, are cletermunued for eac[um halo by a least-square fit to the mean deusities in radial bins up to the virial radii."," 	 The parameters $n$, $\delta_c$, and $r_s$ are determined for each halo by a least-square fit to the mean densities in radial bins up to the virial radii."1125 For the halo Cl6 we obtain an inner slope of ve1.5E. which correspouds to the Moore aud which is iu agreement with the results eive- bv ?..," For the halo Cl6 we obtain an inner slope of $n \approx 1.54$, which corresponds to the Moore-profile and which is in agreement with the results given by \citet{fukushige:01}."1126 Thev analyzed 12 halos with various masses anea found au inner slope of about àz1.5 for all of them., They analyzed 12 halos with various masses and found an inner slope of about $n \approx 1.5$ for all of them.1127 I- contrast. for most clusters of our sample we found sinaller iuncr slopes. see Tab. 1..," In contrast, for most clusters of our sample we found smaller inner slopes, see Tab. \ref{table-halos}."1128" À relaxed spherical halo of collisionless particlesis completely described bv the radial profiles of the density p(r). the radial velocity dispersion a2=(e, v0;:)2. where v; is the mean radial velocity in a spherical shell with mean radius r. aud the anisotropy of the dispersiou ↗∶↓;↽a;⋅≽⋅≽ o>, where o; denotes the taugeutial⋅ velocity⋅⋅ dispersion."," A relaxed spherical halo of collisionless particlesis completely described by the radial profiles of the density $\rho(r)$, the radial velocity dispersion $\sigma_r^2 = \overline{(v_r-\overline{v_r})^2}$, where $\overline{v_r}$ is the mean radial velocity in a spherical shell with mean radius $r$, and the anisotropy of the dispersion $\beta = 1- \sigma_t^2 /\sigma_r^2$ , where $\sigma_t$ denotes the tangential velocity dispersion."1129. The potential can be obtained by mass integration P=GpendrAM(rr?2 (Poisson: equation).: where G denotes the eravitational constant.," The potential can be obtained by mass integration $\Phi = G\, \int^r_0 \, dr M(r) / r^2$ (Poisson equation), where $G$ denotes the gravitational constant."1130 The radial profiles are related by the Jeans equation (?) πρπο σ. my which describes a steady-state halo whose particles move ou collisionless trajectories im a spherical potential selt-consistently generated bv the particle distribution.," The radial profiles are related by the Jeans equation \citep{binney:87}1131 	+ _r^2 	 = 	- 	, 	 which describes a steady-state halo whose particles move on collisionless trajectories in a spherical potential self-consistently generated by the particle distribution."1132 The results of numerical simulations coufiru that dark matter halos ful&ll the Jeaus equation at least up to the virial radius (?).., The results of numerical simulations confirm that dark matter halos fulfill the Jeans equation at least up to the virial radius \citep{thomas:98}. .1133 This leads to the conclusions that (1) the halos are relaxed. (3) the particles in the halos are moving ou," This leads to the conclusions that (i) the halos are relaxed, (ii) the particles in the halos are moving on"1134racius.,radius.1135 In this way our model coltumu density profiles cau be directly compared with stroug lensiug results., In this way our model column density profiles can be directly compared with strong lensing results.1136 In reality. there are baryons aud possibly other forms of dark matter such as massive cold dark matter particles.," In reality, there are baryons and possibly other forms of dark matter such as massive cold dark matter particles."1137 These geueral cases are dealt with by introducing another input parameter. the ratio of the total mass density aud light fermion density. 9.," These general cases are dealt with by introducing another input parameter, the ratio of the total mass density and light fermion density, $\delta$."1138 A1689 studied by Broadhurstοἱal.(2005a.b) is the best studied cluster by both strong aud weak leusiug. for which column cdeusity profile is obtained [rom the core to radii greater than 1 Alpe.," A1689 studied by \citet{TB05A,TB05B} is the best studied cluster by both strong and weak lensing, for which column density profile is obtained from the core to radii greater than 1 Mpc."1139 As a case study. we apply our modeling to this cluster aud constrain the possible combinations of particle properties.," As a case study, we apply our modeling to this cluster and constrain the possible combinations of particle properties."1140 As a natural candidate for light fermions. we consider the case of massive neutriuyn.," As a natural candidate for light fermions, we consider the case of massive neutrinos."1141 The paper is organized as follows., The paper is organized as follows.1142 We first obtain the volume density of A1689 from the observed column deusity profile of Broadhurstetal.(2005b) and show that eV fermious cau be degenerate near the core of this cluster in 822., We first obtain the volume density of A1689 from the observed column density profile of \citet{TB05B} and show that eV fermions can be degenerate near the core of this cluster in 2.1143 Our modeling procedure is described iu 833 aud the properties of input fernuions are discussed in SLL. aud then the results are presented iu 855.," Our modeling procedure is described in 3 and the properties of input fermions are discussed in 4, and then the results are presented in 5."1144 The moclerate degeneracy of unbouud relic ueutrinos aud the plausibility that they cau fall into the cluster core. are cliscussed Lu 866.," The moderate degeneracy of unbound relic neutrinos and the plausibility that they can fall into the cluster core, are discussed in 6."1145 Recently Broadhurst et al., Recently Broadhurst et al.1146 (Broadhliurstetal.2005a.b)| reported. a mass column density profile of the cluster of galaxies. A1689. obtained from gravitational lensing.," \citep{TB05A,TB05B} reported a mass column density profile of the cluster of galaxies, A1689, obtained from gravitational lensing."1147 One of the important properties of the profile is that it has a [lat top., One of the important properties of the profile is that it has a flat top.1148 We propose that this flat-top column density. profile uuieht be explained by the effects of degeneracy pressure of fermionic dark matter., We propose that this flat-top column density profile might be explained by the effects of degeneracy pressure of fermionic dark matter.1149 Here we analyze this proposal., Here we analyze this proposal.1150 First we briefly introduce the main results of Broadhurstetal.(2002a.b)..," First we briefly introduce the main results of \citet{TB05A,TB05B}."1151 In their analysis. 1 corresponds to 129 kpe fh ! Tu B," In their analysis, $^{\prime}$ corresponds to 129 kpc $h^{-1}$ ."1152roadhurstetal.(2005a).. the central 250 kpe /i Lin radius of HST/ACS images were analyzed.," In \citet{TB05A}, the central 250 kpc $h^{-1}$ in radius of multi-color HST/ACS images were analyzed."1153 The mass column density. profile. X(r). is not expressed as a single power law of radius.," The mass column density profile, $\Sigma(r)$, is not expressed as a single power law of radius."1154 The mass column density profile flattens toward the center with a mean slope of dlosX/dlogrze—0.55 within r «2250 kpe . +., The mass column density profile flattens toward the center with a mean slope of $d \log \Sigma / d\log r \approx -0.55$ within $r<$ 250 kpc $h^{-1}$ .1155" Inside the Einstein radius (05zz 20""). they obtained the slope of zz—0.3 (rom the ratio between Op and the radius of the radial critical curve. 0,zz17""."," Inside the Einstein radius $\theta_E\approx 50^{\prime\prime}$ ), they obtained the slope of $\approx -0.3$ from the ratio between $\theta_E$ and the radius of the radial critical curve, $\theta_r\approx 17^{\prime\prime}$."1156" They fit their results with an inner region of an NEW prolile with a relatively high concentration. Cj,=8.2."," They fit their results with an inner region of an NFW profile \citep{NFW96}1157 with a relatively high concentration, $C_{vir} = 8.2$."1158 The mass column density. X(r). is the integral of the volume deusity. p(r). along the line of sight over the entire cluster scale of Mpc.," The mass column density, $\Sigma(r)$, is the integral of the volume density, $\rho(r)$, along the line of sight over the entire cluster scale of Mpc."1159 Iu order to study the possibilityof leriuiiou degeneracy near the center ofthe cluster. we need information ou the volume density. p(r).instead of the," In order to study the possibilityof fermion degeneracy near the center ofthe cluster, we need information on the volume density, $\rho(r)$ instead of the"1160The masses of neutron stars are the most sensitive among all their parameters to the equation of state at high densities.,The masses of neutron stars are the most sensitive among all their parameters to the equation of state at high densities.1161 Therefore. pulsar mass measurements provide one of the key experimental constraints on the theory of ultra-dense matter.," Therefore, pulsar mass measurements provide one of the key experimental constraints on the theory of ultra-dense matter."1162" The masses measured in the pulsar binaries are. clustered around the value 1.4 Mc and have been consider as ""canonical"" for a long time.", The masses measured in the pulsar binaries are clustered around the value 1.4 $M_{\sun}$ and have been consider as “canonical” for a long time.1163 However. in recent years mounting evidence emerged in favor of substantially heavier neutron stars with M€2Mo.," However, in recent years mounting evidence emerged in favor of substantially heavier neutron stars with $M\le 2M_{\sun}$."1164" In particular. the recent discovery of a compact star with a mass of 1.97 M5 measured through the Shapiro delay provides an observationally ""clean"" lower bound on the maximum mass of a compact star (Demorestetal.2010)."," In particular, the recent discovery of a compact star with a mass of 1.97 $M_{\sun}$ measured through the Shapiro delay provides an observationally “clean” lower bound on the maximum mass of a compact star \citep{2010Natur.467.1081D}."1165 On the theoretical side it is now well-established that the emergence of new degrees of freedom at high densities softens the equation of state of matter., On the theoretical side it is now well-established that the emergence of new degrees of freedom at high densities softens the equation of state of matter.1166 For example. allowing for the hyperons ean reduce the maximum mass of à sequence of compact stars below the canonical mass of 1.4 Me.," For example, allowing for the hyperons can reduce the maximum mass of a sequence of compact stars below the canonical mass of 1.4 $M_{\sun}$."1167 A similar reduction may occur if a deconfinement to quark matter takes place. although the softening of the equation of state in this case is less dramatic.," A similar reduction may occur if a deconfinement to quark matter takes place, although the softening of the equation of state in this case is less dramatic."1168 Thus. the observation of 2M mass neutron star is evidence that the ultra-dense matter in neutron stars cannot be soft.Le... agents that will substantially soften the equation of state are potentially excluded.," Thus, the observation of $M_{\sun}$ mass neutron star is evidence that the ultra-dense matter in neutron stars cannot be soft, agents that will substantially soften the equation of state are potentially excluded."1169 We aim to study the equation of state of ultra-dense matter in the light of this recent constraint (Demorestetal.2010).., We aim to study the equation of state of ultra-dense matter in the light of this recent constraint \citep{2010Natur.467.1081D}.1170 We investigate to which extent one can reconcile the nucleonic components such as hyperons and two- and three-flavor quark matter. along with their color superconductivity. with the existence of neutron stars with masses 2M.," We investigate to which extent one can reconcile the non-nucleonic components such as hyperons and two- and three-flavor quark matter, along with their color superconductivity, with the existence of neutron stars with masses $M_{\sun}$."1171 The ralswer(s) to the question above are of fundamental importance. because if hybrid stars featuring quark cores surrounded by a (hyperinuclear mantle exist in nature. they could provide a unique window on the properties of quantum chromodynamics (QCD) at high baryon densities under conditions not attainable in. laboratory experiments (the ultra-dense matter is in equilibrium. is charge neutral and in B-equilibrium with respect to weak interactions).," The answer(s) to the question above are of fundamental importance, because if hybrid stars featuring quark cores surrounded by a (hyper)nuclear mantle exist in nature, they could provide a unique window on the properties of quantum chromodynamics (QCD) at high baryon densities under conditions not attainable in laboratory experiments (the ultra-dense matter is in equilibrium, is charge neutral and in $\beta$ -equilibrium with respect to weak interactions)."1172 Although heavy baryons (mainly == and A hyperons) were considered even before the discovery of pulsars and their identification with the neutron stars1960)... their emergence in the cores of neutron stars is still very elusive.," Although heavy baryons (mainly $\Sigma^{\pm}$ and $\Lambda$ hyperons) were considered even before the discovery of pulsars and their identification with the neutron stars, their emergence in the cores of neutron stars is still very elusive."1173 Treatments based on relativistic density functional methods (Glendenning1985:Glendenning&Moszkowski1991:Weber1999) predict masses that are not much larger than the canonical mass of a neutron star which clearly contradicts modern. observations.," Treatments based on relativistic density functional methods \citep{1985ApJ...293..470G,1991PhRvL..67.2414G,weber_book}1174 predict masses that are not much larger than the canonical mass of a neutron star which clearly contradicts modern observations."1175 [asses on the order of €{δω were obtained in non-relativistic phenomenological models (Balbergetal.1999:Djapo2010).. while microscopic models based on hyperon-nucleon potentials. which include the repulsive three-body forces. predict low maximal masses for hypernuclear stars (Baldoetal.1998.2003a;Vidanaet 2011).," Masses on the order of $\le 1.8 M_{\sun}$ were obtained in non-relativistic phenomenological models \citep{1999ApJS..121..515B,2010PhRvC..81c5803D}, while microscopic models based on hyperon-nucleon potentials, which include the repulsive three-body forces, predict low maximal masses for hypernuclear stars \citep{PhysRev1998,2003astro.ph.12446B,2011EL.....9411002V}."1176 The treatment of deconfined matter at ultra-high densities is. model-dependent., The treatment of deconfined matter at ultra-high densities is model-dependent.1177 We used the. Nambu-Jona-Lasinio (NJL) model to describe the quark matter and its color superconductivity., We used the Nambu–Jona-Lasinio (NJL) model to describe the quark matter and its color superconductivity.1178 The model is à non-perturbative low-energy approximation to QCD. which is anchored in. the low-energy phenomenology of the hadronic spectrum.," The model is a non-perturbative low-energy approximation to QCD, which is anchored in the low-energy phenomenology of the hadronic spectrum."1179 The dynamical symmetry breaking. by which quarks acquire mass. is incorporated in this model. but it lacks confinement.," The dynamical symmetry breaking, by which quarks acquire mass, is incorporated in this model, but it lacks confinement."1180 Our ignorance of the mechanism of confinement requires a free parameter in the theory. which can be identified with the bag constant (the latter need not be the same as in the MIT bag model).," Our ignorance of the mechanism of confinement requires a free parameter in the theory, which can be identified with the bag constant (the latter need not be the same as in the MIT bag model)."1181 Furthermore. it can be eliminated in favor of a more physical quantity - the transition density from (hyperinuclear to quark matter.," Furthermore, it can be eliminated in favor of a more physical quantity - the transition density from (hyper)nuclear to quark matter."1182 Inthe low-density matter a candidate superconducting phase is the two-superconducting-colors (2SC) phase (Bailin&Love1984).. which at sufficiently high densities transforms to the three-flavor color-flavor-locked (CFL) phase (Alfordetal.1999):: our present study includes only these two phases. but we emphasize that the phase structure of matter could be more complicated (Riisteretal. 2005)..," Inthe low-density matter a candidate superconducting phase is the two-superconducting-colors (2SC) phase \citep{1984PhR...107..325B}, which at sufficiently high densities transforms to the three-flavor color-flavor-locked (CFL) phase \citep{1999NuPhB.537..443A}; our present study includes only these two phases, but we emphasize that the phase structure of matter could be more complicated \citep{2005PhRvD..72c4004R}."1183 The separate problem of compact stars made of strange matter with equal number of flavors of quarks greiros2011) will not be considered here., The separate problem of compact stars made of strange matter with equal number of flavors of quarks \citep{2011AIPC.1354...13W} will not be considered here.1184 Early studies of hadron-quark phase transition and. quark superconductivity within the NJL model suggested that no stable stars (in the CFL phase) can be obtained within the standard parameterization of this model (see. e.g... Baldo (2003b))).," Early studies of hadron-quark phase transition and quark superconductivity within the NJL model suggested that no stable stars (in the CFL phase) can be obtained within the standard parameterization of this model (see, , \citet{2003PhLB..562..153B}) )."1185 Recently. NJL-model based stable sequences of hadron-quark stars were obtained for 2SC and CFL matter (Klihnetal.2006:Alford2007) and a," Recently, NJL-model based stable sequences of hadron-quark stars were obtained for 2SC and CFL matter \citep{2006PhRvC..74c5802K,2007Natur.445E...7A} and a"1186Heating of a coronal loop is a fundamental problem in solar physics.,Heating of a coronal loop is a fundamental problem in solar physics.1187 Coronal loops. which are thin thread-like structures seen in coronal emission lines. must be continuously heated to account for their radiative and conductive energy losses.," Coronal loops, which are thin thread-like structures seen in coronal emission lines, must be continuously heated to account for their radiative and conductive energy losses."1188" However. models of coronal loops are not mature enough to reproduce the observations sufficiently 2..2., and ?. show that a static loop model is not consistent with observations."," However, models of coronal loops are not mature enough to reproduce the observations sufficiently \citet{winebarger2002}, \citet{warren2006}, , and \citet{aschwanden2009}1189 show that a static loop model is not consistent with observations."1190 A dynamie model with a collection of impulsive heatings is in better agreement with observations. but still not satisfactory (2?)..," A dynamic model with a collection of impulsive heatings is in better agreement with observations, but still not satisfactory \citep{warren2003,warren2007}."1191 A detailed study of the temporal evolution of coronal loops is therefore crucial for understanding them., A detailed study of the temporal evolution of coronal loops is therefore crucial for understanding them.1192 Observations of nonflaring active regions show that coronal loops are visible over a wide temperature range and are highly variable., Observations of nonflaring active regions show that coronal loops are visible over a wide temperature range and are highly variable.1193 Brightness distribution of EUV emission lines indicates that hot loops (=2κ10° K) are concentrated in the cores of active regions. while lower temperature loops (~1x10° ΚΙ are located on the periphery of the active region (???)..," Brightness distribution of EUV emission lines indicates that hot loops $\geq 2\times 10^6$ K) are concentrated in the cores of active regions, while lower temperature loops $\sim 1\times 10^6$ K) are located on the periphery of the active region \citep{aschwanden2008c,tripathi2008,odwyer2011}. ."1194 Loop-like structures are also seen at transition-region and chromospheric temperatures., Loop-like structures are also seen at transition-region and chromospheric temperatures.1195 ? have shown that cool loops seen at |~5x10° K change significantly within one hour. while hot loops are less variable.," \citet{kjeldsethmoe1998} have shown that cool loops seen at $1\sim5 \times 10^5$ K change significantly within one hour, while hot loops are less variable."1196 ? finds cool plasma (<1x10° K) flowing down along the loop. which he interprets as a result of catastrophic. cooling at the loop top.," \citet{schrijver2001} finds cool plasma $\leq1\times 10^5$ K) flowing down along the loop, which he interprets as a result of catastrophic cooling at the loop top."1197 Numerical simulations shows that frequent occurrence of falling blobs in chromospheric lines. or coronal rain. favors a heating concentrated near the footpomts of a coronal loop (2???)..," Numerical simulations shows that frequent occurrence of falling blobs in chromospheric lines, or coronal rain, favors a heating concentrated near the footpoints of a coronal loop \citep{mueller2003,mueller2004,mueller2005,antolin2010}."1198 Clearly. in order to understand the energy balance of coronal loops. it is important to study both the cooling and heating processes.," Clearly, in order to understand the energy balance of coronal loops, it is important to study both the cooling and heating processes."1199 The Atmospheric Imaging Assembly (AIA:??) on the Solar Dynamics Observatory (SDO) records high-cadence EUV images at multiple temperatures.," The Atmospheric Imaging Assembly \citep[AIA;][]{lemen2011,boerner2011} on the Solar Dynamics Observatory (SDO) records high-cadence EUV images at multiple temperatures."1200 In this paper. we selected nonflaring active regions at the limb and on the disk to study the temporal evolution of coronal loops.," In this paper, we selected nonflaring active regions at the limb and on the disk to study the temporal evolution of coronal loops."

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