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We use the code (Stone Norman 1992); we employ a spherical grid with 0=[0,7/2], the radial grid cells are logarithmically spaced, such that we have adequate resolution at small radius to resolve the onset of the flow.
We use the code (Stone Norman 1992); we employ a spherical grid with $\theta=[0,\pi/2]$, the radial grid cells are logarithmically spaced, such that we have adequate resolution at small radius to resolve the onset of the flow.
'The calculation is an isothermal wind calculation with the sound speed set to c,= 10km s! and the radius scaled to the length scale ry=GM./c2 ie. the radius at which the internal energy of the gas is enough to unbind the gas from the star.
The calculation is an isothermal wind calculation with the sound speed set to $c_s=10$ km $^{-1}$ and the radius scaled to the length scale $r_g=GM_*/c_s^2$ i.e. the radius at which the internal energy of the gas is enough to unbind the gas from the star.
We use a radial range of r=[0.05,40]rg with N,=240 and Ne=50.
We use a radial range of $r=[0.05,40]r_g$ with $N_r=240$ and $N_{\theta}=50$.
The number density at the base (i.e. the density along the 6=7/2 axis) of the wind was calculated semi-analytically by Hollenbach et al. (
The number density at the base (i.e. the density along the $\theta=\pi/2$ axis) of the wind was calculated semi-analytically by Hollenbach et al. (
1994) and scales as R~°/? for R<Ry and as R~*/? outside Ry, as in Font et al. (
1994) and scales as $R^{-3/2}$ for $R<R_g$ and as $R^{-5/2}$ outside $R_g$, as in Font et al. (
2004) and Alexander et al. (
2004) and Alexander et al. (
2008) we adopt the smooth density profile suggested by that varies between the two power laws: where n, is the density at R, which was determined through the numerical calculations of Hollenbachetal.(1994) to be: where 6 is the ionizing luminosity.
2008) we adopt the smooth density profile suggested by \citet{font04} that varies between the two power laws: where $n_g$ is the density at $R_g$ which was determined through the numerical calculations of \citet{hollenbach94} to be: where $\Phi$ is the ionizing luminosity.
We note that this hydrodynamic calculation does not include a cold bound ‘disc’ component, since as discussed above the base density structure of the wind is known a priori.
We note that this hydrodynamic calculation does not include a cold bound `disc' component, since as discussed above the base density structure of the wind is known a priori.
This base density, along with Keplerian rotation is reset at every time-step and the model is allowed to evolve to a steady state launching a wind from the grid's mid-plane (representing the disc's surface).
This base density, along with Keplerian rotation is reset at every time-step and the model is allowed to evolve to a steady state launching a wind from the grid's mid-plane (representing the disc's surface).
As expected, we find excellent agreement with the results of the Fontetal.(2004) and Alexander(2008) calculations.
As expected, we find excellent agreement with the results of the \citet{font04} and \citet{alexander08} calculations.
In Figure 1 we show a plot of the converged wind structure showing that the wind is approximately spherical once it has reached several scale heights, in agreement with our earlier discussion in Section ??..
In Figure \ref{fig:structure} we show a plot of the converged wind structure showing that the wind is approximately spherical once it has reached several scale heights, in agreement with our earlier discussion in Section \ref{model}.
In order to calculate the dust distribution in the wind, we must make some assumptions about the underlying dust distribution in the disc.
In order to calculate the dust distribution in the wind, we must make some assumptions about the underlying dust distribution in the disc.
We adopt a dust to gas mass ratio of 0.01, and a power law grain size distribution of index -3.5 (Mathis, Rumpl Nordsiek, 1977, MRN), with grain sizes ranging from Qmin=5X1073 um to @maz=l1mm, we assume spherical grains with a density of 1g οπι?.
We adopt a dust to gas mass ratio of 0.01, and a power law grain size distribution of index -3.5 (Mathis, Rumpl Nordsiek, 1977, MRN), with grain sizes ranging from $a_{min}$ $\times10^{-3}\mu$ m to $a_{max}$ =1mm, we assume spherical grains with a density of 1g $^{-3}$.
We also assume that the dust is fully mixed within the disc up to the transition between the bound cold disc and the hot EUV heated flow.
We also assume that the dust is fully mixed within the disc up to the transition between the bound cold disc and the hot EUV heated flow.
We then calculate streamlines from the base of the flow to the edge of the grid, then along each streamline, compute the force balance between the drag force (calculated from Equation 1), gravity and the centrifugal force.
We then calculate streamlines from the base of the flow to the edge of the grid, then along each streamline, compute the force balance between the drag force (calculated from Equation 1), gravity and the centrifugal force.
We take the dust grain as entrained if the net force along the streamline is >0.
We take the dust grain as entrained if the net force along the streamline is $>0$.
We then obtain the maximum grain size entrained along the entire streamline
We then obtain the maximum grain size entrained along the entire streamline
wavelength. or frequency. of the radiation. its location on the sky. and the polarization of (he radiation.
wavelength, or frequency, of the radiation, its location on the sky, and the polarization of the radiation.
Measurements of the latter (vo. location and polarization. follow the statistics of direction.
Measurements of the latter two, location and polarization, follow the statistics of direction.
The association ol directional statistics with the measurement of location is obvious. but the application of directional statistics {ο polarization measurements is nol immediately apparent until one recalls that the Stokes parameters ο. U. and. V describe (he orientation of a polarization vector within the Poincaré sphere.
The association of directional statistics with the measurement of location is obvious, but the application of directional statistics to polarization measurements is not immediately apparent until one recalls that the Stokes parameters Q, U, and V describe the orientation of a polarization vector within the Poincaré sphere.
The Stokes parameter V defines (he circular polarization of the radiation ancl establishes the z-coordinate of the polarization vector in the Poincaré sphere.
The Stokes parameter V defines the circular polarization of the radiation and establishes the z-coordinate" of the polarization vector in the Poincaré sphere.
The Stokes parameters Q and U describe the radiations linear polarization and establish the vectors x- and ν- respectively,
The Stokes parameters Q and U describe the radiation's linear polarization and establish the vector's x- and y-coordinates, respectively.
Here. polarization measurements are shown to follow directional statistics. and (hese statistics are applied to polarization observations of radio pulsars.
Here, polarization measurements are shown to follow directional statistics, and these statistics are applied to polarization observations of radio pulsars.
Pulsars are rapidly rotating. highly magnetized neutron stars.
Pulsars are rapidly rotating, highly magnetized neutron stars.
Their rotation periods range between about. Ims and 108. and the strength of the magnetic field at their surfaces ranges from LOS G [or the oldest pulsars to over 101 G [or the voungest.
Their rotation periods range between about 1ms and 10s, and the strength of the magnetic field at their surfaces ranges from $10^8$ G for the oldest pulsars to over $10^{12}$ G for the youngest.
A beam of radio emission is emitted from each of the stars magnetic poles.
A beam of radio emission is emitted from each of the star's magnetic poles.
A pulse of radio emission is observed as (he stars rotation causes the beam (o sweep across an observers line of sight.
A pulse of radio emission is observed as the star's rotation causes the beam to sweep across an observer's line of sight.
Pulsar radio emission is generally thought to originate from charged particles streaming along open magnetic fields lines above the stars magnetic pole. bul unlike other astrophysical raciative processes (e.g. svnchrotron radiation. maser emission. ancl thermal radiation). it is poorly understood.
Pulsar radio emission is generally thought to originate from charged particles streaming along open magnetic fields lines above the star's magnetic pole, but unlike other astrophysical radiative processes (e.g. synchrotron radiation, maser emission, and thermal radiation), it is poorly understood.
Polarization observations of the individiual pulses Irom pulsars are niacde inan attempt to understand the radio emission mechanism and (o study the propagation of radio waves in ultra-strong magnetic fields.
Polarization observations of the individiual pulses from pulsars are made in an attempt to understand the radio emission mechanism and to study the propagation of radio waves in ultra-strong magnetic fields.
Polarization observations of individual pulses (Lyne et al.
Polarization observations of individual pulses (Lyne et al.
1971: Manchester et al.
1971; Manchester et al.
1975: Backer Rankin 1980: Stinebring et al.
1975; Backer Rankin 1980; Stinebring et al.
1984) show that the radiation can be highlv elliplically polarized and hiehlv variable. if not stochastic.
1984) show that the radiation can be highly elliptically polarized and highly variable, if not stochastic.
In many cases. the mean of the polarization position angle varies in an S-shaped pattern across the pulse.
In many cases, the mean of the polarization position angle varies in an S-shaped pattern across the pulse.
But histograms of position angle created from the single pulse observations show (the angles follow the pattern in (wo parallel paths separated by about 90 degrees (Stinebring et al.
But histograms of position angle created from the single pulse observations show the angles follow the pattern in two parallel paths separated by about 90 degrees (Stinebring et al.
1984).
1984).
Furthermore. histograms of fractional linear polarization show that the radiation is significantly depolarized al pulse locations where these orthogonally polarized (OPMSs) modes occur.
Furthermore, histograms of fractional linear polarization show that the radiation is significantly depolarized at pulse locations where these orthogonally polarized (OPMs) modes occur.
The OPMS are thought to be the natural modes of wave propagation in pulsar magnetospheres (Allen Melrose 1982: Barnard Arons 1986).
The OPMs are thought to be the natural modes of wave propagation in pulsar magnetospheres (Allen Melrose 1982; Barnard Arons 1986).
The narrow bandwidths and short sampling intervals used in single pulse observations cause the instrumental noise in these observations to be large.
The narrow bandwidths and short sampling intervals used in single pulse observations cause the instrumental noise in these observations to be large.
The narrow bandwidths are used (to overcome pulse smearing effects caused by the dispersion. measure of. and mulüpath scattering in. the interstellar medium.
The narrow bandwidths are used to overcome pulse smearing effects caused by the dispersion measure of, and multipath scattering in, the interstellar medium.
The short sampling intervals. (vpically of order LOQus. are needed to adecquatelv resolve the short duration radio pulse.
The short sampling intervals, typically of order 100us, are needed to adequately resolve the short duration radio pulse.
The combination of the stochastic nature of the intrinsic. emission
The combination of the stochastic nature of the intrinsic emission
The IR LFs of the three different regions were determined as described in Sect. 3.1,,
The IR LFs of the three different regions were determined as described in Sect. \ref{s:corr},
using completeness and purity corrections that are appropriate for each considered region, and multiplying the counts by the fractions of non-AGN galaxies in each Lig--bin and each region to remove the AGN contribution from the IR LFs.
using completeness and purity corrections that are appropriate for each considered region, and multiplying the counts by the fractions of non-AGN galaxies in each -bin and each region to remove the AGN contribution from the IR LFs.
Error bars were determined via a bootstrap sampling procedure.
Error bars were determined via a bootstrap re-sampling procedure.
The three IR LFs are displayed in the panels of Fig. 12,,
The three IR LFs are displayed in the left-hand panels of Fig. \ref{f:3irlf},
for both the zUΖρ (top panel) and the z sample (bottom panel).
for both the $\rm{z} \cup \rm{z}_p$ (top panel) and the z sample (bottom panel).
Power-law function fits to the three IR LFs are shown as dashed lines, and the best-fitting values of the slope parameter are given in Table 1..
Power-law function fits to the three IR LFs are shown as dashed lines, and the best-fitting values of the slope parameter are given in Table \ref{t:fits}.
The slopes of the three region IR LFs do not differ significantly, but taken at face value they suggest that the filament has a flatter IR LF than both the outskirts and (for the zUzy sample) the core.
The slopes of the three region IR LFs do not differ significantly, but taken at face value they suggest that the filament has a flatter IR LF than both the outskirts and (for the $\rm{z} \cup \rm{z}_p$ sample) the core.
The IR LF of the filament region is flatter because of an excess of LIRGs relative to the other regions.
The IR LF of the filament region is flatter because of an excess of LIRGs relative to the other regions.
This is also apparent from a visual inspection of Fig.
This is also apparent from a visual inspection of Fig.
12 and also of Fig. 11,,
\ref{f:3irlf} and also of Fig. \ref{f:regions},
where we show the spatial positions of all supercluster members in the zUzy sample and indicate the LIRGs with pink symbols (square symbols for LIRGs of the z sample).
where we show the spatial positions of all supercluster members in the $\rm{z} \cup \rm{z}_p$ sample and indicate the LIRGs with pink symbols (square symbols for LIRGs of the z sample).
Fig.
Fig.
12 (left panels) also shows that at lowerLip,, the number densities of IR-emitting galaxies are similar in the core and in the filament regions, and lowest in the outskirts region.
\ref{f:3irlf} (left panels) also shows that at lower, the number densities of IR-emitting galaxies are similar in the core and in the filament regions, and lowest in the outskirts region.
When considering the implications of this comparison, one must take into account that the three selected regions are characterized by different densities of normal galaxies, highest in the core, lowest in the outskirts.
When considering the implications of this comparison, one must take into account that the three selected regions are characterized by different densities of normal galaxies, highest in the core, lowest in the outskirts.
Similarities in the IR LFs of different regions could be caused by a combination of different densities of normal galaxies and different fractions of IR-emitting galaxies among the total.
Similarities in the IR LFs of different regions could be caused by a combination of different densities of normal galaxies and different fractions of IR-emitting galaxies among the total.
Viceversa, different IR LFs could simply reflect differences in the densities of normal galaxies combined with similar IR-emitting galaxy fractions among the total.
Viceversa, different IR LFs could simply reflect differences in the densities of normal galaxies combined with similar IR-emitting galaxy fractions among the total.
It is therefore also important to compare the relative fractions of IR-emitting galaxies in the different regions.
It is therefore also important to compare the relative fractions of IR-emitting galaxies in the different regions.
For this, we must determine the densities of normal galaxies in the three different regions.
For this, we must determine the densities of normal galaxies in the three different regions.
By adopting the same methodology used for a derivation of the IR LF (see Sect. 3.1)),
By adopting the same methodology used for a derivation of the IR LF (see Sect. \ref{s:corr}) ),
we determine the r-band LFs in the three regions.
we determine the $r$ -band LFs in the three regions.
These LFs are well fitted by Schechter functions, and their shapes are not statistically different according to a y? test (?).
These LFs are well fitted by Schechter functions, and their shapes are not statistically different according to a $\chi^2$ test .
. We then integrate these LFs to derive the number densities of r-band selected galaxies with r-band L,>710?Lo.
We then integrate these LFs to derive the number densities of $r$ -band selected galaxies with $r$ -band $\rm{L}_r \geq 7 \, 10^9 \, \rm{L}_{\odot}$.
This luminosity represents the lower limit above which our determinations of the r-band LFs appear to be robust, i.e. independent ofsample choice (the zUzy sample or the z sample).
This luminosity represents the lower limit above which our determinations of the $r$ -band LFs appear to be robust, i.e. independent ofsample choice (the $\rm{z} \cup \rm{z}_p$ sample or the z sample).
It corresponds to a stellar
It corresponds to a stellar
square fit of the data with the general relation I4). by considering in each case a value of (m less than the number of available data points.
square fit of the data with the general relation \ref{velr2n}) ), by considering in each case a value of $m$ less than the number of available data points.
In Figure |. we show the adjusted rotation curves for the four galaxies considered.
In Figure \ref{rotcurv} we show the adjusted rotation curves for the four galaxies considered.
The points with error bars are the observations. as reported in Verheijen&Sancici(9001)... while the solid line is the rotation curve determined from (14)) with the values for the fs, given by the numerical fit.
The points with error bars are the observations, as reported in \cite{VS}, while the solid line is the rotation curve determined from \ref{velr2n}) ) with the values for the $A_{2n}$ given by the numerical fit.
As we can see. the relation (14) fit quite accurately to the observed data of the four galaxies considered.
As we can see, the relation \ref{velr2n}) ) fit quite accurately to the observed data of the four galaxies considered.
Then. from the obtained values for του. the corresponding values of the C's, are determined by using (159) and (17)).
Then, from the obtained values for $A_{2n}$, the corresponding values of the $C_{2n}$ are determined by using \ref{relation}) ) and \ref{constant0}) ).
In Table | we present the values ofC, for the four galaxies as well as the corresponding value of à used in CI).
In Table \ref{tab:c2n} we present the values of $C_{2n}$ for the four galaxies as well as the corresponding value of $m$ used in \ref{velr2n}) ).
In Table 2 we indicate. for each galaxy. the morphological type according to he Hubble's elassitication of galaxies. the radius e in kpc and the otal mass 4. both in ke and in solar mass units (ME. ).
In Table \ref{tab:mass} we indicate, for each galaxy, the morphological type according to the Hubble's classification of galaxies, the radius $a$ in ${\rm kpc}$ and the total mass $\mathcal{M}$, both in ${\rm kg}$ and in solar mass units $\mathcal{M_{\odot}}$ ).
Now. as the set of constants C, it defines completely each particular thin dise model. we can easily compute all the shysical quantities characterizing each galaxy.
Now, as the set of constants $C_{2n}$ it defines completely each particular thin disc model, we can easily compute all the physical quantities characterizing each galaxy.
However. as explicit expressions for the gravitational potential (/?.2) and the surface mass density X(/7) can be easily obtained by using the values of he C's, at expressions (1019) and (123). we will not present them rere.
However, as explicit expressions for the gravitational potential $\Phi (R,z)$ and the surface mass density $\Sigma (R)$ can be easily obtained by using the values of the $C_{2n}$ at expressions \ref{eq:poten}) ) and \ref{density}) ), we will not present them here.
Insteed. we plot in Figure 2. the surface densities for the four galaxies. as functions of the dimensionless radial coordinate Ifa.
Insteed, we plot in Figure \ref{densit} the surface densities for the four galaxies, as functions of the dimensionless radial coordinate ${\widetilde R} = R/a$ .
For the four galaxies we obtain a well behaved surface mass density.having a maximum at the dise center and then decreasing until vanish at the disc edge.
For the four galaxies we obtain a well behaved surface mass density,having a maximum at the disc center and then decreasing until vanish at the disc edge.
In a similar way. we can compute the epiciclic and vertical frequencies by using (22). (24)) and the values of the constants eto, obtained from the numerical fit.
In a similar way, we can compute the epiciclic and vertical frequencies by using \ref{kapr2n}) ), \ref{nur2n}) ) and the values of the constants $A_{2n}$ obtained from the numerical fit.
However. as with the surface mass densities. we will not present the explicit expressions here and. instead. we only show the corresponding plots.
However, as with the surface mass densities, we will not present the explicit expressions here and, instead, we only show the corresponding plots.
So. in Figure 3. we show the plots of the epiciclic frequencies for the four galaxies considered and. in Figure 4.. the corresponding plots of the vertical frequencies.
So, in Figure \ref{epicic}, we show the plots of the epiciclic frequencies for the four galaxies considered and, in Figure \ref{vertic}, the corresponding plots of the vertical frequencies.
From the plots at Figure 3 we can see that only the galaxy NGC4Ol0 presents a small region of radial instability near the disc edge.
From the plots at Figure \ref{epicic} we can see that only the galaxy NGC4010 presents a small region of radial instability near the disc edge.
On the other hand. as it is shown at Figure 4.. the four galaxies are instable against vertical perturbations.
On the other hand, as it is shown at Figure \ref{vertic}, the four galaxies are instable against vertical perturbations.
(DeLuciaetal.200).. it does not coutribute to the existing stellar mass;
\citep{DeLucia04}, it does not contribute to the existing stellar mass.
When accounting for this. we find that the contribution from simaller central galaxies is considerably reduced (the dot-dashed lines in top panels of Fig. 8))
When accounting for this, we find that the contribution from smaller central galaxies is considerably reduced (the dot-dashed lines in top panels of Fig. \ref{fig:contTest}) )
aud is in better agreement with the SAM predictions (particularly for the Durham model).
and is in better agreement with the SAMs predictions (particularly for the Durham model).
This approximated coutribution. however. still appears to be somewhat overestimated. especially in the MPÀ 120del. where the measured coutribution of znaller ceutrals is tiny.
This approximated contribution, however, still appears to be somewhat overestimated, especially in the MPA model, where the measured contribution of smaller centrals is tiny.
As ineutioned already. the simplified estimate also inplicitlv assumes a coustaut SEE for the mereime halos. which in reality does vary with halo mass (sce. e... Fie.
As mentioned already, the simplified estimate also implicitly assumes a constant SFE for the merging halos, which in reality does vary with halo mass (see, e.g., Fig.
b. in this work and Fig.
\ref{fig:Fig10mill50b} in this work and Fig.
10 iu ZCZO7).
10 in ZCZ07).
This cau affect the contribution from snaller ceutral galaxies im two wavs: for a halo whose mass is around the peak of SPE or sinaller. this assiuuptiou might overestimate the contribution. while for larger mass halos if can result in an underestimation (which will result iu a stronger downsizing behavior).
This can affect the contribution from smaller central galaxies in two ways: for a halo whose mass is around the peak of SFE or smaller, this assumption might overestimate the contribution, while for larger mass halos it can result in an underestimation (which will result in a stronger downsizing behavior).
The bottom panels of Figure & compare the rough estimation of the merger contribution from satellites to
The bottom panels of Figure \ref{fig:contTest} compare the rough estimation of the merger contribution from satellites to
The distribution reaches as eacly stae after ~3x101)& or 1000yes.
The distribution reaches a steady state after $\about3\times10^{10}\unit{s}$, or $\about1000\unit{yrs}$.
This is a small fraction of the time speut in pliase 2. sugvesting tiat the iitial conditions are unimportant.
This is a small fraction of the time spent in phase 2, suggesting that the initial conditions are unimportant.
Also shown iu he figure are the opacity and otical deyh alter 10!s. but the curve falls exactly on the curve or 3x10!s aud cannot be disiuguisled in the igure.
Also shown in the figure are the opacity and optical depth after $10^{11}\unit{s}$, but the curve falls exactly on the curve for $3\times10^{10}\unit{s}$, and cannot be distinguished in the figure.
We see that while the opaciy is quite hie first. it drops quickly wheu erains are allowed O grow. aud the steady state op:€icity througho uost of the atmosphere is very much lower than 2iο>| the order of maguitde of interste eral opacity at these temperatures.
We see that while the opacity is quite high at first, it drops quickly when grains are allowed to grow, and the steady state opacity throughout most of the atmosphere is very much lower than $2\unit{cm^2~g^{-1}}$, the order of magnitude of interstellar grain opacity at these temperatures.
Ouly the ower third of the atinosphere (but ~90% of tl lass} is" consistent. with. the low opacity. of ?.. but the optical depth of tLe radiative zo is slightly lower than it would be with their low opacity.
Only the lower third of the atmosphere (but $\about90\%$ of the mass) is consistent with the low opacity of \citeauthor{hubickyj}, but the optical depth of the radiative zone is slightly lower than it would be with their low opacity.
Figure E shows tlie steady sale size distritition of graius in several layers of the atinosphliere. a 0.5Myr. or roughly the middle of phase 2.
Figure \ref{fig:5291nd} shows the steady state size distribution of grains in several layers of the atmosphere, at $0.8\unit{Myr}$, or roughly the middle of phase 2.
Because sinall [wegrains are continuotsly being deposited iu all layers. we expect a large population of small graius everywhere.
Because small grains are continuously being deposited in all layers, we expect a large population of small grains everywhere.
As we move deeper into the atmosphere we fiud more aud more large [n]€alus.
As we move deeper into the atmosphere we find more and more large grains.
These are grains that had time to grow while settling from higher up.
These are grains that had time to grow while settling from higher up.