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The left-hand panels show that the mean v receives contributions from a wide range of overdensities. | The left-hand panels show that the mean $y$ receives contributions from a wide range of overdensities. |
Cooling reduces the contribution from high-density gas in groups and clusters. | Cooling reduces the contribution from high-density gas in groups and clusters. |
Because most of the gas in the simulations is at low overdensity. pre-heating preferentially raises the contribution from that phase. | Because most of the gas in the simulations is at low overdensity, pre-heating preferentially raises the contribution from that phase. |
The hand panels in Figure |. indicate that gas below 10? K and above 105K contributes negligibly to μμ. | The right-hand panels in Figure \ref{f:ytd} indicate that gas below $10^5$ K and above $10^8$ K contributes negligibly to $y_{{\rm mean}}$. |
The mean v distributions have similar shapes in the cooling and non-radiative models and are practically uniform in the range 6.2=log(£/K)7.3 for all runs. | The mean $y$ distributions have similar shapes in the cooling and non-radiative models and are practically uniform in the range $6.2\lesssim \log (T/{\rm K})\lesssim 7.3$ for all runs. |
Gas above —2« 107K produces the same amount of distortion independently of the model considered. | Gas above $\sim 2
\times 10^7$ K produces the same amount of distortion independently of the model considered. |
The heating run shows a sharp peak at T~ 10°K resulting from IGM gas heated to this temperature by the energy injection at z=4. | The pre-heating run shows a sharp peak at $T\simeq
10^6$ K resulting from IGM gas heated to this temperature by the energy injection at $z=4$. |
While pre-heating will indeed insert à new temperature scale. the narrowness of this feature is no doubt an artifact. of our simplified method and would be broadened in reality. | While pre-heating will indeed insert a new temperature scale, the narrowness of this feature is no doubt an artifact of our simplified method and would be broadened in reality. |
Indeed. there is evidence that some of the IGM is cooler than this (Schaye et al. | Indeed, there is evidence that some of the IGM is cooler than this (Schaye et al. |
2000). | 2000). |
Figure 2. shows the rms temperature perturbation σµµς as à function of beam resolution (avy. obtained by averaging the 30 thermal (Rayleigh-Jeans band) and kinetic SZ maps. | Figure \ref{f:sigrms} shows the rms temperature perturbation $\sigma_{{\rm
rms}}$ as a function of beam resolution $\theta_{{\rm FWHM}}$, obtained by averaging the 30 thermal (Rayleigh–Jeans band) and kinetic SZ maps. |
Thedifferent cooling/pre-heating models shift the curves by tens ofpercent. | Thedifferent cooling/pre-heating models shift the curves by tens ofpercent. |
On the angular scalesshown. the kinetic dispersions are a factor ~5 smaller than the thermal. confirming earlier results using lower-resolution simulations (da Silvaet al. | On the angular scalesshown, the kinetic dispersions are a factor $\sim$ 5 smaller than the thermal, confirming earlier results using lower-resolution simulations (da Silva et al. |
2001). | 2001). |
external Theinduced Euclidean space-time isdue to the Euclidean dyonic loops. | = =0 where $\phi$ is the scalar field and $E_{\mu}$ is electric field in $R^4$. |
The natural question concerns (hepossiblemicroscopic description ofthe angular momentum in the Obackground | The shape of the loop can be arbitrary \cite{town}
however the extremization of the angular momentum yields the circular loop. |
in terms ofsome bounces inthe Euclidean space similar to QED. Sincein theD =5 SYM | The dyonic instanton is the BPS state and keeps 1/2 of the initial SUSY. |
one-loop Ποια.The branes branes on their worldvolumes. In the T-dual picture the dvonic instanton gets represented by (he DI-helix. | The BPS formula yields for its mass M= |I| + |vQ_e| where $|I|$ is the instanton charge and $v$ is the vev of the scalar. |
TheDObranes are charged with respect to theeraviphoton fieldaud prevent D2 branes from collaps | The BPS-ness is provided by the combined effect of the scalar, electric field and the "running" of the instantons in the loop. |
ingtoa point. Ilence in the€background wehavea kindοἱ bounce configurations in Euclidean space-time. been developedin [19]. wherethe Nekrasovp | Note that the symmetries supported by the dyonic instantons, that is diagonal $SU(2)$ from left rotations and R-symmetry, coincide with the symmetries kept by the $\Omega$ background. |
artition function was derived in termsof the blowing of ins | Let us describe the dynamical quantum numbers of solution in some details. |
tantons intheproper backeround into the D2— D2 state. Letus emphasize (hat wenecessarilv should QED case the Euclidean space-time. | To this aim it is useful to discuss the worldvolume Lagrangian of the tubular D2 brane of constant radius $R$ in flat Euclidean space-time L= - where $E,B$ are the worldvolume electric and magnetic fields. |
The dvonic instantons can circulardyonic loop which branesare equalion of motion | The corresponding canonical momentum reads as and Hamiltonian density is = There are evident integrals |
The solid squares in Fig. 2(( | The solid squares in Fig. \ref{fig:intro}( ( |
b) show the absorbers whose mmeasurement exist in the literature, and color-coded according to [Zn/H] from -2 to 0. | b) show the absorbers whose measurement exist in the literature, and color-coded according to [Zn/H] from -2 to 0. |
This figure clearly shows that the more metal poor (lighter grey points) are located in a different location as the metal rich (darker grey points). | This figure clearly shows that the more metal poor (lighter grey points) are located in a different location as the metal rich (darker grey points). |
In other words, there is a strong metallicity gradient across the pplane, represented schematically in Fig. 3(( | In other words, there is a strong metallicity gradient across the plane, represented schematically in Fig. \ref{fig:gradient}( ( |
a). | a). |
The metallicity gradient is noted by the vector. | The metallicity gradient is noted by the vector. |
For low ccolumn densities (logNg,< 19.5), there is a lack of metallicity data due to difficulties in measuring [X/H] due to an increasing ionization correction (Pérouxetal.2006;Prochaska2006).. | For low column densities $\log \NHI<19.5$ ), there is a lack of metallicity data due to difficulties in measuring [X/H] due to an increasing ionization correction \citep{PerouxC_06a,ProchaskaJ_06a}. |
Fig. 2(( | Fig. \ref{fig:intro}( ( |
b) shows that sub-DLAs are generally more metal rich than DLAs, a result noted already by many (e.g.Khareetal.2007).. | b) shows that sub-DLAs are generally more metal rich than DLAs, a result noted already by many \citep[e.g.][]{KhareP_07a}. |
However, since the metallicity changes in a subtle way in the pplane, (Fig. 3[[ | However, since the metallicity changes in a subtle way in the plane, (Fig. \ref{fig:gradient}[ [ |
a]), one would expect to have different mean metallicity ([X/H]) for different --selected samples. | a]), one would expect to have different mean metallicity $\langle\Z\rangle$ for different -selected samples. |
This is illustrated in Fig. 3(( | This is illustrated in Fig. \ref{fig:gradient}( ( |
b), where we Nyyplot ([X/H]) for DLAs with logNg,>20.3 (top) and sub-DLAs with logNg,<20.3 (bottom). | b), where we plot $\langle\Z\rangle$ for DLAs with $\log \NHI>20.3$ (top) and sub-DLAs with $\log \NHI<20.3$ (bottom). |
The metallicity iincreases as a function of (a proxy for the velocity width Av) for DLAs. | The metallicity increases as a function of (a proxy for the velocity width $\Delta v$ ) for DLAs. |
The P-value of the Spearman's correlation test is 2x10*, i.e. the correlation is significant at 4-c. | The $P$ -value of the Spearman's correlation test is $2\times10^{-7}$, i.e. the correlation is significant at $>4$ $\sigma$ . |
Moreover, the increase in the mean metallicity lis ~ 0.8-1 dex, which is the increase reported by Ledoux for their DLA-sample. | Moreover, the increase in the mean metallicity is $\sim0.8$ –1 dex, which is the increase reported by \citet{LedouxC_06a} for their DLA-sample. |
On the other hand, for absorbers with log less than 20.3, the mean metallicity appears constant (Fig. Ng,3[[ | On the other hand, for absorbers with $\log \NHI$ less than $20.3$, the mean metallicity appears constant (Fig. \ref{fig:gradient}[ [ |
b], bottom). | b], bottom). |
The Spearman's correlation test gives a P-value much higher (0.10) and shows that the correlation is significant at best at 1.50. | The Spearman's correlation test gives a $P$ -value much higher (0.10) and shows that the correlation is significant at best at $\sigma$. |
Without the one data point atW?7799200.5À... the P-value is higher still: 0.43 and the is not correlated with[X/H]. | Without the one data point at, the $P$ -value is higher still: 0.43 and the is not correlated with. |
. We note that the rrelation reported by Murphyetal.(2007) is explained by the fact that their sample is dominated by systems with ccolumn densities mostly above the DLA threshold Ng,>20.3 (Fig. 2[[ | We note that the relation reported by \citet{MurphyM_07a} is explained by the fact that their sample is dominated by systems with column densities mostly above the DLA threshold $\NHI>20.3$ (Fig. \ref{fig:intro}[ [ |
a]). | a]). |
Thus, the [X/H]-Av and correlations reported by Ledouxetal.(2006) for DLAs and Murphyetal.(2007) are both a ‘selection effect’: it originates from the increased overlap of the metal poor and metal rich systems in the pplane. | Thus, the $\Delta v$ and correlations reported by \citet{LedouxC_06a} for DLAs and \citet{MurphyM_07a} are both a `selection effect': it originates from the increased overlap of the metal poor and metal rich systems in the plane. |
While the fraction of DLAs increases with| this exercise shows that the selection upon is not equivalent to a sselection, as the two sample will have very different properties: the I1--selected sample will be biased towards more metal rich absorbers, while the 1--selected sample will be more metal poor, with a strong metallicity dependence onW?796. | While the fraction of DLAs increases with, this exercise shows that the selection upon is not equivalent to a selection, as the two sample will have very different properties: the -selected sample will be biased towards more metal rich absorbers, while the -selected sample will be more metal poor, with a strong metallicity dependence on. |
. Note that there seems to be no redshift bias in our results: Fig. 2[[ | Note that there seems to be no redshift bias in our results: Fig. \ref{fig:intro}[ [ |
b] looks similar for the zaps«1.6 and Zaps>1.6 sub-samples, with perhaps an overall shift in metallicities which has been before for DLAs and sub-DLAs (Prochaskaetal.2003;Kulkarnietal. 2007).. | b] looks similar for the $z_{\rm abs}<1.6$ and $z_{\rm abs}>1.6$ sub-samples, with perhaps an overall shift in metallicities which has been before for DLAs and sub-DLAs \citep{ProchaskaJ_03b,KulkarniV_07a}. |
Based on these results, we turn towards a physical interpretation. | Based on these results, we turn towards a physical interpretation. |
As we already noted, the ddistribution is bimodal in the pplane (Fig. | As we already noted, the distribution is bimodal in the plane (Fig. |
2aa). | \ref{fig:intro}a a). |
This is particularlyNg ονtrue for systems with W2?798611.5 A. | This is particularly true for systems with $<1.5$. |
.Thisindicatestheremightbetwoclasseso finterveningabsorber. | This indicates there might be two classes of intervening absorbers, probing different physical conditions. |
ccolumndensity, andthebimodalityisalreadypresentintheir sample. | While observational bias may play a role here, the survey of \citet{RaoS_06a} is unbiased in regards to column density, and the bimodality is already present in their sample. |
Given the metallicity gradient shown in the previous section and the absorber distribution in the pplane, we make the following Nyassumptionws to guide our understanding: absorbers in the redmetal-rich shaded region | Given the metallicity gradient shown in the previous section and the absorber distribution in the plane, we make the following assumption to guide our understanding: absorbers in the redmetal-rich shaded region |
In this paper we have constructed an equation of state in (he vicinity of the chiral eritical point. | In this paper we have constructed an equation of state in the vicinity of the chiral critical point. |
It incorporates the correct values of the critical exponents and amplitudes. | It incorporates the correct values of the critical exponents and amplitudes. |
Since only certain. properties of the equation of state are universal. (here is some freedom to vary (he noncritical functional dependence on temperature and density aud to change (he parameters in those functions. | Since only certain properties of the equation of state are universal, there is some freedom to vary the noncritical functional dependence on temperature and density and to change the parameters in those functions. |
The parameterization proposed here matches on to the equation of state al zero barvon density as caleulated in lattice gauge theory. and at zero Lemperalture using reasonable extrapolations of dense nuclear matter. | The parameterization proposed here matches on to the equation of state at zero baryon density as calculated in lattice gauge theory, and at zero temperature using reasonable extrapolations of dense nuclear matter. |
Certainly. refinements and mocifications are possible within (he present framework. | Certainly, refinements and modifications are possible within the present framework. |
The Landau theory of fluctuations away trom equilibrium states was elploved to determine the potential magnitude of the fluctuations one might expect in heavy ion collisions. | The Landau theory of fluctuations away from equilibrium states was employed to determine the potential magnitude of the fluctuations one might expect in heavy ion collisions. |
The magnitude of these f[Iuctuations is quite large. partlv due to finite volume effects but. primarily because (he critical exponent à is much larger (han in standard mean field theories. | The magnitude of these fluctuations is quite large, partly due to finite volume effects but primarily because the critical exponent $\delta$ is much larger than in standard mean field theories. |
This flattens the Landau free enerev as a function of density away [rom the equilibrium densities and hence decreases the cost to fluctuate away [rom them. | This flattens the Landau free energy as a function of density away from the equilibrium densities and hence decreases the cost to fluctuate away from them. |
In the future it would be hiehly desirable to have a parameterization of the equation of state Chat includes not only the behavior near (he critical point but also extends to much hieher temperatures aud densities. | In the future it would be highly desirable to have a parameterization of the equation of state that includes not only the behavior near the critical point but also extends to much higher temperatures and densities. |
Ultimately. lo compare wilh experimental data. it will be necessary (o incorporate this knowledge into dvnamical simulations of heavy ion collisions. | Ultimately, to compare with experimental data, it will be necessary to incorporate this knowledge into dynamical simulations of heavy ion collisions. |
Tam grateful to L. Csernai for discussions. and to both him and Ix. Rajagopal for comments on the manuscript. | I am grateful to L. Csernai for discussions, and to both him and K. Rajagopal for comments on the manuscript. |
This work was supported by the US Department of Energv (DOE) under Grant No. | This work was supported by the US Department of Energy (DOE) under Grant No. |
DE-EGO2-51EBRA0328. | DE-FG02-87ER40328. |
1n this section we investigate several models. based. on standard theories of the Formation of galactic discs. | In this section we investigate several models based on standard theories of the formation of galactic discs. |
These theories are generically based on the idea of (1963) that the specific angular momentum of the material that forms the galactic disc is conserved as it Cools and condenses. | These theories are generically based on the idea of \nocite{mest:63}{ (1963) that the specific angular momentum of the material that forms the galactic disc is conserved as it cools and condenses. |
Since this idea was first applied in the classic work of Fall (1980). many authors have refined this theory V including the effects of the adiabatic contraction of the clark halo. the presence of a bulge. more realistic halo profiles. and disc stability criteria ((Blumenthal 1986: LOST: 1993:Dalcanton. 1997:Mo.Mao. 1908: 1999). | Since this idea was first applied in the classic work of \nocite{fe:80}{ (1980), many authors have refined this theory by including the effects of the adiabatic contraction of the dark halo, the presence of a bulge, more realistic halo profiles, and disc stability criteria \nocite{bffp:86,kruit:87,fpbf:93,dss:97,mmw:98,bosch:99}( 1986; 1987; 1993;, 1997;, 1998; 1999). |
In the simplest of such models. we assume a singular isothermal profile for the dark. matter. halo. neglect. the ellects of the halo contraction on the assembly of the disc. and assume that the profile of the cold eas after collapse has the form of an exponential. | In the simplest of such models, we assume a singular isothermal profile for the dark matter halo, neglect the effects of the halo contraction on the assembly of the disc, and assume that the profile of the cold gas after collapse has the form of an exponential. |
The exponential scale length is then given by the simple expression: where Ag is the dimensionless spin parameter of the halo. and r; is the initial radius of the gas before collapse. | The exponential scale length is then given by the simple expression: _H r_i where $\lambda_H$ is the dimensionless spin parameter of the halo, and $r_i$ is the initial radius of the gas before collapse. |
In N-bocly simulations. the spin parameter Ag for dark matter halos is found to have a log-normal clistribution with à mean ol about 0.05 (Warren 1992). | In $N$ -body simulations, the spin parameter $\lambda_H$ for dark matter halos is found to have a log-normal distribution with a mean of about 0.05 \nocite{warr:92}( 1992). |
X generalization of this model. using an NEW profile for the dark matter halo and including the ellect of halo contraction. has recently been presented by Mo (1998). | A generalization of this model, using an NFW profile for the dark matter halo and including the effect of halo contraction, has recently been presented by \nocite{mmw:98}{ (1998). |
In model EXPL. we assume Aq=0.05 for all halos. take ο—minreoPerr]. and caleulate the scale length Lor each dise from eqn 7.. | In model EXP1, we assume $\lambda_H = 0.05$ for all halos, take $r_i = \min[r_{cool}, r_{vir}]$, and calculate the scale length for each disc from eqn \ref{eqn:rdisc}. |
Note that when this approach is used to model scale lengths. the values that we obtain are in good agreement with observations at redshift zero and redshift ~3 (SP: SPE). | Note that when this approach is used to model scale lengths, the values that we obtain are in good agreement with observations at redshift zero and redshift $\sim 3$ (SP; SPF). |
llowever local observations ((Broeils 1997) find that in gas rich galaxies the LIE disc always has a larger extent than the stellar disc. | However local observations \nocite{br:97}( 1997) find that in gas rich galaxies the HI disc always has a larger extent than the stellar disc. |
To explore this scenario we try a model where the exponential scale length of the gas is given by a multiple of the stellar dise scale length. | To explore this scenario we try a model where the exponential scale length of the gas is given by a multiple of the stellar disc scale length. |
We find multiplving the scale length. calculated from eqn. | We find multiplying the scale length calculated from eqn. |
T hy a [actor of six (model EXPG) produces the best agreement with the kinematic data but can still be rejected at ο95% confidence level. | \ref{eqn:rdisc} by a factor of six (model EXP6) produces the best agreement with the kinematic data but can still be rejected at $> 95\%$ confidence level. |
In model MN. we use the fitting formulae of (1998) to obtain the scale racius. | In model MMW, we use the fitting formulae of \nocite{mmw:98}{ (1998) to obtain the scale radius. |
In this model we do not use the gas content. predicted by the SAMs. but. instead. Following Mo (1998) we assume that the disc mass is a fixed fraction (one tenth) of the total mass of cach halo or sub-halo. | In this model we do not use the gas content predicted by the SAMs, but instead, following \nocite{mmw:98}{ (1998) we assume that the disc mass is a fixed fraction (one tenth) of the total mass of each halo or sub-halo. |
This procedure produces roughly three times more cold eas per halo than the SAAIs as there is no and no hot gas. | This procedure produces roughly three times more cold gas per halo than the SAMs as there is no and no hot gas. |
Thus this model should be seen as an upper limit on the amount of cold gas that is available to form DLAS in the halo mass range we are considering. | Thus this model should be seen as an upper limit on the amount of cold gas that is available to form DLAS in the halo mass range we are considering. |
The spin parameter Àg is chosen randomly from a log-norma distribution. and the exponential scale length is found from eqn τν. | The spin parameter $\lambda_H$ is chosen randomly from a log-normal distribution, and the exponential scale length is found from eqn \ref{eqn:rdisc}. |
Phe main dillerence between our AIMIW model ane he actual model of is that we include sub-halos (multiple galaxies in cach halo). | The main difference between our MMW model and the actual model of \nocite{mmw:98}{ is that we include sub-halos (multiple galaxies in each halo). |
Because do no simulate the merging history of their halos. they assume tha only one galaxy inhabits each halo (which would correspone o our central galaxy). | Because \nocite{mmw:98}{ do not simulate the merging history of their halos, they assume that only one galaxy inhabits each halo (which would correspond to our central galaxy). |
The models of IN96 used the assumption that the initia xolile of the cold gas resulted [rom conservation of angular momentum. and mocelled. star formation according to the empirical law proposed by (1989). | The models of K96 used the assumption that the initial profile of the cold gas resulted from conservation of angular momentum, and modelled star formation according to the empirical law proposed by \nocite{kenn:89}{ (1989). \nocite{kauf:96}{ |
hen found that surface density of the gas clises tended to remain close to the critical surface density. as. in fact observed. | then found that surface density of the gas discs tended to remain close to the critical surface density, as \nocite{kenn:89}{ in fact observed. |
In. our model WENN. based. on. these observations and the results of IX96. we again take the total mass of cold. gas from the SAAIs. and distribute it at the critical density. which for a flat rotation curve is given by :—15. 72 )) t) | In our model KENN, based on these observations and the results of K96, we again take the total mass of cold gas from the SAMs, and distribute it at the critical density, which for a flat rotation curve is given by :=1.5 2 ) ). |
‘Thus for à given Y, this is a Alestel distribution. with | Thus for a given $V_c$ this is a Mestel distribution, with |
the fact that the column density is not the best proxy for the soft X-ray absorbing column density. | the fact that the column density is not the best proxy for the soft X-ray absorbing column density. |
This result immediately suggests that while using Ny, as a proxy for the soft X-ray absorption is reasonable. using the dust column. as suggested by ?.. 1s likely to yield better results not simply because of the higher resolution of the dust maps. but because the dust-to-metals ratio seems to be more constant than the dust-to-gas ratio. | This result immediately suggests that while using $N_\ion{H}{i}$ as a proxy for the soft X-ray absorption is reasonable, using the dust column, as suggested by \citet{1998ApJ...500..525S}, is likely to yield better results not simply because of the higher resolution of the dust maps, but because the dust-to-metals ratio seems to be more constant than the dust-to-gas ratio. |
While this cannot be investigated further here due to the large uncertainty in the ratios we derive. future studies should try to determine the systematic Galactic radial and columi density dependences of the dust-to-metals ratio. | While this cannot be investigated further here due to the large uncertainty in the ratios we derive, future studies should try to determine the systematic Galactic radial and column density dependences of the dust-to-metals ratio. |
This latter point may be important since it is well-known that the depletiot of metals out of the gas phase increases as we move into the disk and into cooler environments (?).. which would obviously be associated with higher column densities. | This latter point may be important since it is well-known that the depletion of metals out of the gas phase increases as we move into the disk and into cooler environments \citep{1996ARA&A..34..279S}, which would obviously be associated with higher column densities. |
It has beer suggested above that the exploration of ? could be extendec by increasing the sample size. | It has been suggested above that the exploration of \citet{2009MNRAS.400.2050G} could be extended by increasing the sample size. |
Such an extension would indeec be worthwhile and allow the Galaxy to be divided into various lines of sight. related to the disk or the bulge. | Such an extension would indeed be worthwhile and allow the Galaxy to be divided into various lines of sight, related to the disk or the bulge. |
A more complete approach might be to use bright extragalactic objects know! to have low host galaxy absorptions. which would allow a census to be taken of sightlines through arbitrary directions in the galaxy. including the halo. | A more complete approach might be to use bright extragalactic objects known to have low host galaxy absorptions, which would allow a census to be taken of sightlines through arbitrary directions in the galaxy, including the halo. |
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