Virial Shocks in Galactic Halos

This paper (Birnboim & Dekel 2004; http://arxiv.org/abs/astro-ph/0302161) performs a global 1-D linear stability analysis of the virial shock in a self-gravitating dark matter halo. The authors relate the pressure and density of the post-shock gas (using $d\ln P/d\ln \rho = \gamma_{\rm eff}$) and perform a stability analysis on the perturbations of the pressure and gravitational forces, assuming hydrostatic equilibrium. $\gamma_{\rm eff}$ depends on the cooling rate; for an adiabatic ideal gas blob $\gamma_{\rm eff}=5/3$. They derive a critical $\gamma_{\rm eff}$ for the shock stability in presence of cooling; only for $\gamma_{\rm eff}>\gamma_{\rm crit}=1.43$ is the post-shock plasma stable. In presence of cooling, the effective adiabatic index is given by
$$\gamma_{\rm eff}=\gamma + \frac{r_s}{2 u_1} \frac{q}{e},$$
where $r_s$ is the shock radius, $u_1$ is the post-shock velocity ($<0$) and $q$ is the cooling rate and $e$ is the internal energy. This instability criterion can also be expressed in terms of the upstream variables and is roughly equivalent to $\frac{t_{\rm ff}}{t_{\rm cool}} \lesssim {\cal O}(1)$. A similar criterion was proposed by Rees & Ostriker 1977 (http://adsabs.harvard.edu/abs/1977MNRAS.179..541R) for efficient cooling of gas to form galaxies. They argued that if $t_{\rm cool}<t_{\rm ff} \sim t_{\rm snd}$, the gas cools to sub-virial temperatures ($10^4$ K), and the cool gas falls on a free-fall time, unimpeded by gas pressure.

Both these papers find that stable/quasi-steady, pressure supported IGM is formed only for a halo mass $\gtrsim 10^{12} M_\odot$. While RO77 and other subsequent papers envisioned a hot, shocked IGM, BD04 showed that a stable virial shock is formed only for $\gtrsim 10^{12} M_\odot$ halos, and that the gas accretes in the code mode (at $\sim 10^4$ K) for lower mass halos, as observed in recent numerical simulations. BD04 also performed 1-D Lagrangian simulations of shock formation with DM + gas, starting from cosmologically consistent initial conditions. Their numerical simulations agree with their linear stability analysis. The critical halo mass for forming stable shock ($\sim 10^{11.5} M_\odot$) is fairly insensitive to metallicity, angular momentum, baryon fraction, power spectrum, etc. An important effect that BD04 may have missed is feedback heating; in presence of  feedback heating the virial shock can become stable as feedback heating provides the post-shock pressure to support the shock.

Recently Dekel and collaborators have argued that cold streams are responsible for star-forming galaxies (SFGs) with SFR~100$M_\odot {\rm yr}^{-1}$; however major mergers are likely responsible for the rarer sub-mm galaxies at z~2 with SFR~1000$M_\odot {\rm yr}^{-1}$. Major mergers are responsible for $< 1/3$ in total star formation.

Classic papers in Astrophysics

I want to read and understand some of the classic papers in Astrophysics and summarize them here, for later reference. Hopefully I get down to this sooner than later. I'll probably choose them based on my current interests and taste. I want to do at least 1 per week.

Galaxy Formation : Environment vs. Halo Mass

Galaxies grow primarily by the cooling of the intergalactic gas accreted by dark matter halos. Numerical simulations have shown that the gas accreting in dark matter halos <~ 10^12 Msun is not heated to the virial temperature, but instead is accreted via the `cold' mode (see http://arxiv.org/abs/astro-ph/0407095). For halos less massive than this critical mass, the cooling time of the gas at the virial radius is shorter than the dynamical time, and thus a hot hydrostatic atmosphere is not formed. This recent paper (http://arxiv.org/abs/1104.5046) argues that, in addition to the halo mass, the environment also plays an important role in galaxy formation. They have simulated two large (~ 20^3 Mp^3) cosmological volumes, one centered on a void (underdensity) and one on a cluster (overdensity), and compared galaxy formation in these different environments. As expected,  stellar/light density is much smaller in the void simulation than in the cluster simulation. Their simulations reproduce galaxy downsizing, i.e., the peak star formation occurs in lower mass halos with decreasing redshift, for both the void and cluster galaxies.

They argue that the ratio of tcool (cooling time at the virial radius) and the Hubble time (halo age), which is roughly a function of entropy and is relatively independent of redshift, determines the specific star-formation rate (sSFR). If tcool/tH is small, sSFR is large and the galactic mass can double in the Hubble time. At high z, because of a large cosmic density, tcool is shorter than tH and sSFR is large for all galaxies, both in void and cluster environments. However, at z=0, not only the massive halos (as predicted by the 'cold mode' scenario), but also the lower mass halos in high temperature/entropy cluster environment, have low sSFR such that they can't double their mass in a Hubble time. Thus, in addition to the halo mass, environment also plays an important role in galaxy formation. But fundamentally it is still tcool/tH which determines sSFR; temperature/entropy in cluster environment is higher and tcool/tH>1, and hence sSFR is suppressed.

Some studies compare tcool/tff and some compare tcool/tH. If there is feedback heating which roughly balances radiative cooling, as in the intracluster medium, the relevant ratio should be tcool/tff. In absence of heating, tcool/tH seems more appropriate. It will be useful to study these important timescales in more detail. Clarification: tcool<tH is absolute minimum requirement (necessary but not sufficient) for efficient cooling; since tcool is minimum at fewx1e5 K, that tcool is an absolute upper limit for efficient star formation.

Many more Jupiters than Stars

In this very exciting paper (http://arxiv.org/abs/1105.3544), based on microlensing experiments which monitor the sudden increase in the luminosity of the Galactic halo stars due to gravitational magnification by a foreground source, the authors have obtained the statistics of lens masses. The duration of the amplification even is ~ (M/M_J)^0.5 days, where M_J is the Jupiter mass. Thus, you need higher cadence  (shorter sampling of the stellar lightcurve) to see smaller mass lenses. The authors find an excess of events at ~ day timescale, corresponding to the Jupiter mass objects. They claim that these Jupiter mass objects are either free-floating, or are farther by >10 AU from the central star, and are more common than main sequence stars by a factor of ~ 2. Out of their 474 evens only 10 have an Einstein time (duration of magnification event) < 2 days; although their number is small the probability of lensing by smaller masses is also lower (proportional to the square of the lens mass), so their real abundance is larger.

The lensing statistics reproduce a good fit to the stellar mass function but requires a bump at the Jupiter mass. The argue that these Jupiter mass planets are kicked out from their stars by dynamical interactions. Another possibility is that  they are Jupiters formed at large distances from their stars, but this is less likely because such systems would have been detected very commonly in nearby directly-imaged planetary systems. With even better cadences they may be able to constraint the number of free-floating lower mass planets. Let wait and watch!

Why are low mass halos not forming stars?

The mass to light ratio of galaxies is minimum for a Galactic mass halo (~1.e12 Msun). For both smaller and larger halo masses the stellar mass, and hence the luminosity, decreases relative to the halo mass. At larger halo masses star formation is believed to be quenched due to AGN feedback, and at lower halo masses momentum feedback by supernovae has been blamed for suppressing star formation. This paper (http://arxiv.org/abs/1105.2376) suggests an alternate possibility for explaining lower star formation efficiency in smaller mass halos (<few 1.e9 Msun; to quench star-formation in galaxies larger than this still requires supernova feedback). It suggests that lower mass halos (with low metallicities and smaller gas column densities) cannot form molecular hydrogen, which is a pre-requisite to form stars according to recent observations and modeling. This is a simulation paper which uses a simplified equilibrium model for molecular gas fraction depending on the UV background, metallicity, dust, neutral hydrogen density, etc. and calculates the star formation rate based on molecular hydrogen fraction. Using this prescription the authors are able to get the reduction in stellar mass fraction in halo masses less than few times 1.e9 solar masses. Their model also predict neutral hydrogen in lower mass halos because it has not been converted in the molecular phase or stars. 

Large Cool-Cores vs. Coronae

Recently it was shown that most clusters have entropy cores (http://arxiv.org/abs/0902.1802) at scales of few 10s of kpc, and if the core entropy is < 30 keV it is very likely to show cool filaments or radio AGN. However, this paper (http://arxiv.org/abs/0904.2006) suggested that the core entropy is not a well-defined quantity in all cases because some clusters show high density, low temperature coronae associated with the central BCG at much smaller scales (< 5 kpc). The paper shows that strong radio emission is seen in all systems with cool gas, either in form of traditional large cool cores or small coronae. Thus, non-cool-core systems which show radio are very likely to be unresolved coronae systems. Now the question arises whether the coronae show cool filaments as the systems with large cool cores do?

Missing Baryon Problem(s)

This (http://arxiv.org/abs/1003.3273) paper talks about two missing baryon problems: one, the global one, that most of the baryons (accounting for all observed sources, stars, cool gas, ICM, Ly alpha forest, etc.) in the universe as a whole are missing. The second missing baryon problem is that most galaxies (like our own) are severely baryon poor. Numerical simulations suggest that rest of the baryons are in the difficult to observe warm hot intergalactic medium (WHIM). This paper argues, based on observation of pulsar dispersion measure, OVII absorption, etc., that most of the baryons are not in the Galactic halo. Moreover, from the lack of correlation between AGN/stellar feedback indicators (e.g., stellar fraction, bulge mass) and the missing baryon fraction from a galaxy, these authors argue that the baryons are not missing because of outflows driven by feedback. Rather the baryons never fell into the dark matter halos in the first place!