lit: The Habitable Epoch of the Early Universe

by A. Loeb.
That's a fantastically crazy paper (by A. Loeb, who's one of the best known names in areas as diverse as gravitational microlensing/black hole evolution/reionisation and 21 cm signal/high-z GRBs/Event Horizon telescope, and many others). He's written several papers about wild ideas before: exploring the (sad and very distant) future of observational cosmology, bio-markers in white dwarf planets' atmospheres, planets of hypervelocity stars, search of artificially-illuminated objects in and beyond the Solar System and cosmology measurements from hypervelocity stars which shows that not all is lost for the future cosmologists.
In this paper he looks at the dawn of the Universe, when it was only ~15 million year old. A. Loeb points out that the temperature of the cosmic microwave background was roughly around 0-30 C then, and therefore liquid water could have existed on any solid surface, meaning that there might have been conditions suitable to life as we know it. In order to form any rocky planet one needs to explode some massive stars before (to get some heavier elements like oxygen, iron, silicium, etc, which are what rocky planets are made of). At that time we're left with the formation of the very first stars in the very first, tiny, dark matter haloes at the far end of the density distribution. Calculations show that the number of such protogalaxies was incredibly small at these redshifts.
However, if we assume that the initial density distribution was not perfectly Gaussian (there are many theories explaining why it might have been the case, although Planck and other observations haven't found any proof of non-gaussianity yet), there might have been some haloes that had formed massive stars by that time.
It's a marvelous article, although AFAIK, it takes much longer than a few Myr for rocky planets to assemble from accretion disks of stars (and cool down due to the decay of radioactive elements..). But think of it: at some time in the history of the Universe the outer space was warm (and at least a million times denser than now).

lit: The Zeldovich approximation: key to understanding Cosmic Web complexity

Hidding, Shandarin et al. 2013: seems interesting, modelling the structure of the cosmic web.

talk: assembly bias

I had volunteered to give a presentation on 'Detection of assembly bias' by Wang, Weinmann, de Lucia and Yang. It went pretty well today, here are the slides. It explains the difference between galaxy bias, halo bias and assembly bias. As one of my supervisors puts it, 'not good news'.

Daily Paper #8: Constraints on the relationship between stellar mass and halo mass at low and high redshift

Title: Constraints on the relationship between stellar mass and halo mass at low and high redshift
Authors: Moster, Somerville et al.
Year: 2009, http://arxiv.org/abs/0903.4682
They give a nice breakdown of the methods used to link the halo properties with those of the galaxy. It is possible to obtain these relations from observations (kinematics, lensing, X-rays), from bottom-up modelling (N-body or SAMs), or by using a statistical approach: obtaining the probability that a halo with a certain mass hosts a certain number of galaxies with some certain properties (luminosity, type, etc.). This way, we don't have to make assumptions about feedback and other poorly-understood processes that plague the SAMs. I'll review the lecture recordings from Jerusalem School, I think the formalism used was explained in detail there.
The goal of this paper is to construct the conditional stellar mass function (as opposed to the conditional luminosity function). Such a function provides the average number of galaxies in a certain stellar mass range that reside in a halo with a mass M -- it can also be viewed as the stellar mass function for the haloes of mass M.
They use a N-body simulation to obtain a population of DM haloes and their merger tree information. The ratio of the halo mass M and the stellar mass M is not constant (due to different feedback processes), so they use a parameterisation of it to fill the haloes with galaxies, and obtain the stellar mass-Mhalo relation.
In order to obtain the conditional mass function, they divide the galaxies into centrals and satellites, parameterising their distribution in two different ways. The total CMF is the combination of the two.
They also obtain the M* -- M_halo relationship for higher redshifts, claiming that 'large halos accrete dark matter faster than large galaxies grow in stellar mass, while the growth of low mass halos is slower than that of the central galaxies they harbor', (see the attached picture).

This paper does not mention the TF relation, however, I wanted to find out more about the M*-Mhalo relation, the ways to determine it and its evolution. It's interesting that the high-mass end of this relation does not evolve much since z=4.

Daily Paper #7: Galaxy groups in the 2dFGRS: the number density of groups

Title: Galaxy groups in the 2dFGRS: the number density of groups
Authors: Eke, Baugh, Cole et al.
Year: 2006, http://adsabs.harvard.edu/abs/2006MNRAS.370.1147E
The authors determine the galaxy groups mass and luminosity functions from 2dFGRS Percolation-Inferred Galaxy Group (2PIGG) catalogue (getting about 29 000 groups). The catalogue and the mock catalogues used to determine and correct for bias are described in Eke 2004 paper.
They obtain dynamical masses of the clusters (I think they use the words 'cluster' and 'group' interchangeably here) from their velocity dispersions, and obtain their luminosities by simply adding up the members' luminosities with weighting to account for spectroscopic incompleteness and galaxies below the flux limit. Then they correct the mass and luminosity functions using the Vmax method. However, they claim that a more robust way to determine the group mass function is deriving it from the luminosity function by multiplying it by a mass-to-light ratio. They also show that the total group luminosity function depends on the group finding algorithm used.
The main goal of the article is to determine the \sigma_8 parameter, but they make a comparison between halo velocities and circular velocities, claiming that the two are similar. The authors claim it is possible to convert a halo luminosity to its circular rotation velocity directly, then convert group luminosities (which are very similar to those of the brightest galaxy of the group) to circular velocities using Bell & de Jong B-band TF relation, and compare the two (see the attached figure).


I think it is an important article, because it is observational, and worth citing while discussing the halo/galaxy velocities issue (the ratio of v_c/v_200 is around 1.2, at least from the simulations, not close to 1 as they find here). Anyway, I'll remember this article in case I have enough time to work on the velocity function.

Daily Paper #6: A physical model of cosmological simulations of galaxy formation

I picked this article for the group meeting presentation, and actually read it, because it is rather relevant.
Title: A physical model of cosmological simulations of galaxy formation
Authors: Vogelsberger, Genel, Sijacki et al.
Year: 2012, http://arxiv.org/pdf/1305.2913v1.pdf
They present galaxy formation simulations using the AREPO code, which is a moving mesh hydro code, claimed to combine the advantages of SPH and semi-analytical models built on top of N-body simulations. What is important, however, is that they include, among other things:
-- BH seeding and growth
-- 3 modes of AGN feedback (thermal, kinetic (radio jets) and EM radiation). The discrepancy between the high-mass end of McCarthy, Schaye et al. TFR and observations I discussed yesterday is probably due to lack of AGN feedback prescriptions.
-- realistic cooling (including metals) with self-shielding
-- realistic enrichment timescales and yields
-- different modes of outflows

The article itself is quite long and rather technical, dealing with the details of the implementation of physics. However, there are some interesting observations. For instance, they discuss the stellar mass function and its relation to feedback, halo mass function and the cosmic SFH. The stellar mass function is 'chewed' by stellar feedback (SN and stellar winds) at the low halo mass end, and by AGN feedback at the higher mass end. It can be viewed as the convolution of the halo mass function with the efficiency with which stars form in these haloes (i.e. feedback mechanisms).

I think this relation is really important -- actually, it shows why the TFR exists, and why there is a knee at the high-mass end. _Why_ the slope, zeropoint and scatter are such are different questions -- but the answer to that should be some combination of the halo concentration (i.e. response to baryons, mostly), details of feedback (which determine the shape of the M* -- Mhalo relation) and the initial halo mass function (i.e. cosmology). The latter also sets the angular momentum of galaxies (Vvir -- Mvir are related, see the description of Dutton 2011).

They reproduce the stellar mass-halo relation, stellar mass function, evolution of the cosmic SFR density, the cosmic stellar mass density, mass-metallicity relation, SDSS luminosity function, M_BH -- M* relation and the Tully-Fisher relation (in the Vcirc -- M* sense, see the other attached plot). They claim (by citing McCarthy & Schaye, and experimenting with different radii) that the precise radius of the velocity measurement is not very important.

They conclude that TFR is not very sensitive to feedback parameters (shown in the plot). However, feedback must be included, otherwise it is not possible to reproduce TFR correctly. They find that the stellar mass in a halo is primarily set by the stellar feedback and radio-mode AGN feedback.

Daily Paper #4: Dark halo response and the stellar initial mass function in early-type and late-type galaxies

Our group meeting ate most of my day, so here's a delayed review. Title: Dark halo response and the stellar initial mass function in early-type and late-type galaxies
Authors: Dutton, Conroy, van den Bosch et al., http://arxiv.org/abs/1012.5859
Year: 2011
The authors try to find the origins of the TF and Faber-Jackson relations, using a big sample of observed galaxies from SDSS, a set of observational scaling relations showing the distribution of baryons in galaxies, with constrains on the DM halo structure from simulations.
They claim in the introduction that the origin of TFR and FJR is the relation between the halo virial velocity and its virial mass, which scales as v_vir \propto M^(1/3). The relation between v_opt (*) and v_vir depends on 3 factors:
-- the contribution of baryons to v_opt
-- the structure of pristine (DM-only) haloes. The halo profiles are well-enough defined by the NFW profile.
-- and the halo response to the disk formation (contraction/expansion)
The biggest source of uncertainty for the first factor is the IMF, as most of the baryonic mass in galaxies (except the low-mass star-forming ones) is in stars.
The third factor, the halo response, is quite uncertain. It can be adiabatic or non-adiabatic contraction, or expansion due to a number of different processes.
They use a large number of observed relations (TF and FJ relations too) to constrain or predict unknown quantities in their analytic model, modelling the DM halo, bulges, disks, gas disks, constructing 3D models of their SDSS sample galaxies (~100 000 LTGs, ~160 000 ETGs).
They construct mass models for all those galaxies using various IMF and assumptions about the halo response. Then they compare them with the observed circular velocity -- stellar mass relations (I do not understand it at this point -- they already used the TFR as a constraint while solving for the halo contraction at a given IMF, so it is inbuilt in their model somehow?).
Nevertheless, they do not reproduce the zero-point of the TFR with the standard Chabrier IMF and standard adiabatic halo contraction model, as the velocity is overpredicted. They claim that it is possible to fix that by either assuming a different IMF, or changing the halo response, or having different halo concentrations (set by formation time or \sigma_8, they claim that both ways to do it do not solve the zero-point problem).
However, they find that early-type and late-type galaxies cannot have the same IMF and halo response. For any given halo response model, ETGs and LTGs must have different IMF normalisations to reproduce the TFR. If we assume a universal IMF, early-type galaxies require stronger halo contraction.
They look into the model circular velocity profiles (see attached) for models that reproduce the TF and FJRs, with Chabrier IMF. The velocity profiles look rather constant at higher radii, reaching the maximum at ~0.3 R_vir. (For the LTGs, they convert the velocity dispersion to v_circ picking a rather simple conversion factor between sqrt(2) and sqrt(3).) They claim that the flatness of the rotation curves does not depend strongly on the IMF and the halo response model, and 'is a natural consequence for galaxies embedded in LCDM haloes'.
Then they discuss possible mechanisms that would account for differences in IMF or halo response for ETGs and LTGs. The halo contraction/expansion may depend on galaxy morphology via a number of processes:
-- adiabatic contraction due to smooth accretion -- results in disk growth and SF, important for LTGs
-- wet major mergers -- result in halo contraction because gas settles in the center of a galaxy, transforms LTGs to ellipticals
-- dry major mergers ( for ETGs) -- halo contraction due to violent relaxation which mixes stars and DM
-- clumpy accretion/minor mergers: halo expansion due to dynamical friction. Clumps must be baryonic, so that's likely to occur at high redshifts (A. Dekel was arguing in Jerusalem that it must be the case).
-- feedback causes halo expansion, more important to LTGs and for higher redshifts.
-- bars -- halo expansion or contraction, not clear.

They sum it all up by saying that the key formation event that distinguishes ETGs from LTGs is a major merger (dry or wet), which causes halo contraction. For LTGs, haloes could expand due to a combination of clumpy cold accretion and intensive feedback.
The IMF may plausibly vary with redshift due to its alleged dependence on ISM temperature via the Jeans mass. Since ETGs form their stars earlier than LTGs, their IMF might be different. They discuss the van Dokkum & Conroy 2008 article on the different IMF at the cores of massive ellipticals, and conclude that this IMF would not fit for the other ETGs well.
All in all, they show that there is a degeneracy between IMF and the halo response to disk formation, and we cannot match the two for ETGs and LTGs if we want to reproduce the TFR. However, I'm puzzled here -- like in the previous Mo, Mao, White article, they do not model galaxy evolution in a self-contained way, and a model cannot show things that are not included in it. Mo, Mao & White include one set of parameters in their article, and get a set dependences on their parameters (like the disk formation time). Here Dutton et al. model rotation curves as functions of other parameters, and get dependence on another set of parameters. I think it's tricky to understand which parameters are really important, because in astrophysics we often have many coupled parameters, and it's not difficult to find correlations between them. It's more difficult to find out which ones are the fundamental ones, which really affect the TFR.
-- a question: what does it mean "TFR is an edge-on projection of the fundamental plane" (p. 323)?
(*) v2.2 for late-type galaxies and some measure of velocity proportional to dispersion at the effective radius for early types

Daily Paper #3: Rotation rates, sizes and star formation efficiencies of a representative population of simulated disc galaxies

I was a bit late today, because I went to see a couple of talks at the HETDEX meeting. A couple of interesting points from there:
-- The LAE people are worried about selection bias arising due to galaxy spins' alignment with the large scale structure (http://arxiv.org/abs/1004.3611)
-- Cluster growth depends not only on the proto-cluster environment (i.e. the immediate neighbourhood), but on super-halo scales as well (it's probably better defined here: http://arxiv.org/abs/1109.6328)

...On to the paper:
Title: Rotation rates, sizes and star formation efficiencies of a representative population of simulated disc galaxies
Authors: McCarthy, Schaye et al.
Year: 2012, http://arxiv.org/abs/1204.5195 They use resimulated (SPH) Millenium sub-regions with selected representative mean densities, including baryonic physics. They include background UV/Xray radiation field that 'reionises' the simulations at z = 9 and the CMB. They model star formation using an effective prescription reproducing the Kennicut's relation and assuming Chabrier IMF, as well as yields and timing of nucleosynthesis and SN feedback.
Then they fit the surface brightness profiles of galaxies in 9 - 11.5 log M* range with a Sersic function and classify their galaxies into disc and spheroid-dominated usin n = 2.5 as the cut.
-- The stellar mass - rotation velocity relation:
They examine this relation for their disk galaxy population (see the attached picture) and compare it with Reyes 2011 observations, claiming that this is the first cosmological hydrodynamical simulation that produces a population of galaxies consistent with the observed TFR. The slope is slightly higher, but in general, the agreement is really good. They use v80 (velocity at 80% light radius) and Vmax as the velocity measures. The velocities at their high-mass range are too big, and they claim that lack of prescription for AGN feedback may explain that.
The authors also discuss the scatter in TF relation, claiming that it is not possible to directly compare observed and simulated TF scatter without careful analysis of selection criteria and observational uncertainties.
Simulated spheroid galaxies follow the TFR well at this mass range, except for the most massive galaxies. The rotation curves of the galaxies with M* > 10.6 are not realistic (due to overcooling, too efficient SF of the highest mass haloes). Their simulated galaxies are also compatible with observed M* - size and star formation efficiency -- M* relations, up to the higher mass range.
One more quantity that simulations are compared with is the ratio of v_circ to v_200. If there is no significant halo expansion/contraction, this ratio should be roughly equal to 1.2 (Duffy 2010 writes more on halo expansion/contraction issue and impact on this ratio). Again, their results agree with this quite well up to log(M*) > 10.5.
They try to reproduce the main galaxy sequence at z = 0, comparing their results with SFR from Galex. Except for the lowest mass galaxies where their resolution is too small, it works well.
The section 4 is an interesting discussion of connection between SF efficiency, stellar mass function and the TF relation. They show that by assuming power-law shapes for halo mass function and stellar mass function in certain stellar mass range where this is valid, it is possible to match haloes (=velocities) and stellar masses using the abundance matching method, and reproduce TFR and SFR efficiency-M200 relations well (and maybe even constrain the faint end of the IMF). The way I understand it, the TFR arises due to the linear (in log-space) match between the halo mass function (set by cosmology) and the stellar mass function (set by IMF, SFR efficiency, thus feedback, etc.). I'll read Mo, van den Bosch and White 2010 for more discussion on this matter.

Daily Paper #2: The Tully-Fisher Zero Point Problem

Today's is a short paper (conference proceedings, just 4 or so pages), dealing with the halo contraction/expansion issue.

Title: The Tully-Fisher Zero Point Problem
Authors: Dutton, van den Bosch & Courteau
Year: 2008, http://arxiv.org/abs/0801.1505

The authors claim that CDM-based disk formation models can reproduce the slope/scatter of the TFR, however, its zeropoint has not been matched. This problem gets even worse if additional constraints (disk sizes, number densities) are imposed.
The TFR zeropoint can be matched in models if the halo contraction or disk self-gravity are not taken into account, or, as is shown in the article, halo contraction is counteracted by baryon feedback. They model an exponential disk in a NFW halo, obtain its luminosity from observed TFR and its scale-length from the size-luminosity relation. Assuming WMAP3 cosmology and a concentration parameter value from simulations, they solve for the virial mass and obtain rotation curves with and without the halo contraction (see the attached plot). The halo-contraction case is in conflict with both theory and observations, meaning that the halo is too small and has too high spin parameter.
They suggest 3 ways to solve this problem:

• -- lower the stellar mass-to-light ratio (but there is no known IMF that could provide that). Also, they claim that baryons at the disk and bulge account for at least half of the v2.2 -- I didn't know that (Courteau 1999, Weiner 2001)!
• -- lower the initial concentration (then the virial radius of a halo is increased) -- but that's incompatible with WMAP3 cosmology.
• -- turn off or reverse halo contraction: disk galaxies do not form in isolated haloes by smooth cooling. Halo contraction can be reversed by:
  • a) Feedback during adiabatic disk formation, if a large fraction of its mass is removed. It would also explain why galaxy formation is so inefficient (I think they mean that the gas is not converted into stars rapidly).
  • b) Dynamic friction between baryons and DM due to bars or large baryonic clumps (do they mean violent disk instabilities here?). They do not explain the details of such a process here, but I think what happens is that baryons transfer some of their angular momentum to the halo due to formation of massive, concentrated, rapidly moving structures.

The interesting message of the article is that the TFR zeropoint can provide clues into baryon feedback (which should also explain the core-cusp problem of DM haloes, at least that was what A. Dekel and J. Primack maintained at the Jerusalem Winter School). That's important.

Daily Paper: The formation of galactic discs

Me and my supervisor agreed that I would read a paper a day and write it up, so I'll be copying the summaries here.

Title: The formation of galactic discs (http://adsabs.harvard.edu/abs/1998MNRAS.295..319M)
Authors: Mo, Mao, White
Year: 1998
It's actually a really important paper -- I'm glad not to have missed it. They model galactic disk formation (of pure exponential ones, though they address influence of a simple bulge model later) in 3 CDM cosmologies. The authors make 4 important assumptions:
1) The mass of a disk is a fixed fraction of its halo
2) The angular momentum of the disk is also a fixed fraction of that of the DM halo (later they find that the specific angular momenta of the disk and halo are similar, so these two ratios should be equal).
3) The disk is thin, has an exponential density profile and is centrifugally supported
4) Real galaxies are dynamically stable disks, i.e. they reject unstable models.

They calculate the halo mass function using Press-Schechter formalism (see Appendix), assume halo angular momentum distribution determined by N-body simulations and a constant mass-to light ratio, and NFW profile. They calculate the total energy of a truncated (to r_200) NFW halo using the virial theorem, the rotation curve corresponding to it (after accounting for adiabatic halo contraction and gravitational disk influence).
See the attached picture (Mo1998_rotcurves.png) for their results. They claim that the shape of a rotation curve depends on 3 parameters only: the halo concentration parameter c(see *), fraction of mass in the disk m_d, and the spin parameter.

There is a lot more in this paper, but they devote a significant section of it to Tully-Fisher relation, explaining the origins of its slope, zeropoint and intrinsic scatter.

• -- slope: They claim that it is a generic prediction of hierarchical structure formation models with CDM-like fluctuation spectra (which set the halo formation times and thus their concentration c distribution).
• -- zeropoint: mostly set on disk mass fraction, mass-to-light radio and the redshift at which a given disk was assembled. They claim that disks must have effectively formed at redshifts close to zero (?), unless we assume an unphysical mass-to-light ratio.
• -- scatter: they analyse possible sources of intrinsic scatter of the disks, and find that:
  • --- a small amount of scatter comes from the spin parameter distribution
  • --- scatter in concentration c also adds scatter to the TF relation (disks at more concentrated haloes spin faster).
  • --- bulge is not included in their model, so bulge luminosity contribution is not accounted for -- that's a source of scatter as well
  • --- mass-to-light ratio may vary, adding some more scatter
  • --- formation times may vary as well, adding even more scatter.

The intrinsic scatter because of the first two factors cannot be smaller than 0.15 mag.
In conclusion, they show that it is possible to derive a realistic TF relation theoretically, however, I'm not sure if that is the only way it could arise? They do not include bulges, which are important for our sample, too. I am also unsure what do they mean with 'effective disk assembly redshift' at z <= 1.

* c == r_200/r_s, here r_200 -- the limiting radius of a halo, defined so that the mean density inside this radius is 200 times larger than the background density, r_s -- the disk scale length.
There is also a brief explanation of the \sigma_8 parameter -- see attached.

lit: Non-linear structure formation

Slides from F. van den Bosch, from a talk given at Jerusalem Winter School.
A Gaussian random field is completely specified by either the two-point correlation function ξ(r), or, equivalently, the power spectrum P(k)

lit: Halo assembly bias

slides by F. van den Bosch.

lit: 2dSWML algorithm, HI mass function

The 1000 Brightest HIPASS Galaxies by Zwaan et al.: has a nice section on Vmax corrections/fitting distribution functions, with a reference to the original Schmidt 1968 article.

Jerusalem WS lecture notes: 13. Galaxy Formation with Inflows and Outflows

By R. Dave, slides here.

• 4 phases of baryons:
  • diffuse
  • unbound shock-heated
  • virial shock-heated (condensed)
  • cool halo gas (condensed)
  • low mas haloes cannot keep their gas
• how gas gets into galaxies:
  • hot mode (shock heating at virial radius, cooling onto disk. slower, limited by cooling time, more spherical)
  • cool mode: more rapid, line emission cooled, filamentary: cold streams (dominant: cold accretion dominates globally, mergers are a small contribution to gas supply: SF is supply-limited)
  • mergers: DM grows by mergers (mass fn is steep), mergers contribute little to gas supply
  • mass dependence of accretion mode: large halos: hot mode, small halos: cold mode, separation at roughly ~10^{11.5} M_{\odot}, with metal cooling -- 10^{12} M_{\odot} -- connection with galaxy bimodality
• shock stability: shocks form up from a certain mass, that's why cold mode dominates (virial shocks cannot form)
• simulations
• accretion w/out feedback overpredicts cold baryon mass (overcooling): conversion efficiency peaks at 10 ^{12}
• red and dead: AGN feedback as the power source, blue: SNe, YSOs
• abundance matching: equate nr density of haloes and galaxies with a given mass -- halo occupation distribution -- galaxies and satellites. Procedure assigns galaxies to haloes, matching halo masses to stellar masses, Behroozi +13 -- peak of conversion efficiency constant at all redshifts.
• galaxies are gas processing factories: raw materials from IGM (infall rate due to gravity)
  • not all infall material ends up in the galaxy -- some gas is prevented from getting into the galaxy, outflow of hot and polluted gas from SF regions (just like in a factory), some outflow material is recaptured -- infall metallicity (\alpha_z in the diagram)
  • resulting SF: mass balance: infall = formed stars + Outflow + gas reservoir change
  • equilibrium condition: reservoir gas is constant over time (from hydro and obs, not true for dwarfs, just for L_{\star}) --> high z galaxies have higher ISM gas fractions
• Inflow: primordial and recycled gas: recycling metallicity vs. SN ejecta metallicity
• SFR: set by 3 baryon cycling parameters:
  • feedback preventing parameter (inflow)
  • outflow mass loading factor (outflow)
  • recycled wind metallicity ratio
• SFH does not depend on (it's expressed in correlations):
  • SF law
  • merger history
  • environment or clustering
  • morphology
  • gas content
• MS of galaxy evolution: SFR vs. M_{\star}:
  • relation should be close to linear, D. Elbaz
  • SFR should grow with z rapidly --> feeding rate change
• feedback parameters:
  • quenching at high mass (AGN?)
  • gravitational heating transition to hot mode (\zeta_{grav}, RD 2012) -- power law all the way to high masses, weak dependence on z
  • wind heating suppress accretion
  • specific SFR: feedback effects
  • gas metallicity relation, its evolution -- gas phase metallicities
• gas content, M_{gas} -- cold gas in the ISM:
  • H_2 gas fraction ~= t_{dep} \cdot sSFR (how much gas is in the ISM that waits to become stars)
  • depletion time t_{dep}
  • t_{dep}: depends on Schmidt law, Kennicutt relation
  • SF law sets t_{dep}, which sets f_{gas} ~ t_{dep}
• the role of merging: second order effect (like environment), sets scatter (e.g. M_{star}-Z relation)
  • first order: smooth accretion
  • second order: stochasticity: clumps (mergers) --> lower Z, higher SFR (signals recent accretion event) --> high star formation points lie below MZ relation
  • dilution time -- explains scatter

lit: a few articles by FvdB

One of our lecturers, Frank van den Bosch, pointed me to a few articles that might be useful for the topics I'm currently studying:
Spatial and kinematic alignments between central and satellite halos
Probing the Intrinsic Shape and Alignment of Dark Matter Haloes using SDSS Galaxy Groups
The Tully-Fisher Zero Point Problem

Jerusalem WS lecture notes: 08. Extended Press-Schechter formalism formalism

by F. van den Bosch, slides here.

• Press - Schechter theory:
  • filters of density fields: Gaussian, top-hat, sharp k-space filter (same, as top-hat, except we end up having a nice box in Fourier space)
  • mass variance
  • halo mass function: how can we assign halo mass to a collapsed region?
  • PS: only half of the mass of the Universe can become collapsed (overdense), but due to smoothing, this is not entirely correct. fudge factor of 2
  • halo mass function: many more small haloes than higher, exponential suppression
• Excursion set (EPS) formalism (Bond et al, ~1991, statistics of peak heights):
  • excursion: locations of space
  • sharp k-space filter: Markovian trajectory
  • http://ned.ipac.caltech.edu/level5/Sept06/Loeb/Loeb4.html
  • all mass elements will eventually sit in a halo of arbitrarily low mass
  • works in a statistical sense, not necessarily correct on a per-halo basis
  • the sharp k-space filter looks ugly in real space (sinc-like)
  • the Spherical Cow
  • simulations: underpredicts number of high-mass haloes, over-predicts low-mass haloes
  • halo finding: how we define the haloes? It changes the halo mass function!
• Ellipsoidal collapse EPS theory:
  • moving barrier up-crossing, mcmc simulations
  • much better agreement w/ simulations
• Halo merger trees:
  • accurately sampling progenitor mass f-n
  • mass conservation
  • impossible to do properly: conditional probabilities, many ways to draw from the distribution
  • tests on the accuracy of merger trees: consistency test, comparison w/ numerical simulation
  mass assembly history:
  • main central galaxy accretes lower mass haloes (subhaloes, which may survive or not)
  • satellite
  • assembly time: main progenitor reaches 1/2 the final mass (more massive haloes assemble later)

Jerusalem WS lecture notes: 06. The First Galaxies and Reionisation

By A. Loeb, with a short, but brilliant skit on adventure and creativity in science, slides uploaded here.

• spectrum of the sky:
• dip: Ly\alpha photons keep the gas coupled to its kinetic temperature
• most of the comoving volume of the Universe is at high redshifts:
• SDSS LRGs: 0.001 of the observable volume of the Universe (Loeb &Wyithe 2008)
• What is the best time to be a cosmologist? At early time, Hubble scale grows, but due to expansion the comoving distance starts to shrink: objects enter and exit the horizon. The optimal cosmic epoch for precision cosmology was at z = 10 (http://arxiv.org/abs/1203.2622)
• http://prl.aps.org/abstract/PRL/v106/i17/e171302
• LF at various redshifts -- DM haloes mass slope
• H, He cooling curve: no excitation at lower energies (T < 10^4), H_2 becomes important at lower T
• Pop. 3.1 stars -- the very first stars, ~10^8 Myr after BB, SF conditions were differented, higher T: ~200K
• Pop 3.2 stars: UV photons ionize surrounding gas --> much more efficient cooling by forming H_2, HD, HD radiative cooling --> gravitational instabilities
• galaxies much more clustered on scales ~100 comoving Mpc than at present -- not many regions exceed the collapse threshold: bias, numerical bottleneck (need large dynamic range)
• at higher redshifts (~8) you need to produce more photons per baryons to keep the IGM reionized
• Pop3 observables:
  • stellar remnants:
  • Pair instability supernovae: best-understood SNe, Cooke et al. 2012. Lasts for years: long duration, luminosity comparable to SN II. 160-240 M_sol progenitors: if you start with a few hundredths M_sol progenitor, winds don't reduce the mass enough to avoid the PI SN. Collisionally-formed stars.
  • Long GRBs: seen to the edge of the obs. Universe, jets are drilling a hole in the star, followed by SN. Cosmological stretch of time: longer observation time
• Ly\alpha forest: probing ISM by QSO spectra
• Spin transition: Harward connection: horn antenna, snowballs, spin temperature, 21 cm tomography, cosmological evolution of the 21cm signal, X-ray heating (stellar mass BHs? X-ray binaries? AGNs?), LOS anisotropy: Kaiser effects, Pritchard & Loeb 2011, 'CMB is old', EDGES experiment: reionisation was not abrupt, EOR signal
• extension to other lines: emission (CO, C, C II) by groups of galaxies: unresolved galaxy survey

Jerusalem WS lecture notes: 03. Structure Formation: From Linear to Non-Linear

Given by Frank van den Bosch, slides here.

• cosmological [over]density field: moments of the PDF
• the ergodic hypothesis: ensemble average is equal to spatial average taken over one realisation of the random field (we only have one Universe, but it consists of many random subvolumes). Basically, spatial correlations decay rapidly w/ separation, so the subvolumes are statistically independent.
• random Gaussian field: distribution of arbitrary set of N points is an N-variate Gaussian. covariance matrix is the 2nd moment: 2-point correlation function. We only need this one moment to specify the N-point probability function.
• 2PCF: 0 for Poisson distribution, != 0 for clustered distribution. Gravity makes things cluster, so we get positive CF for small radii, negative for large radii, then turns towards zero.
• Higher-order CFs: irreducible CFs cannot be obtained from lower order reduced CFs. Connected moments of all higher order CFs are 0 for a Gaussian field: one can use this to test for Gaussianity.
• the matter field in Fourier space: V is volume over which the Universe is assumed to be periodic. k -- modes.
• power spectrum (Z-H)
• Linear perturbation growth: Silk damping: e- and photons are no longer coupled, photons move away, structure starts growing. Jeans length for DM is very low: free streaming. When perturbations become of order unity, growth becomes non-linear.
• Non-linear regime: perturbation theory (and Gaussianity assumption) is no longer valid. Modes couple to each other: no analytic solutions, higher order moments are required for complete specification of the density field: higher-order perturbation theory.
• Numerical simulation, the Halo Model
• Over-simplified model: top-hat spherical collapse. No shell crossing, mass conservation. Evolution depends only on the mass inside the shell. parametric form: implies maximum radius before turnaround. Collapse -- shell crossing, after it mass is not conserved.
• By using linear theory, we can identify regions that had already collapsed.
• Beyond shell crossing: collapse is not spherical, hence BHs don't form. Virialization: halo is in equillibrium as a result. We can compute overdensity of the virialised DM halo: 178: haloes finding at 200.
• Zel'dovich approximation:
  • Lagrangian picture: works in mildly non-linear regime, calculated displacement of particles from the initial conditions.
  • no spherical symmetry is required, mass-conservation is valid until shell crossing.
  • deformation tensor in the initial density field, eigenvalues: positive: contracting coordinate, neg: expansion. No over-simplified geometry, works in qusi-linear regime. Collapse happens first in one direction (largest eigenvalue) --> pancake.
  • ellipsoidal overdensity --> sheet (pancake) -- > filament --> halo (longest axis 'halo formation')
• Relaxation and virialisation:
  • 2 body-relaxation time: time required for a particle to change its E_k by about its initial amount due to 2 body interactions. How can galaxies appear relaxed, if galaxies and haloes have 2body relaxation times larger than t_H. 4 mechanisms:
  • Phase mixing: different phases, same energies: mixing in phase space, goes linearly with time. Completely reversible: no information is lost.
  • chaotic mixing --> the book [MBW]
  • violent relaxation: potential is time-dependent, particles gain or lose energy. Overall, energy distribution is broadened by the process. No segregation by mass, quite opposite to collisional (2-body) relaxation. e.g. stars don't sink to the center. Mixing on coarse-grained level. Self-limiting: no all knowledge of initial conditions is erased.
  • Landau damping --> the book

Jerusalem WS lecture notes: 02. Structure Formation in the Universe

By A. Loeb. I didn't take notes for some reason, so I'll only point to the slides.