lit: evolution of dwarf galaxies: a dynamical perspective

I was tasked with presenting Lelli et al. 2013 in our group meeting. Here are the slides [pdf].

stats: the covariance matrix

The covariance matrix is N-dimensional generalisation of the scalar variance in 1 dimension. Here's a simple explanation of it which I needed in order to code up a test case for fitting a 2D Gaussian with intrinsic scatter.

lit: Some aspects of measurement error in linear regression of astronomical data, Kelly 2007

Kelly 2007:
I describe a Bayesian method to account for measurement errors in linear regression of astronomical data. The method allows for heteroscedastic and possibly correlated measurement errors and intrinsic scatter in the regression relationship. The method is based on deriving a likelihood function for the measured data, and I focus on the case when the intrinsic distribution of the independent variables can be approximated using a mixture of Gaussian functions. I generalize the method to incorporate multiple independent variables, non-detections, and selection effects (e.g., Malmquist bias).

lit: Tonini et al. 2013, on physically meaningful radius for velocity measurements

They define the 'corrected' disk scale-length that includes the bulge potential. Pay attention to this article anyway -- they add a dynamical classificator dimension to the TFR, which is a little bit akin to what I'm doing.

Fitting the Tully-Fisher relation

There's one thing I can't quite wrap my head around while reading literature on the Tully-Fisher relation: why is the fitting always performed in the magnitude-log(velocity) space? It may be easier to fit an expression y = mx + b to data than y = c*x**z, but one would have to deal with asymmetric errors in two dimensions.
I'm currently trying to figure out a way to do the fit in semi-log space, namely, magnitude-velocity space, using errors in both directions and MCMC.

lit: Stellar mass-to-light ratios and the Tully-Fisher relation

I'll have to read this when I get more sleep: iopscience.iop.org/0004-637X/550/1/212

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'.

lit: NFW halo profile properties, relation to TFR

I've a perhaps naive idea to try to obtain the TFR from the halo-stellar mass distribution. Apparently, that's an old thought, but then they didn't have such good halo-stellar mass relation, 'chewed' by AGN and stellar feedback processes on both ends! That's cool.

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 #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.

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: Spins and orientations of haloes in cosmic filaments

Zhang et al., many useful references on methods therein.

lit: Rotational support in galaxies

I was wondering how to derive v_rot/sigma ratio for my sample, here is a review: Rotation and anisotropy of galaxies revisited, by J. Binney.

Fitting a model to data: lit review

Yesterday I showed some preliminary TF results at our group meeting, and it was rightly noted that the straight line fit I made was wrong. I've only included errors in one variable (velocity, obtained by using bootstrapping) in the fit, and made a mess of that by mixing the variables on the plot.
I've been thinking about how to do a proper fit when the data has uncertainties in both directions, and been revisiting this paper by Hogg et al.:
In the astrophysics literature (see, for example, the Tully Fisher literature, there is a tradition, when there are uncertainties in both directions, of fi tting the "forward" and "reverse" relations, that is, fi tting y as a function of x and then x as a function of y, and then splitting the diff erence between the two slopes so obtained, or treating the di fference between the slopes as a systematic uncertainty. This is unjusti ed.

Matplotlib: strings as axis labels

I wanted to make a plot that shows the relation of some galaxy properties vs. their Hubble subtype. The subtypes were saved as strings at my database, I selected them, converted back to numbers. Why back? Because some colleagues of mine, who think in words, classified all the 900 galaxies by their Hubble types, then their classifications were converted into numbers, means and probabilities calculated, and converted back to types.
Anyway, I wanted to have types on my axis, so I did it thus. Here's the plot:

lit: Intrinsic properties of SDSS galaxies

Maller et al.. It's important in many other ways, but here is an interesting excerpt on why TF relation is different:
However, with the notable exception of the Tully-Fisher relation these distributions and relations are traditionally measured in terms of the observed properties of galaxies. That is, the measurements used are K-corrected and corrected for foreground dust extinction, but no correction is attempted to compensate for the viewing angle from which the galaxies are observed. In contrast, the Tully-Fisher relation is not a relationship between a galaxy's observed luminosity and rotation velocity, but a relation between a galaxy luminosity and rotation velocity corrected for inclination. The inclination correction attempts to recover the intrinsic properties of a galaxy and not properties that are measured because of the particular angle from which the galaxy is viewed. For a long time there was great controversy over whether spiral galaxies are optically thin or optically thick (e.g., Holmberg 1958; Disney et al. 1989), but in the early 1990s it was established that galaxies become redder and fainter as they are inclined (e.g., Burstein et al. 1991).

lit: face-on TF relation

Andersen and Bershady 2003:
Hence there is a triple penalty at low inclinations for TF studies: (1) erroneously large inclinations lead to undercorrecting the velocity projection, (2) random errors diverge since photometric disk axis ratio measurements have constant errors as a function of axis ratio, and (3) for long-slit studies, P.A. mismatch will always yield systematic underestimates of the projected rotation speed.