The Radial Distribution of Galactic Satellites. Jacqueline Chen

Transcription

1 The Radial Distribution of Galactic Satellites Jacqueline Chen December 12, 2006

2 Introduction In the hierarchical assembly of dark matter (DM) halos, progenitor halos merge to form larger systems. Some DM halos survive accretion and form a population of subhalos within the virial radius of the larger halo. Baryonic material cools and forms stars in the center of some halos and subhalos, resulting in galaxies and satellite galaxies. Satellite galaxies, then, reflect galaxy formation processes as well as the dissipative processes that destroy subhalos as they fall into a DM halo.

3 Introduction The spatial distribution of galactic satellites can illuminate the relationship between satellite galaxies and dark matter subhalos and aid in developing and testing galaxy formation models. DM halo galaxies subhalos (Nagai & Kravtsov 2005) (Gao et al. 2004) Two different methods of modeling galaxies in simulations result in different spatial distributions compared to the DM halo and subhalo distributions.

4 Results Using Interloper Subtraction Constraints on the spatial distribution of dwarfs in the Local Group suggest a distribution more radially concentrated than dark matter subhalos and inconsistent with the DM halo profile. Constraints on the spatial distribution of satellites beyond the Local Group use large galaxy redshift surveys to create samples of satellite galaxies. The samples, however, are contaminated by interlopers. Projected density satellites selected objects interlopers Interlopers need to be subtracted out of the data in order to constrain the spatial distribution.

5 Interloper Subtraction V max = km/s not void void Interlopers are not uniform in velocity space. primary galaxy isolation criteria Estimating interloper fraction requires better than uniform sampling.

6 Results Using Interloper Subtraction Projected density α projected density: Σ(R) = A R α A Interloper subtracted samples fall between subhalo and DM distributions. (Chen et al. 2006)

7 Introduction An alternate approach to the problem employs the projected cross-correlation of bright and faint galaxies. This approach eliminates the need for cuts to the bright sample by environment and for interloper subtraction. The projected correlation function is the statistical measure of the excess probability over a random distribution of finding pairs of objects at projected separation, r. This can be calculated analytically using the halo model, such that the spatial distribution of faint galaxies around bright galaxies is a free parameter.

8 Data Data is taken from the spectroscopic catalog of the Sloan Digital Sky Survey (SDSS) -- including all of Data Release 4 (DR4) -- with a completeness-weighted area of 5104 square degrees. Samples are drawn from a volume-limited sample of galaxies with redshift less than z= Bright galaxies are chosen with r-band magnitudes between -20 and -21. Faint galaxies have r-band magnitudes between -19 and -18.

9 Correlation Functions The correlation function is the statistical measure of the excess probability over a random distribution of finding pairs of objects at projected separation, r. Using the Landy & Szalay (1993) estimator, the correlation function is: ξ(r p,π) = DD DR RD + RR RR The projected correlation function is: w p (r p ) = 2 ξ(r p,π)dπ

10 Correlation Functions faint autocorrelation bright autocorrelation The bright autocorrelation, faint autocorrelation, and cross-correlation functions and jackknife errors. The minimum separations between fibers in the SDSS is 55 arcsec. At the median redshift, this is 30 kpc/h. The catalog is collision corrected to get to 10 kpc/h.

11 Halo Model 2-halo centralsatellite satellitesatellite The correlation functions can be calculated from the halo mass function, the halo profile, matter power spectrum, and halo bias -- which are calculated in simulations -- and the number and distribution of galaxies in a halo of mass, M, which is fit. The correlation function can be split into two parts: a one-halo term and a two-halo term. In addition, the one-halo term can be split into a centralsatellite term and a satellite-satellite term.

12 Halo Model centralsatellite satellitesatellite 2-halo The analytic correlation function (as in the SDSS data) is power-law-like, although made up of non-power-law terms, which dominate at different radii.

13 HOD The number of galaxies in a halo of mass, M, is parameterized by the halo occupation distribution (HOD). The expected number of central galaxies in a halo is a step-function, such that: N cen = 1, if M M M min max 0, else These 2 parameters M min and M max are calculated. The expected number of satellite galaxies: N sat = M M 1 α exp M cut M M 1, α, and M cut are free parameters.

14 HOD The spatial distribution of galaxies is parameterized by a scaling factor to the concentration of the dark matter halo (NFW profile): c gal = f c dm Two such parameters are used, f and f cross : f represents the scaling for bright and faint satellites in any sized halo. f cross represents the single case of the distribution of faint satellites in halos with a bright central galaxy.

15 HOD centralsatellite satellitesatellite 2-halo For the autocorrelation, all terms depend on f. For the crosscorrelation, only the central-satellite term -- dominant at small projected radii -- depends on f cross, while the other terms depend on f.

16 HOD Free parameters:!! bright sample:!!!! M 1!!!! α!!!! M cut!! faint sample:!!!! M 1!!!! α!!!! M cut!! f!! f cross

17 Tests with Populated Simulations The efficacy of the analysis is tested using a large dark matter simulation of 400 Mpc/h on a side (Warren & Salmon 1993), with a volume 42 times that used in the SDSS samples. The simulation is populated with bright and faint galaxies using a reasonable HOD. The best-fit parameters and their errors are found by MCMC, which samples the parameter space such that the distribution of points follows the underlying probability distribution exactly.

18 Populated Simulations Left: marginalizing over all parameters, the likelihood distribution of each parameter. The true value is offset. Right: The fit to the cross-correlation using the best-fit unmarginalized parameters.

19 Populated Simulations The parameters are degenerate. M 1 α α M 1 α M cut M cut α f cross v. everything f faint v. faint bright v. bright

20 Populated Simulations The degeneracies behave in predictable ways. M 1 α M cut f f cross

21 Populated Simulations The true value of each parameter is offset in predictable ways given the parameterization of the HOD.

22 Populated Simulations The full simulation box is 42 times the volume of the SDSS data. Using subvolumes of 5, 2, and 1 times the volume of the SDSS data broadens the likelihoods.

23 Tests with Populated Simulations Degeneracies result in offsets from true values even in data from a significantly larger volume than in the SDSS data. These degeneracies behave in predictable ways. As the volume of data is decreased, the corresponding constraints on parameter estimation are degraded.

24 Analysis of SDSS Samples Below: The fit to the cross-correlation in the SDSS data using the best-fit unmarginalized parameters. Above: The marginalized likelihoods in the SDSS. The constraints on f cross are consistent with f cross =1 with a broad distribution. The constraints on f are stronger -- ruling out f=2 and peaked somewhat smaller than f=1.

25 Analysis of SDSS Samples Both f and f cross are consistent with 1 -- a spatial distribution of galaxies equivalent to the DM profile of the halos. f cross is not well constrained. The constraints on f are stronger -- ruling out large values like f=2 and peaked somewhat smaller than f=1. Values of f smaller than 1 are consistent with previous studies of the spatial distribution using interloper subtraction methods. In addition, comparing the cross-correlation to weak-lensing measurements (Mandelbaum et al. 2006) of the galaxy-mass crosscorrelation shows results that are generally consistent.

26 Conclusions The spatial distribution of galactic satellites can illuminate the relationship between satellite galaxies and dark matter subhalos and aid in developing and testing galaxy formation models. Simulations show that DM subhalos have a shallower / less concentrated profile than the DM halo profile. Constraints on the spatial distribution of satellites in the Local Group suggest a distribution more radially concentrated than dark matter subhalos and inconsistent with the DM halo profile. Constraints on the spatial distribution of satellites using the crosscorrelation of bright and faint galaxies show general consistency with previous results using interloper subtraction methods, for radial profiles that are consistent with -- and possibly less concentrated than -- DM halo profiles.