A Statistical Semi-Empirical Model: Satellite galaxies in Groups and Clusters

We present STEEL a STatistical sEmi-Empirical modeL designed to probe the distribution of satellite galaxies in groups and clusters. Our fast statistical methodology relies on tracing the abundances of central and satellite haloes via their mass functions at all cosmic epochs with virtually no limitation on cosmic volume and mass resolution. From mean halo accretion histories and subhalo mass functions the satellite mass function is progressively built in time via abundance matching techniques constrained by number densities of centrals in the local Universe. By enforcing dynamical merging timescales as predicted by high-resolution N-body simulations, we obtain satellite distributions as a function of stellar mass and halo mass consistent with current data. We show that stellar stripping, star formation, and quenching play all a secondary role in setting the number densities of massive satellites above $M_*\gtrsim 3\times 10^{10}\, M_{\odot}$. We further show that observed star formation rates used in our empirical model over predict low-mass satellites below $M_*\lesssim 3\times 10^{10}\, M_{\odot}$, whereas, star formation rates derived from a continuity equation approach yield the correct abundances similar to previous results for centrals.Comment: 21 pages, 17 Figures. MNRAS, in pres

Decomposition of homogeneous polynomials with low rank

Let $F$ be a homogeneous polynomial of degree $d$ in $m+1$ variables defined over an algebraically closed field of characteristic zero and suppose that $F$ belongs to the $s$-th secant varieties of the standard Veronese variety $X_{m,d}\subset \mathbb{P}^{{m+d\choose d}-1}$ but that its minimal decomposition as a sum of $d$-th powers of linear forms $M_1, ..., M_r$ is $F=M_1^d+... + M_r^d$ with $r>s$. We show that if $s+r\leq 2d+1$ then such a decomposition of $F$ can be split in two parts: one of them is made by linear forms that can be written using only two variables, the other part is uniquely determined once one has fixed the first part. We also obtain a uniqueness theorem for the minimal decomposition of $F$ if the rank is at most $d$ and a mild condition is satisfied.Comment: final version. Math. Z. (to appear

Comparing PyMorph and SDSS photometry. II. The differences are more than semantics and are not dominated by intracluster light

The Sloan Digital Sky Survey pipeline photometry underestimates the brightnesses of the most luminous galaxies. This is mainly because (i) the SDSS overestimates the sky background and (ii) single or two-component Sersic-based models better fit the surface brightness profile of galaxies, especially at high luminosities, than does the de Vaucouleurs model used by the SDSS pipeline. We use the PyMorph photometric reductions to isolate effect (ii) and show that it is the same in the full sample as in small group environments, and for satellites in the most massive clusters as well. None of these are expected to be significantly affected by intracluster light (ICL). We only see an additional effect for centrals in the most massive halos, but we argue that even this is not dominated by ICL. Hence, for the vast majority of galaxies, the differences between PyMorph and SDSS pipeline photometry cannot be ascribed to the semantics of whether or not one includes the ICL when describing the stellar mass of massive galaxies. Rather, they likely reflect differences in star formation or assembly histories. Failure to account for the SDSS underestimate has significantly biased most previous estimates of the SDSS luminosity and stellar mass functions, and therefore Halo Model estimates of the z ~ 0.1 relation between the mass of a halo and that of the galaxy at its center. We also show that when one studies correlations, at fixed group mass, with a quantity which was not used to define the groups, then selection effects appear. We show why such effects arise, and should not be mistaken for physical effects.Comment: 15 pages, 17 figures, accepted for publication in MNRAS. The PyMorph luminosities and stellar masses are available at https://www.physics.upenn.edu/~ameert/SDSS_PhotDec

The high mass end of the stellar mass function: Dependence on stellar population models and agreement between fits to the light profile

We quantify the systematic effects on the stellar mass function which arise from assumptions about the stellar population, as well as how one fits the light profiles of the most luminous galaxies at z ~ 0.1. When comparing results from the literature, we are careful to separate out these effects. Our analysis shows that while systematics in the estimated comoving number density which arise from different treatments of the stellar population remain of order < 0.5 dex, systematics in photometry are now about 0.1 dex, despite recent claims in the literature. Compared to these more recent analyses, previous work based on Sloan Digital Sky Survey (SDSS) pipeline photometry leads to underestimates of rho_*(> M_*) by factors of 3-10 in the mass range 10^11 - 10^11.6 M_Sun, but up to a factor of 100 at higher stellar masses. This impacts studies which match massive galaxies to dark matter halos. Although systematics which arise from different treatments of the stellar population remain of order < 0.5 dex, our finding that systematics in photometry now amount to only about 0.1 dex in the stellar mass density is a significant improvement with respect to a decade ago. Our results highlight the importance of using the same stellar population and photometric models whenever low and high redshift samples are compared.Comment: 18 pages, 17 figures, accepted for publication in MNRAS. The PyMorph luminosities and stellar masses are available at https://www.physics.upenn.edu/~ameert/SDSS_PhotDec

Foreground Model and Antenna Calibration Errors in the Measurement of the Sky-Averaged \lambda 21 cm Signal at z~20

The most promising near-term observable of the cosmic dark age prior to widespread reionization (z~15-200) is the sky-averaged \lambda 21 cm background arising from hydrogen in the intergalactic medium. Though an individual antenna could in principle detect the line signature, data analysis must separate foregrounds that are orders of magnitude brighter than the \lambda 21 cm background (but that are anticipated to vary monotonically and gradually with frequency). Using more physically motivated models for foregrounds than in previous studies, we show that the intrinsic "spectral smoothness" of the foregrounds is likely not a concern, and that data analysis for an ideal antenna should be able to detect the \lambda 21 cm signal after deprojecting a ~5th order polynomial in log(\nu). However, we find that the foreground signal is corrupted by the frequency-dependent response of a real antenna. The frequency dependence complicates modeling of foregrounds commonly based on the assumption of spectral smoothness. Much of our study focuses on the Large-aperture Experiment to detect the Dark Age (LEDA), which combines both radiometric and interferometric measurements. We show that statistical uncertainty remaining after fitting antenna gain patterns to interferometric measurements does not compromise extraction of the \lambda 21 cm signal for a range of cosmological models after fitting a 7th order polynomial to radiometric data. Our results generalize to most efforts to measure the sky-averaged spectrum.Comment: 12 pages, 12 figures, accepted for publication in ApJ. Accepted version uploade