arXiv subjects

Ravi K. Sheth

Publications and source records attributed to Ravi K. Sheth.

At least 145 records · Page 8Linked to original sources

arXiv2007

On estimating redshift and luminosity distributions in photometric redshift surveys

The luminosity functions of galaxies and quasars provide invaluable information about galaxy and quasar formation. Estimating the luminosity function from magnitude limited samples is relatively straightforward, provided that the distances to the objects in the sample are known accurately; techniques for doing this have been available for about thirty years. However, distances are usually known accurately for only a small subset of the sample. This is true of the objects in the Sloan Digital Sky Survey, and will be increasingly true of the next generation of deep multi-color photometric surveys. Estimating the luminosity function when distances are only known approximately (e.g., photometric redshifts are available, but spectroscopic redshifts are not) is more difficult. I describe two algorithms which can handle this complication: one is a generalization of the V_max algorithm, and the other is a maximum likelihood approach. Because these methods account for uncertainties in the distance estimate, they impact a broader range of studies. For example, they are useful for studying the abundances of galaxies which are sufficiently nearby that the contribution of peculiar velocity to the spectroscopic redshift is not negligible, so only a noisy estimate of the true distance is available. In this respect, peculiar velocities and photometric redshift errors have similar effects. The methods developed here are also useful for estimating the stellar luminosity function in samples where accurate parallax distances are not available.

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arXiv2007

Strong clustering of underdense regions and the environmental dependence of clustering from Gaussian initial conditions

We discuss two slightly counter-intuitive findings about the environmental dependence of clustering in the Sloan Digital Sky Survey. First, we find that the relation between clustering strength and density is not monotonic: galaxies in the densest regions are more strongly clustered than are galaxies in regions of moderate overdensity; galaxies in moderate overdensities are more strongly clustered than are those in moderate underdensities; but galaxies in moderate underdensities are less clustered than galaxies in the least dense regions. We argue that this is natural if clustering evolved gravitationally from a Gaussian field, since the highest peaks and lowest troughs in Gaussian fields are similarly clustered. The precise non-monotonic dependence of galaxy clustering on density is very well reproduced in a mock catalog which is based on a halo-model decomposition of galaxy clustering. Second, the distribution of galaxy counts in our sample is rather well described by a Poisson cluster model. We show that, despite their Poisson nature, correlations with environment are expected in such models. More remarkably, the expected trends are very like those in standard models of halo bias, despite the fact that correlations with environment in these models arise purely from the fact that dense regions are dense because they happen to host more massive halos. This is in contrast to the usual analysis which assumes that it is the large scale environment which determines the halo mass function. [Abridged]

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arXiv2007

The Three-Point Correlation Function of Luminous Red Galaxies in the Sloan Digital Sky Survey

We present measurements of the redshift-space three-point correlation function of 50,967 Luminous Red Galaxies (LRGs) from Data Release 3 (DR3) of the Sloan Digital Sky Survey (SDSS). We have studied the shape dependence of the reduced three-point correlation function (Qz(s,q,theta)) on three different scales, s=4, 7 and 10 h-1 Mpc, and over the range of 1 < q < 3 and 0 < theta < 180. On small scales (s=4 h-1 Mpc), Qz is nearly constant, with little change as a function of q and theta. However, there is evidence for a shallow U-shaped behaviour (with theta) which is expected from theoretical modeling of Qz . On larger scales (s=7 and 10 h-1 Mpc), the U-shaped anisotropy in Qz (with theta) is more clearly detected. We compare this shape-dependence in Qz(s,q,theta) with that seen in mock galaxy catalogues which were generated by populating the dark matter halos in large N-body simulations with mock galaxies using various Halo Occupation Distributions (HOD). We find that the combination of the observed number density of LRGs, the (redshift-space) two-point correlation function and Qz provides a strong constraint on the allowed HOD parameters (M_min, M_1, alpha) and breaks key degeneracies between these parameters. For example, our observed Qz disfavors mock catalogues that overpopulate massive dark matter halos with many LRG satellites. We also estimate the linear bias of LRGs to be b=1.87+/-0.07 in excellent agreement with other measurements.

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arXiv2007

An improved model for the formation times of dark matter haloes

A dark matter halo is said to have formed when at least half its mass hass been assembled into a single progenitor. With this definition, it is possible to derive a simple but useful analytic estimate of the distribution of halo formation times. The standard estimate of this distribution depends on the shape of the conditional mass function--the distribution of progenitor masses of a halo as a function of time. If the spherical collapse model is used to estimate the progenitor mass function, then the formation times one infers systematically underestimate those seen in numerical simulations of hierarchical gravitational clustering. We provide estimates of halo formation which may be related to an ellipsoidal collapse model. These estimates provide a substantially better description of the simulations. We also provide an alternative derivation of the formation time distribution which is based on the assumption that haloes increase their mass through binary mergers only. Our results are useful for models which relate halo structure to halo formation.

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arXiv2006

Bispectrum and Nonlinear Biasing of Galaxies: Perturbation Analysis, Numerical Simulation and SDSS Galaxy Clustering

We consider nonlinear biasing models of galaxies with particular attention to a correlation between linear and quadratic biasing coefficients, b_1 and b_2. We first derive perturbative expressions for b_1 and b_2 in halo and peak biasing models. Then we compute power spectra and bispectra of dark matter particles and halos using N-body simulation data and of volume-limited subsamples of Sloan Digital Sky Survey (SDSS) galaxies, and determine their b_1 and b_2. We find that the values of those coefficients at linear regimes (k<0.2h/Mpc) are fairly insensitive to the redshift-space distortion and the survey volume shape. The resulting normalized amplitudes of bispectra, Q, for equilateral triangles, are insensitive to the values of b_1 implying that b_2 indeed correlates with b_1. The present results explain the previous finding of Kayo et al. (2004) for the hierarchical relation of three-point correlation functions of SDSS galaxies. While the relations between b_1 and b_2 are quantitatively different for specific biasing models, their approximately similar correlations indicate a fairly generic outcome of the biasing due to the gravity in primordial Gaussian density fields.

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arXiv2006

The environmental dependence of galaxy clustering in the Sloan Digital Sky Survey

A generic prediction of hierarchical clustering models is that the mass function of dark haloes in dense regions in the Universe should be top-heavy. We provide a novel test of this prediction using a sample of galaxies drawn from the Sloan Digital Sky Survey. To perform the test, we compare measurements of galaxy clustering in dense and underdense regions. We find that galaxies in dense regions cluster significantly more strongly than those in less dense regions. This is true over the entire 0.1--30 Mpc pair separation range for which we can make accurate measurements. We make similar measurements in realistic mock catalogs in which the only environmental effects are those which arise from the predicted correlation between halo mass and environment. We also provide an analytic halo-model based calculation of the effect. Both the mock catalogs and the analytic calculation provide rather good descriptions of the SDSS measurements. Thus, our results provide strong support for hierarchical models. They suggest that, unless care is taken to study galaxies at fixed mass, correlations between galaxy properties and the surrounding environment are almost entirely due to more fundamental correlations between galaxy properties and host halo mass, and between halo mass and environment.

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arXiv2006

The Probability Distribution of the Lya transmitted flux from a sample of SDSS quasars

We present a measurement of the probability distribution function (PDF) of the transmitted flux in the Lya forest from a sample of 3492 quasars included in the SDSS DR3 data release. Our intention is to investigate the sensitivity of the Lya flux PDF as measured from low resolution and low signal-to-noise data to a number of systematic errors such as uncertainties in the mean flux, continuum and noise estimate. The quasar continuum is described by the superposition of a power law and emission lines. We perform a power law continuum fitting on a spectrum-by-spectrum basis, and obtain an average continuum slope of 0.59 +/- 0.36 in the redshift range 2.5<z<3.5. Taking into account the variation in the continuum indices increases the mean flux by 3 and 7 per cent at z=3 and 2.4, respectively, as compared to the values inferred with a single (mean) continuum slope. We compare our measurements to the PDF obtained with mock lognormal spectra, whose statistical properties have been constrained to match the observed Lya flux PDF and power spectrum of high resolution data. Using our power law continuum fitting and the SDSS pipeline noise estimate yields a poor agreement between the observed and mock PDFs. Allowing for a break in the continuum slope and, more importantly, for residual scatter in the continuum level substantially improves the agreement. A decrease of 10-15 per cent in the mean quasar continuum with a typical rms variance at the 20 per cent level can account for the data, provided that the noise excess correction is no larger than 10 per cent.

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arXiv2006

Environment and the cosmic evolution of star formation

We present a mark correlation analysis of the galaxies in the Sloan Digital Sky Survey using weights provided by MOPED. The large size of the sample permits statistically significant statements about how galaxies with different metallicities and star formation histories are spatially correlated. Massive objects formed a larger fraction of their stars at higher redshifts and over shorter timescales than did less massive objects (sometimes called down-sizing). We find that those galaxies which dominated the cosmic star formation at z~3 are predominantly in clusters today, whereas galaxies which dominate the star formation at z~0 inhabit substantially lower mass objects in less dense regions today. Hence, our results indicate that star formation and chemical enrichment occured first in the denser regions of the Universe, and moved to less dense regions at later times.

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arXiv2005

The Luminosity-Weighted or `Marked' Correlation Function

We present measurements of the redshift-space luminosity-weighted or `marked' correlation function in the SDSS. These are compared with a model in which the luminosity function and luminosity dependence of clustering are the same as that observed, and in which the form of the luminosity-weighted correlation function is entirely a consequence of the fact that massive halos populate dense regions. We do this by using mock catalogs which are constrained to reproduce the observed luminosity function and the luminosity dependence of clustering, as well as by using the language of the redshift-space halo-model. These analyses show that marked correlations may show a signal on large scales even if there are no large-scale physical effects--the statistical correlation between halos and their environment will produce a measureable signal. Our model is in good agreement with the measurements, indicating that the halo mass function in dense regions is top-heavy; the correlation between halo mass and large scale environment is the primary driver for correlations between galaxy properties and environment; and the luminosity of the central galaxy in a halo is different from (in general, brighter than) that of the other objects in the halo. Thus our measurement provides strong evidence for the accuracy of these three standard assumptions of galaxy formation models. These assumptions also form the basis of current halo-model based interpretations of galaxy clustering.

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arXiv2005

Marked correlations in galaxy formation models

The two-point correlation function has been the standard statistic for quantifying how galaxies are clustered. The statistic uses the positions of galaxies, but not their properties. Clustering as a function of galaxy property, be it type, luminosity, color, etc., is usually studied by analysing a subset of the full population, the galaxies in the subset chosen because they have a similar range of properties. We explore an alternative technique---marked correlations---in which one weights galaxies by some property or `mark' when measuring clustering statistics. Marked correlations are particularly well-suited to quantifying how the properties of galaxies correlate with their environment. Therefore, measurements of marked statistics, with luminosity, stellar mass, color, star-formation rate, etc. as the mark, permit sensitive tests of galaxy formation models. We make measurements of such marked statistics in semi-analytic galaxy formation models to illustrate their utility. These measurements show that close pairs of galaxies are expected to be red, to have larger stellar masses, and to have smaller star formation rates. We also show that the simplest unbiased estimator of the particular marked statistic we use extensively is very simple to measure---it does not require construction of a random catalog---and provide an estimate of its variance. Large wide-field surveys of the sky are revolutionizing our view of galaxies and how they evolve. Our results indicate that application of marked statistics to this high quantity of high-quality data will provide a wealth of information about galaxy formation.

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arXiv2005

The halo-model description of marked statistics

Marked statistics allow sensitive tests of how galaxy properties correlate with environment, as well as of how correlations between galaxy properties are affected by environment. A halo-model description of marked correlations is developed, which incorporates the effects which arise from the facts that typical galaxy marks (e.g., luminosity, color, star formation rate, stellar mass) depend on the mass of the parent halo, and that massive haloes extend to larger radii and populate denser regions. Comparison with measured marked statistics in semi-analytic galaxy formation models shows good agreement on scales smaller than a Megaparsec, and excellent agreement on larger scales. The halo-model description shows clearly that the behaviour of some low-order marked statistics on these scales encodes information about the mean galaxy mark as a function of halo mass, but is insensitive to mark-gradients within haloes. Higher-order statistics encode information about higher order moments of the distribution of marks within haloes. This information is obtained without ever having to identify haloes or clusters in the galaxy distribution. On scales smaller than a Megaparsec, the halo-model calculation shows that marked statistics allow sensitive tests of whether or not central galaxies in haloes are a special population. A prescription for including more general mark-gradients in the halo-model description is also provided. The formalism developed here is particularly well-suited to interpretation of marked statistics in astrophysical datasets, because it is phrased in the same language that is currently used to interpret more standard measures of galaxy clustering.

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arXiv2005

The environmental dependence of clustering in hierarchical models

In hierarchical models, density fluctuations on different scales are correlated. This induces correlations between dark halo masses, their formation histories, and their larger-scale environments. In turn, this produces a correlation between galaxy properties and environment. This correlation is entirely statistical in nature. We show how the observed clustering of galaxies can be used to quantify the importance of this statistical correlation relative to other physical effects which may also give rise to correlations between the properties of galaxies and their surroundings. We also develop a halo model description of this environmental dependence of clustering.

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arXiv2005

On Departures From a Power Law in the Galaxy Correlation Function

We measure the projected correlation function w_p(r_p) from the Sloan Digital Sky Survey for a flux-limited sample of 118,000 galaxies and for a volume limited subset of 22,000 galaxies with absolute magnitude M_r<-21. Both correlation functions show subtle but systematic departures from the best-fit power law, in particular a change in slope at r_p~1-2 Mpc/h. These departures are stronger for the volume-limited sample, which is restricted to relatively luminous galaxies. We show that the inflection point in w_p(r_p) can be naturally explained by contemporary models of galaxy clustering, according to which it marks the transition from a large scale regime dominated by galaxy pairs in separate dark matter halos to a small scale regime dominated by galaxy pairs in the same dark matter halo. For example, given the dark halo population predicted by an inflationary cold dark matter scenario, the projected correlation function of the volume-limited sample can be well reproduced by a model in which the mean number of M_r<-21 galaxies in a halo of mass M>M_1=4.74 X 10^{13}\msun/h is _M=(M/M_1)^{0.89}, with 75% of the galaxies residing in less massive, single-galaxy halos. This physically motivated model has the same number of free parameters as a power law, and it fits the w_p(r_p) data better, with a χ^2/d.o.f.=0.93 compared to 6.12 (for 10 degrees of freedom, incorporating the covariance of the correlation function errors). Departures from a power-law correlation function encode information about the relation between galaxies and dark matter halos. Higher precision measurements of these departures for multiple classes of galaxies will constrain galaxy bias and provide new tests of the theory of galaxy formation.

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arXiv2005

Detection of Cosmic Magnification with the Sloan Digital Sky Survey

We present an 8 sigma detection of cosmic magnification measured by the variation of quasar density due to gravitational lensing by foreground large scale structure. To make this measurement we used 3800 square degrees of photometric observations from the Sloan Digital Sky Survey (SDSS) containing \~200,000 quasars and 13 million galaxies. Our measurement of the galaxy-quasar cross-correlation function exhibits the amplitude, angular dependence and change in sign as a function of the slope of the observed quasar number counts that is expected from magnification bias due to weak gravitational lensing. We show that observational uncertainties (stellar contamination, Galactic dust extinction, seeing variations and errors in the photometric redshifts) are well controlled and do not significantly affect the lensing signal. By weighting the quasars with the number count slope, we combine the cross-correlation of quasars for our full magnitude range and detect the lensing signal at >4 sigma in all five SDSS filters. Our measurements of cosmic magnification probe scales ranging from 60 kpc/h to 10 Mpc/h and are in good agreement with theoretical predictions based on the WMAP concordance cosmology. As with galaxy-galaxy lensing, future measurements of cosmic magnification will provide useful constraints on the galaxy-mass power spectrum.

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arXiv2005

Voids in a $Λ$CDM Universe

We study the formation and evolution of voids in the dark matter distribution using various simulations of the popular $Λ$ Cold Dark Matter cosmogony. We identify voids by requiring them to be regions of space with a mean overdensity of -0.8 or less. Each of the simulations contains thousands of voids. The distribution of void sizes in the different simulations shows good agreement. Voids very clearly correspond to minima in the smoothed initial density field. We find a universal void mass profile of the form $ρ(<r)/ρ(r_{\rm eff}) \propto \exp[(r/r_{\rm eff})^α]$ where $r_{\rm eff}$ is the effective radius of a void and $α\sim 2$. The mass function of haloes in voids is steeper than that of haloes that populate denser regions. The abundances of void haloes seem to evolve somewhat more strongly between redshifts $\sim 1$ and 0 than the global abundances of haloes. (abridged)

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arXiv2004

How does clustering depend on environment?

According to the current paradigm, galaxies form and reside in extended cold dark matter (CDM) halos and in turn are key tracers of cosmological structure. Understanding how different types of galaxies occupy halos of different masses is one of the major challenges facing extragalactic astrophysics. The observed galaxy properties depend on the environment surrounding the galaxy. Within the framework of most galaxy formation models the environmental dependence of the galaxy population is mainly due to the change of the halo mass function with large-scale environment. Such models make precise predictions for how galaxy clustering should depend on environment. We will illustrate this by presenting analytical models of dark matter and galaxy clustering along with results obtained from numerical simulations. With these results we can hope to obtain a better understanding of the link between galaxies and dark matter and thereby constrain galaxy formation models.

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arXiv2004

On the environmental dependence of halo formation

A generic prediction of hierarchical gravitational clustering models is that the distribution of halo formation times should depend relatively strongly on halo mass, massive haloes forming more recently, and depend only weakly, if at all, on the large scale environment of the haloes. We present a novel test of this assumption which uses a statistic that proves to be particularly well-suited to detecting and quantifying weak correlations with environment. We find that close pairs of haloes form at slightly higher redshifts than do more widely separated halo pairs, suggesting that haloes in dense regions form at slightly earlier times than do haloes of the same mass in less dense regions. The environmental trends we find are useful for models which relate the properties of galaxies to the formation histories of the haloes which surround them.

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arXiv2004

Formation times and masses of dark matter haloes

The most commonly used definition of halo formation is the time when a halo's most massive progenitor first contains at least half the final mass of its parent. Reasonably accurate formulae for the distribution of formation times of haloes of fixed mass have been available for some time. We use numerical simulations of hierarchical gravitational clustering to test the accuracy of formulae for the mass at formation. We also derive and test a formula for the joint distribution of formation masses and times. The structure of a halo is expected to be related to its accretion history. Our tests show that our formulae for formation masses and times are reasonably accurate, so we expect that they will aid future analytic studies of halo structure.

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