We explore the potential of the kinetic Sunyaev-Zeldovich (kSZ) effect as the cornerstone of a future observational probe for halo spin bias, the secondary dependence of halo clustering on halo spin at fixed halo mass. Using the IllustrisTNG magneto-
hydrodynamical cosmological simulation, we measure both the kSZ and the thermal SZ (tSZ) effects produced by the baryonic content of more than 50,000 haloes within the halo mass range $11 < log_{10} ({rm M_{vir}}/ h^{-1} {rm M_{odot}}) lesssim 14.5$. First, we confirm that the magnitude of both effects depends strongly on the total gas and virial mass of the haloes, and that the integrated kSZ signal displays a significant correlation with the angular momentum of the intra-halo gas, particularly for massive haloes. Second, we show that both the integrated kSZ signal and the ratio of the integrated kSZ and tSZ signals trace total halo spin, even though significant scatter exists. Finally, we demonstrate that, in the absence of observational and instrumental uncertainties, these SZ-related statistics can be used to recover most of the underlying IllustrisTNG halo spin bias signal. Our analysis represents the first attempt to develop a future observational probe for halo spin bias, bringing forward alternative routes for measuring the secondary bias effects.
At $z=0$, higher-spin haloes with masses above $log(text{M}_{text{c}}/h^{-1}text{M}_odot)simeq 11.5$ have a higher bias than lower-spin haloes of the same mass. However, this trend is known to invert below this characteristic crossover mass, $text{M}
_{text{c}}$. In this paper, we measure the redshift evolution and scale dependence of halo spin bias at the low-mass end and demonstrate that the inversion of the signal is entirely produced by the effect of splashback haloes. These low-mass haloes tend to live in the vicinity of significantly more massive haloes, thus sharing their large-scale bias properties. We further show that the location of the redshift-dependent crossover mass scale $text{M}_{text{c}}(z)$ is completely determined by the relative abundance of splashbacks in the low- and high-spin subpopulations. Once splashback haloes are removed from the sample, the intrinsic mass dependence of spin bias is recovered. Since splashbacks have been shown to account for some of the assembly bias signal at the low-mass end, our results unveil a specific link between two different secondary bias trends: spin bias and assembly bias.
The galaxy power spectrum is one of the central quantities in cosmology. It contains information about the primordial inflationary process, the matter clustering, the baryon-photon interaction, the effects of gravity, the galaxy-matter bias, the cosm
ic expansion, the peculiar velocity field, etc.. Most of this information is however difficult to extract without assuming a specific cosmological model, for instance $Lambda$CDM and standard gravity. In this paper we explore instead how much information can be obtained that is independent of the cosmological model, both at background and linear perturbation level. We determine the full set of model-independent statistics that can be constructed by combining two redshift bins and two distinct tracers. We focus in particular on the statistics $r(k,z_1,z_2)$, defined as the ratio of $fsigma_8(z)$ at two redshift shells, and we show how to estimate it with a Fisher matrix approach. Finally, we forecast the constraints on $r$ that can be achieved by future galaxy surveys, and compare it with the standard single-tracer result. We find that $r$ can be measured with a precision from 3 to 11%, depending on the survey. Using two tracers, we find improvements in the constraints up to a factor of two.
We use the improved IllustrisTNG300 magneto-hydrodynamical cosmological simulation to revisit the effect that secondary halo bias has on the clustering of the central galaxy population. With a side length of 205 $h^{-1}$Mpc and significant improvemen
ts on the sub-grid model with respect to the previous Illustris boxes, IllustrisTNG300 allows us to explore the dependencies of galaxy clustering over a large cosmological volume and wide halo-mass range. We show, at high statistical significance, that the halo assembly bias signal (i.e., the secondary dependence of halo bias on halo formation redshift) manifests itself on the clustering of the central galaxy population when this is split by stellar mass, colour, specific star formation rate, and surface density. A significant detection is also obtained for galaxy size: at fixed halo mass, larger central galaxies are more tightly clustered than smaller central galaxies in haloes of mass M$_{rm vir} lesssim 10^{12.5}$ $h^{-1}$M$_{odot}$. This effect, however, seems to be uncorrelated with halo formation time, unlike the rest of the secondary dependencies analysed. We also explore the transmission of the halo spin bias signal, i.e., the secondary dependence of halo bias on halo spin. Although galaxy spin retains little information about the total spin of the halo, the correlation is enough to produce a significant galaxy spin bias signal. We discuss possible ways to probe the spin bias effects with observations.
We use mock galaxy data from the VIMOS Public Extragalactic Redshift Survey (VIPERS) to test the performance of the Multi-Tracer Optimal Estimator (MTOE) of Abramo et al. as a tool to measure the monopoles of the power spectra of multiple tracers of
the large-scale structure, $P^{(0)}_alpha(k)$. We show that MTOE provides more accurate measurements than the standard technique of Feldman, Kaiser & Peacock (FKP), independently of the tracer-selection strategy adopted, on both small and large scales. The largest improvements on individual $P^{(0)}_alpha(k)$ are obtained using a colour-magnitude selection on small scales, due to MTOE being naturally better equipped to deal with shot noise: we report an average error reduction with respect to FKP of $sim$ 40$%$ at $k , [h$ Mpc$^{-1}]gtrsim 0.3$. On large scales ($k[h$ Mpc$^{-1}]lesssim0.1$), the gain in accuracy resulting from cosmic-variance cancellation is $sim$ 10$%$ for the ratios of $P^{(0)}_alpha(k)$. We have carried out a Monte-Carlo Markov Chain analysis to determine the impact of these gains on several quantities derived from $P^{(0)}_alpha(k)$. If we push the measurement to scales $0.3 < k , [h$ Mpc$^{-1}]< 0.5$, the average improvements are $sim$ 30 $%$ for the amplitudes of the monopoles, $sim$ 70 $%$ for the monopole ratios, and $sim$ 20 $%$ for the galaxy biases. Our results highlight the potential of MTOE to shed light upon the physics that operate both on large and small cosmological scales. The effect of MTOE on cosmological constraints using VIPERS data will be addressed in a separate paper.
We show how to obtain constraints on $beta=f/b$, the ratio of the matter growth rate and the bias that quantifies the linear redshift-space distortions, that are independent of the cosmological model, using multiple tracers of large-scale structure.
For a single tracer the uncertainties on $beta$ are constrained by the uncertainties in the amplitude and shape of the power spectrum, which is limited by cosmic variance. However, for two or more tracers this limit does not apply, since taking the ratio of power spectra cosmic variance cancels out, and in the linear (Kaiser) approximation one measures directly the quantity $(1+ beta_1 mu^2)^2/(1+ beta_2 mu^2)^2$, where $mu$ is the angle of a given mode with the line of sight. We provide analytic formulae for the Fisher matrix for one and two tracers, and quantify the signal-to-noise ratio needed to make effective use of the multiple-tracer technique. We also forecast the errors on $beta$ for a survey like Euclid.
Halo bias is the main link between the matter distribution and dark matter halos. In its simplest form, halo bias is determined by halo mass, but there are known additional dependencies on other halo properties which are of consequence for accurate m
odeling of galaxy clustering. Here we present the most precise measurement of these secondary-bias dependencies on halo age, concentration, and spin, for a wide range of halo masses spanning from 10$^{10.7}$ to 10$^{14.7}$ $h^{-1}$ M$_{odot}$. At the high-mass end, we find no strong evidence of assembly bias for masses above M$_{vir}$ $sim10^{14}$ $h^{-1}$ M$_{odot}$. Secondary bias exists, however, for halo concentration and spin, up to cluster-size halos, in agreement with previous findings. For halo spin, we report, for the first time, two different regimes: above M$_{vir}sim$10$^{11.5}$ $h^{-1}$ M$_{odot}$, halos with larger values of spin have larger bias, at fixed mass, with the effect reaching almost a factor 2. This trend reverses below this characteristic mass. In addition to these results, we test, for the first time, the performance of a multi-tracer method for the determination of the relative bias between different subsets of halos. We show that this method increases significantly the signal-to-noise of the secondary-bias measurement as compared to a traditional approach. This analysis serves as the basis for follow-up applications of our multi-tracer method to real data.
In the Halo Model, galaxies are hosted by dark matter halos, while the halos themselves are biased tracers of the underlying matter distribution. Measurements of galaxy correlation functions include contributions both from galaxies in different halos
, and from galaxies in the same halo (the so-called 1-halo terms). We show that, for highly biased tracers, the 1-halo term of the power spectrum obeys a steep scaling relation in terms of bias. We also show that the 1-halo term of the trispectrum has a steep scaling with bias. The steepness of these scaling relations is such that the 1-halo terms can become key contributions to the $n$-point correlation functions, even at large scales. We interpret these results through analytical arguments and semi-analytical calculations in terms of the statistical properties of halos.
Galaxy surveys that map multiple species of tracers of large-scale structure can improve the constraints on some cosmological parameters far beyond the limits imposed by a simplistic interpretation of cosmic variance. This enhancement derives from co
mparing the relative clustering between different tracers of large-scale structure. We present a simple but fully generic expression for the Fisher information matrix of surveys with any (discrete) number of tracers, and show that the enhancement of the constraints on bias-sensitive parameters are a straightforward consequence of this multi-tracer Fisher matrix. In fact, the relative clustering amplitudes between tracers are eigenvectors of this multi-tracer Fisher matrix. The diagonalized multi-tracer Fisher matrix clearly shows that while the effective volume is bounded by the physical volume of the survey, the relational information between species is unbounded. As an application, we study the expected enhancements in the constraints of realistic surveys that aim at mapping several different types of tracers of large-scale structure. The gain obtained by combining multiple tracers is highest at low redshifts, and in one particular scenario we analyzed, the enhancement can be as large as a factor of ~3 for the accuracy in the determination of the redshift distortion parameter, and a factor ~5 for the local non-Gaussianity parameter. Radial and angular distance determinations from the baryonic features in the power spectrum may also benefit from the multi-tracer approach.
Starting from the Fisher matrix for counts in cells, I derive the full Fisher matrix for surveys of multiple tracers of large-scale structure. The key assumption is that the inverse of the covariance of the galaxy counts is given by the naive matrix
inverse of the covariance in a mixed position-space and Fourier-space basis. I then compute the Fisher matrix for the power spectrum in bins of the three-dimensional wavenumber k; the Fisher matrix for functions of position x (or redshift z) such as the linear bias of the tracers and/or the growth function; and the cross-terms of the Fisher matrix that expresses the correlations between estimations of the power spectrum and estimations of the bias. When the bias and growth function are fully specified, and the Fourier-space bins are large enough that the covariance between them can be neglected, the Fisher matrix for the power spectrum reduces to the widely used result that was first derived by Feldman, Kaiser and Peacock (1994). Assuming isotropy, an exact calculation of the Fisher matrix can be performed in the case of a constant-density, volume-limited survey. I then show how the exact Fisher matrix in the general case can be obtained in terms of a series of volume-limited surveys.
