arXiv subjects

Kwan Chuen Chan

Publications and source records attributed to Kwan Chuen Chan.

34 records · Page 2Linked to original sources

arXiv2020

Measurement of Void Bias Using Separate Universe Simulations

Cosmic voids are biased tracers of the large-scale structure of the universe. Separate universe simulations (SUS) enable accurate measurements of this biasing relation by implementing the peak-background split (PBS). In this work, we apply the SUS technique to measure the void bias parameters. We confirm that the PBS argument works well for underdense tracers. The response of the void size distribution depends on the void radius. For voids larger (smaller) than the size at the peak of the distribution, the void abundance responds negatively (positively) to a long wavelength mode. The linear bias from the SUS is in good agreement with the cross power spectrum measurement on large scales. Using the SUS, we have detected the quadratic void bias for the first time in simulations. We find that $ b_2 $ is negative when the magnitude of $ b_1 $ is small, and that it becomes positive and increases rapidly when $ |b_1| $ increases. We compare the results from voids identified in the halo density field with those from the dark matter distribution, and find that the results are qualitatively similar, but the biases generally shift to the larger voids sizes.

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arXiv2019

Constraint of Void Bias on Primordial non-Gaussianity

We study the large-scale bias parameter of cosmic voids with primordial non-Gaussian (PNG) initial conditions of the local type. In this scenario, the dark matter halo bias exhibits a characteristic scale dependence on large scales, which has been recognized as one of the most promising probes of the local PNG. Using a suite of $N$-body simulations with Gaussian and non-Gaussian initial conditions, we find that the void bias features scale-dependent corrections on large scales, similar to its halo counterpart. We find excellent agreement between the numerical measurement of the PNG void bias and the general peak-background split prediction. Contrary to halos, large voids anti-correlate with the dark matter density field, and the large-scale Gaussian void bias ranges from positive to negative values depending on void size and redshift. Thus, the information in the clustering of voids can be complementary to that of the halos. Using the Fisher matrix formalism for multiple tracers, we demonstrate that including the scale-dependent bias information from voids, constraints on the PNG parameter $f_{\rm NL}$ can be tightened by a factor of two compared to the accessible information from halos alone, when the sampling density of tracers reaches $4 \times 10^{-3} \, h^3 \mathrm{Mpc}^{-3} $.

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arXiv2018

Bispectrum Supersample Covariance

Modes with wavelengths larger than the survey window can have significant impact on the covariance within the survey window. The supersample covariance has been recognized as an important source of covariance for the power spectrum on small scales, and it can potentially be important for the bispectrum covariance as well. In this paper, using the response function formalism, we model the supersample covariance contributions to the bispectrum covariance and the cross covariance between the power spectrum and the bispectrum. The supersample covariances due to the long wavelength density and tidal perturbations are investigated, and the tidal contribution is a few orders of magnitude smaller than the density one because in configuration space the bispectrum estimator involves angular averaging and the tidal response function is anisotropic. The impact of the super-survey modes is quantified using numerical measurements with periodic box and subbox setups. For the matter bispectrum, the ratio between the supersample covariance correction and the small scale covariance, which can be computed using a periodic box, is roughly an order of magnitude smaller than that for the matter power spectrum. This is because for the bispectrum, the small scale non-Gaussian covariance is significantly larger than that for the power spectrum. For the cross covariance, the supersample covariance is as important as for the power spectrum covariance. The supersample covariance prediction with the halo model response function is in good agreement with numerical results.

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arXiv2017

Effective Window Function for Lagrangian Halos

The window function for protohalos in Lagrangian space is often assumed to be a tophat in real space. We measure this profile directly and find that it is more extended than a tophat but less extended than a Gaussian; its shape is well-described by rounding the edges of the tophat by convolution with a Gaussian that has a scale length about 5 times smaller. This effective window $W_{\rm eff}$ is particularly simple in Fourier space, and has an analytic form in real space. Together with the excursion set bias parameters, $W_{\rm eff}$ describes the scale-dependence of the Lagrangian halo-matter cross correlation up to $kR_{\rm Lag} \sim 10 $, where $R_{\rm Lag}$ is the Lagrangian size of the protohalo. Moreover, with this $W_{\rm eff}$, all the spectral moments of the power spectrum are finite, allowing a straightforward estimate of the excursion set peak mass function. This estimate requires a prescription of the critical overdensity enclosed within a protohalo if it is to collapse, which we calibrate from simulations. We find that the resulting estimate of halo abundances is only accurate to about 20%, and we discuss why: A tophat in `infall time' towards the protohalo center need not correspond to a tophat in the initial spatial distribution, so models in which infall rather than smoothed overdensity is the relevant variable may be more accurate.

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arXiv2017

Shot noise and biased tracers: a new look at the halo model

Shot noise is an important ingredient to any measurement or theoretical modeling of discrete tracers of the large scale structure. Recent work has shown that the shot noise in the halo power spectrum becomes increasingly sub-Poissonian at high mass. Interestingly, while the halo model predicts a shot noise power spectrum in qualitative agreement with the data, it leads to an unphysical white noise in the cross halo-matter and matter power spectrum. In this work, we show that absorbing all the halo model sources of shot noise into the halo fluctuation field leads to meaningful predictions for the shot noise contributions to halo clustering statistics and remove the unphysical white noise from the cross halo-matter statistics. Our prescription straightforwardly maps onto the general bias expansion, so that the renormalized shot noise terms can be expressed as combinations of the halo model shot noises. Furthermore, we demonstrate that non-Poissonian contributions are related to volume integrals over correlation functions and their response to long-wavelength density perturbations. This leads to a new class of consistency relations for discrete tracers, which appear to be satisfied by our reformulation of the halo model. We test our theoretical predictions against measurements of halo shot noise bispectra extracted from a large suite of numerical simulations. Our model reproduces qualitatively the observed sub-Poissonian noise, although it underestimates the magnitude of this effect.

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arXiv2017

Assessment of the Information Content of the Power Spectrum and Bispectrum

The covariance matrix of the matter and halo power spectrum and bispectrum are studied. Using a large suite of simulations, we find that the non-Gaussianity in the covariance is significant already at mildly nonlinear scales. We compute the leading disconnected non-Gaussian correction to the matter bispectrum covariance using perturbation theory, and find that the corrections result in good agreement in the mildly nonlinear regime. The shot noise contribution to the halo power spectrum and bispectrum covariance is computed using the Poisson model, and the model yields decent agreement with simulation results. However, when the shot noise is estimated from the individual realization, which is usually done in reality, we find that the halo covariance is substantially reduced and gets close to the Gaussian covariance. This is because most of the non-Gaussianity in the covariance arises from the fluctuations in the Poisson shot noise. We use the measured non-Gaussian covariance to access the information content of the power spectrum and bispectrum. The signal-to-noise ratio, S/N, of the matter and halo power spectrum levels off in the mildly nonlinear regime, $k \sim 0.1 - 0.2 \,\mathrm{Mpc} h^{-1}$. In the nonlinear regime the S/N of the matter and halo bispectrum increases but much slower than the Gaussian results suggest. We find that both the S/N for power spectrum and bispectrum are overestimated by the Gaussian covariances, but the problem being much more serious for the bispectrum. Because the bispectrum is affected strongly by nonlinearity and shot noise, inclusion of the bispectrum only adds modest amount of S/N compared to that of the power spectrum.

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arXiv2017

Consistency relations for the Lagrangian halo bias and their implications

The protohalo patches from which halos form are defined by a number of constraints imposed on the Lagrangian dark matter density field. Each of these constraints contributes to biasing the spatial distribution of the protohalos relative to the matter. We show how measurements of this spatial distribution -- linear combinations of protohalo bias factors -- can be used to make inferences about the physics of halo formation. Our analysis exploits the fact that halo bias factors satisfy consistency relations which encode this physics, and that these relations are the same even for sub-populations in which assembly bias has played a role. We illustrate our methods using a model in which three parameters matter: a density threshold, the local slope and the curvature of the smoothed density field. The latter two are nearly degenerate; our approach naturally allows one to build an accurate effective two-parameter model for which the consistency relations still apply. This, with an accurate description of the smoothing window, allows one to describe the protohalo-matter cross-correlation very well, both in Fourier and configuration space. We then use our determination of the large scale bias parameters together with the consistency relations, to estimate the enclosed density and mean slope on the Lagrangian radius scale of the protohalos. Direct measurements of these quantities, made on smaller scales than those on which the bias parameters are typically measured, are in good agreement.

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arXiv2016

Squeezing the halo bispectrum: a test of bias models

We study the halo-matter cross bispectrum in the presence of primordial non-Gaussianity of the local type. We restrict ourselves to the squeezed limit, for which the calculation are straightforward, and perform the measurements in the initial conditions of N-body simulations, to mitigate the contamination induced by nonlinear gravitational evolution. Interestingly, the halo-matter cross bispectrum is not trivial even in this simple limit as it is strongly sensitive to the scale-dependence of the quadratic and third-order halo bias. Therefore, it can be used to test biasing prescriptions. We consider three different prescription for halo clustering: excursion set peaks (ESP), local bias and a model in which the halo bias parameters are explicitly derived from a peak-background split. In all cases, the model parameters are fully constrained with statistics other than the cross bispectrum. We measure the cross bispectrum involving one halo fluctuation field and two mass overdensity fields for various halo masses and collapse redshifts. We find that the ESP is in reasonably good agreement with the numerical data, while the other alternatives we consider fail in various cases. This suggests that the scale-dependence of halo bias also is a crucial ingredient to the squeezed limit of the halo bispectrum.

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arXiv2015

Halo Profile Evolution and Velocity Bias

We propose a simple model that elucidates the generation of halo velocity bias. The fluid equation approximation is often adopted in modelling the evolution of the halo density field. In this approach, halos are often taken to be point particles even though in reality they are finite-sized objects. In this paper, we generalize the fluid equation approximation to halos to include the finite extent of halos by taking into account the halo profile. We compute the perturbation of the halo density and velocity field to second order and find that the profile correction gives rise to $k^2$ correction terms in Fourier space. These corrections are more important for velocity than for density. In particular, the profile correction generates $k^2$ correction term in the velocity bias and the correction terms do not decay away in the long term limit, but it is not constant. We model the halo profile evolution using the spherical collapse model. We also measure the evolution of proto-halo profile at various redshifts numerically. We find that the spherical collapse model gives a reasonable description of the numerical profile evolution. Static halo profile is often adopted in modelling halos in theories such as the excursion set theory. Our work highlights the importance of including the profile evolution in the calculations.

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arXiv2014

Large-Scale Clustering of Cosmic Voids

We study the clustering of voids using $N$-body simulations and simple theoretical models. The excursion-set formalism describes fairly well the abundance of voids identified with the watershed algorithm, although the void formation threshold required is quite different from the spherical collapse value. The void cross bias $b_{\rm c} $ is measured and its large-scale value is found to be consistent with the peak background split results. A simple fitting formula for $b_{\rm c} $ is found. We model the void auto-power spectrum taking into account the void biasing and exclusion effect. A good fit to the simulation data is obtained for voids with radii $\gtrsim$ 30 Mpc/$h$, especially when the void biasing model is extended to 1-loop order. However, the best-fit bias parameters do not agree well with the peak-background split results. Being able to fit the void auto-power spectrum is particularly important not only because it is the direct observable in galaxy surveys, but also our method enables us to treat the bias parameters as nuisance parameters, which are sensitive to the techniques used to identify voids.

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arXiv2014

Measuring nonlocal Lagrangian peak bias

We investigate nonlocal Lagrangian bias contributions involving gradients of the linear density field, for which we have predictions from the excursion set peak formalism. We begin by writing down a bias expansion which includes all the bias terms, including the nonlocal ones. Having checked that the model furnishes a reasonable fit to the halo mass function, we develop a 1-point cross-correlation technique to measure bias factors associated with 2-distributed quantities. We validate the method with numerical realizations of peaks of Gaussian random fields before we apply it to N-body simulations. We focus on the lowest (quadratic) order nonlocal contributions. We can reproduce our measurement of χ_{10} if we allow for an offset between the Lagrangian halo center-of-mass and the peak position. The sign and magnitude of χ_{10} is consistent with Lagrangian haloes sitting near linear density maxima. The resulting contribution to the halo bias can safely be ignored for M = 10^13 Msun/h, but could become relevant at larger halo masses. For the second nonlocal bias χ_{01} however, we measure a much larger magnitude than predicted by our model. We speculate that some of this discrepancy might originate from nonlocal Lagrangian contributions induced by nonspherical collapse.

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arXiv2014

Helmholtz Decomposition of the Lagrangian Displacement

Lagrangian displacement field $Ψ$ is the central object in Lagrangian perturbation theory (LPT). LPT is very successful at high redshifts, but it performs poorly at low redshifts due to severe shell crossing. To understand and quantify the effects of shell crossing, we extract $Ψ$ from N-body simulation and decompose it into scalar and vector parts. We find that at late time the power spectrum of the scalar part agrees with 1-loop results from LPT at large scales, while the power in small scales is much suppressed due to shell crossing. At z=0, the power spectrum of $Ψ$ is 10% lower than the 1-loop results at k = 0.1 h/Mpc. Shell crossing also generates the vector contribution in $Ψ$, although its effect is subdominant in comparison with the power suppression in the scalar part. At z=0, the vector part contributes 10% to the total power spectrum of $Ψ$ at k = 1 h/Mpc, while only 1% is expected from the vector contribution in LPT. We also examine the standard LPT recipes and some of its variants. In one of the variants, we include a power suppression factor in the displacement potential to take into account the power suppression in small scales after shell crossing. However, these simple phenomenological approaches are found to yield limited improvement compared to the standard LPT after the onset of shell crossing.

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arXiv2013

Bias deconstructed: Unravelling the scale dependence of halo bias using real space measurements

We explore the scale dependence of halo bias using real space cross-correlation measurements in N-body simulations and in Pinocchio, an algorithm based on Lagrangian Perturbation Theory. Recent work has shown how to interpret such real space measurements in terms of k-dependent bias in Fourier space, and how to remove the k-dependence to reconstruct the k-independent peak-background split halo bias parameters. We compare our reconstruction of the linear bias, which requires no free parameters, with previous estimates from N-body simulations which were obtained directly in Fourier space at large scales, and find very good agreement. Our reconstruction of the quadratic bias is similarly parameter-free, although in this case there are no previous Fourier space measurements to compare with. Our analysis of N-body simulations explicitly tests the predictions of the excursion set peaks (ESP) formalism of Paranjape et al. (2013) for the scale dependence of bias; we find that the ESP predictions accurately describe our measurements. In addition, our measurements in Pinocchio serve as a useful, successful consistency check between Pinocchio and N-body simulations that is not accessible to traditional measurements.

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arXiv2013

Non-local Lagrangian bias

Halos are biased tracers of the dark matter distribution. It is often assumed that the patches from which halos formed are locally biased with respect to the initial fluctuation field, meaning that the halo-patch fluctuation field can be written as a Taylor series in that of the dark matter. If quantities other than the local density influence halo formation, then this Lagrangian bias will generically be nonlocal; the Taylor series must be performed with respect to these other variables as well. We illustrate the effect with Monte-Carlo simulations of a model in which halo formation depends on the local shear (the quadrupole of perturbation theory), and provide an analytic model which provides a good description of our results. Our model, which extends the excursion set approach to walks in more than one dimension, works both when steps in the walk are uncorrelated, as well as when there are correlations between steps. For walks with correlated steps, our model includes two distinct types of nonlocality: one is due to the fact that the initial density profile around a patch which is destined to form a halo must fall sufficiently steeply around it -- this introduces k-dependence to even the linear bias factor, but otherwise only affects the monopole of the clustering signal. The other is due to the surrounding shear field; this affects the quadratic and higher order bias factors, and introduces an angular dependence to the clustering signal. In both cases, our analysis shows that these nonlocal Lagrangian bias terms can be significant, particularly for massive halos; they must be accounted for in analyses of higher order clustering such as the halo bispectrum in Lagrangian or Eulerian space. Although we illustrate these effects using halos, our analysis and conclusions also apply to the other constituents of the cosmic web -- filaments, sheets and voids.

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arXiv2012

Halo Sampling, Local Bias and Loop Corrections

We develop a new test of local bias, by constructing a locally biased halo density field from sampling the dark matter-halo distribution. Our test differs from conventional tests in that it preserves the full scatter in the bias relation and it does not rely on perturbation theory. We put forward that bias parameters obtained using a smoothing scale R can only be applied to computing the halo power spectrum at scales k ~ 1/R. Our calculations can automatically include the running of bias parameters and give vanishingly small loop corrections at low-k. Our proposal results in much better agreement of the sampling and perturbation theory results with simulations. In particular, unlike the standard interpretation of local bias in the literature, our treatment of local bias does not generate a constant power in the low-k limit. We search for extra noise in the Poisson corrected halo power spectrum at wavenumbers below its turn-over and find no evidence of significant positive noise (as predicted by the standard interpretation) while we find evidence of negative noise coming from halo exclusion for very massive halos. Using perturbation theory and our non-perturbative sampling technique we also demonstrate that nonlocal bias effects discovered recently in simulations impact the power spectrum only at the few percent level in the weakly nonlinear regime.

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arXiv2012

Gravity and Large-Scale Non-local Bias

The relationship between galaxy and matter overdensities, bias, is most often assumed to be local. This is however unstable under time evolution, we provide proofs under several sets of assumptions. In the simplest model galaxies are created locally and linearly biased at a single time, and subsequently move with the matter (no velocity bias) conserving their comoving number density (no merging). We show that, after this formation time, the bias becomes unavoidably non-local and non-linear at large scales. We identify the non-local gravitationally induced fields in which the galaxy overdensity can be expanded, showing that they can be constructed out of the invariants of the deformation tensor (Galileons). In addition, we show that this result persists if we include an arbitrary evolution of the comoving number density of tracers. We then include velocity bias, and show that new contributions appear, a dipole field being the signature at second order. We test these predictions by studying the dependence of halo overdensities in cells of fixed matter density: measurements in simulations show that departures from the mean bias relation are strongly correlated with the non-local gravitationally induced fields identified by our formalism. The effects on non-local bias seen in the simulations are most important for the most biased halos, as expected from our predictions. The non-locality seen in the simulations is not fully captured by assuming local bias in Lagrangian space. Accounting for these effects when modeling galaxy bias is essential for correctly describing the dependence on triangle shape of the galaxy bispectrum, and hence constraining cosmological parameters and primordial non-Gaussianity. We show that using our formalism we remove an important systematic in the determination of bias parameters from the galaxy bispectrum, particularly for luminous galaxies. (abridged)

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