arXiv subjects

Zachary Slepian

Publications and source records attributed to Zachary Slepian.

At least 37 records · Page 2Linked to original sources

arXiv2024

A Model for the Redshift-Space Galaxy 4-Point Correlation Function

The field of cosmology is entering an epoch of unparalleled wealth of observational data thanks to galaxy surveys such as DESI, Euclid, and Roman. Therefore, it is essential to have a firm theoretical basis that allows the effective analysis of the data. With this purpose, we compute the nonlinear, gravitationally-induced connected galaxy 4-point correlation function (4PCF) at the tree level in Standard Perturbation Theory (SPT), including redshift-space distortions (RSD). We begin from the trispectrum and take its inverse Fourier transform into configuration space, exploiting the isotropic basis functions of Cahn & Slepian (2023). We ultimately reduce the configuration-space expression to low-dimensional radial integrals of the power spectrum. This model will enable the use of the BAO feature in the connected 4PCF to sharpen our constraints on the expansion history of the Universe. It will also offer an additional avenue for determining the galaxy bias parameters, and thus tighten our cosmological constraints by breaking degeneracies. Survey geometry can be corrected in the 4PCF, and many systematics are localized, which is an advantage over data analysis with the trispectrum.

astro-ph.CO↗

arXiv2024

First Measurements of the 4-Point Correlation Function of Magnetohydrodynamic Turbulence as a Novel Probe of the Interstellar Medium

In the Interstellar Medium (ISM), gas and dust evolve under magnetohydrodynamic (MHD) turbulence. This produces dense, non-linear structures that then seed star formation. Observationally and theoretically, turbulence is quantified by summary statistics such as the 2-Point Correlation Function (2PCF) or its Fourier-space analog the power spectrum. These cannot capture the non-Gaussian correlations coming from turbulence's highly non-linear nature. We here for the first time apply the 4-Point Correlation Function (4PCF) to turbulence, measuring it on a large suite of MHD simulations that mirror, as well as currently possible, the conditions expected in the ISM. The 4PCF captures the dependence of correlations between quadruplets of density points on the geometry of the tetrahedron they form. Using a novel functionality added to the \textsc{sarabande} code specifically for this work, we isolate the purely non-Gaussian piece of the 4PCF. We then explore simulations with a range of pressures, $P$, and magnetic fields, $B$ (but without self-gravity); these are quantified by different sonic $(M_{\rm S})$ and Alfvénic $(M_{\rm A})$ Mach numbers. We show that the 4PCF has rich behavior that can in future be used as a diagnostic of ISM conditions. We also show that a large-scale coherent magnetic field leads to parity-odd modes of the 4PCF, a clean test of magnetic field coherence with observational ramifications. All our measurements of the 4PCF (10 $M_{\rm S}, M_{\rm A}$ combinations, 9 time-slices for each, 34 4PCF modes for each) are made public for the community to explore.

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arXiv2024

On a Generating Function for the Isotropic Basis Functions and Other Connected Results

Recently isotropic basis functions of $N$ unit vector arguments were presented; these are of significant use in measuring the N-Point Correlation Functions (NPCFs) of galaxy clustering. Here we develop the generating function for these basis functions -- $i.e.$ that function which, expanded in a power series, has as its angular part the isotropic functions. We show that this can be developed using basic properties of the plane wave. A main use of the generating function is as an efficient route to obtaining the Cartesian basis expressions for the isotropic functions. We show that the methods here enable computing difficult overlap integrals of multiple spherical Bessel functions, and we also give related expansions of the Dirac Delta function into the isotropic basis. Finally, we outline how the Cartesian expressions for the isotropic basis functions might be used to enable a faster NPCF algorithm on the CPU.

astro-ph.IM↗

arXiv2024

An automated method to detect and characterise semi-resolved star clusters

We present a novel method for automatically detecting and characterising semi-resolved star clusters: clusters where the observational point-spread function (PSF) is smaller than the cluster's radius, but larger than the separations between individual stars. We apply our method to a 1.77 deg$^2$ field located in the Large Magellanic Cloud (LMC) using the VISTA survey of the Magellanic Clouds (VMC), which surveyed the LMC in the $YJK_\text{s}$ bands. Our approach first models the position-dependent PSF to detect and remove point sources from deep $K_\text{s}$ images; this leaves behind extended objects such as star clusters and background galaxies. We then analyse the isophotes of these extended objects to characterise their properties, perform integrated photometry, and finally remove any spurious objects this procedure identifies. We demonstrate our approach in practice on a deep VMC $K_\text{s}$ tile that contains the most active star-forming regions in the LMC: 30 Doradus, N158, N159, and N160. We select this tile because it is the most challenging for automated techniques due both to crowding and nebular emission. We detect 682 candidate star clusters, with an estimated contamination rate of 13% from background galaxies and chance blends of physically unrelated stars. We compare our candidates to publicly available James Webb Space Telescope data and find that at least 80% of our detections appear to be star clusters.

astro-ph.GA↗

arXiv2024

Can Baryon Acoustic Oscillations Illuminate the Parity-Violating Galaxy 4PCF?

Measurements of the galaxy 4-Point Correlation Function (4PCF) from theSloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey (SDSS BOSS) have recently found strong statistical evidence for parity violation. If this signal is of genuine physical origin, it must stem from beyond-Standard Model physics, most likely during the very early Universe, prior to decoupling ($z$$\sim$$1,020$). Since the Baryon Acoustic Oscillation (BAO) features imprint at decoupling, they are expected in the parity-odd galaxy 4PCF, and so detecting them would be an additional piece of evidence that the signal is genuine. We demonstrate in a toy parity-violating model how the BAO imprint on the parity-odd 4PCF. We then outline how to perform a model-independent search for BAO in the odd 4PCF, desirable since, if the signal is real, we may not know for some time what model of e.g. inflation is producing it. If BAO are detected in the parity-odd sector, they can be used as a standard ruler as is already done in the 2PCF and 3PCF. We derive a simple formula relating the expected precision on the BAO scale to the overall parity-odd detection significance. Pursuing BAO in the odd 4PCF of future redshift surveys such as DESI, Euclid, Spherex, and Roman will be a valuable additional avenue to determine if parity violation in the distribution of galaxies is of genuine cosmological origin.

astro-ph.CO↗

arXiv2024

Parity-Odd Power Spectra: Concise Statistics for Cosmological Parity Violation

We introduce the Parity-Odd Power (POP) spectra, a novel set of observables for probing parity violation in cosmological $N$-point statistics. POP spectra are derived from composite fields obtained by applying nonlinear transformations, involving also gradients, curls, and filtering functions, to a scalar field. This compresses the parity-odd trispectrum into a power spectrum. These new statistics offer several advantages: they are computationally fast to construct, estimating their covariance is less demanding compared to estimating that of the full parity-odd trispectrum, and they are simple to model theoretically. We measure the POP spectra on simulations of a scalar field with a specific parity-odd trispectrum shape. We compare these measurements to semi-analytic theoretical calculations and find agreement. We also explore extensions and generalizations of these parity-odd observables.

astro-ph.CO↗

arXiv2024

Algorithm to Produce a Density Field with Given Two, Three, and Four-Point Correlation Functions

Here we show how to produce a 3D density field with a given set of higher-order correlation functions. Our algorithm enables producing any desired two-point, three-point, and four-point functions, including odd-parity for the latter. We note that this algorithm produces the desired correlations about a set of ``primary'' points, matched to how the spherical-harmonic-based algorithms ENCORE and CADENZA measure them. These ``primary points'' must be used as those around which the correlation functions are measured. We also generalize the algorithm to i) $N$-point correlations with $N>4$, ii) dimensions other than 3, and iii) beyond scalar quantities. This algorithm should find use in verifying analysis pipelines for higher-order statistics in upcoming galaxy redshift surveys such as DESI, Euclid, Roman, and Spherex, as well as intensity mapping. In particular it may be helpful in searches for parity violation in the 4PCF of these samples, for which producing initial conditions for N-body simulations is both costly and highly model-dependent at present, and so alternative methods such as that developed here are desirable

astro-ph.CO↗

arXiv2023

Triple-Spherical Bessel Function Integrals with Exponential and Gaussian Damping: Towards an Analytic N-Point Correlation Function Covariance Model

Spherical Bessel functions appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different weighting functions (which appear as toy models of a given physical observable, such as the galaxy power spectrum) is useful. Here we present a generalization of a recursion-based method for evaluating such integrals. It gives relatively simple closed-form results in terms of Legendre functions (for the exponentially-damped case) and Gamma, incomplete Gamma functions, and hypergeometric functions (for the Gaussian-damped case). We also present a new, non-recursive method to evaluate integrals of products of spherical Bessel functions with Gaussian damping in terms of incomplete Gamma functions and hypergeometric functions.

math-ph↗

arXiv2023

GTC Follow-up Observations of Very Metal-Poor Star Candidates from DESI

The observations from the Dark Energy Spectroscopic Instrument (DESI) will significantly increase the numbers of known extremely metal-poor stars by a factor of ~ 10, improving the sample statistics to study the early chemical evolution of the Milky Way and the nature of the first stars. In this paper we report high signal-to-noise follow-up observations of 9 metal-poor stars identified during the DESI commissioning with the Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS) instrument on the 10.4m Gran Telescopio Canarias (GTC). The analysis of the data using a well-vetted methodology confirms the quality of the DESI spectra and the performance of the pipelines developed for the data reduction and analysis of DESI data.

astro-ph.SR↗

arXiv2023

Measurement of Parity-Odd Modes in the Large-Scale 4-Point Correlation Function of SDSS BOSS DR12 CMASS and LOWZ Galaxies

A tetrahedron is the simplest shape that cannot be rotated into its mirror image in 3D. The 4-Point Correlation Function (4PCF), which quantifies excess clustering of quartets of galaxies over random, is the lowest-order statistic sensitive to parity violation. Each galaxy defines one vertex of the tetrahedron. Parity-odd modes of the 4PCF probe an imbalance between tetrahedra and their mirror images. We measure these modes from the largest currently available spectroscopic samples, the 280,067 Luminous Red Galaxies (LRGs) of the Baryon Oscillation Spectroscopic Survey (BOSS) DR12 LOWZ ($\bar{z} = 0.32$) and the 803,112 LRGS of BOSS DR12 CMASS ($\bar{z} = 0.57$). In LOWZ we find $3.1σ$ evidence for a non-zero parity-odd 4PCF, and in CMASS we detect a parity-odd 4PCF at $7.1σ$. Gravitational evolution alone does not produce this effect; parity-breaking in LSS, if cosmological in origin, must stem from the epoch of inflation. We have explored many sources of systematic error and found none that can produce a spurious parity-odd \textit{signal} sufficient to explain our result. Underestimation of the \textit{noise} could also lead to a spurious detection. Our reported significances presume that the mock catalogs used to calculate the covariance sufficiently capture the covariance of the true data. We have performed numerous tests to explore this issue. The odd-parity 4PCF opens a new avenue for probing new forces during the epoch of inflation with 3D LSS; such exploration is timely given large upcoming spectroscopic samples such as DESI and Euclid.

astro-ph.CO↗

arXiv2022

Accelerating BAO Scale Fitting Using Taylor Series

The Universe is currently undergoing accelerated expansion driven by dark energy. Dark energy's essential nature remains mysterious: one means of revealing it is by measuring the Universe's size at different redshifts. This may be done using the Baryon Acoustic Oscillation (BAO) feature, a standard ruler in the galaxy 2-Point Correlation Function (2PCF). In order to measure the distance scale, one dilates and contracts a template for the 2PCF in a fiducial cosmology, using a scaling factor $α$. The standard method for finding the best-fit $α$ is to compute the likelihood over a grid of roughly 100 values of it. This approach is slow; in this work, we propose a significantly faster way. Our method writes the 2PCF as a polynomial in $α$ by Taylor-expanding it about $α= 1$, exploiting that we know the fiducial cosmology sufficiently well that $α$ is within a few percent of unity. The likelihood resulting from this expansion may then be analytically solved for the best-fit $α$. Our method is 48-85$\times$ faster than a directly comparable approach in which we numerically minimize $α$, and $\sim$$12,000 \times$ faster than the standard iterative method. Our work will be highly enabling for upcoming large-scale structure redshift surveys such as that by Dark Energy Spectroscopic Instrument (DESI).

astro-ph.CO↗

arXiv2022

SARABANDE: 3/4 Point Correlation Functions with Fast Fourier Transforms

We present a new $\texttt{python}$ package SARABANDE for measuring 3 & 4 Point Correlation Functions (3/4 PCFs) in $\mathcal{O}(N_{\rm g} \log N_{\rm g})$ time using Fast Fourier Transforms (FFTs), with $N_{\rm g}$ the number of grid points used for the FFT. SARABANDE can measure both projected and full 3 and 4 PCFs on gridded 2D and 3D datasets. The general technique is to generate suitable angular basis functions on an underlying grid, radially bin these to create kernels, and convolve these kernels with the original gridded data to obtain expansion coefficients about every point simultaneously. These coefficients are then combined to give us the 3/4 PCF as expanded in our basis. We apply SARABANDE to simulations of the Interstellar Medium (ISM) to show the results and scaling of calculating both the full and projected 3/4 PCFs.

astro-ph.IM↗

arXiv2022

The MegaMapper: A Stage-5 Spectroscopic Instrument Concept for the Study of Inflation and Dark Energy

In this white paper, we present the MegaMapper concept. The MegaMapper is a proposed ground-based experiment to measure Inflation parameters and Dark Energy from galaxy redshifts at $2<z<5$. In order to achieve path-breaking results with a mid-scale investment, the MegaMapper combines existing technologies for critical path elements and pushes innovative development in other design areas. To this aim, we envision a 6.5-m Magellan-like telescope, with a newly designed wide field, coupled with DESI spectrographs, and small-pitch robots to achieve multiplexing of at least 26,000. This will match the expected achievable target density in the redshift range of interest and provide a 10x capability over the existing state-of the art, without a 10x increase in project budget.

astro-ph.IM↗

arXiv2022

A Spectroscopic Road Map for Cosmic Frontier: DESI, DESI-II, Stage-5

In this white paper, we present an experimental road map for spectroscopic experiments beyond DESI. DESI will be a transformative cosmological survey in the 2020s, mapping 40 million galaxies and quasars and capturing a significant fraction of the available linear modes up to z=1.2. DESI-II will pilot observations of galaxies both at much higher densities and extending to higher redshifts. A Stage-5 experiment would build out those high-density and high-redshift observations, mapping hundreds of millions of stars and galaxies in three dimensions, to address the problems of inflation, dark energy, light relativistic species, and dark matter. These spectroscopic data will also complement the next generation of weak lensing, line intensity mapping and CMB experiments and allow them to reach their full potential.

astro-ph.CO↗

arXiv2022

Efficient Computation of $N$-point Correlation Functions in $D$ Dimensions

We present efficient algorithms for computing the $N$-point correlation functions (NPCFs) of random fields in arbitrary $D$-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences, and provide a natural tool to describe stochastic processes. algorithms for computing the NPCF components have $\mathcal{O}(n^N)$ complexity (for a data set containing $n$ particles); their application is thus computationally infeasible unless $N$ is small. By projecting the statistic onto a suitably-defined angular basis, we show that the estimators can be written in a separable form, with complexity $\mathcal{O}(n^2)$, or $\mathcal{O}(n_{\rm g}\log n_{\rm g})$ if evaluated using a Fast Fourier Transform on a grid of size $n_{\rm g}$. Our decomposition is built upon the $D$-dimensional hyperspherical harmonics; these form a complete basis on the $(D-1)$-sphere and are intrinsically related to angular momentum operators. Concatenation of $(N-1)$ such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. As $N$ and $D$ grow, the number of basis components quickly becomes large, providing a practical limitation to this (and all other) approaches: however, the dimensionality is greatly reduced in the presence of symmetries; for example, isotropic correlation functions require only states of zero combined angular momentum. We provide a \textsc{Julia} package implementing our estimators, and show how they can be applied to a variety of scenarios within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.

astro-ph.IM↗

arXiv2021

On a General Method for Resolving Integrals of Multiple Spherical Bessel Functions Against Power Laws into Distributions

We here present a method of performing integrals of products of spherical Bessel functions (SBFs) weighted by a power-law. Our method, which begins with double-SBF integrals, exploits a differential operator $\hat{D}$ defined via Bessel's differential equation. Application of this operator raises the power-law in steps of two. We also here display a suitable base integral expression to which this operator can be applied for both even and odd cases. We test our method by showing that it reproduces previously-known solutions. Importantly, it also goes beyond them, offering solutions in terms of singular distributions, Heaviside functions, and Gauss's hypergeometric,$\;_2{\rm F}_1$ for $all$ double-SBF integrals with positive semi-definite integer power-law weight. We then show how our method for double-SBF integrals enables evaluating $arbitrary$ triple-SBF overlap integrals, going beyond the cases currently in the literature. This in turn enables reduction of arbitrary quadruple, quintuple, and sextuple-SBF integrals and beyond into tractable forms.

math.CA↗

arXiv2021

Clustering in Massive Neutrino Cosmologies via Eulerian Perturbation Theory

We introduce an Eulerian Perturbation Theory to study the clustering of tracers for cosmologies in the presence of massive neutrinos. Our approach is based on mapping recently-obtained Lagrangian Perturbation Theory results to the Eulerian framework. We add Effective Field Theory counterterms, IR-resummations and a biasing scheme to compute the one-loop redshift-space power spectrum. To assess our predictions, we compare the power spectrum multipoles against synthetic halo catalogues from the Quijote simulations, finding excellent agreement on scales $k\lesssim 0.25 \,h \text{Mpc}^{-1}$. One can obtain the same fitting accuracy using higher wave-numbers, but then the theory fails to give a correct estimation of the linear bias parameter. We further discuss the implications for the tree-level bispectrum. Finally, calculating loop corrections is computationally costly, hence we derive an accurate approximation wherein we retain only the main features of the kernels, as produced by changes to the growth rate. As a result, we show how FFTLog methods can be used to further accelerate the loop computations with these reduced kernels.

astro-ph.CO↗

arXiv2021

A Test for Cosmological Parity Violation Using the 3D Distribution of Galaxies

We show that the galaxy 4-Point Correlation Function (4PCF) can test for cosmological parity violation. The detection of cosmological parity violation would reflect previously unknown forces present at the earliest moments of the Universe. Recent developments both in rapidly evaluating galaxy $N$-Point Correlation Functions (NPCFs) and in determining the corresponding covariance matrices make the search for parity violation in the 4PCF possible in current and upcoming surveys such as those undertaken by Dark Energy Spectroscopic Instrument (DESI), the $Euclid$ satellite, and the Vera C. Rubin Observatory (VRO).

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