arXiv subjects

Mark C. Neyrinck

Publications and source records attributed to Mark C. Neyrinck.

At least 37 records · Page 2Linked to original sources

arXiv2015

The Persistent Percolation of Single-Stream Voids

We study the nature of voids defined as single-stream regions that have not undergone shell-crossing. We use ORIGAMI to determine the cosmic web morphology of each dark matter particle in a suite of cosmological $N$-body simulations, which explicitly calculates whether a particle has crossed paths with others along multiple sets of axes and does not depend on a parameter or smoothing scale. The theoretical picture of voids is that of expanding underdensities with borders defined by shell-crossing. We find instead that locally underdense single-stream regions are not bounded on all sides by multi-stream regions, thus they percolate, filling the simulation volume; we show that the set of multi-stream particles also percolates. This percolation persists to high resolution, where the mass fraction of single-stream voids is low, because the volume fraction remains high; we speculate on the fraction of collapsed mass in the continuum limit of infinite resolution. By introducing a volume threshold parameter to define underdense void "cores", we create a catalog of ORIGAMI voids which consist entirely of single-stream particles and measure their percolation properties, volume functions, and average densities.

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arXiv2014

An Origami Approximation to the Cosmic Web

The powerful Lagrangian view of structure formation was essentially introduced to cosmology by Zel'dovich. In the current cosmological paradigm, a dark-matter-sheet 3D manifold, inhabiting 6D position-velocity phase space, was flat (with vanishing velocity) at the big bang. Afterward, gravity stretched and bunched the sheet together in different places, forming a cosmic web when projected to the position coordinates. Here, I explain some properties of an origami approximation, in which the sheet does not stretch or contract (an assumption that is false in general), but is allowed to fold. Even without stretching, the sheet can form an idealized cosmic web, with convex polyhedral voids separated by straight walls and filaments, joined by convex polyhedral nodes. The nodes form in 'polygonal' or 'polyhedral' collapse, somewhat like spherical/ellipsoidal collapse, except incorporating simultaneous filament and wall formation. The origami approximation allows phase-space geometries of nodes, filaments, and walls to be more easily understood, and may aid in understanding spin correlations between nearby galaxies. This contribution explores kinematic origami-approximation models giving velocity fields for the first time.

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arXiv2014

Star Formation Isochrone Surfaces: Clues on Star Formation Quenching in Dense Environments

The star formation history of galaxies is a complex process usually considered to be stochastic in nature, for which we can only give average descriptions such as the color-density relation. In this work we follow star-forming gas particles in a hydrodynamical N-body simulation back in time in order to study their initial spatial configuration. By keeping record of the time when a gas particle started forming stars we can produce gas-star isochrone surfaces delineating the surfaces of accreting gas that begin producing stars at different times. These accretion surfaces are closely packed inside dense regions, intersecting each other, and as a result galaxies inside proto-clusters stop accreting gas early, naturally explaining the color dependence on density. The process described here has a purely gravitational / geometrical origin, arguably operating at a more fundamental level than complex processes such as AGN and supernovae, and providing a conceptual origin for the color-density relation.

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arXiv2014

Kinematic Morphology of Large-scale Structure: Evolution from Potential to Rotational Flow

As an alternative way of describing the cosmological velocity field, we discuss the evolution of rotational invariants constructed from the velocity gradient tensor. Compared with the traditional divergence-vorticity decomposition, these invariants, defined as coefficients of characteristic equation of the velocity gradient tensor, enable a complete classification of all possible flow patterns in the dark-matter comoving frame, including both potential and vortical flows. We show that this tool, first introduced in turbulence two decades ago, proves to be very useful in understanding the evolution of the cosmic web structure, and in classifying its morphology. Before shell-crossing, different categories of potential flow are highly associated with cosmic web structure, because of the coherent evolution of density and velocity. This correspondence is even preserved at some level when vorticity is generated after shell-crossing. The evolution from the potential to vortical flow can be traced continuously by these invariants. With the help of this tool, we show that the vorticity is generated in a particular way that is highly correlated with the large-scale structure. This includes a distinct spatial distribution and different types of alignment between cosmic web and vorticity direction for various vortical flows. Incorporating shell-crossing into closed dynamical systems is highly non-trivial, but we propose a possible statistical explanation for some of these phenomena relating to the internal structure of the three-dimensional invariants space.

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arXiv2014

Transformationally decoupling clustering and tracer bias

Gaussianizing transformations are used statistically in many non-cosmological fields, but in cosmology, we are only starting to apply them. Here I explain a strategy of analyzing the 1-point function (PDF) of a spatial field, together with the 'essential' clustering statistics of the Gaussianized field, which are invariant to a local transformation. In cosmology, if the tracer sampling is sufficient, this achieves two important goals. First, it can greatly multiply the Fisher information, which is negligible on nonlinear scales in the usual $δ$ statistics. Second, it decouples clustering statistics from a local bias description for tracers such as galaxies.

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arXiv2014

A halo bias function measured deeply into voids without stochasticity

We study the relationship between dark-matter haloes and matter in the MIP $N$-body simulation ensemble, which allows precision measurements of this relationship, even deeply into voids. What enables this is a lack of discreteness, stochasticity, and exclusion, achieved by averaging over hundreds of possible sets of initial small-scale modes, while holding fixed large-scale modes that give the cosmic web. We find (i) that dark-matter-halo formation is greatly suppressed in voids; there is an exponential downturn at low densities in the otherwise power-law matter-to-halo density bias function. Thus, the rarity of haloes in voids is akin to the rarity of the largest clusters, and their abundance is quite sensitive to cosmological parameters. The exponential downturn appears both in an excursion-set model, and in a model in which fluctuations evolve in voids as in an open universe with an effective $Ω_m$ proportional to a large-scale density. We also find that (ii) haloes typically populate the average halo-density field in a super-Poisson way, i.e. with a variance exceeding the mean; and (iii) the rank-order-Gaussianized halo and dark-matter fields are impressively similar in Fourier space. We compare both their power spectra and cross-correlation, supporting the conclusion that one is roughly a strictly-increasing mapping of the other. The MIP ensemble especially reveals how halo abundance varies with `environmental' quantities beyond the local matter density; (iv) we find a visual suggestion that at fixed matter density, filaments are more populated by haloes than clusters.

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arXiv2014

A Possible Cold Imprint of Voids on the Microwave Background Radiation

We measure the average temperature decrement on the cosmic microwave background (CMB) produced by voids selected in the SDSS DR7 spectroscopic redshift galaxy catalog, spanning redshifts $0<z<0.44$. We find an imprint of amplitude between 2.6 and 2.9$μK$ as viewed through a compensated top-hat filter scaled to the radius of each void; we assess the statistical significance of the imprint at ~2$σ$. We make crucial use of $N$-body simulations to calibrate our analysis. As expected, we find that large voids produce cold spots on the CMB through the Integrated Sachs-Wolfe (ISW) effect. However, we also find that small voids in the halo density field produce hot spots, because they reside in contracting, larger-scale overdense regions. This is an important effect to consider when stacking CMB imprints from voids of different radius. We have found that the same filter radius that gives the largest ISW signal in simulations also yields close to the largest detected signal in the observations. However, although it is low in significance, our measured signal is much higher-amplitude than expected from ISW in the concordance $Λ$CDM universe. The discrepancy is also at the ~2$σ$ level. We have demonstrated that our result is robust against the varying of thresholds over a wide range.

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arXiv2013

ORIGAMI: Delineating Cosmic Structures with Phase-Space Folds

Structures like galaxies and filaments of galaxies in the Universe come about from the origami-like folding of an initially flat three-dimensional manifold in 6D phase space. The ORIGAMI method identifies these structures in a cosmological simulation, delineating the structures according to their outer folds. Structure identification is a crucial step in comparing cosmological simulations to observed maps of the Universe. The ORIGAMI definition is objective, dynamical and geometric: filament, wall and void particles are classified according to the number of orthogonal axes along which dark-matter streams have crossed. Here, we briefly review these ideas, and speculate on how ORIGAMI might be useful to find cosmic voids.

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arXiv2013

Ringing the initial Universe: the response of overdensity and transformed-density power spectra to initial spikes

We present an experiment in which we 'ring' a set of cosmological N-body-simulation initial conditions, placing spikes in the initial power spectrum at different wavenumber bins. We then measure where these spikes end up in the final conditions. In the usual overdensity power spectrum, most sensitive to contracting and collapsing dense regions, initial power on slightly non-linear scales (k ~ 0.3 h/Mpc) smears to smaller scales, coming to dominate the initial power once there. Log-density and Gaussianized-density power spectra, sensitive to low-density (expanding) and high-density regions, respond differently: initial spikes spread symmetrically in scale, both upward and downward. In fact, in the power spectrum of 1/(1 + δ), spikes migrate to larger scales, showing the magnifying effect of voids on small-scale modes. These power spectra show much greater sensitivity to small-scale initial features. We also test the difference between an approximation of the Ly-α flux field, and its Gaussianized form, and give a toy model that qualitatively explains the symmetric power spreading in Gaussianized-density power spectra. Also, we discuss how to use this framework to estimate power-spectrum covariance matrices. This can be used to track the fate of information in the Universe, that takes the form of initial degrees of freedom, one random spike per initial mode.

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arXiv2012

Removing BAO-peak Shifts with Local Density Transforms

Large-scale bulk flows in the Universe distort the initial density field, broadening the baryon-acoustic-oscillation (BAO) feature that was imprinted when baryons were strongly coupled to photons. Additionally, there is a small shift inward in the peak of the conventional overdensity correlation function, a mass-weighted statistic. This shift occurs when high density peaks move toward each other. We explore whether this shift can be removed by applying to the density field a transform (such as a logarithm) that gives fairer statistical weight to fluctuations in underdense regions. Using configuration-space perturbation theory in the Zel'dovich approximation, we find that the log-density correlation function shows a much smaller inward shift in the position of the BAO peak at low redshift than is seen in the overdensity correlation function. We also show that if the initial, Lagrangian density of matter parcels could be estimated at their Eulerian positions, giving a displaced-initial-density field, its peak shift would be even smaller. In fact, a transformed field that accentuates underdensities, such as the reciprocal of the density, pushes the peak the other way, outward. In our model, these shifts in the peak position can be attributed to shift terms, involving the derivative of the linear correlation function, that entirely vanish in this displaced-initial-density field.

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arXiv2012

Quantifying distortions of the Lagrangian dark-matter mesh in cosmology

We examine the Lagrangian divergence of the displacement field, arguably a more natural object than the density in a Lagrangian description of cosmological large-scale structure. This quantity, which we denote ψ, quantifies the stretching and distortion of the initially homogeneous lattice of dark-matter particles in the universe. ψ encodes similar information as the density, but the correspondence has subtleties. It corresponds better to the log-density A than the overdensity δ. A Gaussian distribution in ψ produces a distribution in A with slight skewness; in δ, we find that in many cases the skewness is further increased by 3. A local spherical-collapse-based (SC) fit found by Bernardeau gives a formula for ψ's particle-by-particle behavior that works quite well, better than applying Lagrangian perturbation theory (LPT) at first or second (2LPT) order. In 2LPT, there is a roughly parabolic relation between initial and final ψ that can give overdensities in deep voids, so low-redshift, high-resolution 2LPT realizations should be used with caution. The SC fit excels at predicting ψ until streams cross; then, for particles forming haloes, ψ plummets as in a waterfall to -3. This gives a new method for producing N-particle realizations. Compared to LPT realizations, such SC realizations give reduced stream-crossing, and better visual and 1-point-PDF correspondence to the results of full gravity. LPT, on the other hand, predicts large-scale flows and the large-scale power-spectrum amplitude better, unless an empirical correction is added to the SC formula.

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arXiv2012

Origami constraints on the initial-conditions arrangement of dark-matter caustics and streams

In a cold-dark-matter universe, cosmological structure formation proceeds in rough analogy to origami folding. Dark matter occupies a three-dimensional 'sheet' of free- fall observers, non-intersecting in six-dimensional velocity-position phase space. At early times, the sheet was flat like an origami sheet, i.e. velocities were essentially zero, but as time passes, the sheet folds up to form cosmic structure. The present paper further illustrates this analogy, and clarifies a Lagrangian definition of caustics and streams: caustics are two-dimensional surfaces in this initial sheet along which it folds, tessellating Lagrangian space into a set of three-dimensional regions, i.e. streams. The main scientific result of the paper is that streams may be colored by only two colors, with no two neighbouring streams (i.e. streams on either side of a caustic surface) colored the same. The two colors correspond to positive and negative parities of local Lagrangian volumes. This is a severe restriction on the connectivity and therefore arrangement of streams in Lagrangian space, since arbitrarily many colors can be necessary to color a general arrangement of three-dimensional regions. This stream two-colorability has consequences from graph theory, which we explain. Then, using N-body simulations, we test how these caustics correspond in Lagrangian space to the boundaries of haloes, filaments and walls. We also test how well outer caustics correspond to a Zel'dovich-approximation prediction.

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arXiv2012

Tessellating the cosmological dark-matter sheet: origami creases in the universe and ways to find them

Tessellations are valuable both conceptually and for analysis in the study of the large-scale structure of the universe. They provide a conceptual model for the 'cosmic web,' and are of great use to analyze cosmological data. Here we describe tessellations in another set of coordinates, of the initially flat sheet of dark matter that gravity folds up in rough analogy to origami. The folds that develop are called caustics, and they tessellate space into stream regions. Tessellations of the dark-matter sheet are also useful in simulation analysis, for instance for density measurement, and to identify structures where streams overlap.

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arXiv2012

ORIGAMI: Delineating Halos using Phase-Space Folds

We present the ORIGAMI method of identifying structures, particularly halos, in cosmological N-body simulations. Structure formation can be thought of as the folding of an initially flat three-dimensional manifold in six-dimensional phase space. ORIGAMI finds the outer folds that delineate these structures. Halo particles are identified as those that have undergone shell-crossing along 3 orthogonal axes, providing a dynamical definition of halo regions that is independent of density. ORIGAMI also identifies other morphological structures: particles that have undergone shell-crossing along 2, 1, or 0 orthogonal axes correspond to filaments, walls, and voids respectively. We compare this method to a standard Friends-of-Friends halo-finding algorithm and find that ORIGAMI halos are somewhat larger, more diffuse, and less spherical, though the global properties of ORIGAMI halos are in good agreement with other modern halo-finding algorithms.

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arXiv2012

On the inadequacy of N-point correlation functions to describe nonlinear cosmological fields: explicit examples and connection to simulations

Motivated by recent results on lognormal statistics showing that the moment hierarchy of a lognormal variable completely fails at capturing its information content in the large variance regime, we discuss in this work the inadequacy of the hierarchy of correlation functions to describe a correlated lognormal field, which provides a roughly accurate description of the non-linear cosmological matter density field. We present families of fields having the same hierarchy of correlation functions than the lognormal field at all orders. This explicitly demonstrates the little studied though known fact that the correlation function hierarchy never provides a complete description of a lognormal field, and that it fails to capture information in the non-linear regime, where other simple observables are left totally unconstrained. We discuss why perturbative, Edgeworth-like approaches to statistics in the non-linear regime, common in cosmology, can never reproduce or predict that effect, and why it is however generic for tailed fields, hinting at a breakdown of the perturbation theory based on the field fluctuations. We make a rough but successful quantitative connection to N-body simulations results, that showed that the spectrum of the log-density field carries more information than the spectrum of the field entering the non-linear regime.

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arXiv2011

Straightening the Density-Displacement Relation with a Logarithmic Transform

We investigate the use of a logarithmic density variable in estimating the Lagrangian displacement field, motivated by the success of a logarithmic transformation in restoring information to the matter power spectrum. The logarithmic relation is an extension of the linear relation, motivated by the continuity equation, in which the density field is assumed to be proportional to the divergence of the displacement field; we compare the linear and logarithmic relations by measuring both of these fields directly in a cosmological N-body simulation. The relative success of the logarithmic and linear relations depends on the scale at which the density field is smoothed. Thus we explore several ways of measuring the density field, including Cloud-In-Cell smoothing, adaptive smoothing, and the (scale-independent) Delaunay tessellation, and we use both a Fourier space and a geometrical tessellation approach to measuring the divergence. We find that the relation between the divergence of the displacement field and the density is significantly tighter with a logarithmic density variable, especially at low redshifts and for very small (~2 Mpc/h) smoothing scales. We find that the grid-based methods are more reliable than the tessellation-based method of calculating both the density and the divergence fields, though in both cases the logarithmic relation works better in the appropriate regime, which corresponds to nonlinear scales for the grid-based methods and low densities for the tessellation-based method.

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arXiv2011

Rejuvenating the Matter Power Spectrum III: The Cosmology Sensitivity of Gaussianized Power Spectra

It was recently shown that applying a Gaussianizing transform, such as a logarithm, to the nonlinear matter density field extends the range of useful applicability of the power spectrum by a factor of a few smaller. Such a transform dramatically reduces nonlinearities in both the covariance and the shape of the power spectrum. Here, analyzing Coyote Universe real-space dark matter density fields, we investigate the consequences of these transforms for cosmological parameter estimation. The power spectrum of the log-density provides the tightest cosmological parameter error bars (marginalized or not), giving a factor of 2-3 improvement over the conventional power spectrum in all five parameters tested. For the tilt, n_s, the improvement reaches a factor of 5. Similar constraints are achieved if the log-density power spectrum and conventional power spectrum are analyzed together. Rank-order Gaussianization seems just as useful as a log transform to constrain n_s, but not other parameters. Dividing the overdensity by its dispersion in few-Mpc cells, while it diagonalizes the covariance matrix, does not seem to help with parameter constraints. We also provide a code that emulates these power spectra over a range of concordance cosmological models.

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arXiv2011

Gaussianization: Enhancing the Statistical Power of the Power Spectrum

The power spectrum is widely used in astronomy, to analyze temporal or spatial structure. In cosmology, it is used to quantify large-scale structure (LSS) and the cosmic microwave background (CMB). This is because the power spectrum completely quantifies Gaussian random fields, which the CMB and LSS fields seem to be at early epochs. However, at late epochs and small scales, cosmological density fields become highly non-Gaussian. The power spectrum loses power to describe LSS and CMB fields on small scales, most obviously through high covariance in the power spectrum as a function of scale. Practically, this significantly degrades constraints that observations can place on cosmological parameters. However, if a nonlinear transformation that produces a (more) Gaussian 1-point distribution is applied to a field, the extra covariance in the field's power spectrum can be dramatically reduced. In the case of the roughly lognormal low-redshift matter density field, a log transform accomplishes this. Applying a log transform to the density field before measuring the power spectrum also tightens cosmological parameter constraints by a factor of several.

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