Shaun Hotchkiss

University of Sussex, Brighton, England, United Kingdom

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Publications (22)101.16 Total impact

  • Seshadri Nadathur, Shaun Hotchkiss
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    ABSTRACT: Cosmic voids may be very useful in testing fundamental aspects of cosmology. Yet observationally voids can only be seen as regions with a deficit of bright galaxies. To study how biased galaxies trace matter underdensities and how the properties of voids depend on those of the tracer galaxy population, we use a $\Lambda$CDM N-body simulation populated with mock galaxies based on the halo occupation distribution (HOD) model. We identify voids in these mocks using the ZOBOV void finder and measure their abundances, sizes, tracer densities, and dark matter content. To separate the effects of bias from those of sampling density, we do the same for voids traced by randomly down-sampled subsets of the dark matter particles in the simulation. We find that galaxy bias reduces the total number of voids by $\sim50\%$ and can dramatically change their size distribution. The matter content of voids in biased and unbiased tracers also differs. Using simulations to accurately estimate the cosmological constraints that can be obtained from voids therefore requires the use of realistic mock galaxy catalogues. We discuss aspects of the dark matter content of voids that can be deduced from properties of the tracer distribution, such as the void size and the minimum tracer number density. In particular we consider the compensation of the total mass deficit in voids and find that the distinction between over- and under-compensated voids is not a function of void size alone, as has previously been suggested. However, we find a simple linear relationship between the average density of tracers in the void and the total mass compensation on much larger scales. The existence of this linear relationship holds independent of the bias and sampling density of the tracers. This provides a universal tool to classify void environments and will be important for the use of voids in observational cosmology.
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    Seshadri Nadathur, Shaun Hotchkiss
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    ABSTRACT: The statistical study of voids in the matter distribution promises to be an important tool for precision cosmology, but there are known discrepancies between theoretical models of voids and the voids actually found in large simulations or galaxy surveys. The empirical properties of observed voids are also not well understood. In this paper we study voids in an N-body simulation, using the ZOBOV watershed algorithm. As in other studies, we use sets of subsampled dark matter particles as tracers to identify voids, but we use the full-resolution simulation output to measure dark matter densities at the identified locations. Voids span a wide range of sizes and densities, but there is a clear trend towards larger voids containing deeper density minima, a trend which is expected for all watershed void finders. We also find that the tracer density at void locations is smaller than the true density, and that this relationship depends on the sampling density of tracers. We show that fitting functions given in the literature fail to match the density profiles of voids either quantitatively or qualitatively. The average enclosed density contrast within watershed voids varies widely with both the size of the void and the minimum density within it, but is always far from the shell-crossing threshold expected from theoretical models. Voids with deeper density minima also show much broader density profiles. We discuss the implications of these results for the excursion set approach to modelling such voids.
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    ABSTRACT: We discuss the universality and self-similarity of void density profiles, for voids in realistic mock luminous red galaxy (LRG) catalogues from the Jubilee simulation, as well as in void catalogues constructed from the SDSS LRG and Main Galaxy samples. Voids are identified using a modified version of the ZOBOV watershed transform algorithm, with additional selection cuts. We find that voids in simulation are self-similar, meaning that their average rescaled profile does not depend on the void size, or -- within the range of the simulated catalogue -- on the redshift. Comparison of the profiles obtained from simulated and real voids shows an excellent match. The profiles of real voids also show a universal behaviour over a wide range of galaxy luminosities, number densities and redshifts. This points to a fundamental property of the voids found by the watershed algorithm, which can be exploited in future studies of voids.
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    ABSTRACT: The discovery of a void of size $\sim200\;h^{-1}$Mpc and average density contrast of $\sim-0.1$ aligned with the Cold Spot direction has been recently reported. It has been argued that, although the first-order integrated Sachs-Wolfe (ISW) effect of such a void on the CMB is small, the second-order Rees-Sciama (RS) contribution exceeds this by an order of magnitude and can entirely explain the observed Cold Spot temperature profile. In this paper we examine this surprising claim using both an exact calculation with the spherically symmetric Lema\^itre--Tolman--Bondi metric, and perturbation theory about a background Friedmann--Robertson--Walker (FRW) metric. We show that both approaches agree well with each other, and both show that the dominant temperature contribution of the postulated void is an unobservable dipole anisotropy. If this dipole is subtracted, we find that the remaining temperature anisotropy is dominated by the linear ISW signal, which is orders of magnitude larger than the second-order RS effect, and that the total magnitude is too small to explain the observed Cold Spot profile. We calculate the density and size of a void that would be required to explain the Cold Spot, and show that the probability of existence of such a void is essentially zero in $\Lambda$CDM. We identify the importance of \emph{a posteriori} selection effects in the identification of the Cold Spot, but argue that even after accounting for them, a supervoid explanation of the Cold Spot is always disfavoured relative to a random statistical fluctuation on the last scattering surface.
    Physical Review D 08/2014; 90(10). DOI:10.1103/PhysRevD.90.103510 · 4.86 Impact Factor
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    ABSTRACT: The stacked density profile of cosmic voids in the galaxy distribution provides an important tool for the use of voids for precision cosmology. We study the density profiles of voids identified using the ZOBOV watershed transform algorithm in realistic mock luminous red galaxy (LRG) catalogues from the Jubilee simulation, as well as in void catalogues constructed from the SDSS LRG and Main Galaxy samples. We compare different methods for reconstructing density profiles scaled by the void radius and show that the most commonly used method based on counts in shells and simple averaging is statistically flawed as it underestimates the density in void interiors. We provide two alternative methods that do not suffer from this effect; one based on Voronoi tessellations is also easily able to account from artefacts due to finite survey boundaries and so is more suitable when comparing simulation data to observation. Using this method we show that voids in simulation are exactly self-similar, meaning that their average rescaled profile does not depend on the void size. Within the range of our simulation we also find no redshift dependence of the profile. Comparison of the profiles obtained from simulated and real voids shows an excellent match. The profiles of real voids also show a universal behaviour over a wide range of galaxy luminosities, number densities and redshifts. This points to a fundamental property of the voids found by the watershed algorithm, which can be exploited in future studies of voids.
    Monthly Notices of the Royal Astronomical Society 07/2014; 449(4). DOI:10.1093/mnras/stv513 · 5.23 Impact Factor
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    ABSTRACT: We examine the integrated Sachs-Wolfe (ISW) imprint of voids and superclusters on the cosmic microwave background. We first study results from the Jubilee N-body simulation, which models the full-sky ISW signal from structures out to redshift z=1.4 and provides a mock luminous red galaxy (LRG) catalogue, to confirm that the expected signal in the concordance \Lambda CDM model is very small and likely to always be much smaller than the anisotropies arising at the last scattering surface. Any current detections of such an imprint cannot, therefore, be caused by an ISW effect in a \Lambda CDM universe. Using the simulation as a guide, we then look for the signal using a catalogue of voids and superclusters from the Sloan Digital Sky Survey. We find a result that is consistent with the \Lambda CDM model, i.e. a signal consistent with zero.
    Monthly Notices of the Royal Astronomical Society 05/2014; 446(2). DOI:10.1093/mnras/stu2072 · 5.23 Impact Factor
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    ABSTRACT: We examine the integrated Sachs-Wolfe (ISW) imprint of voids and superclusters on the cosmic microwave background. We first study results from the Jubilee N-body simulation, which models the full-sky ISW signal from structures out to redshift z=1.4 and provides a mock luminous red galaxy (LRG) catalogue, to confirm that the expected signal in the concordance \Lambda CDM model is very small and likely to always be much smaller than the anisotropies arising at the last scattering surface. Any current detections of such an imprint cannot, therefore, be caused by an ISW effect in a \Lambda CDM universe. Using the simulation as a guide, we then look for the signal using a catalogue of voids and superclusters from the Sloan Digital Sky Survey. We find a result that is consistent with the \Lambda CDM model, i.e. a signal consistent with zero.
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    ABSTRACT: We present initial results from the Jubilee Integrated Sachs-Wolfe (ISW) project, which models the expected Λ cold dark matter ISW effect in the Jubilee simulation. The simulation volume is (6 h-1 Gpc)3, allowing power on very large scales to be incorporated into the calculation. Haloes are resolved down to a mass of 1.5 × 1012 h-1 M☉, which allows us to derive a catalogue of mock Luminous Red Galaxies (LRGs) for cross-correlation analysis with the ISW signal. We find the ISW effect observed on a projected sky to grow stronger at late times with the evolution of the ISW power spectrum matching expectations from linear theory. Maps of the gravitational-lensing effect are calculated using the same potential as for the ISW. We calculate the redshift dependence of the ISW-LRG cross-correlation signal for a full-sky survey with no noise considerations. For ℓ < 30, the signal is strongest for lower redshift bins (z ̃ 0.2-0.5), whereas for ℓ > 30, the signal is best observed with surveys covering z ̃ 0.6-1.0.
    Monthly Notices of the Royal Astronomical Society 01/2014; 438(1). DOI:10.1093/mnras/stt2208 · 5.23 Impact Factor
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    Seshadri Nadathur, Shaun Hotchkiss
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    ABSTRACT: Sutter et al. have responded to the criticisms we made of their cosmic void catalogue in our recent paper presenting an alternative catalogue (Nadathur & Hotchkiss 2013). Unfortunately, their response contains several statements which are incorrect, as we point out in this note.
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    Seshadri Nadathur, Shaun Hotchkiss
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    ABSTRACT: The study of the interesting cosmological properties of voids in the Universe depends on the efficient and robust identification of such voids in galaxy redshift surveys. Recently, Sutter et al. (2012) have published a public catalogue of voids in the Sloan Digital Sky Survey Data Release 7 main galaxy and luminous red galaxy samples, using the void-finding algorithm ZOBOV, which is based on the watershed transform. We examine the properties of this catalogue and show that it suffers from several inconsistencies and errors, including the identification of some extremely overdense regions as voids. As a result, cosmological results obtained using this catalogue need to be reconsidered. We provide instead an alternative, self-consistent, public catalogue of voids in the same galaxy data, obtained from using an improved version of the same watershed transform algorithm. We provide a more robust method of dealing with survey boundaries and masks, as well as with a radially varying selection function, which means that our method can be applied to any other survey. We discuss some basic properties of the voids thus discovered, and describe how further information may be obtained from the catalogue. In addition, we apply an inversion of the algorithm to the same data to obtain a corresponding catalogue of large-scale overdense structures, or "superclusters".
    Monthly Notices of the Royal Astronomical Society 10/2013; 440(2). DOI:10.1093/mnras/stu349 · 5.23 Impact Factor
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    Samuel Flender, Shaun Hotchkiss
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    ABSTRACT: We investigate the hemispherical power asymmetry in the cosmic microwave background on small angular scales. We find an anomalously high asymmetry in the multipole range l=601-2048, with a naive statistical significance of 6.5 sigma. However, we show that this extreme anomaly is simply a coincidence of three other effects, relativistic power modulation, edge effects from the mask applied, and inter-scale correlations. After correcting for all of these effects, the significance level drops to ~1 sigma, i.e., there is no anomalous intrinsic asymmetry in the small angular scales. Using this null result, we derive a constraint on a potential dipolar modulation amplitude, A(k)<0.0045 on the ~10 Mpc-scale, at 95% C.L. This new constraint must be satisfied by any theoretical model attempting to explain the hemispherical asymmetry at large angular scales.
    Journal of Cosmology and Astroparticle Physics 07/2013; DOI:10.1088/1475-7516/2013/09/033 · 5.88 Impact Factor
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    Samuel Flender, Shaun Hotchkiss, Seshadri Nadathur
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    ABSTRACT: A detection of the stacked integrated Sachs-Wolfe (ISW) signal in the CMB of rare superstructures identified in the SDSS Luminous Red Galaxy catalogue has been reported at very high statistical significance. The magnitude of the observed signal has previously been argued to be more than 3 standard deviations larger than the theoretical \Lambda CDM expectation. However, this calculation was made in the linear approximation, and relied on assumptions that may potentially have caused the \Lambda CDM expectation to be underestimated. Here we update the theoretical model calculation and compare it with an analysis of ISW maps obtained from N-body simulations of a \Lambda CDM universe. The differences between model predictions and the map analyses are found to be small and cannot explain the discrepancy with observation, which remains at >3 s.d. significance. We discuss the cosmological significance of this anomaly and speculate on the potential of alternative models to explain it.
    Journal of Cosmology and Astroparticle Physics 12/2012; 2013(02). DOI:10.1088/1475-7516/2013/02/013 · 5.88 Impact Factor
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    Ian Harrison, Shaun Hotchkiss
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    ABSTRACT: We consider methods with which to answer the question "is any observed galaxy cluster too unusual for Lambda-CDM?" After emphasising that many previous attempts to answer this question will overestimate the confidence level at which Lambda-CDM can be ruled out, we outline a consistent approach to these rare clusters, which allows the question to be answered. We define three statistical measures, each of which are sensitive to changes in cluster populations arising from different modifications to the cosmological model. We also use these properties to define the 'equivalent mass at redshift zero' for a cluster --- the mass of an equally unusual cluster today. This quantity is independent of the observational survey in which the cluster was found, which makes it an ideal proxy for ranking the relative unusualness of clusters detected by different surveys. These methods are then used on a comprehensive sample of observed galaxy clusters and we confirm that all are less than 2-sigma deviations from the Lambda-CDM expectation. Whereas we have only applied our method to galaxy clusters, it is applicable to any isolated, collapsed, halo. As motivation for future surveys, we also calculate where in the mass redshift plane the rarest halo is most likely to be found, giving information as to which objects might be the most fruitful in the search for new physics.
    Journal of Cosmology and Astroparticle Physics 10/2012; 2013(07). DOI:10.1088/1475-7516/2013/07/022 · 5.88 Impact Factor
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    Seshadri Nadathur, Shaun Hotchkiss, Subir Sarkar
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    ABSTRACT: A crucial diagnostic of the ΛCDM cosmological model is the integrated Sachs-Wolfe (ISW) effect of large-scale structure on the cosmic microwave background (CMB). The ISW imprint of superstructures of size ∼ 100 h−1Mpc at redshift z ∼ 0.5 has been detected with > 4σ significance, however it has been noted that the signal is much larger than expected. We revisit the calculation using linear theory predictions in ΛCDM cosmology for the number density of superstructures and their radial density profile, and take possible selection effects into account. While our expected signal is larger than previous estimates, it is still inconsistent by > 3σ with the observation. If the observed signal is indeed due to the ISW effect then huge, extremely underdense voids are far more common in the observed universe than predicted by ΛCDM.
    Journal of Cosmology and Astroparticle Physics 06/2012; 2012(06):042-042. DOI:10.1088/1475-7516/2012/06/042 · 5.88 Impact Factor
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    Ben Hoyle, Raul Jimenez, Licia Verde, Shaun Hotchkiss
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    ABSTRACT: We critically investigate current statistical tests applied to high redshift clusters of galaxies in order to test the standard cosmological model and describe their range of validity. We carefully compare a sample of high-redshift, massive, galaxy clusters with realistic Poisson sample simulations of the theoretical mass function, which include the effect of Eddington bias. We compare the observations and simulations using the following statistical tests: the distributions of ensemble and individual existence probabilities (in the > M, > z sense), the redshift distributions, and the 2d Kolmogorov-Smirnov test. Using seemingly rare clusters from Hoyle et al. (2011), and Jee et al. (2011) and assuming the same survey geometry as in Jee et al. (2011, which is less conservative than Hoyle et al. 2011), we find that the ( > M, > z) existence probabilities of all clusters are fully consistent with ΛCDM. However assuming the same survey geometry, we use the 2d K-S test probability to show that the observed clusters are not consistent with being the least probable clusters from simulations at > 95% confidence, and are also not consistent with being a random selection of clusters, which may be caused by the non-trivial selection function and survey geometry. Tension can be removed if we examine only a X-ray selected sub sample, with simulations performed assuming a modified survey geometry.
    Journal of Cosmology and Astroparticle Physics 02/2012; 2012(02):009-009. DOI:10.1088/1475-7516/2012/02/009 · 5.88 Impact Factor
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    ABSTRACT: We address the issue of cosmological backreaction from non-linear structure formation by constructing an approximation for the time evolved metric of a dust dominated universe based on a gradient expansion. Our metric begins as a perturbation of a flat Friedmann-Robertson-Walker state described by a nearly scale invariant, Gaussian, power-law distribution, and evolves in time until non-linear structures have formed. After describing and attempting to control for certain complications in the implementation of this approach, this metric then forms a working model of the universe. We numerically calculate the evolution of the average scale factor in this model and hence the backreaction. We argue that, despite its limitations, this model is more realistic than previous models that have confronted the issue of backreaction. We find that the \emph{instantaneous} effects of backreaction in this model could be as large as $\sim10%$ of the background. This suggests that a proper understanding of the \emph{cumulative} effects of backreaction could be crucial for precision cosmology and any future exploration of the dark sector.
    Journal of Cosmology and Astroparticle Physics 12/2011; 2012(03). DOI:10.1088/1475-7516/2012/03/026 · 5.88 Impact Factor
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    ABSTRACT: The detection of primordial gravitational waves, or tensor perturbations, would be regarded as compelling evidence for inflation. The canonical measure of this is the ratio of tensor to scalar perturbations, r. For single-field slow-roll models of inflation with small field excursions, the Lyth bound dictates that if the evolution of the slow-roll parameter epsilon is monotonic, the tensor-to-scalar ratio must be below observationally detectable levels. We describe how non-monotonic evolution of epsilon can evade the Lyth bound and generate observationally large r, even with small field excursions. This has consequences for the scalar power spectrum as it necessarily predicts an enhancement in the spectrum at very small scales and significant scale-dependent running at CMB scales. This effect has not been appropriately accounted for in previous analyses. We describe a mechanism that will generically produce the required behaviour in epsilon and give an example of this mechanism arising in a well-motivated small-field model. This model can produce r\geq0.05 while satisfying all current observational constraints.
    Journal of Cosmology and Astroparticle Physics 10/2011; 2012(02). DOI:10.1088/1475-7516/2012/02/008 · 5.88 Impact Factor
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    Shaun Hotchkiss
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    ABSTRACT: I show that the most common method of quantifying the likelihood that an extreme galaxy cluster could exist is biased and can result in false claims of tension with LambdaCDM. This common method uses the probability that at least one cluster could exist above the mass and redshift of an observed cluster. I demonstrate the existence of the bias using sample cluster populations, describe its origin and explain how to remove it. I then suggest potentially more suitable and unbiased measures of the rareness of individual clusters. Each different measure will be most sensitive to different possible types of new physics. I show how to generalise these measures to quantify the total `rareness' of a set of clusters. It is seen that, when mass uncertainties are marginalised over, there is no tension between the standard LambdaCDM cosmological model and the existence of any observed set of clusters. As a case study, I apply these rareness measures to sample cluster populations generated using primordial density perturbations with a non-Gaussian spectrum.
    Journal of Cosmology and Astroparticle Physics 05/2011; 7(07). DOI:10.1088/1475-7516/2011/07/004 · 5.88 Impact Factor
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    Kari Enqvist, Shaun Hotchkiss, Olli Taanila
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    ABSTRACT: There are observations of at least 14 high-redshift massive galaxy clusters, which have an extremely small probability with a purely Gaussian initial curvature perturbation. Here we revisit the estimation of the contribution of non-Gaussianities to the cluster mass function and point out serious problems that have resulted from the application of the mass function out of the range of its validity. We remedy the situation and show that the values of fNL previously claimed to completely reconcile (i.e. at ~ 100% confidence) the existence of the clusters with ΛCDM are unphysically small. However, for WMAP cosmology and at 95% confidence, we arrive at the limit fNL411, which is similar to previous estimates. We also explore the possibility of a large gNL as the reason for the observed excess of the massive galaxy clusters. This scenario, gNL > 2 × 106, appears to be in more agreement with CMB and LSS limits for the non-Gaussianity parameters and could also provide an explanation for the overabundance of large voids in the early universe.
    Journal of Cosmology and Astroparticle Physics 04/2011; 2011(04):017. DOI:10.1088/1475-7516/2011/04/017 · 5.88 Impact Factor
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    ABSTRACT: Number counts of massive high-redshift clusters provide a window to study primordial non-Gaussianity. The current quality of data, however, forces the statistical analysis to probe a region of parameter space -- the extreme tail of the mass function -- which is neither accessible in any of the currently available theoretical prescriptions for calculating the mass function, nor calibrated in N-body simulations. In this work we present a new analytical prescription for calculating a "resummed" non-Gaussian halo mass function, which is constructed to remain stable in the extreme tail. We show that the prescription works well in the parameter regime that has been currently explored in simulations. We then use Fisher matrix techniques to compare our prescription with an extrapolated fit to N-body simulations, which has recently been used to obtain constraints from data collected by the South Pole Telecope. We show that for the current data, both prescriptions would lead to statistically consistent constraints. As the data improve, however, there is a possibility of introducing a statistically significant bias in the constraints due to the choice of prescription, especially if non-Gaussianity is scale dependent and becomes relatively large on cluster scales. It would then be necessary to test the accuracy of the prescriptions in N-body simulations that can probe clusters with high masses and redshifts in the presence of large non-Gaussianity.
    Physical review D: Particles and fields 04/2011; 84(2). DOI:10.1103/PhysRevD.84.023517 · 4.86 Impact Factor

Publication Stats

263 Citations
101.16 Total Impact Points

Institutions

  • 2013–2014
    • University of Sussex
      • • Astronomy Centre
      • • Department of Physics and Astronomy
      Brighton, England, United Kingdom
  • 2011–2013
    • University of Helsinki
      • Department of Physics
      Helsinki, Uusimaa, Finland
  • 2012
    • Bielefeld University
      • Faculty of Physics
      Bielefeld, North Rhine-Westphalia, Germany
  • 2008
    • Universidad Nacional Autónoma de México
      • Institute of Physical Science
      Ciudad de México, The Federal District, Mexico