# Signatures of the Primordial Universe from Its Emptiness: Measurement of Baryon Acoustic Oscillations from Minima of the Density Field

Francisco-Shu Kitaura, Chia-Hsun Chuang, Yu Liang, Cheng Zhao, Charling

Tao, Sergio Rodriguez-Torres, Daniel J. Eisenstein, Hector Gil-Marin, Jean-Paul Kneib, Cameron Mcbride, et al.

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To cite this version:

Francisco-Shu Kitaura, Chia-Hsun Chuang, Yu Liang, Cheng Zhao, Charling Tao, et al. "Signatures of the Primordial Universe from Its Emptiness: Measurement of Baryon Acoustic Oscillations from Minima of the Density Field. Physical Review Letters, 2016, 116 (17), pp.171301. 10.1103/Phys-RevLett.116.171301. hal-01440693

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# Signatures of the Primordial Universe from Its Emptiness: Measurement of Baryon Acoustic Oscillations from Minima of the Density Field

Francisco-Shu Kitaura,¹,* Chia-Hsun Chuang,¹ Yu Liang,² Cheng Zhao,² Charling Tao,²,³

Sergio Rodríguez-Torres,⁴,⁵,⁶ Daniel J. Eisenstein,⁷ Héctor Gil-Marín,⁸,⁹ Jean-Paul Kneib,¹⁰,¹¹

Cameron McBride,⁷ Will J. Percival,¹² Ashley J. Ross,¹²,¹³ Ariel G. Sánchez,¹⁴ Jeremy Tinker,¹⁵

Rita Tojeiro,¹⁶ Mariana Vargas-Magana,¹⁷ and Gong-Bo Zhao¹⁸,¹²

¹Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482 Potsdam, Germany

²Tsinghua Center of Astrophysics and Department of Physics, Tsinghua University, Beijing 100084, China

³Aix-Marseille Université, CNRS/IN2P3, CPPM UMR 7346, 13288 Marseille, France

⁴Instituto de Física Teórica, (UAM/CSIC), Universidad Autónoma de Madrid, Cantoblanco, E-28049 Madrid, Spain

⁵Campus of International Excellence UAM+CSIC, Cantoblanco, E-28049 Madrid, Spain

⁶Departamento de Física Teórica M8, Universidad Autonoma de Madrid (UAM), Cantoblanco, E-28049, Madrid, Spain

⁷Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, USA

⁸Sorbonne Universits, Institut Lagrange de Paris (ILP), 98 bis Boulevard Arago, 75014 Paris, France

⁹Laboratoire de Physique Nuclaire et de Hautes Energies, Université Pierre et Marie Curie,
4 Place Jussieu, Tour 22, 1er tage, 75005 Paris, France

¹⁰Laboratoire d'Astrophysique, Ecole Polytechnique Fedérale de Lausanne, CH-1015 Lausanne, Switzerland

¹¹Aix Marseille Université, CNRS, LAM (Laboratoire d'Astrophysique de Marseille) UMR 7326, F-13388, Marseille, France

¹²Institute of Cosmology & Gravitation, University of Portsmouth, Dennis Sciama Building, Portsmouth PO1 3FX, United Kingdom

¹³Center for Cosmology and AstroParticle Physics, The Ohio State University, Columbus, Ohio 43210, USA

¹⁴Max-Planck-Institut für Extraterrestrische Physik, Postfach 1312, Giessenbachstraße, 85741 Garching, Germany

¹⁵Center for Cosmology and Particle Physics, New York University, 4 Washington Place, New York, New York 10003, USA

¹⁶University of St. Andrews, North Haugh, St. Andrews Fife, KY16 9SS, United Kingdom

¹⁷Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, México

¹⁸National Astronomy Observatories, Chinese Academy of Science, Beijing, 100012, People's Republic of China
(Received 13 November 2015; revised manuscript received 22 March 2016; published 25 April 2016)

Sound waves from the primordial fluctuations of the Universe imprinted in the large-scale structure, called baryon acoustic oscillations (BAOs), can be used as standard rulers to measure the scale of the Universe. These oscillations have already been detected in the distribution of galaxies. Here we propose to measure BAOs from the troughs (minima) of the density field. Based on two sets of accurate mock halo catalogues with and without BAOs in the seed initial conditions, we demonstrate that the BAO signal cannot be obtained from the clustering of classical disjoint voids, but it is clearly detected from overlapping voids. The latter represent an estimate of all troughs of the density field. We compute them from the empty circumsphere centers constrained by tetrahedra of galaxies using Delaunay triangulation. Our theoretical models based on an unprecedented large set of detailed simulated void catalogues are remarkably well confirmed by observational data. We use the largest recently publicly available sample of luminous red galaxies from SDSS-III BOSS DR11 to unveil for the first time a $> 3\sigma$ BAO detection from voids in observations. Since voids are nearly isotropically expanding regions, their centers represent the most quiet places in the Universe, keeping in mind the cosmos origin and providing a new promising window in the analysis of the cosmological large-scale structure from galaxy surveys.

DOI: 10.1103/PhysRevLett.116.171301

In the primordial baryon-photon plasma of our Universe, overpressured regions triggered sound waves that stalled at the recombination epoch, imprinting spheres of overdensity fluctuations, measurable in the matter power spectrum as an oscillatory pattern, the so-called baryon acoustic oscillations (BAOs). Any dark matter tracer should encode this signal in its spatial distribution either at early or late cosmic times after cosmic evolution [1–4]. In fact, these oscillations have already been detected in the cosmic microwave background anisotropies [5–8], in the distribution of

galaxies [9–14], and more recently in the distribution of the Lyman alpha forest [15–17]. For a review on BAOs and their cosmological implications, see Aubourg et al. [18].

Their characteristic scale can be used as a standard ruler to measure the evolving scale of the Universe and to constrain the nature of its driving force, the dark energy component. For this reason a large number of surveys have focused on measuring BAOs or have included them as an integral part of their science, such as the 2dFGRS [19], the SDSS [20], the WiggleZ [21], the BOSS [22], the
SDSS-IV/eBOSS, the DESI/BigBOSS [23], the DES [24], the LSST [25], the J-PAS [26], the 4MOST [27], or the EUCLID survey [28].

Ever since the first detection of the giant Boötes void in 1981 [29] and with the nascent era of galaxy surveys, more evidence for the existence of voids has been found. The presence of voids in the large-scale structure was considered a manifestation of cosmological structure formation transforming the homogeneous Universe into a complex cosmic web structure. This picture was confirmed through numerical simulations (see, e.g., Refs. [30–32]). The classification of voids based on galaxy surveys has turned into a common practice; see, e.g., the CfA [33,34], the IRAS [35], Las Campanas [36], the PSCz [37], the 2dFRGS [38–40], the DEEP2 [41], the 2MRS [42], the SDSS survey [43–48], and the VIMOS survey [49]. Nevertheless, voids are usually considered to be very large rare objects, as compared to galaxies. Their probability distribution function can be used to constrain cosmology in an analogous way to galaxy clusters [50]. The statistics of voids has been studied for a long time (see, e.g., Refs. [51–55]), and an excursion set formalism analogous to the one describing the formation of halos (the compact collapsed dark matter objects hosting galaxies) has been developed [56–59]. Those studies hint towards a hierarchical picture, in which voids can form merger trees through cosmic evolution [60]. Considerable efforts have been made to understand the nature and evolution of voids through theoretical studies with semianalytic studies (see, e.g., Refs. [61,62]) and simulations (see, e.g., Refs. [63–69]).

Nevertheless, there are many different definitions of voids [56,66,67,70–80], which do not necessarily agree with each other (see, e.g., Ref. [81]).

From a practical perspective, voids have recently been proposed to give additional cosmological constraints, not only according to their statistics but also according to their shape. The void ellipticity was proposed to probe dark energy [82–85] and to make the Alcock-Paczyński test [86]. In particular, voids can be used to test gravity (see, e.g., Refs. [84,87,88]) dynamical dark energy [84], coupled dark energy [89], and modified gravity [87,90]. They can also be used to measure the Sachs Wolfe effect [91]. However, their sparse population and low signal-to-noise ratio have made them less interesting for clustering analysis. Little work can be found on the measurement of the correlation function of voids; see, however, Refs. [92–94] and, in particular, the recent pioneering study on observations [95].

In this Letter, we propose, for the first time, using the troughs of the density field (from now on called void tracers), meaning the minima in the overdensity field, to obtain additional measurements of the BAOs from the ones corresponding to galaxies. We have developed a Delaunay triangulation void finder based on empty circumspheres constrained by tetrahedra of galaxies Zhao *et al.* [96].

Our voids are close to the classical definition as spherical underdense regions (see, e.g., Refs. [40,51]), including, however, as a crucial difference, overlapping spheres, since we are interested in the distribution of troughs of the density field and account, in this way, for the shape of empty regions.

Our definition crucially increases the statistics of void tracers by about 2 orders of magnitude in contrast to previous studies, in which voids are treated as large connected regions that do not overlap at all or overlap only marginally (see, e.g., Refs. [40,94,95]). The speed of the DIVE void finder has been crucial for this project taking only of the order of minutes to find all the void tracers associated with about half a million objects and with little memory requirements (on a single core: ~18 mins and ~5 Gb, respectively).

In Liang *et al.* [97], we have studied, for the first time, the BAO signal with this void definition on mock catalogues predicting a characteristic correlation function, which includes dips on scales smaller and larger than the BAO peak. These features were exploited to develop a model-independent signal-to-noise estimator, used in turn to determine the radius cuts that provide the optimal signal-to-noise ratio for the BAO signal.

In this Letter we aim to extend the signal-to-noise estimator to detect the BAO signal from voids based on observational data.

To this end, first we define a control sample of accurate mock galaxy catalogues performed with the PATCHY code [98]. In particular, we have produced 100 mocks for each of the following cases: catalogues with and without baryon acoustic oscillations (“wiggle” and “nonwiggle” cases, respectively) in the initial conditions used to simulate structure formation. In particular, we consider complete samples of halos (main and subhalos) in cubic volumes of $(2.5 \ h^{-1} \ \text{Gpc})^3$ with number density $3.5 \times 10^{-4} \ h^3 \ \text{Mpc}^{-3}$, similar to the one of the BOSS CMASS galaxy sample at a mean redshift $z = 0.56$. The parameters of the PATCHY code have been calibrated with the large BigMultiDark N-body simulation [99] to accurately match the two- and the three-point statistics (such parameters can be found in Ref. [100]). The cosmological parameters have been consistently chosen to be within $\Lambda$ cold dark matter Planck cosmology with $\Omega_M = 0.307115$, $\Omega_b = 0.048206$, $\sigma_8 = 0.8288$, $n_s = 0.9611$, and a Hubble constant ($H_0 = 100 \ h \ \text{km s}^{-1} \ \text{Mpc}^{-1}$) given by $h = 0.6777$.

The accuracy of these catalogues has been further demonstrated in several recent papers [101,102].

We have run the DIVE void finder for circumspheres with radii $\ge 16 \ h^{-1} \ \text{Mpc}$ on these sets of catalogues in real space and computed the corresponding correlation functions. The results do not show any signal in the nonwiggle case, as expected, while the wiggle case shows a significant BAO signal (see Fig. 1). Hence, both sets of simulations demonstrate that the BAO signal from voids is really
<figure><img src="image_3.png" /><figcaption>FIG. 1. Correlation functions for the set of 100 PATCHY (full cubic volume at mean redshift 0.56) void tracer mock catalogues (without observational effects) based on seed perturbations with and without BAOs. *Upper panel:* Mean and variance for the following cases: (1) with BAOs, blue solid line and blue error bars, respectively; (2) without BAOs (“nonwiggle”), black solid line and black error bars, respectively. *Lower panel:* Corresponding residual (red solid line and red error bars).</figcaption></figure>

present in our mock catalogues, and we confirm the findings in Liang *et al.* [97]. The two dips around the BAO peak and a singularity around the size (diameter) of the smallest void ($\sim 30 h^{-1}$ Mpc) due to the void exclusion effect can also be clearly seen in Fig. 1. Importantly, the BAO peak is not only seen in the residual after extracting the nonwiggle from the wiggle mock catalogues (see lower panel in Fig. 1) but directly in the correlation function based on the catalogues containing the BAO signal in the seed perturbations (see upper panel in Fig. 1). This is not the case when analyzing disjoint voids (see Fig. 2). The oscillation patterns seen in the correlation functions are not related to the BAOs but are due to hard sphere exclusion effects when the filling factor is high (see [103]), as they can be found both in the wiggle and nonwiggle mock catalogues. There are only tiny differences in the modulation of these oscillations caused by BAOs, which can only be found in the residuals with large error bars (compare upper and lower panels in Fig. 2).

<figure><img src="image_4.png" /><figcaption>FIG. 2. Same as Fig. 1 for disjoint voids.</figcaption></figure>

We have verified that the majority of the void tracers considered are located in expanding regions and that they are anticorrelated to the halos, hereby demonstrating that our definition of voids yields additional tracers of the large-scale structure (see Ref. [96]).

To detect the void tracer BAO signature in observations, we need to consider mocks resembling the BOSS DR11 CMASS sample in our analysis, including survey geometry, radial selection effects, bias evolution, and redshift space distortions (RSDs).

This work uses data from the Data Release DR11 [104] of the Baryon Oscillation Spectroscopic Survey (BOSS) [105]. The BOSS survey uses the SDSS 2.5 meter telescope at Apache Point Observatory [106], and the spectra are obtained using the double-armed BOSS spectrograph [107]. The data are then reduced using the algorithms described in Ref. [108]. The target selection of the CMASS and LOWZ samples, together with the algorithms used to create large scale structure catalogues (the MKSAMPLE code), are presented in Reid *et al.* [109].

We compute the voids (with radii $\ge 16 h^{-1}$ Mpc) and the corresponding correlation functions for 1,000 BOSS DR11 CMASS MULTIDARK PATCHY mocks [110]. These galaxy mocks have been calibrated with N-body based reference catalogues from the BIGMULTIDARK simulation [111] and made publicly available [112]. The radius cut was determined to provide the optimal signal-to-noise ratio for the BAO signal (see Ref. [97]).

We follow the methodology presented in Liang *et al.* [97] to deal with the survey geometry and radial selection function. In particular, we use the angular mask from the DR11 galaxy catalogue to filter out the voids identified outside the survey area to construct the observed DR11 void catalogue and the corresponding set of synthetic BOSS DR11 CMASS MULTIDARK PATCHY void light-cone catalogues. To compute the two-point correlation functions, we need to construct a random void catalogue with the same geometry (in both angular and radius directions) as the BOSS DR11 CMASS data. To that purpose we combine 50 BOSS DR11 CMASS MULTIDARK PATCHY void catalogues and reassign the redshift randomly picked from observed data (a.k.a. shuffle method, e.g., see Ref. [14]). This procedure will produce random void catalogues with geometry consistent with the observed data. We avoid using the random galaxy catalogue for the random void catalogue since the distribution of the voids is different, especially at the boundaries of the survey.

Our analysis relies on a factor 2–2.5 more troughs than galaxies (for CMASS North: 1,212,393 troughs—voids with radii $\ge 16 h^{-1}$ Mpc—vs 566,940 galaxies; and for CMASS South: 472,868 troughs vs 188,582 galaxies). As an example, for the CMASS North we would only have 48,000 disjoint voids.

Finally, we take the BOSS DR11 data and apply the same analysis algorithms, using the same settings. A plot of
<figure><img src="image_5.png" /><figcaption>FIG. 3. Sky projection in right ascension (RA) and declination (DEC) of the BOSS DR11 CMASS LRGs (red symbols) and the corresponding void tracer (blue symbols) catalogues. Upper panel: Northern galactic cap (NGC). Lower panel: Southern galactic cap (SGC). Void tracers obtained in unobserved regions or holes in the mask (caused by, e.g., stars) have accordingly been removed.</figcaption></figure>

the sky projection of the galaxies and their corresponding void tracers clearly illustrates how these tracers trace different regions of the cosmic web (see Fig. 3). The result of these computations shows a remarkable agreement between the theoretical prediction and the observations even towards large scales in contrast to galaxies (see Fig. 4). Here we use the wiggle and nonwiggle simulations to construct the templates of the fitting models to estimate the significance of the BAO detection.

We make a cubic spline fit from the wiggle and non-wiggle PATCHY mock correlation function, $\xi_w(s)$ and $\xi_{nw}(s)$, respectively, with $s$ being the separation between two void tracers based on the galaxy distribution in redshift space. These two functions are the basis to construct the wiggle model and nonwiggle models for determining the BAO significance. In particular, we apply the following models in the fitting range $60 < r < 160 h^{-1}$ Mpc. First, we show a wiggle model:

$$ \xi_{\text{th}}(s) = A[\xi_w(s/\alpha) - \xi_{\text{nw}}(s/\alpha)] + \xi_{\text{nw}}(s/\alpha) + a_0 + a_1/s + a_2/s^2, \quad (1) $$

<figure><img src="image_6.png" /><figcaption>FIG. 4. Correlation functions for the BOSS DR11 CMASS void tracer catalogue (black error bars) and the mean (blue line) and $1\sigma$ region (blue shaded) of the corresponding 1,000 light-cone (including evolution from redshift 0.43 to 0.7) MULTI-DARK PATCHY DR11 CMASS mock void catalogues (including observational effects: survey geometry, mask, radial selection function, and redshift-space distortions). The wiggle and nonwiggle best fitting models are represented by the red and black solid lines, respectively.</figcaption></figure>

where $\alpha$ is the rescaling factor of BAO, $A$ is the BAO damping factor, and the polynomial models the systematics for the overall shape following Anderson et al. [14]. Second, we show a nonwiggle model:

$$ \xi_{\text{th}}(s) = \xi_{\text{nw}}(s/\alpha) + a_0 + a_1/s + a_2/s^2, \quad (2) $$

which can be obtained from setting $A=0$ in the wiggle model Eq. (1).

As in Anderson et al. [14], we use a template with fixed cosmology. The measurement of $\alpha$ can be interpreted as the ratio between the spherically averaged distance scale $D_V(z) \equiv [cz(1+z)2D_A(z)2H^{-1}(z)]^{1/3}$ to the pivot redshift ($z=0.57$) and the sound horizon scale $rs$ at drag epoch with respect to the fiducial model, $\alpha = [D_V/r_s]/[D_V/r_s]_{\text{fid}}$, where $D_A(z)$ is the angular diameter distance and $H(z)$ is the Hubble parameter. In general, a theoretical correlation function model should be constructed with parameters $\{\Omega_M h^2, n_s, \Omega_b h^2, \alpha\}$, where $\alpha$ absorbs the information of dark energy and curvature. In practice, one might ignore the uncertainties of $n_s$ and $\Omega_b h^2$ since they are tightly constrained by CMB. While fixing $\Omega_M h^2$, we can only measure some quantity which is insensitive to $\Omega_M h^2$. Therefore, $\alpha$ should be interpreted as $D_V/r_s$, which is uncorrelated to $\Omega_M h^2$ (e.g., see Table 2 in Ref. [113]).

The significance of the detection was computed from the difference of the best wiggle and nonwiggle fits yielding a chi-squared per degrees of freedom of $\chi^2/\text{dof} = 9.9/15$ for the wiggle model and $\chi^2/\text{dof} = 20.1/16$ for the nonwiggle model. In particular, we measured $\alpha$ by marginalizing over the amplitude $A$, obtaining $\alpha = 1.000 \pm 0.022$. Converting this finding to an effective distance at $z=0.57$ would correspond to $2057 \pm 45$ Mpc, which is compatible with
the finding from galaxies alone (see Ref. [14], which found 2056 ± 20 Mpc). One should note that the chi-squared distribution is not very Gaussian for voids. We would therefore take this measurement as a first-order estimate and work on more robust measurements in forthcoming papers.

Relying on these models we find a BAO detection with a significance of $3.2\sigma$ (see Fig. 4). We have used the covariance matrices derived from the set of 1,000 mocks to do this analysis analogously to Anderson et al. [14]. As a first approximation we assume in the wiggle and nonwiggle models that RSDs can be modeled by a damping term. We plan to investigate RSDs in detail in future work. Incompleteness, veto mask, and the fiber collision are taken into account in the DR11 CMASS mock catalogues and, accordingly, in the void catalogue computations. We do not see in the CMASS void correlation function any strong systematic effects, i.e., strong deviations in the correlation function towards large scales, as it was seen with the CMASS galaxy correlation function [114,115]. The correlation function behaves very much like the theoretical correlation function from the light-cone mocks. With the optimal radius cut used in this study, we found that the number density of voids is insensitive to the number density of galaxies (see Fig. 4 in Ref. [96]). This would explain why a varying number density of galaxies caused by stellar density systematics does not have a significant impact on the void density across the sky.

Questions arise when we measure the clustering of voids: What is the information gain from void tracers directly computed from the distribution of galaxies? And how covariant are these tracers to the galaxies themselves? The construction of void troughs follows the intuitive physical picture of filling the gaps complementary to the high density peaks occupied by the galaxies. Luminous red galaxies (LRGs) are known to reside in high density regions (see, e.g., Ref. [100]). We are thus extending the information on the density fluctuations ($\delta = \rho/\bar{\rho} - 1$) to underdense regions ($\delta < 0$), which based on this galaxy distribution are otherwise set to a constant value ($\delta = -1$). Less massive objects, such as emission line galaxies, could also be used to define underdense regions, but an extended definition with some stellar mass threshold may be required for the estimation of troughs. We note that small voids are equivalent to groups of quartets of galaxies residing in high density regions (see Ref. [96]) and, hence, are expected to deliver redundant information to the galaxies themselves. This is not the case for the large voids considered in this study. In fact, it is clear that the Delaunay voids we construct from tetrahedra of galaxies encode higher order statistics, further constrained by imposing the circum-spheres to be empty, which strongly depends on gravita-tional evolution of the morphology of the cosmic web and hence on all the n-point statistics of the density field (in particular, the three-point statistics; see Ref. [116]).

Moreover, our prior knowledge on the radius cut selecting empty circumspheres located in expanding void regions, based on tidal field computations of the underlying dark matter field in simulations (see Ref. [96]), implicitly incorporates knowledge on the void regions beyond the one present in the galaxy distribution. By analyzing the clustering of the troughs (constructed upon the galaxies) we are including higher order information (see Ref. [51]), potentially circumventing a more complicated mathemati-cal formalism needed to extract the full information encoded in the three-dimensional distribution of galaxies. This is supported by recent theoretical work, demonstrating that most of the information gained in BAO reconstruction comes from the three-point statistics with some contribu-tions from the four-point statistics [117], and depends on the environment [118]. In fact, a recent work has presented a $2.8\sigma$ detection of BAOs from the three-point correlation function based on BOSS DR12 [119].

The actual information gain we can get from combining void tracers with galaxies in a multitracer analysis remains to be investigated, including whether voids will improve the cosmological constraints from galaxy clustering alone. This analysis may yield little added value in the presence of data covering the underdense cosmic density field, with, e.g., considerably higher number densities than that pro-vided by LRGs. Nevertheless, since void tracers are expected to be less affected by gravitational pull, BAO reconstruction techniques [120] could be less necessary for these tracers, and they may thus yield a less cosmology-dependent estimate of the linear correlation function. We will investigate this in future work.

The authors thank Michael Wood-Vasey, Christian Wagner, Marcos Pellejero Ibañez, Juan E. Betancort-Rijo, Anatoly Klypin, Gustavo Yepes, and Francisco Prada for useful discussions. F. S. K. thanks the Leibniz Society for support. Y. L., C. T., and C. Z. acknowledge support from Tsinghua University through a 985 grant, 973 programme 2013CB834906, NSFC Grants No. 11033003 and No. 11173017, Sino French CNRS-CAS International Laboratories LIA Origins, and FCPPL. R. T. thanks the STFC for support. H. G. M. thanks the Labex ILP (Reference No. ANR-10-LABX-63), part of the Idex SUPER, for support, receiving financial state aid managed by the Agence Nationale de la Recherche, as part of the programme Investissements d'avenir under Reference No. ANR-11-IDEX-0004-02. G. Z. is supported by the Strategic Priority Research Program of the Chinese Academy of Sciences Grant No. XDB09000000. The authors are also thankful for the access to computing facilities at Barcelona (MareNostrum), LRZ (Supermuc), AIP (erebos), CCIN2P3 (Quentin Le Boulc'h), and Tsinghua University. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office
of Science. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration, including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/ Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.

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