David W. Hogg

Carnegie Mellon University, Pittsburgh, Pennsylvania, United States

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Publications (286)956.82 Total impact

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    ABSTRACT: Astronomical observations are affected by several kinds of noise, each with its own causal source; there is photon noise, stochastic source variability, and residuals coming from imperfect calibration of the detector or telescope. The precision of NASA Kepler photometry for exoplanet science---the most precise photometric measurements of stars ever made---appears to be limited by unknown or untracked variations in spacecraft pointing and temperature, and unmodeled stellar variability. Here we present the Causal Pixel Model (CPM) for Kepler data, a data-driven model intended to capture variability but preserve transit signals. The CPM works at the pixel level so that it can capture very fine-grained information about the variation of the spacecraft. The CPM predicts each target pixel value from a large number of pixels of other stars sharing the instrument variabilities while not containing any information on possible transits in the target star. In addition, we use the target star's future and past (auto-regression). By appropriately separating, for each data point, the data into training and test sets, we ensure that information about any transit will be perfectly isolated from the model. The method has four hyper-parameters (the number of predictor stars, the auto-regressive window size, and two L2-regularization amplitudes for model components), which we set by cross-validation. We determine a generic set of hyper-parameters that works well for most of the stars and apply the method to a corresponding set of target stars. We find that we can consistently outperform (for the purposes of exoplanet detection) the Kepler Pre-search Data Conditioning (PDC) method for exoplanet discovery.
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    ABSTRACT: Several long, dynamically cold stellar streams have been observed around the Milky Way Galaxy, presumably formed from the tidal disruption of globular clusters. In integrable potentials---where all orbits are dynamically regular---tidal debris phase-mixes close to the orbit of the progenitor system. However, cosmological simulations of structure formation suggest that the Milky Way's dark matter halo is expected not to be fully integrable; an appreciable fraction of orbits will be chaotic. This paper examines the influence of chaos on the phase-space morphology of cold tidal streams. We find very stark results: Streams in chaotic regions look very different from those in regular regions. We find that streams (simulated using test particle ensembles of nearby orbits) can be sensitive to chaos on a much shorter time-scale than any standard prediction (from the Lyapunov or frequency-diffusion times). For example, on a weakly chaotic orbit with a chaotic timescale predicted to be >1000 orbital periods (>1000 Gyr), the resulting stellar stream is, after just a few 10's of orbits, substantially more diffuse than any formed on a nearby but regular orbit. We find that the enhanced diffusion of the stream stars can be understood by looking at the variance in orbital frequencies of orbit ensembles centered around the parent (progenitor) orbit. Our results suggest that long, cold streams around our Galaxy must exist only on regular (or very nearly regular) orbits; they potentially provide a map of the regular regions of the Milky Way potential. This suggests a promising new direction for the use of tidal streams to constrain the distribution of dark matter around our Galaxy.
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    ABSTRACT: We describe a method for removing the effect of confounders in order to reconstruct a latent quantity of interest. The method, referred to as half-sibling regression, is inspired by recent work in causal inference using additive noise models. We provide a theoretical justification and illustrate the potential of the method in a challenging astronomy application.
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    ABSTRACT: The extended Kepler mission, K2, is now providing photometry of new fields every three months in a search for transiting planets. In a recent study, Foreman-Mackey and collaborators presented a list of 36 planet candidates orbiting 31 stars in K2 Campaign 1. In this contribution, we present stellar and planetary properties for all systems. We combine ground-based seeing-limited survey data and adaptive optics imaging with an automated transit analysis scheme to validate 18 candidates as planets and identify 6 candidates as likely false positives. Of particular interest is EPIC 201912552, a bright (K=8.9) M2 dwarf hosting a 2.24 \pm 0.25 Earth radius planet with an equilibrium temperature of 271 \pm 16 K and an orbital period of 33 days. We also present two new open-source software packages that enabled this analysis: isochrones, a flexible tool for fitting theoretical stellar models to observational data to determine stellar properties, and vespa, a new general-purpose procedure to calculate false positive probabilities and statistically validate transiting exoplanets.
    The Astrophysical Journal 03/2015; 809(1). DOI:10.1088/0004-637X/809/1/25 · 6.28 Impact Factor
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    ABSTRACT: We have undertaken the largest systematic study of the high-mass stellar initial mass function (IMF) to date using the optical color-magnitude diagrams (CMDs) of 85 resolved, young (4 Myr < t < 25 Myr), intermediate mass star clusters (10^3-10^4 Msun), observed as part of the Panchromatic Hubble Andromeda Treasury (PHAT) program. We fit each cluster's CMD to measure its mass function (MF) slope for stars >2 Msun. For the ensemble of clusters, the distribution of stellar MF slopes is best described by $\Gamma=+1.45^{+0.03}_{-0.06}$ with a very small intrinsic scatter. The data also imply no significant dependencies of the MF slope on cluster age, mass, and size, providing direct observational evidence that the measured MF represents the IMF. This analysis implies that the high-mass IMF slope in M31 clusters is universal with a slope ($\Gamma=+1.45^{+0.03}_{-0.06}$) that is steeper than the canonical Kroupa (+1.30) and Salpeter (+1.35) values. Using our inference model on select Milky Way (MW) and LMC high-mass IMF studies from the literature, we find $\Gamma_{\rm MW} \sim+1.15\pm0.1$ and $\Gamma_{\rm LMC} \sim+1.3\pm0.1$, both with intrinsic scatter of ~0.3-0.4 dex. Thus, while the high-mass IMF in the Local Group may be universal, systematics in literature IMF studies preclude any definitive conclusions; homogenous investigations of the high-mass IMF in the local universe are needed to overcome this limitation. Consequently, the present study represents the most robust measurement of the high-mass IMF slope to date. We have grafted the M31 high-mass IMF slope onto widely used sub-solar mass Kroupa and Chabrier IMFs and show that commonly used UV- and Halpha-based star formation rates should be increased by a factor of ~1.3-1.5 and the number of stars with masses >8 Msun are ~25% fewer than expected for a Salpeter/Kroupa IMF. [abridged]
    The Astrophysical Journal 02/2015; 806(2). DOI:10.1088/0004-637X/806/2/198 · 6.28 Impact Factor
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    ABSTRACT: Photometry of stars from the K2 extension of NASA's Kepler mission is afflicted by systematic effects caused by small (few-pixel) drifts in the telescope pointing and other spacecraft issues. We present a method for searching K2 light curves for evidence of exoplanets by simultaneously fitting for these systematics and the transit signals of interest. This method is more computationally expensive than standard search algorithms but we demonstrate that it can be efficiently implemented and used to discover transit signals. We apply this method to the full Campaign 1 dataset and report a list of 36 planet candidates transiting 31 stars, along with an analysis of the pipeline performance and detection efficiency based on artificial signal injections and recoveries. For all planet candidates, we present posterior distributions on the properties of each system based strictly on the transit observables.
    The Astrophysical Journal 02/2015; 806(2). DOI:10.1088/0004-637X/806/2/215 · 6.28 Impact Factor
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    ABSTRACT: Using the example of the tidal stream of the Milky Way globular cluster Palomar 5 (Pal 5), we demonstrate how observational data on streams can be efficiently reduced in dimensionality and modeled in a Bayesian framework. Our approach combines detection of stream overdensities by a Difference-of-Gaussians process with fast streakline models, a continuous likelihood function built from these models, and inference with MCMC. By generating $\approx10^7$ model streams, we show that the geometry of the Pal 5 debris yields powerful constraints on the solar position and motion, the Milky Way and Pal 5 itself. All 10 model parameters were allowed to vary over large ranges without additional prior information. Using only SDSS data and a few radial velocities from the literature, we find that the distance of the Sun from the Galactic Center is $8.30\pm0.25$ kpc, and the transverse velocity is $253\pm16$ km/s. Both estimates are in excellent agreement with independent measurements of these quantities. Assuming a standard disk and bulge model, we determine the Galactic mass within Pal 5's apogalactic radius of 19 kpc to be $(2.1\pm0.4)\times10^{11}$ M$_\odot$. Moreover, we find the potential of the dark halo with a flattening of $q_z = 0.95^{+0.16}_{-0.12}$ to be essentially spherical within the radial range that is effectively probed by Pal 5. We also determine Pal 5's mass, distance and proper motion independently from other methods, which enables us to perform vital cross-checks. We conclude that with more observational data and by using additional prior information, the precision of this method can be significantly increased.
    The Astrophysical Journal 02/2015; 803(2). DOI:10.1088/0004-637X/803/2/80 · 6.28 Impact Factor
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    ABSTRACT: New spectroscopic surveys offer the promise of consistent stellar parameters and abundances ('stellar labels') for hundreds of thousands of stars in the Milky Way: this poses a formidable spectral modeling challenge. In many cases, there is a sub-set of reference objects for which the stellar labels are known with high(er) fidelity. We take advantage of this with The Cannon, a new data-driven approach for determining stellar labels from spectroscopic data. The Cannon learns from the 'known' labels of reference stars how the continuum-normalized spectra depend on these labels by fitting a flexible model at each wavelength; then, The Cannon uses this model to derive labels for the remaining survey stars. We illustrate The Cannon by training the model on only 543 stars in 19 clusters as reference objects, with Teff, log g and [Fe/H] as the labels, and then applying it to the spectra of 56,000 stars from APOGEE DR10. The Cannon is very accurate. Its stellar labels compare well to the stars for which APOGEE pipeline (ASPCAP) labels are provided in DR10, with rms differences that are basically identical to the stated ASPCAP uncertainties. Beyond the reference labels, The Cannon makes no use of stellar models nor any line-list, but needs a set of reference objects that span label-space. The Cannon performs well at lower signal-to-noise, as it delivers comparably good labels even at one ninth the APOGEE observing time. We discuss the limitations of The Cannon and its future potential, particularly, to bring different spectroscopic surveys onto a consistent scale of stellar labels.
    The Astrophysical Journal 01/2015; 808(1). DOI:10.1088/0004-637X/808/1/16 · 6.28 Impact Factor
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    ABSTRACT: The third generation of the Sloan Digital Sky Survey (SDSS-III) took data from 2008 to 2014 using the original SDSS wide-field imager, the original and an upgraded multi-object fiber-fed optical spectrograph, a new near-infrared high-resolution spectrograph, and a novel optical interferometer. All the data from SDSS-III are now made public. In particular, this paper describes Data Release 11 (DR11) including all data acquired through 2013 July, and Data Release 12 (DR12) adding data acquired through 2014 July (including all data included in previous data releases), marking the end of SDSS-III observing. Relative to our previous public release (DR10), DR12 adds one million new spectra of galaxies and quasars from the Baryon Oscillation Spectroscopic Survey (BOSS) over an additional 3000 sq. deg of sky, more than triples the number of H-band spectra of stars as part of the Apache Point Observatory (APO) Galactic Evolution Experiment (APOGEE), and includes repeated accurate radial velocity measurements of 5500 stars from the Multi-Object APO Radial Velocity Exoplanet Large-area Survey (MARVELS). The APOGEE outputs now include measured abundances of 15 different elements for each star. In total, SDSS-III added 5200 sq. deg of ugriz imaging; 155,520 spectra of 138,099 stars as part of the Sloan Exploration of Galactic Understanding and Evolution 2 (SEGUE-2) survey; 2,497,484 BOSS spectra of 1,372,737 galaxies, 294,512 quasars, and 247,216 stars over 9376 sq. deg; 618,080 APOGEE spectra of 156,593 stars; and 197,040 MARVELS spectra of 5,513 stars. Since its first light in 1998, SDSS has imaged over 1/3 the Celestial sphere in five bands and obtained over five million astronomical spectra.
    The Astrophysical Journal Supplement Series 01/2015; 219(1). DOI:10.1088/0067-0049/219/1/12 · 14.14 Impact Factor
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    ABSTRACT: We present a modular, extensible framework for the spectroscopic inference of physical parameters based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints (pixels) into the residual spectrum. In the limit of high signal-to-noise data with large spectral range that is common for stellar parameter estimation, that covariant structure can bias the parameter determinations. We have designed a likelihood function formalism to account for the structure of the covariance matrix, utilizing the machinery of Gaussian process kernels. We specifically address the common problem of mismatches in model spectral line strengths (with respect to data) due to intrinsic model imperfections (e.g., in the atomic or molecular data, or radiative transfer treatment) by developing a novel local covariance kernel framework that identifies and self-consistently downweights pathological spectral line "outliers." By fitting multiple spectra in a hierarchical manner, these local kernels provide a mechanism to learn about and build data-driven corrections to synthetic model spectral libraries. The application of this method, implemented as a freely available open source code, is demonstrated by fitting the high resolution optical (V-band) spectrum of WASP-14, an F5 dwarf with a transiting exoplanet, and the moderate resolution near-infrared (K-band) spectrum of Gliese 51, an M5 dwarf.
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    ABSTRACT: We present first results from the third GRavitational lEnsing Accuracy Testing (GREAT3) challenge, the third in a sequence of challenges for testing methods of inferring weak gravitational lensing shear distortions from simulated galaxy images. GREAT3 was divided into experiments to test three specific questions, and included simulated space- and ground-based data with constant or cosmologically-varying shear fields. The simplest (control) experiment included parametric galaxies with a realistic distribution of signal-to-noise, size, and ellipticity, and a complex point spread function (PSF). The other experiments tested the additional impact of realistic galaxy morphology, multiple exposure imaging, and the uncertainty about a spatially-varying PSF; the last two questions will be explored in Paper II. The 24 participating teams competed to estimate lensing shears to within systematic error tolerances for upcoming Stage-IV dark energy surveys, making 1525 submissions overall. GREAT3 saw considerable variety and innovation in the types of methods applied. Several teams now meet or exceed the targets in many of the tests conducted (to within the statistical errors). We conclude that the presence of realistic galaxy morphology in simulations changes shear calibration biases by $\sim 1$ per cent for a wide range of methods. Other effects such as truncation biases due to finite galaxy postage stamps, and the impact of galaxy type as measured by the S\'{e}rsic index, are quantified for the first time. Our results generalize previous studies regarding sensitivities to galaxy size and signal-to-noise, and to PSF properties such as seeing and defocus. Almost all methods' results support the simple model in which additive shear biases depend linearly on PSF ellipticity.
    Monthly Notices of the Royal Astronomical Society 12/2014; 450(3). DOI:10.1093/mnras/stv781 · 5.23 Impact Factor
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    ABSTRACT: Point estimators for the shearing of galaxy images induced by gravitational lensing involve a complex inverse problem in the presence of noise, pixelization, and model uncertainties. We present a probabilistic forward modeling approach to gravitational lensing inference that has the potential to mitigate the biased inferences in most common point estimators and is practical for upcoming lensing surveys. The first part of our statistical framework requires specification of a likelihood function for the pixel data in an imaging survey given parameterized models for the galaxies in the images. We derive the lensing shear posterior by marginalizing over all intrinsic galaxy properties that contribute to the pixel data (i.e., not limited to galaxy ellipticities) and learn the distributions for the intrinsic galaxy properties via hierarchical inference with a suitably flexible conditional probabilitiy distribution specification. We use importance sampling to separate the modeling of small imaging areas from the global shear inference, thereby rendering our algorithm computationally tractable for large surveys. With simple numerical examples we demonstrate the improvements in accuracy from our importance sampling approach, as well as the significance of the conditional distribution specification for the intrinsic galaxy properties when the data are generated from an unknown number of distinct galaxy populations with different morphological characteristics.
    The Astrophysical Journal 11/2014; 807(1). DOI:10.1088/0004-637X/807/1/87 · 6.28 Impact Factor
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    Dustin Lang · David W. Hogg · David J. Schlegel
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    ABSTRACT: We present photometry of images from the Wide-Field Infrared Survey Explorer (WISE; Wright et al. 2010) of over 400 million sources detected by the Sloan Digital Sky Survey (SDSS; York et al. 2000). We use a "forced photometry" technique, using measured SDSS source positions, star-galaxy separation and galaxy profiles to define the sources whose fluxes are to be measured in the WISE images. We perform photometry with The Tractor image modeling code, working on our "unWISE" coaddds and taking account of the WISE point-spread function and a noise model. The result is a measurement of the flux of each SDSS source in each WISE band. Many sources have little flux in the WISE bands, so often the measurements we report are consistent with zero. However, for many sources we get three- or four-sigma measurements; these sources would not be reported by the WISE pipeline and will not appear in the WISE catalog, yet they can be highly informative for some scientific questions. In addition, these small-signal measurements can be used in stacking analyses at catalog level. The forced photometry approach has the advantage that we measure a consistent set of sources between SDSS and WISE, taking advantage of the resolution and depth of the SDSS images to interpret the WISE images; objects that are resolved in SDSS but blended together in WISE still have accurate measurements in our photometry. Our results, and the code used to produce them, are publicly available at http://unwise.me.
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    ABSTRACT: High dynamic-range imagers aim to block out or null light from a very bright primary star to make it possible to detect and measure far fainter companions; in real systems a small fraction of the primary light is scattered, diffracted, and unocculted. We introduce S4, a flexible data-driven model for the unocculted (and highly speckled) light in the P1640 spectroscopic coronograph. The model uses Principal Components Analysis (PCA) to capture the spatial structure and wavelength dependence of the speckles but not the signal produced by any companion. Consequently, the residual typically includes the companion signal. The companion can thus be found by filtering this error signal with a fixed companion model. The approach is sensitive to companions that are of order a percent of the brightness of the speckles, or up to $10^{-7}$ times the brightness of the primary star. This outperforms existing methods by a factor of 2-3 and is close to the shot-noise physical limit.
    The Astrophysical Journal 08/2014; 794(2). DOI:10.1088/0004-637X/794/2/161 · 6.28 Impact Factor
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    ABSTRACT: We present a new method for determining the Galactic gravitational potential based on forward modeling of tidal stellar streams. We use this method to test the performance of smooth and static analytic potentials in representing realistic dark matter halos, which have substructure and are continually evolving by accretion. Our FAST-FORWARD method uses a Markov Chain Monte Carlo algorithm to compare, in 6D phase space, an "observed" stream to models created in trial analytic potentials. We analyze a large sample of streams evolved in the Via Lactea II (VL2) simulation, which represents a realistic Galactic halo potential. The recovered potential parameters are in agreement with the best fit to the global, present-day VL2 potential. However, merely assuming an analytic potential limits the dark matter halo mass measurement to an accuracy of 5 to 20%, depending on the choice of analytic parametrization. Collectively, mass estimates using streams from our sample reach this fundamental limit, but individually they can be highly biased. Individual streams can both under- and overestimate the mass, and the bias is progressively worse for those with smaller perigalacticons, motivating the search for tidal streams at galactocentric distances larger than 70 kpc. We estimate that the assumption of a static and smooth dark matter potential in modeling of the GD-1 and Pal5-like streams introduces an error of up to 50% in the Milky Way mass estimates.
    The Astrophysical Journal 06/2014; 795(1). DOI:10.1088/0004-637X/795/1/94 · 6.28 Impact Factor
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    ABSTRACT: No true extrasolar Earth analog is known. Hundreds of planets have been found around Sun-like stars that are either Earth-sized but on shorter periods, or else on year-long orbits but somewhat larger. Under strong assumptions, exoplanet catalogs have been used to make an extrapolated estimate of the rate at which Sun-like stars host Earth analogs. These studies are complicated by the fact that every catalog is censored by non-trivial selection effects and detection efficiencies, and every property (period, radius, etc.) is measured noisily. Here we present a general hierarchical probabilistic framework for making justified inferences about the population of exoplanets, taking into account survey completeness and, for the first time, observational uncertainties. We are able to make fewer assumptions about the distribution than previous studies; we only require that the occurrence rate density be a smooth function of period and radius (employing a Gaussian process). By applying our method to synthetic catalogs, we demonstrate that it produces more accurate estimates of the whole population than standard procedures based on weighting by inverse detection efficiency. We apply the method to an existing catalog of small planet candidates around G dwarf stars (Petigura et al. 2013). We confirm a previous result that the radius distribution changes slope near Earth's radius. We find that the rate density of Earth analogs is about 0.02 (per star per natural logarithmic bin in period and radius) with large uncertainty. This number is much smaller than previous estimates made with the same data but stronger assumptions.
    The Astrophysical Journal 06/2014; 795(1). DOI:10.1088/0004-637X/795/1/64 · 6.28 Impact Factor
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    Dustin Lang · David W. Hogg · Bernhard Scholkopf
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    ABSTRACT: We describe a system that builds a high dynamic-range and wide-angle image of the night sky by combining a large set of input images. The method makes use of pixel-rank information in the individual input images to improve a "consensus" pixel rank in the combined image. Because it only makes use of ranks and the complexity of the algorithm is linear in the number of images, the method is useful for large sets of uncalibrated images that might have undergone unknown non-linear tone mapping transformations for visualization or aesthetic reasons. We apply the method to images of the night sky (of unknown provenance) discovered on the Web. The method permits discovery of astronomical objects or features that are not visible in any of the input images taken individually. More importantly, however, it permits scientific exploitation of a huge source of astronomical images that would not be available to astronomical research without our automatic system.
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    ABSTRACT: The dark matter halo of the Milky Way is expected to be triaxial and filled with substructure. It is hoped that streams or shells of stars produced by tidal disruption of stellar systems will provide precise measures of the gravitational potential to test these predictions. We develop a method for inferring the Galactic potential with tidal streams based on the idea that the stream stars were once close in phase space. Our method can flexibly adapt to any form for the Galactic potential: it works in phase-space rather than action-space and hence relies neither on our ability to derive actions nor on the integrability of the potential. Our model is probabilistic, with a likelihood function and priors on the parameters. The method can properly account for finite observational uncertainties and missing data dimensions. We test our method on synthetic datasets generated from N-body simulations of satellite disruption in a static, multi-component Milky Way including a triaxial dark matter halo with observational uncertainties chosen to mimic current and near-future surveys of various stars. We find that with just four well-measured stream stars, we can infer properties of a triaxial potential with precisions of order 5-7 percent. Without proper motions we obtain 15 percent constraints on potential parameters and precisions around 25 percent for recovering missing phase-space coordinates. These results are encouraging for the eventual goal of using flexible, time-dependent potential models combined with larger data sets to unravel the detailed shape of the dark matter distribution around the Milky Way.
    The Astrophysical Journal 05/2014; 794(1). DOI:10.1088/0004-637X/794/1/4 · 6.28 Impact Factor
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    ABSTRACT: The Ly$\alpha$ forest flux probability distribution function (PDF) is an established probe of the intergalactic medium (IGM) astrophysics, especially the temperature-density relationship of the IGM. We measure the flux PDF from 3393 Baryon Oscillations Spectroscopic Survey (BOSS) quasars from SDSS Data Release 9, and compare with mock spectra that include careful modeling of the noise, continuum, and astrophysical uncertainties. The BOSS flux PDFs, measured at $\langle z \rangle = [2.3,2.6,3.0]$, are compared with PDFs created from mock spectra drawn from a suite of hydrodynamical simulations that sample the IGM temperature-density relationship, $\gamma$, and temperature at mean-density, $T_0$, where $T(\Delta) = T_0 \Delta^{\gamma-1}$. We find that a significant population of partial Lyman-limit systems with a column-density distribution slope of $\beta_\mathrm{pLLS} \sim -2$ are required to explain the data at the low-flux end of flux PDF, while uncertainties in the mean \lya\ forest transmission affect the high-flux end. After modelling the LLSs and marginalizing over mean-transmission uncertainties, we find that $\gamma=1.6$ best describes the data over our entire redshift range, although constraints on $T_0$ are affected by systematic uncertainties. Isothermal or inverted temperature-density relationships ($\gamma \leq 1$) are disfavored at a significance of over 4$\sigma$.
    The Astrophysical Journal 05/2014; 799(2). DOI:10.1088/0004-637X/799/2/196 · 6.28 Impact Factor

Publication Stats

19k Citations
956.82 Total Impact Points

Institutions

  • 2014
    • Carnegie Mellon University
      • Department of Physics
      Pittsburgh, Pennsylvania, United States
    • Columbia University
      New York City, New York, United States
    • The Ohio State University
      Columbus, Ohio, United States
  • 2007–2014
    • NYU Langone Medical Center
      New York, New York, United States
  • 2001–2014
    • CUNY Graduate Center
      New York, New York, United States
    • Fermi National Accelerator Laboratory (Fermilab)
      Batavia, Illinois, United States
  • 2012
    • Pennsylvania State University
      • Department of Astronomy and Astrophysics
      University Park, Maryland, United States
  • 2011
    • Universität Heidelberg
      Heidelburg, Baden-Württemberg, Germany
    • New York University
      New York, New York, United States
    • Vanderbilt University
      • Department of Physics and Astronomy
      Nashville, Michigan, United States
  • 2008–2011
    • Max Planck Institute for Astronomy
      Heidelburg, Baden-Württemberg, Germany
  • 2009
    • York University
      • Department of Physics and Astronomy
      Toronto, Ontario, Canada
  • 2007–2009
    • Princeton University
      • Department of Astrophysical Sciences
      Princeton, New Jersey, United States
  • 1996–2008
    • California Institute of Technology
      • Department of Astronomy
      Pasadena, California, United States
  • 2002–2007
    • Johns Hopkins University
      • Department of Physics and Astronomy
      Baltimore, Maryland, United States
  • 2006
    • The Catholic University of America
      • Department of Physics
      Washington, Washington, D.C., United States
  • 2005
    • The University of Arizona
      • Department of Astronomy
      Tucson, Arizona, United States
  • 1999–2001
    • Institute for Advanced Study
      Princeton Junction, New Jersey, United States
  • 1994
    • University of Toronto
      Toronto, Ontario, Canada
  • 1991
    • Massachusetts Institute of Technology
      • Department of Physics
      Cambridge, Massachusetts, United States