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J. Richard Gott III

Publications and source records attributed to J. Richard Gott III.

At least 37 records · Page 2Linked to original sources

Transformation of Morphology and Luminosity Classes of the SDSS Galaxies

We present a unified picture on the evolution of galaxy luminosity and morphology. Galaxy morphology is found to depend critically on the local environment set up by the nearest neighbor galaxy in addition to luminosity and the large scale density. When a galaxy is located farther than the virial radius from its closest neighbor, the probability for the galaxy to have an early morphological type is an increasing function only of luminosity and the local density due to the nearest neighbor ($ρ_n$). The tide produced by the nearest neighbor is thought to be responsible for the morphology transformation toward the early type at these separations. When the separation is less than the virial radius, i.e. when $ρ_n > ρ_{\rm virial}$, its morphology depends also on the neighbor's morphology and the large-scale background density over a few Mpc scales ($ρ_{20}$) in addition to luminosity and $ρ_n$. The early type probability keeps increasing as $ρ_n$ increases if its neighbor is an early type. But the probability decreases as $ρ_n$ increases when the neighbor is a late type. The cold gas streaming from the late type neighbor can be the reason for the morphology transformation toward late type. The overall early-type fraction increases as $ρ_{20}$ increases when $ρ_n > ρ_{\rm virial}$. This can be attributed to the hot halo gas of the neighbor which is confined by the pressure of the ambient medium held by the background mass. We have also found that galaxy luminosity depends on $ρ_n$, and that the isolated bright galaxies are more likely to be recent merger products. We propose a scenario that a series of morphology and luminosity transformation occur through distant interactions and mergers, which results in the morphology--luminosity--local density relation.

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Flexion and Skewness in Map Projections of the Earth

Tissot indicatrices have provided visual measures of local area and isotropy distortions. Here we show how large scale distortions of flexion (bending) and skewness (lopsidedness) can be measured. Area and isotropy distortions depend on the map projection metric, flexion and skewness, which manifest themselves on continental scales, depend on the first derivatives of the metric. We introduce new indicatrices that show not only area and isotropy distortions but flexion and skewness as well. We present a table showing error measures for area, isotropy, flexion, skewness, distances, and boundary cuts allowing us to compare different world map projections. We find that the Winkel-Tripel projection (already adopted for world maps by the National Geographic), has low distortion on most measures and excellent quality overall.

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Environmental Dependence of Properties of Galaxies in the Sloan Digital Sky Survey

We investigate the dependence of physical properties of galaxies brighter than M_r=-18.0 in the SDSS on environment, as measured by local density using an adaptive smoothing kernel. We find that variations of galaxy properties with environment are almost entirely due to the dependence of morphology and luminosity on environment. Because galaxy properties depend not only on luminosity but also on morphology, it is clear that galaxy properties cannot be determined solely by dark halo mass. When morphology and luminosity are fixed, other physical properties, such as color, color-gradient, concentration, size, velocity dispersion, and star formation rate, are nearly independent of local density. The only feature is the sharp decrease of late type fraction above the critical luminosity of about M_r=-21.3 in the morphology versus luminosity relation. Weak residual dependences on environment include that of the color of late-types (bluer at lower density) and of the L-sigma relation of early-types (larger dispersion at higher density for bright galaxies). The early-type fraction is a monotonically increasing function of local density and luminosity. The morphology-density- luminosity relation should be a key constraint on galaxy formation models. We demonstrate that the dependence on environment of the morphology of galaxie originates from variations in density on effective Gaussian smoothing scales much smaller than 12 h^{-1}Mpc. We find that galaxy morphology varies both with density measured on an effective Gaussian smoothing scale of 4.7 h^{-1} Mpc and on distance to the nearest bright galaxy (particularly, for about 0.2 h^{-1}Mpc). We propose a mechanism that the morphology of galaxies in galaxy systems is transformed by the tidal force.

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Topology of structure in the Sloan Digital Sky Survey: model testing

We measure the three-dimensional topology of large-scale structure in the Sloan Digital Sky Survey (SDSS). This allows the genus statistic to be measured with unprecedented statistical accuracy. The sample size is now sufficiently large to allow the topology to be an important tool for testing galaxy formation models. For comparison, we make mock SDSS samples using several state-of-the-art N-body simulations: the Millennium run of Springel et al. (2005)(10 billion particles), Kim & Park (2006) CDM models (1.1 billion particles), and Cen & Ostriker (2006) hydrodynamic code models (8.6 billion cell hydro mesh). Each of these simulations uses a different method for modeling galaxy formation. The SDSS data show a genus curve that is broadly characteristic of that produced by Gaussian random phase initial conditions. Thus the data strongly support the standard model of inflation where Gaussian random phase initial conditions are produced by random quantum fluctuations in the early universe. But on top of this general shape there are measurable differences produced by non-linear gravitational effects (cf. Matsubara 1994), and biasing connected with galaxy formation. The N-body simulations have been tuned to reproduce the power spectrum and multiplicity function but not topology, so topology is an acid test for these models. The data show a ``meatball'' shift (only partly due to the Sloan Great Wall of Galaxies; this shift also appears in a sub-sample not containing the Wall) which differs at the 2.5σlevel from the results of the Millennium run and the Kim & Park dark halo models, even including the effects of cosmic variance.

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Genus Topology of the Cosmic Microwave Background from the WMAP 3-Year Data

We have independently measured the genus topology of the temperature fluctuations in the cosmic microwave background seen in the Wilkinson Microwave Anisotropy Probe (WMAP) 3-year data. A genus analysis of the WMAP data indicates consistency with Gaussian random-phase initial conditions, as predicted by standard inflation. We set 95% confidence limits on non-linearities of -101 < f_{nl} < 107. We also find that the observed low l (l <= 8) modes show a slight anti-correlation with the Galactic foreground, but not exceeding 95% confidence, and that the topology defined by these modes is consistent with that of a Gaussian random-phase distribution (within 95% confidence).

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Map Projections Minimizing Distance Errors

It is useful to have mathematical criteria for evaluating errors in map projections. The Chebyshev criterion for minimizing rms (root mean square) local scale factor errors for conformal maps has been useful in developing conformal map projections of continents. Any local error criterion will be minimized ultimately by map projections with multiple interruptions, on which some pairs of points that are close on the globe are far apart on the map. Since it is as bad to have two points on the map at two times their proper separation as to have them at half their proper separation, it is the rms logarithmic distance, s, between random points in the mapped region that we will minimize. The best previously known projection of the entire sphere for distances is the Lambert equal-area azimuthal with an rms logarithmic distance error of s=0.343. For comparison, the Mercator has s=0.444, and the Mollweide has s=0.390. We present new projections: the "Gott equal-area elliptical" with perfect shapes on the central meridian, the "Gott-Mugnolo equal-area elliptical" and the "Gott-Mugnolo azimuthal" with rms logarithmic distance errors of s=0.365, s=0.348, and s=0.341 respectively, which improve on previous projections of their type. The "Gott-Mugnolo azimuthal" has the lowest distance errors of any map and is produced by a new technique using "forces" between pairs of points on a map which make them move so as to minimize s. The "Gott equal-area elliptical" projection produces a particularly attractive map of Mars, and the "Gott-Mugnolo azimuthal" projection produces an interesting map of the moon.

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Percolation Galaxy Groups and Clusters in the SDSS Redshift Survey: Identification, Catalogs, and the Multiplicity Function

We identify galaxy groups and clusters in volume-limited samples of the SDSS redshift survey, using a redshift-space friends-of-friends algorithm. We optimize the friends-of-friends linking lengths to recover galaxy systems that occupy the same dark matter halos, using a set of mock catalogs created by populating halos of N-body simulations with galaxies. Extensive tests with these mock catalogs show that no combination of perpendicular and line-of-sight linking lengths is able to yield groups and clusters that simultaneously recover the true halo multiplicity function, projected size distribution, and velocity dispersion. We adopt a linking length combination that yields, for galaxy groups with ten or more members: a group multiplicity function that is unbiased with respect to the true halo multiplicity function; an unbiased median relation between the multiplicities of groups and their associated halos; a spurious group fraction of less than ~1%; a halo completeness of more than ~97%; the correct projected size distribution as a function of multiplicity; and a velocity dispersion distribution that is ~20% too low at all multiplicities. These results hold over a range of mock catalogs that use different input recipes of populating halos with galaxies. We apply our group-finding algorithm to the SDSS data and obtain three group and cluster catalogs for three volume-limited samples that cover 3495.1 square degrees on the sky. We correct for incompleteness caused by fiber collisions and survey edges, and obtain measurements of the group multiplicity function, with errors calculated from realistic mock catalogs. These multiplicity function measurements provide a key constraint on the relation between galaxy populations and dark matter halos.

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Cleaned Three-Year WMAP CMB Map: Magnitude of the Quadrupole and Alignment of Large Scale Modes

[Abridged] We have produced a cleaned map of the Wilkinson Microwave Anisotropy Probe (WMAP) 3-year data using an improved foreground subtraction technique. We perform an internal linear combination (ILC) to subtract the Galactic foreground emission from the temperature fluctuations observed by the WMAP. We divide the whole sky into hundreds of pixel groups with similar foreground spectral indices over a range of WMAP frequencies, apply the ILC for each group, and obtain a CMB map with foreground emission effectively reduced. With the resulting foreground-reduced ILC map, we have investigated the known anomalies in CMB maps at large scales. The quadrupole and the octopole powers measured from our ILC map are δT_2^2 = 276_{-126}^{+94} uK^2 and δT_3^2 = 952_{-83}^{+64} uK^2, respectively. The measured quadrupole power is lower than the value expected in the concordance LCDM model (1250 uK^2), in which the probability of finding a quadrupole power lower than the measured value is 5.7%. We have confirmed that the quadrupole and the octopole are strongly aligned with angle θ_{23} = 11.8_{-8.0}^{+6.4} degree, and are planar with high planarity parameters t=0.98_{-0.02}^{+0.02} for l=2 and t=0.91_{-0.03}^{+0.02} for l=3. The observed angular separation θ_{23} is marginally statistically significant because the probability of finding the angular separation as low as the observed value is 4.3%. However, the observed planarity is not statistically significant. The probability of observing such a planarity as high as the measured t values is over 18%. The ILC simulations show that the residual foreground emission in the ILC map does not affect the estimated values significantly.

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A Map of the Universe

We have produced a new conformal map of the universe illustrating recent discoveries, ranging from Kuiper belt objects in the Solar system, to the galaxies and quasars from the Sloan Digital Sky Survey. This map projection, based on the logarithm map of the complex plane, preserves shapes locally, and yet is able to display the entire range of astronomical scales from the Earth's neighborhood to the cosmic microwave background. The conformal nature of the projection, preserving shapes locally, may be of particular use for analyzing large scale structure. Prominent in the map is a Sloan Great Wall of galaxies 1.37 billion light years long, 80% longer than the Great Wall discovered by Geller and Huchra and therefore the largest observed structure in the universe.

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Topology Analysis of the Sloan Digital Sky Survey: I. Scale and Luminosity Dependences

We measure the topology of volume-limited galaxy samples selected from a parent sample of 314,050 galaxies in the Sloan Digital Sky Survey(SDSS), which is now complete enough to describe the fully three-dimensional topology and its dependence on galaxy properties. We compare the observed genus statistic Gν_f) to predictions for a Gaussian random field and to the genus measured for mock surveys constructed from new large-volume simulations of the LambdaCDM cosmology. In this analysis we carefully examine the dependence of the observed genus statistic on the Gaussian smoothing scale R_G from 3.5 to 11 h^-1Mpc and on the luminosity of galaxies over the range -22.50<M_r<-18.5. The void multiplicity A_V is less than unity at all smoothing scales. Because A_V cannot become less than 1 through gravitational evolution, this result provides strong evidence for biased galaxy formation in low density environments. We also find clear evidence of luminosity bias of topology within the volume-limited sub-samples. The shift parameter Delta nu indicates that the genus of brighter galaxies shows a negative shift toward a ``meatball'' (i.e. cluster-dominated) topology, while faint galaxies show a positive shift toward a ``bubble'' (i.e. void-dominated) topology. The transition from negative to positive shift occurs approximately at the characteristic absolute magnitude M_{r*}=-20.4. Even in this analysis of the largest galaxy sample to date, we detect the influence of individual large-scale structures, as the shift parameter Delta nu and cluster multiplicity A_C reflect (at ~3 sigma) the presence of the Sloan Great Wall and a X-shaped structure which runs for several hundred Mpc across the survey volume.

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Minkowski Functionals of SDSS galaxies I : Analysis of Excursion Sets

We present a first morphometric investigation of a preliminary sample from the SDSS of 154287 galaxies with apparent magnitude 14.5<m_r<17.5 and redshift 0.001<z<0.4. We measure the Minkowski Functionals, which are a complete set of morphological descriptors. To account for the complicated wedge--like geometry of the present survey data, we construct isodensity contour surfaces from the galaxy positions in redshift space and employ two complementary methods of computing the Minkowski Functionals. We find that the observed Minkowski Functionals for SDSS galaxies are consistent with the prediction of a Lambda--dominated spatially--flat Cold Dark Matter model with random--Gaussian initial conditions, within the cosmic variance estimated from the corresponding mock catalogue. We expect that future releases of the SDSS survey will allow us to distinguish morphological differences in the galaxy distribution with regard to different morphological type and luminosity ranges.

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Effects of Gravitational Evolution, Biasing, and Redshift Space Distortion on Topology

We have studied the dependence of topology of large scale structure on tracer, gravitational evolution, redshift space distortion, and cosmology. A series of large N-body simulations of the $Λ$CDM and SCDM models that have evolved 1.1 or 8.6 billion particles, are used in the study. Evolution of the genus statistic, used as a topology measure, from redshift 8 to 0 is accurately calculated over a wide range of smoothing scales using the simulations. The tracers of large scale structure considered are the CDM matter, biased peaks in the initial density field, dark halos, and `galaxies' populating the dark halos in accordance with a Halo Occupation Distribution (HOD) model. We have found that the effects of biasing, gravitational evolution, and initial conditions on topology of large scale structure are all comparable. The redshift space distortion effects are relatively small down to about 5 $h^{-1}$Mpc for all tracers except for the high threshold part of the genus curve. The gravitational effects are found to be well-modeled by the analytic perturbation theory when the CDM matter distribution is considered. But the direction of gravitational evolution of topology can be even reversed for different tracers. For example, the shift parameter of the genus curve evolves in opposite directions for matter and HOD `galaxies' at large scales. At small scales there are interesting deviations of the genus curve of dark halos and `galaxies' from that of matter in our initially Gaussian simulations. The deviations should be understood as due to combined effects of gravitational evolution and biasing.

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Where Did The Moon Come From?

The current standard theory of the origin of the Moon is that the Earth was hit by a giant impactor the size of Mars causing ejection of iron poor impactor mantle debris that coalesced to form the Moon. But where did this Mars-sized impactor come from? Isotopic evidence suggests that it came from 1AU radius in the solar nebula and computer simulations are consistent with it approaching Earth on a zero-energy parabolic trajectory. But how could such a large object form in the disk of planetesimals at 1AU without colliding with the Earth early-on before having a chance to grow large or before its or the Earth's iron core had formed? We propose that the giant impactor could have formed in a stable orbit among debris at the Earth's Lagrange point $L_4$ (or $L_5$). We show such a configuration is stable, even for a Mars-sized impactor. It could grow gradually by accretion at $L_4$ (or $L_5$), but eventually gravitational interactions with other growing planetesimals could kick it out into a chaotic creeping orbit which we show would likely cause it to hit the Earth on a zero-energy parabolic trajectory. This paper argues that this scenario is possible and should be further studied.

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Non-Gaussian Error Distribution of Hubble Constant Measurements

We construct the error distribution of Hubble constant ($H_0$) measurements from Huchra's compilation of 461 measurements of $H_0$ and the WMAP experiment central value $H_0$ = 71 km s$^{-1}$ Mpc$^{-1}$. This error distribution is non-Gaussian, with significantly larger probability in the tails of the distribution than predicted by a Gaussian distribution. The 95.4 % confidence limits are 7.0 $σ$ in terms of the quoted errors. It is remarkably well described by either a widened $n = 2$ Student's $t$ distribution or a widened double exponential distribution. These conclusions are unchanged if we use instead the central value $H_0$ = 67 km s$^{-1}$ Mpc$^{-1}$ found from a median statistics analysis of a major subset of $H_0$ measurements used here.

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Genus Topology of the Cosmic Microwave Background from WMAP

We have independently measured the genus topology of the temperature fluctuations in the cosmic microwave background seen by the Wilkinson Microwave Anisotropy Probe (WMAP). A genus analysis of the WMAP data indicates consistency with Gaussian random-phase initial conditions, as predicted by standard inflation.

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An Eternal Time Machine in 2+1 Dimensional anti-de Sitter Space

2+1 dimensional anti-de Sitter space has been the subject of much recent investigation. Studies of the behaviour of point particles in this space have given us a greater understanding of the BTZ black hole solutions produced by topological identification of adS isometries. In this paper, we present a new configuration of two orbiting massive point particles that leads to an ``eternal'' time machine, where closed timelike curves fill the entire space. In contrast to previous solutions, this configuration has no event or chronology horizons. Another interesting feature is that there is no lower bound on the relative velocities of the point masses used to construct the time machine; as long as the particles exceed a certain mass threshold, an eternal time machine will be produced.

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Three-Dimensional Genus Statistics of Galaxies in the SDSS Early Data Release

We present the first analysis of three-dimensional genus statistics for the SDSS EDR galaxy sample. Due to the complicated survey volume and the selection function, analytic predictions of the genus statistics for this sample are not feasible, therefore we construct extensive mock catalogs from N-body simulations in order to compare the observed data with model predictions. This comparison allows us to evaluate the effects of a variety of observational systematics on the estimated genus for the SDSS sample, including the shape of the survey volume, the redshift distortion effect, and the radial selection function due to the magnitude limit. The observed genus for the SDSS EDR galaxy sample is consistent with that predicted by simulations of a $Λ$-dominated spatially-flat cold dark matter model. Standard ($Ω_0=1$) cold dark matter model predictions do not match the observations. We discuss how future SDSS galaxy samples will yield improved estimates of the genus.

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Two-Dimensional Topology of the Sloan Digital Sky Survey

We present the topology of a volume-limited sample of 11,884 galaxies, selected from an apparent-magnitude limited sample of over 100,000 galaxies observed as part of the Sloan Digital Sky Survey (SDSS). The data currently cover three main regions on the sky: one in the Galactic north and one in the south, both at zero degrees declination, and one area in the north at higher declination. Each of these areas covers a wide range of survey longitude but a narrow range of survey latitude, allowing the two dimensional genus to be measured. The genus curves of the SDSS sub-samples are similar, after appropriately normalizing these measurements for the different areas. We sum the genus curves from the three areas to obtain the total genus curve of the SDSS. The total curve has a shape similar to the genus curve derived from mock catalogs drawn from the Hubble Volume Lambda CDM simulation and is similar to that of a Gaussian random field. Likewise, comparison with the genus of the 2dFGRS, after normalization for the difference in area, reveals remarkable similarity in the topology of these samples. We test for the effects of galaxy type segregation by splitting the SDSS data into thirds, based on the u^*- r^* colors of the galaxies, and measure the genus of the reddest and bluest sub-samples. This red/blue split in u^*- r^* is essentially a split by morphology (Strateva et al. 2001). We find that the genus curve for the reddest galaxies exhibits a ``meatball'' shift of the topology -- reflecting the concentration of red galaxies in high density regions -- compared to the bluest galaxies and the full sample, in agreement with predictions from simulations.

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