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Joel Primack

Publications and source records attributed to Joel Primack.

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Accelerating Dust Temperature Calculations with Graphics Processing Units

When calculating the infrared spectral energy distributions (SEDs) of galaxies in radiation-transfer models, the calculation of dust grain temperatures is generally the most time-consuming part of the calculation. Because of its highly parallel nature, this calculation is perfectly suited for massively parallel general-purpose Graphics Processing Units (GPUs). This paper presents an implementation of the calculation of dust grain equilibrium temperatures on GPUs in the Monte-Carlo radiation transfer code Sunrise, using the CUDA API. The GPU can perform this calculation 69 times faster than the 8 CPU cores, showing great potential for accelerating calculations of galaxy SEDs.

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A New Era in Extragalactic Background Light Measurements: The Cosmic History of Accretion, Nucleosynthesis and Reionization

(Brief Summary) What is the total radiative content of the Universe since the epoch of recombination? The extragalactic background light (EBL) spectrum captures the redshifted energy released from the first stellar objects, protogalaxies, and galaxies throughout cosmic history. Yet, we have not determined the brightness of the extragalactic sky from UV/optical to far-infrared wavelengths with sufficient accuracy to establish the radiative content of the Universe to better than an order of magnitude. Among many science topics, an accurate measurement of the EBL spectrum from optical to far-IR wavelengths, will address: What is the total energy released by stellar nucleosynthesis over cosmic history? Was significant energy released by non-stellar processes? Is there a diffuse component to the EBL anywhere from optical to sub-millimeter? When did first stars appear and how luminous was the reionization epoch? Absolute optical to mid-IR EBL spectrum to an astrophysically interesting accuracy can be established by wide field imagingat a distance of 5 AU or above the ecliptic plane where the zodiacal foreground is reduced by more than two orders of magnitude.

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Flat-Cored Dark Matter in Cuspy Clusters of Galaxies

Sand, Treu, & Ellis (2002) have measured the central density profile of cluster MS2137-23 with gravitational lensing and velocity dispersion and removed the stellar contribution with a reasonable M/L. The resulting dark matter distribution within r<50 kpc was fitted by a density cusp of r^{-beta} with beta=0.35. This stands in an apparent contradiction to the CDM prediction of beta~1, and the disagreement worsens if adiabatic compression of the dark matter by the infalling baryons is considered. Following El-Zant, Shlosman & Hoffman (2001), we argue that dynamical friction acting on galaxies moving within the dark matter background counters the effect of adiabatic compression by transfering the orbital energy of galaxies to the dark matter, thus heating up and softening the central density cusp. Using N-body simulations of massive solid clumps moving in clusters we show that indeed the inner dark matter distribution flattens (with beta approx 0.35 for a cluster like MS2137-23) when the galaxies spiral inward. We find as a robust result that while the dark matter distribution becomes core-like, the overall mass distribution preserves its cuspy nature, in agreement with X-ray and lensing observations of clusters.

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A New Non-Parametric Approach to Galaxy Morphological Classification

We present two new non-parametric methods for quantifying galaxy morphology: the relative distribution of the galaxy pixel flux values (the Gini coefficient or G) and the second-order moment of the brightest 20% of the galaxy's flux (M20). We test the robustness of G and M20 to decreasing signal-to-noise and spatial resolution, and find that both measures are reliable to within 10% at average signal-to-noise per pixel greater than 3 and resolutions better than 1000 pc and 500 pc, respectively. We have measured G and M20, as well as concentration (C), asymmetry (A), and clumpiness (S) in the rest-frame near-ultraviolet/optical wavelengths for 150 bright local "normal" Hubble type galaxies (E-Sd) galaxies and 104 0.05 < z < 0.25 ultra-luminous infrared galaxies (ULIRGs).We find that most local galaxies follow a tight sequence in G-M20-C, where early-types have high G and C and low M20 and late-type spirals have lower G and C and higher M20. The majority of ULIRGs lie above the normal galaxy G-M20 sequence, due to their high G and M20 values. Their high Gini coefficients arise from very bright nuclei, while the high second-order moments are produced by multiple nuclei and bright tidal tails. All of these features are signatures of recent and on-going mergers and interactions. We also find that in combination with A and S, G is more effective than C at distinguishing ULIRGs from the "normal" Hubble-types. Finally, we measure the morphologies of 45 1.7 < z < 3.8 galaxies from HST NICMOS observations of the Hubble Deep Field North. We find that many of the z $\sim$ 2 galaxies possess G and A higher than expected from degraded images of local elliptical and spiral galaxies, and have morphologies more like low-redshift single nucleus ULIRGs.

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Generating Hot Gas in Simulations of Disk-Galaxy Major Mergers

We report on the merger-induced generation of a shock-heated gas wind and formation of a remnant gas halo in simulations of colliding disk galaxies. The simulations use cosmologically motivated initial conditions and include the effects of radiative cooling, star formation, stellar feedback and the non-adiabatic heating of gas. The non-adiabatic heating, i.e. shocks, generated in the final merger forces gas out of the central region of the merger remnant and into the dark-matter halo. We demonstrate that the amount of heating depends on the size of the progenitor disk galaxy as well as the initial orbit the galaxies are placed on. Based upon these dependencies, we motivate a possible recipe for including this effect in semi-analytic models of galaxy formation.

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Resolving the Structure of Cold Dark Matter Halos II

We study the effects of mass and force resolution on the density profiles of galaxy-size Cold Dark Matter (CDM) halos in a flat, low-density cosmological model with vacuum energy. We show thatalthough increasing the mass and force resolution allows us to probe deeper into the inner halo regions, it does not lead to steeper inner density profiles. Instead, the halo profiles converge at scales larger than four times the formal resolution or the radius containing more than 200 particles, whichever is larger. In the simulations presented in this paper, we are able to probe density profile of a relaxed isolated galaxy-size halo at scales r=(0.005-1)r_vir. We find that the density distribution can be well approximated by the profile suggested by Moore etal (1998): rho= x^{-1.5}(1+x^{1.5})^-1, where x=r/r_s and r_s is the characteristic radius. The analytical profile proposed by Navarro et al. (1996) rho= x^{-1}(1+x)^-2, also provides a good fit, with the same relative errors of about 10% for radii larger than 1% of the virial radius. Both analytical profiles fit equally well because for high-concentration galaxy-size halos the differences between these profiles become significant only at scales well below 0.01r_vir. We also find that halos of similar mass may have somewhat different parameters (characteristic radius, maximum rotation velocity, etc.) and shapes of their density profiles. We associate this scatter in properties with differences in halo merger histories and the amount of substructure present in the analyzed halos.

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Inclination Effects in Spiral Galaxy Gravitational Lensing

Spheroidal components of spiral galaxies have been considered the only dynamically important component in gravitational lensing studies thus far. Here we point out that including the disk component can have a significant effect, depending on the disk inclination, on a variety of lensing properties that are relevant to present studies and future surveys. As an example, we look at the multiple image system B1600+434, recently identified as being lensed by a spiral galaxy. We find that including the disk component one can understand the fairly large image separation as being due to the inclination of a typical spiral, rather than the presence of a very massive halo. The fairly low magnification ratio can also be readily understood if the disk is included. We also discuss how such lensed systems might allow one to constrain parameters of spiral galaxies such as a disk-to-halo mass ratio, and disk mass scale length. Another example we consider is the quasar multiple-lensing cross section, which we find can increase many-fold at high inclination for a typical spiral. Finally, we discuss the changes in the gravitational lensing effects on damped Lyman alpha systems (DLAS) when disk lensing is included.

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Linearizing the Observed Power Spectrum

Reconstruction of the linear power spectrum from observational data provides a way to compare cosmological models to a large amount of data, as Peacock & Dodds (1994, 1996) have shown. By applying the appropriate corrections to the observational power spectrum it is possible to recover the underlying linear power spectrum for any cosmological model. Using extensive N-body simulations we demonstrate that the method is applicable to a wide range of cosmological models. However, we find that the recovery of the linear power spectrum from observations following PD94 is misleading because the corrections are model- dependent. When we apply the proper corrections for a given model to the observational power spectrum, we find that no model in our test group recovers the linear power spectrum well for the bias suggested by PD94 between Abell, Radio, Optical, and IRAS catalogs 4.5:1.9:1.3:1, with b_IRAS=1. When we allow b_IRAS to vary we find that: (i)CHDM models give very good fits to observations if optically-selected galaxies are slightly biased b_Opt=1.1 (ii) Most LCDM models give worse but acceptable fits if blue galaxies are considerably antibiased: 0.6<b_Opt<0.9 and fail if optical galaxies are biased. (iii)There is a universal shape of the recovered linear power spectrum of all LCDM models over their entire range of explored wavenumbers,0.01<k<0.6h\Mpc. Recovered spectra of CDM and CHDM models are nearly the same as that of LCDM in the region 0.01<k<0.2h/Mpc but diverge from this spectrum at higher k.

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The Best Theory of Cosmic Structure Formation is Cold + Hot Dark Matter (CHDM)

I have been asked to make the case here that CHDM is the best theory of cosmic structure formation, and indeed I believe that it is the best of all those I have considered if the cosmological matter density is near critical and if the expansion rate is not too large (i.e. $h \equiv H_0/(100 \kmsMpc) \lsim 0.6$). I discuss CHDM together with its chief competitor among CDM variants, low-$Ω_0$ CDM with a cosmological constant ($Λ$CDM). $Λ$CDM with $Ω_0 \sim 0.3$ has the possible virtue of allowing a higher expansion rate H_0 for a given cosmic age t_0, but the defect of predicting too much fluctuation power on small scales. Also, except for the $H_0-t_0$ problem, there is not a shred of evidence in favor of a nonzero cosmological constant, only increasingly stringent observational upper bounds on it. CHDM has less power on small scales, in good agreement with data, although it remains to be seen whether it predicts early enough galaxy formation to be compatible with the latest high-redshift data. I also briefly compare CHDM to other CDM variants such as Warm Dark Matter (WDM) and tilted CDM. CHDM has the advantage among $Ω=1$ CDM-type models of requiring little or no tilt, which appears to be an advantage in fitting recent small-angle CMB anisotropy data. The presence of a hot component that clusters less than cold dark matter lowers the effective $Ω_0$ that would be measured on small scales, which appears to be in accord with observations, and it may also avoid the discrepancy between the high central density of dark matter halos from CDM simulations compared to evidence from rotation curves of dwarf spiral galaxies.

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Cosmological Structure Formation With and Without Hot Dark Matter

Cold + Hot Dark Matter (CHDM) is perhaps the best theory of cosmic structure formation {\it if} the cosmological matter density is near critical (i.e., $Ω_0 \approx 1$) and {\it if} the expansion rate is not too large (i.e. $h \equiv H_0/(100 \kmsMpc) \lsim 0.6$). I discuss CHDM together with its chief competitor among CDM variants, low-$Ω_0$ CDM with a cosmological constant (\lcdm). \lcdm\ with $Ω_0 \sim 0.3$ has the possible virtue of allowing a higher expansion rate $H_0$ for a given cosmic age $t_0$, but the defect of predicting too much fluctuation power on small scales. Also, except for the $H_0-t_0$ problem, there is not a shred of evidence in favor of a nonzero cosmological constant, only increasingly stringent observational upper bounds on it. CHDM has less power on small scales, in good agreement with data, although it remains to be seen whether it predicts early enough galaxy formation to be compatible with the latest high-redshift data. CHDM has the advantage among $Ω=1$ CDM-type models of requiring little or no tilt, which appears to be an advantage in fitting recent small-angle cosmic microwave background anisotropy data. The presence of a hot component that clusters less than cold dark matter lowers the effective $Ω_0$ that would be measured on small scales, which appears to be in accord with observations, and it may also avoid the discrepancy between the high central density of dark matter halos from CDM simulations compared to evidence from rotation curves of dwarf spiral galaxies.

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Filament and Shape Statistics: A Quantitative Comparison of Cold + Hot and Cold Dark Matter Cosmologies vs. CfA1 Data

A new class of geometric statistics for analyzing galaxy catalogs is presented. Filament statistics quantify filamentarity and planarity in large scale structure in a manner consistent with catalog visualizations. These statistics are based on sequences of spatial links which follow local high-density structures. From these link sequences we compute the discrete curvature, planarity, and torsion. Filament statistics are applied to CDM and CHDM ($Ω_ν= 0.3$) simulations of Klypin \etal (1996), the CfA1-like mock redshift catalogs of Nolthenius, Klypin and Primack (1994, 1996), and the CfA1 catalog. We also apply the moment-based shape statistics developed by Babul \& Starkman (1992), Luo \& Vishniac (1995), and Robinson \& Albrecht (1996) to these same catalogs, and compare their robustness and discriminatory power versus filament statistics. For 100 Mpc periodic simulation boxes ($H_0 = 50$ km s$^{-1}$ Mpc$^{-1}$), we find discrimination of $\sim 4σ$ (where $σ$ represents resampling errors) between CHDM and CDM for selected filament statistics and shape statistics, including variations in the galaxy identification scheme. Comparing the CfA1 data versus the models does not yield a conclusively favored model; no model is excluded at more than a $\sim 2σ$ level for any statistic, not including cosmic variance which could further degrade the discriminatory power. We find that CfA1 discriminates between models poorly mainly due to its sparseness and small number of galaxies, not due to redshift distortion, magnitude limiting, or geometrical effects. We anticipate that the proliferation of large redshift surveys and simulations will enable the statistics presented here to provide robust discrimination between large-scale structure in various cosmological models.

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Dark Matter and Cosmology: CDM with a Cosmological Constant ($Λ$CDM) vs. CDM with Hot Dark Matter (CHDM)

Here we discuss what are perhaps the two most popular variants of CDM that might agree with the data: \lcdm\ and CHDM. While the predictions of COBE-normalized \lcdm\ and CHDM both agree well with the available data on scales of $\sim 10$ to $100 \hMpc$, each has potential virtues and defects. \lcdm\ with $Ω_0 \sim 0.3$ has the possible virtue of allowing a higher expansion rate $H_0$ for a given cosmic age $t_0$, but the defect of predicting too much fluctuation power on small scales. CHDM has less power on small scales, so its predictions appear to be in good agreement with data on the galaxy distribution, but it remains to be seen whether it predicts early enough galaxy formation to be compatible with the latest high-redshift data. Also, two very recent observational results favor high cosmic density, and thus favor $Ω=1$ models such as CHDM over \lcdm\ --- (1) the positive deceleration parameter $q_0>0$ measured using high-redshift Type Ia supernovae, and (2) the low primordial deuterium/hydrogen ratio measured in two different quasar absorption spectra. We try to identify ``best'' variants of both \lcdm\ and CHDM, and discuss critical observational tests for both models.

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Small-Scale Power Spectrum and Correlations in LCDM

Cosmological models with a positive cosmological constant and $Ω_0<1$ have a number of attractive features. A larger Hubble constant, which can be compatible with the recent HST estimate, and a large fraction of baryon density in galaxy clusters make them current favorites. Early galaxy formation also is considered as a welcome feature of these models But early galaxy formation implies that fluctuations on few megaparsec scales spent more time in the nonlinearregime, as compared with standard Cold Dark Matter (CDM) or Cold+Hot Dark Matter models. This results in excessive clustering on small scales. We show that a typical LCDM model with $H_0=70$ km/s/Mpc, $Ω_0=0.3$ normalized to COBE on large scales and compatible with the number-density of galaxy clusters, predicts a power spectrum of galaxy clustering in real space which is too high: {\it at least} twice larger than CfA estimates (Park \etal 1994) and 3 times larger than APM estimates (Baugh \& Efstathiou 1994) for wavenumbers $k=(0.4-1)h/{\rm Mpc}$. This conclusion holds if we assume either that galaxies trace the dark matter ($σ_8\approx 1.1$ for this model) or just that a region with higher density produces more galaxies than a region with lower density. The only way to reconcile the model with the observed power spectrum is to assume that regions with high dark matter density produce fewer galaxies than regions with low density. Theoretically this is possible, but it seems very unlikely: X-ray emission from groups and clusters indicates that places with a large density of dark matter produce a large number of galaxies. Since it follows that the low- $Ω$ LCDM models are in serious trouble, we discuss which LCDM models have the best hope of surviving the confrontation with available observational data.

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Filament Statistics: A Quantitative Comparison of Cold + Hot and Cold Dark Matter Cosmologies with CfA1 Data

A new class of geometric statistics for analyzing galaxy catalogs is presented. {\it Filament statistics} quantify filamentarity and planarity in large scale structure in a manner consistent with catalog visualizations. These statistics are based on sequences of spatial links which follow local high-density structures. From these link sequences we compute the discrete curvature, planarity, and torsion. Filament statistics are applied to CDM and CHDM ($Ω_ν= 0.3$) simulations of Klypin \etal (1995), the CfA1-like sky catalogs of Nolthenius, Klypin and Primack (1994, 1995), and the CfA1 catalog. For 100 Mpc periodic simulation boxes ($H_0 = 50$ km s$^{-1}$ Mpc$^{-1}$), we find robust discrimination of over 4$σ$ (where $σ$ represents resampling errors) between CHDM and CDM. The {\it reduced filament statistics} show that CfA1 data is intermediate between CHDM and CDM, but more consistent with the CHDM models. Filament statistics provide robust and discriminatory shape statistics with which to test cosmological simulations of various models against present and future redshift survey data.

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Damped Lyman Alpha Systems vs. Cold + Hot Dark Matter

Damped Ly$α$ systems provide possibly the most significant evidence for early structure formation, and thus a stringent constraint on the Cold + Hot Dark Matter (CHDM) cosmology. Using the numbers of halos in N-body simulations to normalize Press-Schechter (PS) estimates of the number densities of protogalaxies as a function of redshift, we find that CHDM with $Ω_c/Ω_ν/Ω_b = 0.6/0.3/0.1$ is compatible with the damped Ly$α$ data only at $z<2.5$, but that it is probably incompatible with data at $z>3$. The predictions of CHDM are quite sensitive to the neutrino fraction. We find that $Ω_c/Ω_ν/Ω_b = 0.725/0.20/0.075$ is compatible with the $z>3$ data. With one massive neutrino species, this corresponds to lowering the neutrino mass from 7.0 to 4.7 eV, for $H_0=50\kmsMpc$ and $T=2.726$ K. By analysing our numerical simulations with different resolutions and box sizes as well as those of Ma \& Bertchinger (1994), we show that for the CHDM models with $Ω_ν$=0.2--0.3 the PS approximation should be used with Gaussian filter with $δ_c=1.3-1.4$ if one tries to recover the total mass of a collapsed halo and to include nonlinear effects, due to waves both longer and shorter than those within the simulation box.

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Damped Lyman Alpha Systems vs. Cold + Hot Dark Matter

Although the Cold + Hot Dark Matter (CHDM) cosmology provides perhaps the best fit of any model to all the available data at the current epoch, CHDM produces structure at relatively low redshifts and thus could be ruled out if there were evidence for formation of massive objects at high redshifts. Damped Ly$α$ systems are abundant in quasar absorption spectra and thus provide possibly the most significant evidence for early structure formation, and thus perhaps the most stringent constraint on CHDM. Using the numbers of halos in N-body simulations to normalize Press-Schechter estimates of the number densities of protogalaxies as a function of redshift, we find that CHDM with $Ω_c/Ω_ν/Ω_b = 0.6/0.3/0.1$ is compatible with the damped Ly$α$ data at $\le 2.5$, but that it is probably incompatible with the limited $z>3$ damped Ly$α$ data. The situation is uncertain because there is very little data for $z>3$, and also it is unclear whether all damped Ly$α$ systems are associated with collapsed protogalaxies. The predictions of CHDM are quite sensitive to the hot (neutrino) fraction, and we find that $Ω_c/Ω_ν/Ω_b = 0.675/0.25/0.075$ is compatible even with the $z>3$ data. This corresponds to lowering the neutrino mass from 6.8 to 5.7 eV, for $H_0=50\kmsMpc$. In CHDM, the higher redshift damped Ly$α$ systems are predicted to have lower masses, which can be checked by measuring the velocity widths of the associated metal line systems.

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Structure Formation with Cold + Hot Dark Matter

We report results from high-resolution particle-mesh (PM) N-body simulations of structure formation in an $Ω=1$ cosmological model with a mixture of Cold plus Hot Dark Matter (C+HDM) having $Ω_{\rm cold}=0.6$, $Ω_ν=0.3$, and $Ω_{\rm baryon}=0.1$. We present analytic fits to the C+HDM power spectra for both cold and hot ($ν$) components, which provide initial conditions for our nonlinear simulations. In order to sample the neutrino velocities adequately, these simulations included six times as many neutrino particles as cold particles. Our simulation boxes were 14, 50, and 200~Mpc cubes (with $H_0=50$ km s$^{-1}$ Mpc$^{-1}$); we also did comparison simulations for Cold Dark Matter (CDM) in a 50~Mpc box. C+HDM with linear bias factor $b=1.5$ is consistent both with the COBE data and with the galaxy correlations we calculate. We find the number of halos as a function of mass and redshift in our simulations; our results for both CDM and C+HDM are well fit by a Press-Schechter model. The number density of galaxy-mass halos is smaller than for CDM, especially at redshift $z>2$, but the numbers of cluster-mass halos are comparable. We also find that on galaxy scales the neutrino velocities and flatter power spectrum in C+HDM result in galaxy pairwise velocities that are in good agreement with the data, and about 30\% smaller than in CDM with the same biasing factor. On scales of several tens of Mpc, the C+HDM streaming velocities are considerably larger than CDM. Thus C+HDM looks promising as a model of structure formation.

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