Showing papers in "The Astrophysical Journal in 2002"

The slope of the black hole mass versus velocity dispersion correlation

Abstract: Observations of nearby galaxies reveal a strong correlation between the mass of the central dark object MBH and the velocity dispersionof the host galaxy, of the form logðMBH=M� Þ¼ � þ � logð�=� 0Þ; how- ever, published estimates of the slopespan a wide range (3.75-5.3). Merritt & Ferrarese have argued that low slopes (d4) arise because of neglect of random measurement errors in the dispersions and an incorrect choice for the dispersion of the Milky Way Galaxy. We show that these explanations and several others account for at most a small part of the slope range. Instead, the range of slopes arises mostly because of sys- tematic differences in the velocity dispersions used by different groups for the same galaxies. The origin of these differences remains unclear, but we suggest that one significant component of the difference results from Ferrarese & Merritt's extrapolation of central velocity dispersions to re= 8( re is the effective radius) using an empirical formula. Another component may arise from dispersion-dependent systematic errors in the mea- surements. A new determination of the slope using 31 galaxies yields � ¼ 4:02 � 0:32, � ¼ 8:13 � 0:06 for � 0 ¼ 200 km s � 1 . The MBH-� relation has an intrinsic dispersion in log MBH that is no larger than 0.25-0.3 dex and may be smaller if observational errors have been underestimated. In an appendix, we present a simple kinematic model for the velocity-dispersion profile of the Galactic bulge. Subject headings: black hole physics — galaxies: bulges — galaxies: fundamental parameters — galaxies: nuclei — Galaxy: bulge — Galaxy: kinematics and dynamics

Analytic Light Curves for Planetary Transit Searches

Abstract: We present exact analytic formulae for the eclipse of a star described by quadratic or nonlinear limb darkening. In the limit that the planet radius is less than a tenth of the stellar radius, we show that the exact light curve can be well approximated by assuming the region of the star blocked by the planet has constant surface brightness. We apply these results to the Hubble Space Telescope observations of HD 209458, showing that the ratio of the planetary to stellar radii is 0.1207 ± 0.0003. These formulae give a fast and accurate means of computing light curves using limb-darkening coefficients from model atmospheres that should aid in the detection, simulation, and parameter fitting of planetary transits.

The Nucleosynthetic Signature of Population III

Abstract: Growing evidence suggests that the first generation of stars may have been quite massive (~100-300 M?). Could these stars have left a distinct nucleosynthetic signature? We explore the nucleosynthesis of helium cores in the mass range MHe = 64-133 M?, corresponding to main-sequence star masses of approximately 140-260 M?. Above MHe = 133 M?, without rotation and using current reaction rates, a black hole is formed, and no nucleosynthesis is ejected. For lighter helium core masses, ~40-63 M?, violent pulsations occur, induced by the pair instability and accompanied by supernova-like mass ejection, but the star eventually produces a large iron core in hydrostatic equilibrium. It is likely that this core, too, collapses to a black hole, thus cleanly separating the heavy-element nucleosynthesis of pair instability supernovae from those of other masses, both above and below. Indeed, black hole formation is a likely outcome for all Population III stars with main-sequence masses between about 25 and 140 M? (MHe = 9-63 M?) as well as those above 260 M?. Nucleosynthesis in pair instability supernovae varies greatly with the mass of the helium core. This core determines the maximum temperature reached during the bounce. At the upper range of exploding core masses, a maximum of 57 M? of 56Ni is produced, making these the most energetic and the brightest thermonuclear explosions in the universe. Integrating over a distribution of masses, we find that pair instability supernovae produce a roughly solar distribution of nuclei having even nuclear charge (Si, S, Ar, etc.) but are remarkably deficient in producing elements with odd nuclear charge?Na, Al, P, V, Mn, etc. This is because there is no stage of stable post-helium burning to set the neutron excess. Also, essentially no elements heavier than zinc are produced owing to a lack of s- and r-processes. The Fe/Si ratio is quite sensitive to whether the upper bound on the initial mass function is over 260 M? or somewhere between 140 and 260 M?. When the yields of pair instability supernovae are combined with reasonable estimates of the nucleosynthesis of Population III stars from 12 to 40 M?, this distinctive pattern of deficient production of odd-Z elements persists. Some possible strategies for testing our predictions are discussed.

Detection of an Extrasolar Planet Atmosphere

Abstract: We report high-precision spectrophotometric observations of four planetary transits of HD 209458, in the region of the sodium resonance doublet at 589.3 nm. We find that the photometric dimming during transit in a bandpass centered on the sodium feature is deeper by (2.32 ± 0.57) × 10-4 relative to simultaneous observations of the transit in adjacent bands. We interpret this additional dimming as absorption from sodium in the planetary atmosphere, as recently predicted from several theoretical modeling efforts. Our model for a cloudless planetary atmosphere with a solar abundance of sodium in atomic form predicts more sodium absorption than we observe. There are several possibilities that may account for this reduced amplitude, including reaction of atomic sodium into molecular gases and/or condensates, photoionization of sodium by the stellar flux, a low primordial abundance of sodium, and the presence of clouds high in the atmosphere.

Concentrations of Dark Halos from Their Assembly Histories

Abstract: We study the relation between the density profiles of dark matter halos and their mass assembly histories using a statistical sample of halos in a high-resolution N-body simulation of the ΛCDM cosmology. For each halo at z = 0, we identify its merger history tree and determine concentration parameters cvir for all progenitors, thus providing a structural merger tree for each halo. We fit the mass accretion histories by a universal function with one parameter, the formation epoch ac, defined when the log mass accretion rate d log M/d log a falls below a critical value S. We find that late-forming galaxies tend to be less concentrated, such that cvir "observed" at any epoch ao is strongly correlated with ac via cvir = c1ao/ac. Scatter about this relation is mostly due to measurement errors in cvir and ac, implying that the actual spread in cvir for halos of a given mass can be mostly attributed to scatter in ac. We demonstrate that this relation can also be used to predict the mass and redshift dependence of cvir and the scatter about the median cvir(M, z) using accretion histories derived from the extended Press-Schechter (EPS) formalism, after adjusting for a constant offset between the formation times as predicted by EPS and as measured in the simulations; this new ingredient can thus be easily incorporated into semianalytic models of galaxy formation. The correlation found between halo concentration and mass accretion rate suggests a physical interpretation: for high mass infall rates, the central density is related to the background density; when the mass infall rate slows, the central density stays approximately constant, and the halo concentration just grows as Rvir. Because of the direct connection between halo concentration and velocity rotation curves and because of probable connections between halo mass assembly history and star formation history, the tight correlation between these properties provides an essential new ingredient for galaxy formation modeling.

The Stellar Initial Mass Function from Turbulent Fragmentation

Abstract: In this paper they conclude that turbulent fragmentation is unavoidable in super-sonically turbulent molecular clouds, and given the success of the present model to predict the observed shape of the Stellar IMF, they conclude that turbulent fragmentation is essential to the origin of the stellar IMF.

Three-Dimensional Interaction between a Planet and an Isothermal Gaseous Disk. I. Corotation and Lindblad Torques and Planet Migration

Abstract: Gravitational interaction between a planet and a three-dimensional isothermal gaseous disk is studied. In the present paper we mainly examine the torque on a planet and the resultant radial migration of the planet. A planet excites density waves at Lindblad and corotation resonances and experiences a negative torque by the density waves, which causes a rapid inward migration of the planet during its formation in a protoplanetary disk. We formulate the linear wave excitation in three-dimensional isothermal disks and calculate the torques of Lindblad resonances and corotation resonances. For corotation resonances, a general torque formula is newly derived, which is also applicable to two-dimensional disks. The new formula succeeds in reproducing numerical results on the corotation torques, which do not agree with the previously well-known formula. The net torque of the inner and the outer Lindblad resonances (i.e., the differential Lindblad torque) is caused by asymmetry such as the radial pressure gradient and the scale height variation. In three-dimensional disks, the differential Lindblad torques are generally smaller than those in two-dimensional disks. Especially, the effect of a pressure gradient becomes weak. The scale height variation, which is a purely three-dimensional effect, makes the differential Lindblad torque decrease. As a result, the migration time of a planet is obtained as of the order of 106 yr for an Earth-size planet at 5 AU for a typical disk model, which is longer than the result of two-dimensional calculation by the factor of 2 or 3. The reflected waves from disk edges, which are neglected in the torque calculation, can further weaken the disk-planet interaction.

The Formation of the First Stars. I. The Primordial Star-forming Cloud

Abstract: To constrain the nature of the very first stars, we investigate the collapse and fragmentation of primordial, metal-free gas clouds. We explore the physics of primordial star formation by means of three-dimensional simulations of the dark matter and gas components, using smoothed particle hydrodynamics, under a wide range of initial conditions, including the initial spin, the total mass of the halo, the redshift of virialization, the power spectrum of the DM fluctuations, the presence of HD cooling, and the number of particles employed in the simulation. We find characteristic values for the temperature, T ~ a few 100 K, and the density, n ~ 103-104 cm-3, characterizing the gas at the end of the initial free-fall phase. These values are rather insensitive to the initial conditions. The corresponding Jeans mass is MJ ~ 103 M?. The existence of these characteristic values has a robust explanation in the microphysics of H2 cooling, connected to the minimum temperature that can be reached with the H2 coolant, and to the critical density at which the transition takes place between levels being populated according to non-LTE (NLTE), and according to LTE. In all cases, the gas dissipatively settles into an irregular, central configuration that has a filamentary and knotty appearance. The fluid regions with the highest densities are the first to undergo runaway collapse due to gravitational instability, and to form clumps with initial masses ~103 M?, close to the characteristic Jeans scale. These results suggest that the first stars might have been quite massive, possibly even very massive with M* 100 M?. After a gas element has undergone runaway collapse, and has reached densities in excess of 108 cm-3, a sink particle is created. This procedure allows us to follow the evolution of the overall system beyond the point where the first nonlinear region would otherwise force the calculation to a halt. These later evolutionary stages, during which the clumps grow in mass due to accretion and merging with other clumps, are quite sensitive to the initial conditions. The key process in building up very massive clumps, with masses up to a few times 104 M?, is merging between clumps. Since the merging rate sensitively depends on the density of the gas, halos with the highest degree of central concentration are able to assemble the most massive clumps. Among these are halos with a low spin (? 0.01), and with DM fluctuations imprinted according to a white-noise spectrum.

The Infrared Spectral Energy Distribution of Normal Star-forming Galaxies: Calibration at Far-Infrared and Submillimeter Wavelengths

Abstract: New far-infrared and submillimeter data are used to solidify and to extend to long wavelengths the empirical calibration of the infrared spectral energy distribution (SED) of normal star-forming galaxies. As was found by Dale and coworkers in 2001, a single parameter family, characterized by fν(60 μm)/fν(100 μm), is adequate to describe the range of normal galaxy SEDs observed by the Infrared Astronomical Satellite and Infrared Space Observatory from 3 to 100 μm. However, predictions based on the first-generation models at longer wavelengths (122-850 μm) are increasingly overluminous compared to the data for smaller fν(60 μm)/fν(100 μm), or alternatively, for weaker global interstellar radiation fields. After slightly modifying the far-infrared/submillimeter dust emissivity in those models as a function of the radiation field intensity to better match the long-wavelength data, a suite of SEDs from 3 μm to 20 cm in wavelength is presented. Results from relevant applications are also discussed, including submillimeter-based photometric redshift indicators, the infrared energy budget and simple formulae for recovering the bolometric infrared luminosity, and dust mass estimates in galaxies. Regarding the latter, since galaxy infrared SEDs are not well described by single blackbody curves, the usual methods of estimating dust masses can be grossly inadequate. The improved model presented herein is used to provide a more accurate relation between infrared luminosity and dust mass.

The Mass Function of an X-Ray Flux-Limited Sample of Galaxy Clusters

Abstract: A new X-ray-selected and X-ray flux-limited galaxy cluster sample is presented. Based on the ROSAT All-Sky Survey, the 63 brightest clusters with galactic latitude |bII| ? 20? and flux fX(0.1-2.4keV) ? 2 ? 10-11ergss-1cm-2 have been compiled. Gravitational masses have been determined utilizing intracluster gas density profiles, derived mainly from ROSAT PSPC pointed observations, and gas temperatures, as published mainly from ASCA observations, assuming hydrostatic equilibrium. This sample and an extended sample of 106 galaxy clusters is used to establish the X-ray luminosity-gravitational mass relation. From the complete sample the galaxy cluster mass function is determined and used to constrain the mean cosmic matter density and the amplitude of mass fluctuations. Comparison to Press-Schechter type model mass functions in the framework of cold dark matter cosmological models and a Harrison-Zeldovich initial density fluctuation spectrum yields the constraints ?m = 0.12 and ?8 = 0.96 (90% c.l.). Various possible systematic uncertainties are quantified. Adding all identified systematic uncertainties to the statistical uncertainty in a worst-case fashion results in an upper limit ?m < 0.31. For comparison to previous results a relation ?8 = 0.43? is derived. The mass function is integrated to show that the contribution of mass bound within virialized cluster regions to the total matter density is small; i.e., ?cluster = 0.012 for cluster masses larger than 6.4 ? 1013 h M?.

A measurement by BOOMERANG of multiple peaks in the angular power spectrum of the cosmic microwave background

Abstract: This paper presents a measurement of the angular power spectrum of the cosmic microwave background from l = 75 to l = 1025 (~10' to 24) from a combined analysis of four 150 GHz channels in the BOOMERANG experiment. The spectrum contains multiple peaks and minima, as predicted by standard adiabatic inflationary models in which the primordial plasma undergoes acoustic oscillations. These results, in concert with other types of cosmological measurements and theoretical models, significantly constrain the values of ?tot, ?bh2, ?ch2, and ns.

A Comprehensive Study of Binary Compact Objects as Gravitational Wave Sources: Evolutionary Channels, Rates, and Physical Properties

Abstract: A new generation of ground-based interferometric detectors for gravitational waves is currently under construction or has entered the commissioning phase (Laser Interferometer Gravitational-wave Observatory [LIGO], VIRGO, GEO600, TAMA300). The purpose of these detectors is to observe gravitational waves from astrophysical sources and help improve our understanding of the source origin and physical properties. In this paper we study the most promising candidate sources for these detectors: inspiraling double compact objects. We use population synthesis methods to calculate the properties and coalescence rates of compact object binaries: double neutron stars, black hole-neutron star systems, and double black holes. We also examine the formation channels available to double compact object binaries. We explicitly account for the evolution of low-mass helium stars and investigate the possibility of common-envelope evolution involving helium stars as well as two evolved stars. As a result we identify a significant number of new formation channels for double neutron stars, in particular, leading to populations with very distinct properties. We discuss the theoretical and observational implications of such populations, but we also note the need for hydrodynamical calculations to settle the question of whether such common-envelope evolution is possible. We also present and discuss the physical properties of compact object binaries and identify a number of robust, qualitative features as well as their origin. Using the calculated coalescence rates we compare our results to earlier studies and derive expected detection rates for LIGO. We find that our most optimistic estimate for the first LIGO detectors reach a couple of events per year and our most pessimistic estimate for advanced LIGO detectors exceed 10 events per year.

Updated and Expanded OPAL Equation-of-State Tables: Implications for Helioseismology

Abstract: We are in the process of updating and extending the OPAL equation-of-state (EOS) and opacity data to include low-mass stars. The EOS part of that effort now is complete, and the results are described herein. The new data cover main-sequence stars having mass � 0.1 M� . As a result of the more extreme matter conditions encountered with low-mass stars, we have added new physics. The electrons are now treated as relativistic, and we have improved our treatment of molecules. We also consider the implications of the new results for helioseismology.

The Halo Occupation Distribution: Toward an Empirical Determination of the Relation between Galaxies and Mass

Abstract: We investigate galaxy bias in the framework of the halo occupation distribution (HOD), which defines the bias of a population of galaxies by the conditional probability P(N|M) that a dark matter halo of virial mass M contains N galaxies, together with prescriptions that specify the relative spatial and velocity distributions of galaxies and dark matter within halos. By populating the halos of a cosmological N-body simulation using a variety of HOD models, we examine the sensitivity of different galaxy clustering statistics to properties of the HOD. The galaxy correlation function responds to different aspects of P(N|M) on different scales. Obtaining the observed power-law form of ξg(r) requires rather specific combinations of HOD parameters, implying a strong constraint on the physics of galaxy formation; the success of numerical and semianalytic models in reproducing this form is entirely nontrivial. Other clustering statistics such as the galaxy-mass correlation function, the bispectrum, the void probability function, the pairwise velocity dispersion, and the group multiplicity function are sensitive to different combinations of HOD parameters and thus provide complementary information about galaxy bias. We outline a strategy for determining the HOD empirically from redshift survey data. This method starts from an assumed cosmological model, but we argue that cosmological and HOD parameters will have nondegenerate effects on galaxy clustering, so that a substantially incorrect cosmological model will not reproduce the observations for any choice of HOD. Empirical determinations of the HOD as a function of galaxy type from the Two-Degree Field (2dF) and Sloan Digital Sky Survey (SDSS) redshift surveys will provide a detailed target for theories of galaxy formation, insight into the origin of galaxy properties, and sharper tests of cosmological models.

Triaxial modeling of halo density profiles with high-resolution N-body simulations

Abstract: We present a detailed nonspherical modeling of dark matter halos on the basis of a combined analysis of high-resolution halo simulations (12 halos with N ~ 106 particles within their virial radius) and large cosmological simulations (five realizations with N = 5123 particles in a 100 h-1 Mpc box size). The density profiles of those simulated halos are well approximated by a sequence of the concentric triaxial distribution with their axis directions being fairly aligned. We characterize the triaxial model quantitatively by generalizing the universal density profile, that has previously been discussed only in the framework of the spherical model. We obtain a series of practically useful fitting formulae in applying the triaxial model: the mass and redshift dependence of the axis ratio, the mean of the concentration parameter, and the probability distribution functions of the axis ratio and the concentration parameter. These accurate fitting formulae form a complete description of the triaxial density profiles of halos in cold dark matter models. Our current description of the dark halos will be particularly useful in predicting a variety of nonsphericity effects, to a reasonably reliable degree, including the weak and strong lens statistics, the orbital evolution of galactic satellites and triaxiality of galactic halos, and the nonlinear clustering of dark matter. In addition, this provides a useful framework for the nonspherical modeling of the intracluster gas, which is crucial in discussing the gas and temperature profiles of X-ray clusters and the Hubble constant estimated via the Sunyaev-Zeldovich effect.

Nucleosynthesis in massive stars with improved nuclear and stellar physics

Abstract: We present the first calculations to follow the evolution of all stable nuclei and their radioactive progeni- tors in stellar models computed from the onset of central hydrogen burning through explosion as Type II supernovae. Calculations are performed for Population I stars of 15, 19, 20, 21, and 25 Musing the most recently available experimental and theoretical nuclear data, revised opacity tables, neutrino losses, and weak interaction rates and taking into account mass loss due to stellar winds. A novel '' adaptive '' reaction net- work is employed with a variable number of nuclei (adjusted each time step) ranging from � 700 on the main sequence to e2200 during the explosion. The network includes, at any given time, all relevant isotopes from hydrogen through polonium (Z ¼ 84). Even the limited grid of stellar masses studied suggests that overall good agreement can be achieved with the solar abundances of nuclei between 16 O and 90 Zr. Interesting dis- crepancies are seen in the 20 Mmodel and (so far, only in that model) are a consequence of the merging of the oxygen, neon, and carbon shells about a day prior to core collapse. We find that, in some stars, most of the '' p-process '' nuclei can be produced in the convective oxygen-burning shell moments prior to collapse; in others, they are made only in the explosion. Serious deficiencies still exist in all cases for the p-process isotopes of Ru and Mo. Subject headings: nuclear reactions, nucleosynthesis, abundances — stars: evolution — supernovae: general On-line material: machine-readable tables

Master of the cosmic microwave background anisotropy power spectrum: a fast method for statistical analysis of large and complex cosmic microwave background data sets

Abstract: We describe a fast and accurate method for estimation of the cosmic microwave background (CMB) anisotropy angular power spectrum—Monte Carlo Apodized Spherical Transform Estimator (MASTER). Originally devised for use in the interpretation of the BOOMERANG experimental data, MASTER is both a computationally efficient method suitable for use with the currently available CMB data sets (already large in size, despite covering small fractions of the sky, and affected by inhomogeneous and correlated noise) and a very promising application for the analysis of very large future CMB satellite mission products.

The Ghost of Sagittarius and Lumps in the Halo of the Milky Way

Abstract: We identify new structures in the halo of the Milky Way from positions, colors, and magnitudes of five million stars detected in the Sloan Digital Sky Survey. Most of these stars are within 126 of the celestial equator. We present color-magnitude diagrams (CMDs) for stars in two previously discovered, tidally disrupted structures. The CMDs and turnoff colors are consistent with those of the Sagittarius dwarf galaxy, as had been predicted. In one direction, we are even able to detect a clump of red stars, similar to that of the Sagittarius dwarf, from stars spread across 110 deg2 of sky. Focusing on stars with the colors of F turnoff objects, we identify at least five additional overdensities of stars. Four of these may be pieces of the same halo structure, which would cover a region of the sky at least 40° in diameter, at a distance of 11 kpc from the Sun (18 kpc from the center of the Galaxy). The turnoff is significantly bluer than that of thick-disk stars, yet the stars lie closer to the Galactic plane than a power-law spheroid predicts. We suggest two models to explain this new structure. One possibility is that this new structure could be a new dwarf satellite of the Milky Way, hidden in the Galactic plane and in the process of being tidally disrupted. The other possibility is that it could be part of a disklike distribution of stars which is metal-poor, with a scale height of approximately 2 kpc and a scale length of approximately 10 kpc. The fifth overdensity, which is 20 kpc away, is some distance from the Sagittarius dwarf streamer orbit and is not associated with any known Galactic structure. We have tentatively identified a sixth overdensity in the halo. If this sixth structure is instead part of a smooth distribution of halo stars (the spheroid), then the spheroid must be very flattened, with axial ratio q = 0.5. It is likely that there are many smaller streams of stars in the Galactic halo.

Active Galactic Nucleus Black Hole Masses and Bolometric Luminosities

Abstract: Black hole mass, along with mass accretion rate, is a fundamental property of active galactic nuclei (AGNs). Black hole mass sets an approximate upper limit to AGN energetics via the Eddington limit. We collect and compare all AGN black hole mass estimates from the literature; these 177 masses are mostly based on the virial assumption for the broad emission lines, with the broad-line region size determined from either reverberation mapping or optical luminosity. We introduce 200 additional black hole mass estimates based on properties of the host galaxy bulges, using either the observed stellar velocity dispersion or the fundamental plane relation to infer σ; these methods assume that AGN hosts are normal galaxies. We compare 36 cases for which black hole mass has been generated by different methods and find, for individual objects, a scatter as high as a couple of orders of magnitude. The less direct the method, the larger the discrepancy with other estimates, probably due to the large scatter in the underlying correlations assumed. Using published fluxes, we calculate bolometric luminosities for 234 AGNs and investigate the relation between black hole mass and luminosity. In contrast to other studies, we find no significant correlation of black hole mass with luminosity, other than those induced by circular reasoning in the estimation of black hole mass. The Eddington limit defines an approximate upper envelope to the distribution of luminosities, but the lower envelope depends entirely on the sample of AGNs included. For any given black hole mass, there is a range in Eddington ratio of up to 3 orders of magnitude.

Degree Angular Scale Interferometer First Results: A Measurement of the Cosmic Microwave Background Angular Power Spectrum

Abstract: We present measurements of anisotropy in the cosmic microwave background (CMB) from the first season of observations with the Degree Angular Scale Interferometer (DASI). The instrument was deployed at the South Pole in the austral summer 1999-2000, and we made observations throughout the following austral winter. We present a measurement of the CMB angular power spectrum in the range 100 < l < 900 in nine bands with fractional uncertainties in the range 10%-20% and dominated by sample variance. In this paper, we review the formalism used in the analysis, in particular the use of constraint matrices to project out contaminants such as ground and point source signals and to test for correlations with diffuse foreground templates. We find no evidence of foregrounds other than point sources in the data, and we find a maximum likelihood temperature spectral index β = -0.1 ± 0.2 (1 σ), consistent with CMB. We detect a first peak in the power spectrum at l ~ 200, in agreement with previous experiments. In addition, we detect a peak in the power spectrum at l ~ 550 and power of similar magnitude at l ~ 800, which are consistent with the second and third harmonic peaks predicted by adiabatic inflationary cosmological models.

Constraining Cosmological Parameters Based on Relative Galaxy Ages

Abstract: We propose to use relative galaxy ages as a means of constraining cosmological parameters. By measuring the age difference between two ensembles of passively evolving galaxies at somewhat different redshifts, one could determine the derivative of redshift with respect to cosmic time, dz/dt. At high redshifts, z ~ 1-2, this measurement would constrain the equation of state of the dark energy, while at low redshifts, z 0.2, it would determine the Hubble constant, H0. Furthermore, we show that d2z/dt2 directly tracks the equation of state of the dark energy; thus, measurements of this quantity at low redshifts can be used to constrain it. The selected galaxies need to be passively evolving on a time much longer than their age difference.

The Relationship between Gas Content and Star Formation in Molecule-rich Spiral Galaxies

Abstract: We investigate the relationship between H I, H2, and the star formation rate (SFR) using azimuthally averaged data for seven CO-bright spiral galaxies. Contrary to some earlier studies based on global fluxes, we find that ΣSFR exhibits a much stronger correlation with Σ than with Σ, as Σ saturates at a value of ~ 10 M☉ pc-2 or even declines for large ΣSFR. Hence, the good correlation between ΣSFR and the total (H I+H2) gas surface density Σgas is driven by the molecular component in these galaxies, with the observed relation between ΣSFR and Σ following a Schmidt-type law of index nmol ≈ 0.8 if a uniform extinction correction is applied or nmol ≈ 1.4 for a radially varying correction dependent on gas density. The corresponding Schmidt law indices for Σgas versus ΣSFR are 1.1 and 1.7 for the two extinction models, in rough agreement with previous studies of the disk-averaged star formation law. An alternative to the Schmidt law, in which the gas depletion timescale is proportional to the orbital timescale, is also consistent with the data if radially varying extinction corrections are applied. We find no clear evidence for a link between the gravitational instability parameter for the gas disk (Qg) and the SFR, and we suggest that Qg be considered a measure of the gas fraction. This implies that for a state of marginal gravitational stability to exist in galaxies with low gas fractions, it must be enforced by the stellar component. In regions where we have both H I and CO measurements, the ratio of H I to H2 surface density scales with radius as roughly R1.5, and we suggest that the balance between H I and H2 is determined primarily by the midplane interstellar pressure. These results favor a "law" of star formation in quiescent disks in which the ambient pressure and metallicity control the formation of molecular clouds from H I, with star formation then occurring at a roughly constant rate per unit H2 mass.

ΛCDM-based Models for the Milky Way and M31. I. Dynamical Models

Abstract: We apply standard disk formation theory with adiabatic contraction within cuspy halo models predicted by the standard cold dark matter (?CDM) cosmology. The resulting models are confronted with the broad range of observational data available for the Milky Way and M31 galaxies. We find that there is a narrow range of parameters that can satisfy the observational constraints, but within this range, the models score remarkably well. Our favored models have virial masses of 1012 and 1.6 ? 1012 M? for the Galaxy and for M31, respectively, average spin parameters ? ? 0.03-0.05, and concentrations Cvir = 10-17, typical for halos of this mass in the standard ?CDM cosmology. The models require neither dark matter modifications nor flat cores to fit the observational data. We explore two types of models, with and without the exchange of angular momentum between the dark matter and the baryons. The models without exchange give reasonable rotation curves, fulfill constraints in the solar neighborhood, and satisfy constraints at larger radii, but they may be problematic for fast rotating central bars. We explore models in which the baryons experience additional contraction due to loss of angular momentum to the surrounding dark matter. These models produce similar global properties, but the dark matter is only a 25% of the total mass in the central 3 kpc region, allowing a fast rotating bar to persist. According to preliminary calculations, our model galaxies probably have sufficient baryonic mass in the central ~3.5 kpc to reproduce recent observational values of the optical depth to microlensing events toward the Galactic center. Our dynamical models unequivocally require that about 50% of all the gas inside the virial radius must not be in the disk or in the bulge, a result that is obtained naturally in standard semianalytic models. Assuming that the Milky Way is typical, we investigate whether the range of virial masses allowed by our dynamical models is compatible with constraints from the galaxy luminosity function. We find that if the Milky Way has a luminosity MK = -24.0, then these constraints are satisfied, but if it is more luminous (as expected if it lies on the Tully-Fisher relation), then the predicted space density is larger than the observed space density of galaxies of the corresponding luminosity by a factor of 1.5-2. We conclude that observed rotation curves and dynamical properties of normal spiral galaxies appear to be consistent with standard ?CDM.

Statistics, Handle with Care: Detecting Multiple Model Components with the Likelihood Ratio Test

Abstract: The likelihood ratio test (LRT) and the related F-test, popularized in astrophysics by Eadie and coworkers in 1971, Bevington in 1969, Lampton, Margon, & Bowyer, in 1976, Cash in 1979, and Avni in 1978, do not (even asymptotically) adhere to their nominal χ2 and F-distributions in many statistical tests common in astrophysics, thereby casting many marginal line or source detections and nondetections into doubt. Although the above authors illustrate the many legitimate uses of these statistics, in some important cases it can be impossible to compute the correct false positive rate. For example, it has become common practice to use the LRT or the F-test to detect a line in a spectral model or a source above background despite the lack of certain required regularity conditions. (These applications were not originally suggested by Cash or by Bevington.) In these and other settings that involve testing a hypothesis that is on the boundary of the parameter space, contrary to common practice, the nominal χ2 distribution for the LRT or the F-distribution for the F-test should not be used. In this paper, we characterize an important class of problems in which the LRT and the F-test fail and illustrate this nonstandard behavior. We briefly sketch several possible acceptable alternatives, focusing on Bayesian posterior predictive probability values. We present this method in some detail since it is a simple, robust, and intuitive approach. This alternative method is illustrated using the gamma-ray burst of 1997 May 8 (GRB 970508) to investigate the presence of an Fe K emission line during the initial phase of the observation. There are many legitimate uses of the LRT and the F-test in astrophysics, and even when these tests are inappropriate, there remain several statistical alternatives (e.g., judicious use of error bars and Bayes factors). Nevertheless, there are numerous cases of the inappropriate use of the LRT and similar tests in the literature, bringing substantive scientific results into question.

Electrodynamics of Magnetars: Implications for the Persistent X-Ray Emission and Spin-down of the Soft Gamma Repeaters and Anomalous X-Ray Pulsars

Abstract: We consider the structure of neutron star magnetospheres threaded by large-scale electrical currents and the effect of resonant Compton scattering by the charge carriers (both electrons and ions) on the emergent X-ray spectra and pulse profiles. In the magnetar model for the soft gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs), these currents are maintained by magnetic stresses acting deep inside the star, which generate both sudden disruptions (SGR outbursts) and more gradual plastic deformations of the rigid crust. We construct self-similar force-free equilibria of the current-carrying magnetosphere with a power-law dependence of magnetic field on radius, ∝ r-(2+p), and show that a large-scale twist of field lines softens the radial dependence of the magnetic field to p < 1. The spin-down torque acting on the star is thereby increased in comparison with an orthogonal vacuum dipole. We comment on the strength of the surface magnetic field in the SGR and AXP sources, as inferred from their measured spin-down rates, and the implications of this model for the narrow measured distribution of spin periods. A magnetosphere with a strong twist [B/Bθ = O(1) at the equator] has an optical depth ~1 to resonant cyclotron scattering, independent of frequency (radius), surface magnetic field strength, or charge/mass ratio of the scattering charge. When electrons and ions supply the current, the stellar surface is also heated by the impacting charges at a rate comparable to the observed X-ray output of the SGR and AXP sources, if Bdipole ~ 1014 G. Redistribution of the emerging X-ray flux at the cyclotron resonance will strongly modify the emerging pulse profile and, through the Doppler effect, generate a nonthermal tail to the X-ray spectrum. We relate the sudden change in the pulse profile of SGR 1900+14 following the 1998 August 27 giant flare to an enhanced optical depth at the electron cyclotron resonance resulting from a sudden twist imparted to the external magnetic field during the flare. The self-similar structure of the magnetosphere should generate frequency-independent profiles; more complicated pulse profiles may reflect the presence of higher multipoles, ion cyclotron scattering, or possibly nonresonant Compton scattering of O-mode photons by pair-loaded currents.

Galaxy clustering in early sloan digital sky survey redshift data

Abstract: We present the first measurements of clustering in the Sloan Digital Sky Survey (SDSS) galaxy redshift survey. Our sample consists of 29,300 galaxies with redshifts 5700 km s-1 ≤ cz ≤ 39,000 km s-1, distributed in several long but narrow (25-5°) segments, covering 690 deg2. For the full, flux-limited sample, the redshift-space correlation length is approximately 8 h-1 Mpc. The two-dimensional correlation function ξ(rp,π) shows clear signatures of both the small-scale, fingers-of-God distortion caused by velocity dispersions in collapsed objects and the large-scale compression caused by coherent flows, though the latter cannot be measured with high precision in the present sample. The inferred real-space correlation function is well described by a power law, ξ(r) = (r/6.1 ± 0.2 h-1 Mpc)-1.75±0.03, for 0.1 h-1 Mpc ≤ r ≤ 16 h-1 Mpc. The galaxy pairwise velocity dispersion is σ12 ≈ 600 ± 100 km s-1 for projected separations 0.15 h-1 Mpc ≤ rp ≤ 5 h-1 Mpc. When we divide the sample by color, the red galaxies exhibit a stronger and steeper real-space correlation function and a higher pairwise velocity dispersion than do the blue galaxies. The relative behavior of subsamples defined by high/low profile concentration or high/low surface brightness is qualitatively similar to that of the red/blue subsamples. Our most striking result is a clear measurement of scale-independent luminosity bias at r 10 h-1 Mpc: subsamples with absolute magnitude ranges centered on M* - 1.5, M*, and M* + 1.5 have real-space correlation functions that are parallel power laws of slope ≈-1.8 with correlation lengths of approximately 7.4, 6.3, and 4.7 h-1 Mpc, respectively.

Properties of Relativistic Jets in Gamma-Ray Burst Afterglows

Abstract: We extend our calculation of physical parameters of gamma-ray burst (GRB) jets by modeling the broadband emission of the afterglows 970508, 980519, 991208, 000926, 000418, and 010222. Together with 990123, 990510, 991216, and 000301c, there are 10 well-observed afterglows for which the initial opening angle of the GRB jet can be constrained. The jet energies (after the GRB phase) obtained for this set of afterglows are within one decade around 5 × 1050 ergs. With the exception of 000418, which requires a jet wider than rad, the jet initial half-angle in the other cases ranges from 2? to 20?. We find that in half of the cases, a homogeneous ambient medium accommodates the afterglow emission better than the windlike r-2 profile medium expected around massive stars. The two types of media give fits of comparable quality in four cases, with a wind medium providing a better description only for 970508. The circumburst densities we obtain are in the 0.1-100 cm-3 range, with the exception of 990123, for which it is below 10-2 cm-3. If in all 10 cases the observed GRB durations are a good measure of the ejecta deceleration timescale, then the parameters obtained here lead to jet Lorentz factors at the deceleration radius between 70 and 300, anticorrelated with the jet initial aperture, and jet masses around 10-6 M? . Our results on the jet energy, opening Lorentz factor, and evacuation of material until breakout provide constraints on theoretical models of GRB jets.

Systematic Molecular Differentiation in Starless Cores

Abstract: We present evidence that low-mass starless cores, the simplest units of star formation, are systematically differentiated in their chemical composition. Some molecules, including CO and CS, almost vanish near the core centers, where the abundance decreases by at least 1 or 2 orders of magnitude with respect to the value in the outer core. At the same time, the N2H+ molecule has a constant abundance, and the fraction of NH3 increases toward the core center. Our conclusions are based on a systematic study of five mostly round starless cores (L1498, L1495, L1400K, L1517B, and L1544), which we have mapped in C18O (1-0), CS (2-1), N2H+ (1-0), NH3 (1, 1) and (2, 2), and the 1.2 mm continuum [complemented with C17O (1-0) and C34S (2-1) data for some systems]. For each core we have built a spherically symmetric model in which the density is derived from the 1.2 mm continuum, the kinetic temperature is derived from NH3, and the abundance of each molecule is derived using a Monte Carlo radiative transfer code, which simultaneously fits the shape of the central spectrum and the radial profile of integrated intensity. Regarding the cores for which we have C17O (1-0) and C34S (2-1) data, the model fits these observations automatically when the standard isotopomer ratio is assumed. As a result of this modeling, we also find that the gas kinetic temperature in each core is constant at approximately 10 K. In agreement with previous work, we find that if the dust temperature is also constant, then the density profiles are centrally flattened, and we can model them with a single analytic expression. We also find that for each core the turbulent line width seems constant in the inner 0.1 pc. The very strong abundance drop of CO and CS toward the center of each core is naturally explained by the depletion of these molecules onto dust grains at densities of (2-6) × 104 cm-3. N2H+ seems unaffected by this process up to densities of several times 105 cm-3, or even 106 cm-3, while the NH3 abundance may be enhanced by its lack of depletion and by reactions triggered by the disappearance of CO from the gas phase. With the help of the Monte Carlo modeling, we show that chemical differentiation automatically explains the discrepancy between the sizes of CS and NH3 maps, a problem that has remained unexplained for more than a decade. Our models, in addition, show that a combination of radiative transfer effects can give rise to the previously observed discrepancy in the line width of these two tracers. Although this discrepancy has been traditionally interpreted as resulting from a systematic increase of the turbulent line width with radius, our models show that it can arise in conditions of constant gas turbulence.

A Textbook Example of a Bow Shock in the Merging Galaxy Cluster 1E 0657–56

Abstract: The Chandra image of the merging, hot galaxy cluster 1E 0657-56 reveals a bow shock propagating in front of a bullet-like gas cloud just exiting the disrupted cluster core. This is the first clear example of a shock front in a cluster. From the jumps in the gas density and temperature at the shock, the Mach number of the bullet-like cloud is 2-3. This corresponds to a velocity of 3000-4000 km s-1 relative to the main cluster, which means that the cloud traversed the core just 0.1-0.2 Gyr ago. The 6-7 keV bullet appears to be a remnant of a dense cooling flow region once located at the center of a merging subcluster whose outer gas has been stripped by ram pressure. The bullet's shape indicates that it is near the final stage of being destroyed by ram pressure and gasdynamic instabilities, as the subcluster galaxies move well ahead of the cool gas. The unique simplicity of the shock front and bullet geometry in 1E 0657-56 may allow a number of interesting future measurements. The cluster's average temperature is 14-15 keV but shows large spatial variations. The hottest gas (T > 20 keV) lies in the region of the radio halo enhancement and extensive merging activity involving subclusters other than the bullet.

Dense Cores in Dark Clouds. XIV. N2H+ (1-0) Maps of Dense Cloud Cores

Abstract: We present results of an extensive mapping survey of N2H+ (1-0) in about 60 low-mass cloud cores already mapped in the NH3 (1, 1) inversion transition line. The survey has been carried out at the FCRAO antenna with an angular resolution of 54'', about 1.5 times finer than the previous ammonia observations made at the Haystack telescope. The comparison between N2H+ and NH3 maps shows strong similarities in the size and morphology of the two molecular species, indicating that they are tracing the same material, especially in starless cores. Cores with stars typically have map sizes about a factor of 2 smaller for N2H+ than for NH3, indicating the presence of denser and more centrally concentrated gas compared to starless cores. The mean aspect ratio is ~2. Significant correlations are found between NH3 and N2H+ column densities and excitation temperatures in starless cores, but not in cores with stars, suggesting a different chemical evolution of the two species. Starless cores are less massive ( 3 M☉) than cores with stars ( 9 M☉). Velocity gradients range between 0.5 and 6 km s-1 pc-1, similar to what has been found with NH3 data, and the ratio β of rotational kinetic energy to gravitational energy has magnitudes between ~10-4 and 0.07, indicating that rotation is not energetically dominant in the support of the cores. Local velocity gradients show significant variation in both magnitude and direction, suggesting the presence of complex motions not interpretable as simple solid-body rotation. Integrated intensity profiles of starless cores present a central flattening and are consistent with a spherically symmetric density law n r-α, where α = 1.2 for r rbreak, with rbreak ~ 0.03 pc. Cores with stars are better modeled with single density power laws with α ≥ 2, in agreement with observations of submillimeter continuum emission. Line widths change across the core, but we did not find a general trend: there are cores with significant positive as well as negative linear correlations between Δv and the impact parameter b. The deviation in line width correlates with the mean line width, suggesting that the line of sight contains ~10 coherence lengths. The corresponding value of the coherence length, ~0.01 pc, is similar to the expected cutoff wavelength for MHD waves. This similarity may account for the increased coherence of line widths on small scales. Despite finer angular resolution, the majority of N2H+ and NH3 maps show a similar simple structure, with single peaks and no elongation.