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THE DENSITY PROFILES OF MASSIVE, RELAXED GALAXY CLUSTERS. I. THE TOTAL DENSITY OVER THREE DECADES IN RADIUS

Clusters of galaxies are excellent locations to probe the distribution of baryons and dark matter (DM) over a wide range of scales. We study a sample of seven massive (M {sub 200} = 0.4-2 Multiplication-Sign 10{sup 15} M {sub Sun }), relaxed galaxy clusters with centrally located brightest cluster galaxies (BCGs) at z = 0.2-0.3. Using the observational tools of strong and weak gravitational lensing, combined with resolved stellar kinematics within the BCG, we measure the total radial density profile, comprising both dark and baryonic matter, over scales of {approx_equal} 3-3000 kpc. We present Keck spectroscopy yielding seven new spectroscopic redshifts of multiply imaged sources and extended stellar velocity dispersion profiles of the BCGs. Lensing-derived mass profiles typically agree with independent X-ray estimates within {approx_equal} 15%, suggesting that departures from hydrostatic equilibrium are small and that the clusters in our sample (except A383) are not strongly elongated or compressed along the line of sight. The inner logarithmic slope {gamma}{sub tot} of the total density profile measured over r/r {sub 200} = 0.003-0.03, where {rho}{sub tot}{proportional_to}r{sup -{gamma}{sub t}{sub o}{sub t}}, is found to be nearly universal, with a mean ({gamma}{sub tot}) = 1.16 {+-} 0.05(random){sup +0.05} {sub -0.07} (systematic) and an intrinsic scatter {sigma}{sub {gamma}} < 0.13 (68% confidence). This is further supported by the very homogeneous shape of the observed velocity dispersion profiles, which are mutually consistent after a simple scaling. Remarkably, this slope agrees closely with high-resolution numerical simulations that contain only DM, despite the significant contribution of stellar mass on the scales we probe. The Navarro-Frenk-White profile characteristic of collisionless cold DM is a better description of the total mass density at radii {approx}> 5-10 kpc than that of DM alone. Hydrodynamical simulations that include baryons, cooling, and feedback currently provide a poorer match. We discuss the significance of our findings for understanding the physical processes governing the assembly of BCGs and cluster cores, particularly the influence of baryons on the inner DM halo.

79 ASTRONOMY AND ASTROPHYSICS↗

THE DENSITY DISTRIBUTION IN TURBULENT BISTABLE FLOWS

We numerically study the volume density probability distribution function (n-PDF) and the column density probability distribution function ({Sigma}-PDF) resulting from thermally bistable turbulent flows. We analyze three-dimensional hydrodynamic models in periodic boxes of 100 pc by side, where turbulence is driven in the Fourier space at a wavenumber corresponding to 50 pc. At low densities (n {approx}< 0.6 cm{sup -3}), the n-PDF is well described by a lognormal distribution for an average local Mach number ranging from {approx}0.2 to {approx}5.5. As a consequence of the nonlinear development of thermal instability (TI), the logarithmic variance of the distribution of the diffuse gas increases with M faster than in the well-known isothermal case. The average local Mach number for the dense gas (n {approx}> 7.1 cm{sup -3}) goes from {approx}1.1 to {approx}16.9 and the shape of the high-density zone of the n-PDF changes from a power law at low Mach numbers to a lognormal at high M values. In the latter case, the width of the distribution is smaller than in the isothermal case and grows slower with M. At high column densities, the {Sigma}-PDF is well described by a lognormal for all of the Mach numbers we consider and, due to the presence of TI, the width of the distribution is systematically larger than in the isothermal case but follows a qualitatively similar behavior as M increases. Although a relationship between the width of the distribution and M can be found for each one of the cases mentioned above, these relations are different from those of the isothermal case.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

THE KINEMATICS AND IONIZATION OF NUCLEAR GAS CLOUDS IN CENTAURUS A

Neumayer et al. established the existence of a blueshifted cloud in the core of Centaurus A, within a few parsecs of the nucleus and close to the radio jet. We propose that the cloud has been impacted by the jet, and that it is in the foreground of the jet, accounting for its blueshifted emission on the southern side of the nucleus. We consider both shock excitation and photoionization models for the excitation of the cloud. Shock models do not account for the [Si VI] and [Ca VIII] emission line fluxes. However, X-ray observations indicate a source of ionizing photons in the core of Centaurus A; photoionization by the inferred flux incident on the cloud can account for the fluxes in these lines relative to Brackett-{gamma}. The power-law slope of the ionizing continuum matches that inferred from synchrotron models of the X-rays. The logarithm of the ionization parameter is -1.9, typical of that in Seyfert galaxies and consistent with the value proposed for dusty ionized plasmas. The model cloud density depends upon the Lorentz factor of the blazar and the inclination of our line of sight to the jet axis. For acute inclinations, the inferred density is consistent with expected cloud densities. However, for moderate inclinations of the jet to the line of sight, high Lorentz factors imply cloud densities in excess of 10{sup 5} cm{sup -3} and very low filling factors, suggesting that models of the gamma-ray emission should incorporate jet Lorentz factors {approx}< 5.

79 ASTRONOMY AND ASTROPHYSICS↗

SUNYAEV-ZEL'DOVICH-MEASURED PRESSURE PROFILES FROM THE BOLOCAM X-RAY/SZ GALAXY CLUSTER SAMPLE

We describe Sunyaev-Zel'dovich (SZ) effect measurements and analysis of the intracluster medium (ICM) pressure profiles of a set of 45 massive galaxy clusters imaged using Bolocam at the Caltech Submillimeter Observatory. We deproject the average pressure profile of our sample into 13 logarithmically spaced radial bins between 0.07R{sub 500} and 3.5R{sub 500}, and we find that a generalized Navarro, Frenk, and White (gNFW) profile describes our data with sufficient goodness-of-fit and best-fit parameters (C{sub 500}, {alpha}, {beta}, {gamma}, P{sub 0} = 1.18, 0.86, 3.67, 0.67, 4.29). We use X-ray data to define cool-core and disturbed subsamples of clusters, and we constrain the average pressure profiles of each of these subsamples. We find that, given the precision of our data, the average pressure profiles of disturbed and cool-core clusters are consistent with one another at R {approx}> 0.15R{sub 500}, with cool-core systems showing indications of higher pressure at R {approx}< 0.15R{sub 500}. In addition, for the first time, we place simultaneous constraints on the mass scaling of cluster pressure profiles, their ensemble mean profile, and their radius-dependent intrinsic scatter between 0.1R{sub 500} and 2.0R{sub 500}. The scatter among profiles is minimized at radii between {approx_equal} 0.2R{sub 500} and {approx_equal} 0.5R{sub 500}, with a value of {approx_equal} 20%. These results for the intrinsic scatter are largely consistent with previous analyses, most of which have relied heavily on X-ray derived pressures of clusters at significantly lower masses and redshifts compared to our sample. Therefore, our data provide further evidence that cluster pressure profiles are largely universal with scatter of {approx_equal} 20%-40% about the universal profile over a wide range of masses and redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗

THE EFFECTS OF RADIATIVE TRANSFER ON THE PROBABILITY DISTRIBUTION FUNCTIONS OF MOLECULAR MAGNETOHYDRODYNAMIC TURBULENCE

We study the effects of radiative transfer on the probability distribution functions (PDFs) of simulations of magnetohydrodynamic turbulence in the widely studied {sup 13}CO 2-1 transition. We find that the integrated intensity maps generally follow a log-normal distribution, with the cases that have {tau} Almost-Equal-To 1 best matching the PDF of the column density. We fit a two-dimensional variance-sonic Mach number relationship to our logarithmic PDFs of the form {sigma}{sub ln}{sup 2}{sub ({Sigma}/{Sigma}0}) = A x ln(1+b{sup 2}M{sub s}{sup 2}) and find that, for parameter b = 1/3, parameter A depends on the radiative transfer environment. We also explore the variance, skewness, and kurtosis of the linear PDFs finding that higher moments reflect both higher sonic Mach number and lower optical depth. Finally, we apply the Tsallis incremental PDF function and find that the fit parameters depend on both Mach numbers, but also are sensitive to the radiative transfer parameter space, with the {tau} Almost-Equal-To 1 case best fitting the incremental PDF of the true column density. We conclude that, for PDFs of low optical depth cases, part of the gas is always subthermally excited so that the spread of the line intensities exceeds the spread of the underlying column densities and hence the PDFs do not reflect the true column density. Similarly, PDFs of optically thick cases are dominated by the velocity dispersion and therefore do not represent the true column density PDF. Thus, in the case of molecules like carbon monoxide, the dynamic range of intensities, structures observed, and, consequently, the observable PDFs are less determined by turbulence and more often determined by radiative transfer effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

THE GRAVITATIONAL DRAG FORCE ON AN EXTENDED OBJECT MOVING IN A GAS

Using axisymmetrical numerical simulations, we revisit the gravitational drag felt by a gravitational Plummer sphere with mass M and core radius R{sub s} moving at constant velocity V{sub 0} through a background homogeneous medium of adiabatic gas. Since the potential is non-diverging, there is no gas removal due to accretion. When R{sub s} is larger than the Bondi radius R{sub B} , the perturbation is linear at every point and the drag force is well fitted by the time-dependent Ostriker's formula with r{sub min} = 2.25R{sub s} , where r{sub min} is the minimum impact parameter in the Coulomb logarithm. In the deep nonlinear supersonic regime (R{sub s} << R{sub B} ), the minimum radius is no longer related to R{sub s} but to R{sub B} . We find r{sub min}=3.3M{sup -2.5}R{sub B} for Mach numbers of the perturber between 1.5 and 4, although r{sub min}= 2M{sup -2}R{sub B}=2GM/V{sup 2}{sub 0} also provides a good fit at M>2. As a consequence, the drag force does not depend sensitively on the nonlinearity parameter A, defined as R{sub B} /R{sub s} , for A values larger than a certain critical value A{sub cr}. We show that our generalized Ostriker's formula for the drag force is more accurate than the formula suggested by Kim and Kim.

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STELLAR MASS-GAP AS A PROBE OF HALO ASSEMBLY HISTORY AND CONCENTRATION: YOUTH HIDDEN AMONG OLD FOSSILS

We investigate the use of the halo mass-gap statistic—defined as the logarithmic difference in mass between the host halo and its most massive satellite subhalo—as a probe of halo age and concentration. A cosmological N-body simulation is used to study N ∼ 25, 000 group/cluster-sized halos in the mass range 10{sup 12.5} < M{sub halo}/M{sub ☉} < 10{sup 14.5}. In agreement with previous work, we find that halo mass-gap is related to halo formation time and concentration. On average, older and more highly concentrated halos have larger halo mass-gaps, and this trend is stronger than the mass-concentration relation over a similar dynamic range. However, there is a large amount of scatter owing to the transitory nature of the satellite subhalo population, which limits the use of the halo mass-gap statistic on an object-by-object basis. For example, we find that 20% of very large halo mass-gap systems (akin to {sup f}ossil groups{sup )} are young and have likely experienced a recent merger between a massive satellite subhalo and the central subhalo. We relate halo mass-gap to the observable stellar mass-gap via abundance matching. Using a galaxy group catalog constructed from the Sloan Digital Sky Survey Data Release 7, we find that the star formation and structural properties of galaxies at fixed mass show no trend with stellar mass-gap. This is despite a variation in halo age of ≈2.5 Gyr over ≈1.2 dex in stellar mass-gap. Thus, we find no evidence to suggest that the halo formation history significantly affects galaxy properties.

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Comparison of time/phase lags in the hard state and plateau state of GRS 1915+105

We investigate the complex behavior of energy- and frequency-dependent time/phase lags in the plateau state and the radio-quiet hard (χ) state of GRS 1915+105. In our timing analysis, we find that when the source is faint in the radio, quasi-periodic oscillations (QPOs) are observed above 2 Hz and typically exhibit soft lags (soft photons lag hard photons), whereas QPOs in the radio-bright plateau state are found below 2.2 Hz and consistently show hard lags. The phase lag at the QPO frequency is strongly anti-correlated with that frequency, changing sign at 2.2 Hz. However, the phase lag at the frequency of the first harmonic is positive and nearly independent of that frequency at ∼0.172 rad, regardless of the radio emission. The lag energy dependence at the first harmonic is also independent of radio flux. However, the lags at the QPO frequency are negative at all energies during the radio-quiet state, but lags at the QPO frequency during the plateau state are positive at all energies and show a 'reflection-type' evolution of the lag energy spectra with respect to the radio-quiet state. The lag energy dependence is roughly logarithmic, but there is some evidence for a break around 4-6 keV. Finally, the Fourier-frequency-dependent phase lag spectra are fairly flat during the plateau state, but increase from negative to positive during the radio-quiet state. We discuss the implications of our results in light of some generic models.

79 ASTRONOMY AND ASTROPHYSICS↗

Astrometry and spatio-kinematics of H{sub 2}O masers in the massive star-forming region NGC 6334I(North) with VERA

We measured the trigonometric parallax of an H{sub 2}O maser source associated with the massive star-forming region NGC 6334I(North), hereafter as NGC 6334I(N), with the VLBI Exploration of Radio Astrometry. The derived annual parallax is 0.789 ± 0.161 mas, corresponding to a distance of 1.26{sub −0.21}{sup +0.33} kpc. Using the new distance, we recalculated the physical parameters (masses and luminosities) of the dust continuum cores in the region, and the revised parameters are only ∼50% of their originally reported values. We also traced 23 relative proper motions of the H{sub 2}O masers associated with SMA1 (central millimeter source in the region) between epochs, which exhibit an average amplitude of maser proper motion of ∼2.03 mas yr{sup –1} (∼12.22 km s{sup –1}), tracing a bipolar outflow. The bipolar outflow structure extends through ∼600 mas (∼720 AU), with a dynamical timescale of ∼295 yr. Using an expanding flow model, we derived the most plausible dynamical center of the outflow, pointing to SMA1b (1.3 cm and 7 mm continuum source) as the outflow driving source. Based on our results and other existing parallax results, we derive the pitch angles of the Sagittarius arm as 6.°2 ± 5.°4 along the Galactic longitude range of ∼0.°7 – ∼40.°1 assuming a perfect logarithmic spiral. We derived the peculiar motion of NGC 6334I(N) to be –4 ± 1 km s{sup –1} toward the Galactic center, 8 ± 2 km s{sup –1} in the direction of the Galactic rotation, and 25 ± 2 km s{sup –1} toward the Galactic north pole.

79 ASTRONOMY AND ASTROPHYSICS↗

Solar flare composition and thermodynamics from RESIK X-ray spectra

Previous estimates of the solar flare abundances of Si, S, Cl, Ar, and K from the RESIK X-ray crystal spectrometer on board the CORONAS-F spacecraft were made on the assumption of isothermal X-ray emission. We investigate the effect on these estimates by relaxing this assumption and instead determining the differential emission measure (DEM) or thermal structure of the emitting plasma by re-analyzing RESIK data for a GOES class M1.0 flare on 2002 November 14 (SOL2002-11-14T22:26) for which there was good data coverage. The analysis method uses a maximum-likelihood (Withbroe-Sylwester) routine for evaluating the DEM. In a first step, called here AbuOpt, an optimized set of abundances of Si, S, Ar, and K is found that is consistent with the observed spectra. With these abundances, the DEM evolution during the flare is found. The abundance optimization leads to revised abundances of silicon and sulfur in the flare plasma: A(S) = 6.94 ± 0.06 and A(Si) = 7.56 ± 0.08 (on a logarithmic scale with A(H) = 12). Previously determined abundances of Ar, K, and Cl from an isothermal assumption are still the preferred values. During the flare's maximum phase, the X-ray-emitting plasma has a basically two-temperature structure, with the cooler plasma with approximately constant temperature (3-6 MK) and a hotter plasma with temperature 16-21 MK. Using imaging data from the RHESSI hard X-ray spacecraft, the emission volume of the hot plasma is deduced from which lower limits of the electron density N{sub e} and the thermal content of the plasma are given.

79 ASTRONOMY AND ASTROPHYSICS↗

3D-HST+CANDELS: The evolution of the galaxy size-mass distribution since z = 3

Spectroscopic+photometric redshifts, stellar mass estimates, and rest-frame colors from the 3D-HST survey are combined with structural parameter measurements from CANDELS imaging to determine the galaxy size-mass distribution over the redshift range 0 < z < 3. Separating early- and late-type galaxies on the basis of star-formation activity, we confirm that early-type galaxies are on average smaller than late-type galaxies at all redshifts, and we find a significantly different rate of average size evolution at fixed galaxy mass, with fast evolution for the early-type population, R {sub eff}∝(1 + z){sup –1.48}, and moderate evolution for the late-type population, R {sub eff}∝(1 + z){sup –0.75}. The large sample size and dynamic range in both galaxy mass and redshift, in combination with the high fidelity of our measurements due to the extensive use of spectroscopic data, not only fortify previous results but also enable us to probe beyond simple average galaxy size measurements. At all redshifts the slope of the size-mass relation is shallow, R{sub eff}∝M{sub ∗}{sup 0.22}, for late-type galaxies with stellar mass >3 × 10{sup 9} M {sub ☉}, and steep, R{sub eff}∝M{sub ∗}{sup 0.75}, for early-type galaxies with stellar mass >2 × 10{sup 10} M {sub ☉}. The intrinsic scatter is ≲0.2 dex for all galaxy types and redshifts. For late-type galaxies, the logarithmic size distribution is not symmetric but is skewed toward small sizes: at all redshifts and masses, a tail of small late-type galaxies exists that overlaps in size with the early-type galaxy population. The number density of massive (∼10{sup 11} M {sub ☉}), compact (R {sub eff} < 2 kpc) early-type galaxies increases from z = 3 to z = 1.5-2 and then strongly decreases at later cosmic times.

79 ASTRONOMY AND ASTROPHYSICS↗

Dependence of the outer density profiles of halos on their mass accretion rate

We present a systematic study of the density profiles of ΛCDM halos, focusing on the outer regions, 0.1 < r/R {sub vir} < 9. We show that the median and mean profiles of halo samples of a given peak height exhibit significant deviations from the universal analytic profiles discussed previously in the literature, such as the Navarro-Frenk-White and Einasto profiles, at radii r ≳ 0.5R {sub 200m}. In particular, at these radii the logarithmic slope of the median density profiles of massive or rapidly accreting halos steepens more sharply than predicted. The steepest slope of the profiles occurs at r ≈ R {sub 200m}, and its absolute value increases with increasing peak height or mass accretion rate, reaching slopes of –4 and steeper. Importantly, we find that the outermost density profiles at r ≳ R {sub 200m} are remarkably self-similar when radii are rescaled by R {sub 200m}. This self-similarity indicates that radii defined with respect to the mean density are preferred for describing the structure and evolution of the outer profiles. However, the inner density profiles are most self-similar when radii are rescaled by R {sub 200c}. We propose a new fitting formula that describes the median and mean profiles of halo samples selected by their peak height or mass accretion rate with accuracy ≲ 10% at all radii, redshifts, and masses we studied, r ≲ 9R {sub vir}, 0 < z < 6, and M {sub vir} > 1.7 × 10{sup 10} h {sup –1} M {sub ☉}. We discuss observational signatures of the profile features described above and show that the steepening of the outer profile should be detectable in future weak-lensing analyses of massive clusters. Such observations could be used to estimate the mass accretion rate of cluster halos.

79 ASTRONOMY AND ASTROPHYSICS↗

Early-type galaxy core phase densities

Early-type galaxies have projected central density brightness profile logarithmic slopes, γ', ranging from about 0 to 1. We show that γ' is strongly correlated, r = 0.83, with the coarse grain phase density of the galaxy core, Q {sub 0} ≡ ρ/σ{sup 3}. The luminosity-γ' correlation is much weaker, r = –0.51. Q {sub 0} also serves to separate the distribution of steep core profiles, γ' > 0.5, from shallow profiles, γ' < 0.3, although there are many galaxies of intermediate slope, at intermediate Q {sub 0}, in a volume-limited sample. The transition phase density separating the two profile types is approximately 0.003 M {sub ☉} pc{sup –3} km{sup –3} s{sup 3}, which is also where the relation between Q {sub 0} and core mass shows a change in slope, the rotation rate of the central part of the galaxy increases, and the ratio of the black hole to core mass increases. These relations are considered relative to the globular cluster inspiral core buildup and binary black hole core scouring mechanisms for core creation and evolution. Mass-enhanced globular cluster inspiral models have quantitative predictions that are supported by data, but no single model yet completely explains the correlations.

79 ASTRONOMY AND ASTROPHYSICS↗

The black hole mass function derived from local spiral galaxies

We present our determination of the nuclear supermassive black hole (SMBH) mass function for spiral galaxies in the local universe, established from a volume-limited sample consisting of a statistically complete collection of the brightest spiral galaxies in the southern (δ < 0°) hemisphere. Our SMBH mass function agrees well at the high-mass end with previous values given in the literature. At the low-mass end, inconsistencies exist in previous works that still need to be resolved, but our work is more in line with expectations based on modeling of black hole evolution. This low-mass end of the spectrum is critical to our understanding of the mass function and evolution of black holes since the epoch of maximum quasar activity. The sample is defined by a limiting luminosity (redshift-independent) distance, D{sub L} = 25.4 Mpc (z = 0.00572) and a limiting absolute B-band magnitude, M{sub B}=−19.12. These limits define a sample of 140 spiral galaxies, with 128 measurable pitch angles to establish the pitch angle distribution for this sample. This pitch-angle distribution function may be useful in the study of the morphology of late-type galaxies. We then use an established relationship between the logarithmic spiral arm pitch angle and the mass of the central SMBH in a host galaxy in order to estimate the mass of the 128 respective SMBHs in this volume-limited sample. This result effectively gives us the distribution of mass for SMBHs residing in spiral galaxies over a lookback time, t{sub L} ≤ 82.1 h{sub 67.77}{sup −1} Myr and contained within a comoving volume, V{sub C} = 3.37 × 10{sup 4} h{sub 67.77}{sup −3} Mpc{sup 3}. We estimate that the density of SMBHs residing in spiral galaxies in the local universe is ρ=5.54{sub −2.73}{sup +6.55} × 10{sup 4} h{sub 67.77}{sup 3} M{sub ☉} Mpc{sup –3}. Thus, our derived cosmological SMBH mass density for spiral galaxies is Ω{sub BH}=4.35{sub −2.15}{sup +5.14} × 10{sup –7} h{sub 67.77}. Assuming that black holes grow via baryonic accretion, we predict that 0.0020{sub −0.0010}{sup +0.0023} h{sub 67.77}{sup 3} % of the universal baryonic inventory (Ω{sub BH}/ω{sub b}) is confined within nuclear SMBHs at the center of spiral galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

SpArcFiRe: Scalable automated detection of spiral galaxy arm segments

Given an approximately centered image of a spiral galaxy, we describe an entirely automated method that finds, centers, and sizes the galaxy (possibly masking nearby stars and other objects if necessary in order to isolate the galaxy itself) and then automatically extracts structural information about the spiral arms. For each arm segment found, we list the pixels in that segment, allowing image analysis on a per-arm-segment basis. We also perform a least-squares fit of a logarithmic spiral arc to the pixels in that segment, giving per-arc parameters, such as the pitch angle, arm segment length, location, etc. The algorithm takes about one minute per galaxies, and can easily be scaled using parallelism. We have run it on all ∼644,000 Sloan objects that are larger than 40 pixels across and classified as 'galaxies'. We find a very good correlation between our quantitative description of a spiral structure and the qualitative description provided by Galaxy Zoo humans. Our objective, quantitative measures of structure demonstrate the difficulty in defining exactly what constitutes a spiral 'arm', leading us to prefer the term 'arm segment'. We find that pitch angle often varies significantly segment-to-segment in a single spiral galaxy, making it difficult to define the pitch angle for a single galaxy. We demonstrate how our new database of arm segments can be queried to find galaxies satisfying specific quantitative visual criteria. For example, even though our code does not explicitly find rings, a good surrogate is to look for galaxies having one long, low-pitch-angle arm—which is how our code views ring galaxies. SpArcFiRe is available at http://sparcfire.ics.uci.edu.

79 ASTRONOMY AND ASTROPHYSICS↗

The Next Generation Virgo Cluster Survey. V. modeling the dynamics of M87 with the made-to-measure method

We study the dynamics of the giant elliptical galaxy M87 from the central to the outermost regions with the made-to-measure (M2M) method. We use a new catalog of 922 globular cluster line-of-sight velocities extending to a projected radius of 180 kpc (equivalent to 25 M87 effective radii), and SAURON integral field unit data within the central 2.4 kpc. There are 263 globular clusters, mainly located beyond 40 kpc, newly observed by the Next Generation Virgo Survey. For the M2M modeling, the gravitational potential is taken as a combination of a luminous matter potential with a constant stellar mass-to-light ratio and a dark matter potential modeled as a logarithmic potential. Our best-fit dynamical model returns a stellar mass-to-light ratio in the I band of M/L{sub I} = 6.0 ± 0.3 M{sub ⊙} L{sub ⊙}{sup −1} with a dark matter potential scale velocity of 591 ± 50 km s{sup –1} and scale radius of 42 ± 10 kpc. We determine the total mass of M87 within 180 kpc to be (1.5 ± 0.2) × 10{sup 13} M {sub ☉}. The mass within 40 kpc is smaller than previous estimates determined using globular cluster kinematics that did not extend beyond ∼45 kpc. With our new globular cluster velocities at much larger radii, we see that globular clusters around 40 kpc show an anomalously large velocity dispersion which affected previous results. The mass we derive is in good agreement with that inferred from ROSAT X-ray observation out to 180 kpc. Within 30 kpc our mass is also consistent with that inferred from Chandra and XMM-Newton X-ray observations, while within 120 kpc it is about 20% smaller. The model velocity dispersion anisotropy β parameter for the globular clusters in M87 is small, varying from –0.2 at the center to 0.2 at ∼40 kpc, and gradually decreasing to zero at ∼120 kpc.

79 ASTRONOMY AND ASTROPHYSICS↗

Trigonometric parallaxes of star forming regions in the Scutum spiral arm

We report measurements of trigonometric parallaxes for six high-mass star-forming regions in the Scutum spiral arm of the Milky Way as part of the BeSSeL Survey. Combining our measurements with 10 previous measurements from the BeSSeL Survey yields a total sample of 16 sources in the Scutum arm with trigonometric parallaxes in the Galactic longitude range from 5° to 32°. Assuming a logarithmic spiral model, we estimate a pitch angle of 19.°8 ± 3.°1 for the Scutum arm, which is larger than pitch angles reported for other spiral arms. The high pitch angle of the arm may be due to the arm's proximity to the Galactic bar. The Scutum arm sources show an average peculiar motion of 4 km s{sup –1} slower than the Galactic rotation and 8 km s{sup –1} toward the Galactic center. While the direction of this non-circular motion has the same sign as determined for sources in other spiral arms, the motion toward the Galactic center is greater for the Scutum arm sources.

79 ASTRONOMY AND ASTROPHYSICS↗

Exoplanet population inference and the abundance of Earth analogs from noisy, incomplete catalogs

No true extrasolar Earth analog is known. Hundreds of planets have been found around Sun-like stars that are either Earth-sized but on shorter periods, or else on year-long orbits but somewhat larger. Under strong assumptions, exoplanet catalogs have been used to make an extrapolated estimate of the rate at which Sun-like stars host Earth analogs. These studies are complicated by the fact that every catalog is censored by non-trivial selection effects and detection efficiencies, and every property (period, radius, etc.) is measured noisily. Here we present a general hierarchical probabilistic framework for making justified inferences about the population of exoplanets, taking into account survey completeness and, for the first time, observational uncertainties. We are able to make fewer assumptions about the distribution than previous studies; we only require that the occurrence rate density be a smooth function of period and radius (employing a Gaussian process). By applying our method to synthetic catalogs, we demonstrate that it produces more accurate estimates of the whole population than standard procedures based on weighting by inverse detection efficiency. We apply the method to an existing catalog of small planet candidates around G dwarf stars. We confirm a previous result that the radius distribution changes slope near Earth's radius. We find that the rate density of Earth analogs is about 0.02 (per star per natural logarithmic bin in period and radius) with large uncertainty. This number is much smaller than previous estimates made with the same data but stronger assumptions.

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