Chung-Pei Ma

REVISITING THE SCALING RELATIONS OF BLACK HOLE MASSES AND HOST GALAXY PROPERTIES

New kinematic data and modeling efforts in the past few years have substantially expanded and revised dynamical measurements of black hole masses (M ?) at the centers of nearby galaxies. Here we compile an updated sample of 72 black holes and their host galaxies, and present revised scaling relations between M ? and stellar velocity dispersion (?), V-band luminosity (L), and bulge stellar mass (M bulge), for different galaxy subsamples. Our best-fitting power-law relations for the full galaxy sample are log10(M ?) = 8.32 + 5.64log10(?/200 km s?1), log10(M ?) = 9.23 + 1.11log10(L/1011 L ?), and log10(M ?) = 8.46 + 1.05log10(M bulge/1011 M ?). A log-quadratic fit to the M ?-? relation with an additional term of ?2 [log10(?/200 km s?1)]2 gives ?2 = 1.68 ? 1.82 and does not decrease the intrinsic scatter in M ?. Including 92 additional upper limits on M ? does not change the slope of the M ?-? relation. When the early- and late-type galaxies are fit separately, we obtain similar slopes of 5.20 and 5.06 for the M ?-? relation but significantly different intercepts?M ? in early-type galaxies are about two times higher than in late types at a given sigma. Within early-type galaxies, our fits to M ?(?) give M ? that is about two times higher in galaxies with central core profiles than those with central power-law profiles. Our M ?-L and M ?-M bulge relations for early-type galaxies are similar to those from earlier compilations, and core and power-law galaxies yield similar L- and M bulge-based predictions for M ?. When the conventional quadrature method is used to determine the intrinsic scatter in M ?, our data set shows weak evidence for increased scatter at M bulge < 1011 M ? or LV < 1010.3 L ?, while the scatter stays constant for 1011 < M bulge < 1012.3 M ? and 1010.3 < LV < 1011.5 L ?. A Bayesian analysis indicates that a larger sample of M ? measurements would be needed to detect any statistically significant trend in the scatter with galaxy properties.

The merger rates and mass assembly histories of dark matter haloes in the two Millennium simulations

We construct merger trees of dark matter haloes and quantify their merger rates and mass growth rates using the joint data set from the Millennium and Millennium-II simulations. The finer resolution of the Millennium-II simulation has allowed us to extend our earlier analysis of halo merger statistics to an unprecedentedly wide range of descendant halo mass (10 10 ≲ M 0 ≲ 10 15 M ⊙ ), progenitor mass ratio (10 -5 ≲ ξ ≤ 1) and redshift (0 ≤ z ≲ 15). We update our earlier fitting form for the mean merger rate per halo as a function of M 0 , ξ and z. The overall behaviour of this quantity is unchanged: the rate per unit redshift is nearly independent of z out to z ~ 15; the dependence on halo mass is weak (∝ Mg 0.13 0 ); and it is nearly a power law in the progenitor mass ratio (∝ ξ -2 ). We also present a simple and accurate fitting formula for the mean mass growth rate of haloes as a function of mass and redshift. This mean rate is 46 M ⊙ yr -1 for 10 12 M ⊙ haloes at z = 0, and it increases with mass as ∝ M 1.1 and with redshift as (1 + z) 2.5 (for z ≳ 1). When the fit for the mean mass growth rate is integrated over a halos history, we find excellent match to the mean mass assembly histories of the simulated haloes. By combining merger rates and mass assembly histories, we present results for the number of mergers over a halos history and the statistics of the redshift of the last major merger.

Dynamical friction and galaxy merging time‐scales

The time-scale for galaxies within merging dark matter haloes to merge with each other is an important ingredient in galaxy formation models. Accurate estimates of merging time-scales are required for predictions of astrophysical quantities such as black hole binary merger rates, the build-up of stellar mass in central galaxies and the statistical properties of satellite galaxies within dark matter haloes. In this paper, we study the merging time-scales of extended dark matter haloes using N-body simulations. We compare these results to standard estimates based on the Chandrasekhar theory of dynamical friction. We find that these standard predictions for merging time-scales, which are often used in semi-analytic galaxy formation models, are systematically shorter than those found in simulations. The discrepancy is approximately a factor of 1.7 for M sat /M host ≈ 0.1 and becomes larger for more disparate satellite-to-host mass ratios, reaching a factor of ∼3.3 for M sat /M host ≈ 0.01. Based on our simulations, we propose a new, easily implementable fitting formula that accurately predicts the time-scale for an extended satellite to sink from the virial radius of a host halo down to the halos centre for a wide range of M sat /M host and orbits. Including a central bulge in each galaxy changes the merging time-scale by ≤10 per cent. To highlight one concrete application of our results, we show that merging time-scales often used in the literature overestimate the growth of stellar mass by satellite accretion by ≈40 per cent, with the extra mass gained in low mass ratio mergers.

Deriving the Nonlinear Cosmological Power Spectrum and Bispectrum from Analytic Dark Matter Halo Profiles and Mass Functions

We present an analytic model for the fully nonlinear two- and three-point correlation functions of the cosmological mass density field, and their Fourier transforms, the mass power spectrum and bispectrum. The model is based on physical properties of dark matter halos, with the three main model inputs being analytic halo density profiles, halo mass functions, and halo-halo spatial correlations, each of which has been well studied in the literature. We demonstrate that this new model can reproduce the power spectrum and bispectrum computed from cosmological simulations of both an n = -2 scale-free model and a low-density cold dark matter model. To enhance the dynamic range of these large simulations, we use the synthetic-halo replacement technique of Ma & Fry, in which the original halos with numerically softened cores are replaced by synthetic halos of realistic density profiles. At high wavenumbers, our model predicts a slope for the nonlinear power spectrum different from the often-used fitting formulas in the literature based on the stable-clustering assumption. Our model also predicts a three-point amplitude, Q, that is scale dependent, in contrast to the popular hierarchical clustering assumption. This model provides a rapid way to compute the mass power spectrum and bispectrum over all length scales where the input halo properties are valid. It also provides a physical interpretation of the clustering properties of matter in the universe.

Two ten-billion-solar-mass black holes at the centres of giant elliptical galaxies

Observational work conducted over the past few decades indicates that all massive galaxies have supermassive black holes at their centres. Although the luminosities and brightness fluctuations of quasars in the early Universe suggest that some were powered by black holes with masses greater than 10 billion solar masses, the remnants of these objects have not been found in the nearby Universe. The giant elliptical galaxy Messier 87 hosts the hitherto most massive known black hole, which has a mass of 6.3 billion solar masses. Here we report that NGC 3842, the brightest galaxy in a cluster at a distance from Earth of 98 megaparsecs, has a central black hole with a mass of 9.7 billion solar masses, and that a black hole of comparable or greater mass is present in NGC 4889, the brightest galaxy in the Coma cluster (at a distance of 103 megaparsecs). These two black holes are significantly more massive than predicted by linearly extrapolating the widely used correlations between black-hole mass and the stellar velocity dispersion or bulge luminosity of the host galaxy. Although these correlations remain useful for predicting black-hole masses in less massive elliptical galaxies, our measurements suggest that different evolutionary processes influence the growth of the largest galaxies and their black holes.

The nearly universal merger rate of dark matter haloes in ΛCDM cosmology

We construct merger trees from the largest data base of dark matter haloes to date provided by the Millennium Simulation to quantify the merger rates of haloes over a broad range of descendant halo mass (10 12 ≤ M 0 ≤ 1015 M ⊙ ), progenitor mass ratio (10 -3 ≤ ξ ≤ 1), and redshift (0 ≤ z ≤ 6). We find the mean merger rate per halo, Bin, to have very simple dependence on M 0 , ξ, and z, and propose a universal fitting form for B/n that is accurate to 10-20 per cent. Overall, B/n depends very weakly on the halo mass (oc M 0 0 .08) and scales as a power law in the progenitor mass ratio (oc ξ -2 ) for minor mergers (ξ ≤ 0.1) with a mild upturn for major mergers. As a function of time, we find the merger rate per Gyr to evolve roughly as (1 + z) nm with r m = 2-2.3, while the rate per unit redshift is nearly independent of z. Several tests are performed to assess how our merger rates are affected by e.g. the time interval between Millennium outputs, binary versus multiple progenitor mergers, and mass conservation and diffuse accretion during mergers. In particular, we find halo fragmentations to be a general issue in merger tree construction from N-body simulations and compare two methods for handling these events. We compare our results with predictions of two analytical models for halo mergers based on the extended Press-Schechter (EPS) model and the coagulation theory. We find that the EPS model overpredicts the major merger rates and underpredicts the minor merger rates by up to a factor of a few.

Red mergers and the assembly of massive elliptical galaxies: the fundamental plane and its projections

Several recent observations suggest that gas-poor (dissipationless) mergers of elliptical galaxies contribute significantly to the build-up of the massive end of the red sequence at z? 1. We perform a series of major merger simulations to investigate the spatial and velocity structure of the remnants of such mergers. Regardless of orbital energy or angular momentum, we find that the stellar remnants lie on the fundamental plane defined by their progenitors, a result of virial equilibrium with a small tilt due to an increasing central dark matter fraction. However, the locations of merger remnants in the projections of the fundamental plane - the Faber-Jackson and R e -M * relations - depend strongly on the merger orbit, and the relations steepen significantly from the canonical scalings (L ∝ σ 4 e and R e ∝ M 0.6 * ) for mergers on radial orbits. This steepening arises because stellar bulges on orbits with lower angular momentum lose less energy via dynamical friction on the dark matter haloes than do bulges on orbits with substantial angular momentum. This results in a less tightly bound remnant bulge with a smaller velocity dispersion and a larger effective radius. Our results imply that the projections of the fundamental plane - but not necessarily the plane itself - provide a powerful way of investigating the assembly history of massive elliptical galaxies, including the brightest cluster galaxies at or near the centres of galaxy clusters. We argue that most massive ellipticals are formed by anisotropic merging and that their fundamental plane projections should thus differ noticeably from those of lower mass ellipticals even though they should lie on the same fundamental plane. Current observations are consistent with this conclusion. The steepening in the L-σ e relation for luminous ellipticals may also be reflected in a corresponding steepening in the M BH-σe relation for massive black holes.

Metallicities and Physical Conditions in Star-forming Galaxies at z ~ 1.0-1.5*

We present a study of the mass-metallicity (M-Z) relation and H II region physical conditions in a sample of 20 star-forming galaxies at 1.0 < z < 1.5 drawn from the DEEP2 Galaxy Redshift Survey. We find a correlation between stellar mass and gas-phase oxygen abundance in the sample and compare it with the one observed among UV-selected z ~ 2 star-forming galaxies and local objects from the Sloan Digital Sky Survey (SDSS). This comparison, based on the same empirical abundance indicator, demonstrates that the zero point of the M-Z relationship evolves with redshift, in the sense that galaxies at fixed stellar mass become more metal-rich at lower redshift. Measurements of [O III]/Hβ and [N II]/Hα emission-line ratios show that, on average, objects in the DEEP2 1.0 < z < 1.5 sample are significantly offset from the excitation sequence observed in nearby H II regions and SDSS emission-line galaxies. In order to fully understand the causes of this offset, which is also observed in z ~ 2 star-forming galaxies, we examine in detail the small fraction of SDSS galaxies that have similar diagnostic ratios to those of the DEEP2 sample. Some of these galaxies indicate evidence for AGN and/or shock activity, which may give rise to their unusual line ratios and contribute to Balmer emission lines at the level of ~20%. Others indicate no evidence for AGN or shock excitation yet are characterized by higher electron densities and temperatures, and therefore interstellar gas pressures, than typical SDSS star-forming galaxies of similar stellar mass. These anomalous objects also have higher concentrations and starformation rate surface densities, which are directly connected to higher interstellar pressure. Higher star formation rate surface densities, interstellar pressures, and H II region ionization parameters may also be common at high redshift. These effects must be taken into account when using strong-line indicators to understand the evolution of heavy elements in galaxies. When such effects are included, the inferred evolution of the M-Z relation out to z ~ 2 is more significant than previous estimates.

Chemical Abundances of DEEP2 Star-forming Galaxies at z~1.0-1.5*

We present the results of near-infrared spectroscopic observations for a sample of 12 star-forming galaxies at 1.0 1 DEEP2 galaxies in our sample are significantly offset from the excitation sequence observed in nearby H II regions and SDSS emission-line galaxies. This offset implies that physical conditions are different in the H II regions of distant galaxies hosting intense star formation, and may affect the chemical abundances derived from strong-line ratios for such objects.

The merger rate of galaxies in the Illustris Simulation: a comparison with observations and semi-empirical models

We have constructed merger trees for galaxies in the Illustris simulation by directly tracking the baryonic content of subhaloes. These merger trees are used to calculate the galaxy–galaxy merger rate as a function of descendant stellar mass, progenitor stellar mass ratio, and redshift. We demonstrate that the most appropriate definition for the mass ratio of a galaxy–galaxy merger consists in taking both progenitor masses at the time when the secondary progenitor reaches its maximum stellar mass. Additionally, we avoid effects from ‘orphaned’ galaxies by allowing some objects to ‘skip’ a snapshot when finding a descendant, and by only considering mergers which show a well-defined ‘infall’ moment. Adopting these definitions, we obtain well-converged predictions for the galaxy–galaxy merger rate with the following main features, which are qualitatively similar to the halo–halo merger rate except for the last one: a strong correlation with redshift that evolves as ∼(1 + z)^(2.4–2.8), a power law with respect to mass ratio, and an increasing dependence on descendant stellar mass, which steepens significantly for descendant stellar masses greater than ∼2 × 10^(11)M_⊙. These trends are consistent with observational constraints for medium-sized galaxies (M* ≳ 10^(10) M_⊙), but in tension with some recent observations of the close pair fraction for massive galaxies (M* ≳ 10^(11) M_⊙), which report a nearly constant or decreasing evolution with redshift. Finally, we provide a fitting function for the galaxy–galaxy merger rate which is accurate over a wide range of stellar masses, progenitor mass ratios, and redshifts.