Dissecting the quasar main sequence: insight from host galaxy properties

The diverse properties of broad-line quasars appear to follow a well-defined main sequence along which the optical FeII strength increases. It has been suggested that this sequence is mainly driven by the Eddington ratio (L/L_Edd) of the black hole (BH) accretion. Shen & Ho demonstrated with quasar clustering analysis that the average BH mass decreases with increasing FeII strength when quasar luminosity is fixed, consistent with this suggestion. Here we perform an independent test by measuring the stellar velocity dispersion sigma* (hence the BH mass via the M-sigma* relation) from decomposed host spectra in low-redshift Sloan Digital Sky Survey quasars. We found that at fixed quasar luminosity, sigma* systematically decreases with increasing FeII strength, confirming that Eddington ratio increases with FeII strength. We also found that at fixed luminosity and FeII strength, there is little dependence of sigma* on the broad Hbeta FWHM. These new results reinforce the framework put forward by Shen & Ho that Eddington ratio and orientation govern most of the diversity seen in broad-line quasar properties.Comment: ApJL in press; 5 pages and 4 figure

On the Eccentricity Distribution of Exoplanets from Radial Velocity Surveys

We investigate the estimation of orbital parameters by least-$\chi^2$ Keplerian fits to radial velocity (RV) data using synthetic data sets. We find that while the fitted period is fairly accurate, the best-fit eccentricity and $M_p\sin i$ are systematically biased upward from the true values for low signal-to-noise ratio $K/\sigma\lesssim 3$ and moderate number of observations $N_{\rm obs}\lesssim 60$, leading to a suppression of the number of nearly circular orbits. Assuming intrinsic distributions of orbital parameters, we generate a large number of mock RV data sets and study the selection effect on the eccentricity distribution. We find the overall detection efficiency only mildly decreases with eccentricity. This is because although high eccentricity orbits are more difficult to sample, they also have larger RV amplitudes for fixed planet mass and orbital semi-major axis. Thus the primary source of uncertainties in the eccentricity distribution comes from biases in Keplerian fits to detections with low-amplitude and/or small $N_{\rm obs}$, rather than from selection effects. Our results suggest that the abundance of low-eccentricity exoplanets may be underestimated in the current sample and we urge caution in interpreting the eccentricity distributions of low-amplitude detections in future RV samples.Comment: Accepted for publication in Ap

The diversity of quasars unified by accretion and orientation

Quasars are rapidly accreting supermassive black holes at the center of massive galaxies. They display a broad range of properties across all wavelengths, reflecting the diversity in the physical conditions of the regions close to the central engine. These properties, however, are not random, but form well-defined trends. The dominant trend is known as Eigenvector 1, where many properties correlate with the strength of optical iron and [OIII] emission. The main physical driver of Eigenvector 1 has long been suspected to be the quasar luminosity normalized by the mass of the hole (the Eddington ratio), an important quantity of the black hole accretion process. But a definitive proof has been missing. Here we report an analysis of archival data that reveals that Eddington ratio indeed drives Eigenvector 1. We also find that orientation plays a significant role in determining the observed kinematics of the gas, implying a flattened, disklike geometry for the fast-moving clouds close to the hole. Our results show that most of the diversity of quasar phenomenology can be unified with two simple quantities, Eddington ratio and orientation.Comment: This is the author's version of the work; 18 pages including Supplementary Information; to appear in the 11 September 2014 issue of Nature at http://dx.doi.org/10.1038/nature1371

Optimal regularity of minimal graphs in the hyperbolic space

We discuss the global regularity of solutions $f$ to the Dirichlet problem for minimal graphs in the hyperbolic space when the boundary of the domain $\Omega\subset\mathbb R^n$ has a nonnegative mean curvature and prove an optimal regularity $f\in C^{\frac{1}{n+1}}(\bar{\Omega})$. We can improve the H\"older exponent for $f$ if certain combinations of principal curvatures of the boundary do not vanish, a phenomenon observed by F.-H. Lin.Comment: Accepted by Calc. Var. Partial Differential Equation

Fluctuation Induced First Order Phase Transitions

We study a $U(N)\times U(N)$ symmetric scalar field model in four and three dimensions. First, using our data in four dimensions in the weak coupling region, we demonstrate explicitly that the observed first order phase transition is induced by quantum fluctuations. Next, based on the renormalization group and our new simulation results in three dimensions we argue that even if the $U_A(1)$ symmetry is restored below the critical temperature the QCD finite temperature chiral phase transition for two flavor could be extremely weak first order. Contribution to Lattice '93 proceedings. Needs espcrc2.sty file (included). Search Figure1.ps, Figure2.ps, ... for postscript files.Comment: 3 pages, 4 postscript figures attached. Preprint BUHEP-93-2