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 lightcurve 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 HST 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 lightcurves using limbdarkening coefficients from model atmospheres which should aid in the detection, simulation, and parameter fitting of planetary transits.

We present 2603 spectra of 462 nearby Type Ia supernovae (SNe Ia), including 2065 previously unpublished spectra, obtained during 1993-2008 through the Center for Astrophysics Supernova Program. There are on average eight spectra for each of the 313 SNe Ia with at least two spectra. Most of the spectra were obtained with the FAST spectrograph at the Fred Lawrence Whipple Observatory 1.5 m telescope and reduced in a consistent manner, making this data set well suited for studies of SN Ia spectroscopic diversity. Using additional data from the literature, we study the spectroscopic and photometric properties of SNe Ia as a function of spectroscopic class using the classification schemes of Branch et al. and Wang et al. The width-luminosity relation appears to be steeper for SNe Ia with broader lines, although the result is not statistically significant with the present sample. Based on the evolution of the characteristic Si ii λ6355 line, we propose improved methods for measuring velocity gradients, revealing a larger range than previously suspected, from ∼0 to ∼400 km s −1 day −1 considering the instantaneous velocity decline rate at maximum light. We find a weaker and less significant correlation between Si ii velocity and intrinsic B − V color at maximum light than reported by Foley et al., owing to a more comprehensive treatment of uncertainties and host galaxy dust. We study the extent of nuclear burning and the presence of unburnt carbon in the outermost layers of the ejecta and report new detections of C ii λ6580 in 23 early-time SN Ia spectra. The frequency of C ii detections is not higher in SNe Ia with bluer colors or narrower light curves, in conflict with the recent results of Thomas et al. Based on nebular spectra of 27 SNe Ia, we find no relation between the FWHM of the iron emission feature at ∼4700 Å and Δm 15 (B) after removing the two low-luminosity SN 1986G and SN 1991bg, suggesting that the peak luminosity is not strongly dependent on the kinetic energy of the explosion for most SNe Ia. Finally, we confirm the correlation of velocity shifts in some nebular lines with the intrinsic B − V color of SNe Ia at maximum light, although several outliers suggest a possible non-monotonic behavior for the largest blueshifts.

From Sloan Digital Sky Survey u' g' r' i' z' imaging, we estimate the stellar masses of the host galaxies of 70 low redshift SN Ia (0.015 < z < 0.08) from the hosts' absolute luminosities and mass-to-light ratios. These nearby SN were discovered largely by searches targeting luminous galaxies, and we find that their host galaxies are substantially more massive than the hosts of SN discovered by the flux-limited Supernova Legacy Survey. Testing four separate light curve fitters, we detect ∼2.5σ correlations of Hubble residuals with both host galaxy size and stellar mass, such that SN Ia occurring in physically larger, more massive hosts are ∼10% brighter after light curve correction. The Hubble residual is the deviation of the inferred distance modulus to the SN, calculated from its apparent luminosity and light curve properties, away from the expected value at the SN redshift. Marginalizing over linear trends in Hubble residuals with light curve parameters shows that the correlations cannot be attributed to a light curve-dependent calibration error. Combining 180 higher-redshift ESSENCE, SNLS, and HigherZ SN with 30 nearby SN whose host masses are less than 10 10.8 M in a cosmology fit yields 1 + w = 0.22−0.108 , while a combination where the 30 nearby SN instead have host masses greater than 10 10.8 M yields 1 + w = −0.03−0.143 . Progenitor metallicity, stellar population age, and dust extinction correlate with galaxy mass and may be responsible for these systematic effects. Host galaxy measurements will yield improved distances to SN Ia.

We have constructed a comprehensive statistical model for Type Ia supernova (SN Ia) light curves spanning optical through near infrared (NIR) data. A hierarchical framework coherently models multiple random and uncertain effects, including intrinsic supernova light curve covariances, dust extinction and reddening, and distances. An improved BayeSN MCMC code computes probabilistic inferences for the hierarchical model by sampling the global probability density of parameters describing individual supernovae and the population. We have applied this hierarchical model to optical and NIR data of 127 SN Ia from PAIRITEL, CfA3, CSP, and the literature. We find an apparent population correlation between the host galaxy extinction A V and the the ratio of total-to-selective dust absorption R V . For SN with low dust extinction, A V 0.4, we find R V ≈ 2.5 − 2.9, while at high extinctions, A V 1, low values of R V < 2 are favored. The NIR luminosities are excellent standard candles and are less sensitive to dust extinction. They exhibit low correlation with optical peak luminosities, and thus provide independent information on distances. The combination of NIR and optical data constrains the dust extinction and improves the predictive precision of individual SN Ia distances by about 60%. Using cross-validation, we estimate an rms distance modulus prediction error of 0.11 mag for SN with optical and NIR data versus 0.15 mag for SN with optical data alone. Continued study of SN Ia in the NIR is important for improving their utility as precise and accurate cosmological distance indicators.