Constructing A Flexible Likelihood Function For Spectroscopic Inference

We present a modular, extensible likelihood framework for spectroscopic inference based on synthetic model spectra. The subtraction of an imperfect model from a continuously sampled spectrum introduces covariance between adjacent datapoints (pixels) into the residual spectrum. For the high signal-to-noise data with large spectral range that is commonly employed in stellar astrophysics, that covariant structure can lead to dramatically underestimated parameter uncertainties (and, in some cases, biases). We construct a likelihood function that accounts for the structure of the covariance matrix, utilizing the machinery of Gaussian process kernels. This framework specifically address the common problem of mismatches in model spectral line strengths (with respect to data) due to intrinsic model imperfections (e.g., in the atomic/molecular databases or opacity prescriptions) by developing a novel local covariance kernel formalism that identifies and self-consistently downweights pathological spectral line "outliers." By fitting many spectra in a hierarchical manner, these local kernels provide a mechanism to learn about and build data-driven corrections to synthetic spectral libraries. An open-source software implementation of this approach is available at http://iancze.github.io/Starfish, including a sophisticated probabilistic scheme for spectral interpolation when using model libraries that are sparsely sampled in the stellar parameters. We demonstrate some salient features of the framework by fitting the high resolution $V$-band spectrum of WASP-14, an F5 dwarf with a transiting exoplanet, and the moderate resolution $K$-band spectrum of Gliese 51, an M5 field dwarf.Comment: Accepted to ApJ. Incorporated referees' comments. New figures 1, 8, 10, 12, and 14. Supplemental website: http://iancze.github.io/Starfish

Weak Gravitational Lensing of High-Redshift 21 cm Power Spectra

We describe the effects of weak gravitational lensing by cosmological large scale structure on the diffuse emission of 21 centimeter radiation from neutral hydrogen at high redshifts during the era of reionization. The ability to observe radial information through the frequency, and thus three-dimensional regions of the background radiation at different redshifts, suggests that 21 cm studies may provide a useful context for studying weak lensing effects. We focus on the gravitational lensing effects on both the angular power spectra and the intrinsic, three-dimensional power spectra. We present a new approach for calculating the weak lensing signature based on integrating differential Fourier-space shells of the deflection field and approximating the magnification matrix. This method is applied to reionization models of the 21 cm spectra up to small angular scales over a range in redshift. The effect on the angular power spectrum is typically < 1% on small angular scales, and very small on scales corresponding to the feature imprinted by reionization bubbles, due to the near-scale invariance of the angular power spectrum of the 21 cm signal on these scales. We describe the expected effect of weak lensing on three-dimensional 21 cm power spectra, and show that lensing creates aspherical perturbations to the intrinsic power spectrum which depend on the polar angle of the wavevector. The effect on the 3D power spectrum is < 1% on scales k < 0.1 h/Mpc, but can be > 1% for highly inclined modes for k > 1 h/Mpc. The angular variation of the lensing effect on these scales is well described by a quartic polynomial in the cosine of the polar angle. The detection of the gravitational lensing effects on 21 cm power spectra will require very sensitive, high resolution observations by future low-frequency radio arrays.Comment: 18 pages, 10 figures; submitting to Ap

GausSN: Bayesian Time-Delay Estimation for Strongly Lensed Supernovae

We present GausSN, a Bayesian semi-parametric Gaussian Process (GP) model for time-delay estimation with resolved systems of gravitationally lensed supernovae (glSNe). GausSN models the underlying light curve non-parametrically using a GP. Without assuming a template light curve for each SN type, GausSN fits for the time delays of all images using data in any number of wavelength filters simultaneously. We also introduce a novel time-varying magnification model to capture the effects of microlensing alongside time-delay estimation. In this analysis, we model the time-varying relative magnification as a sigmoid function, as well as a constant for comparison to existing time-delay estimation approaches. We demonstrate that GausSN provides robust time-delay estimates for simulations of glSNe from the Nancy Grace Roman Space Telescope and the Vera C. Rubin Observatory's Legacy Survey of Space and Time (Rubin-LSST). We find that up to 43.6% of time-delay estimates from Roman and 52.9% from Rubin-LSST have fractional errors of less than 5%. We then apply GausSN to SN Refsdal and find the time delay for the fifth image is consistent with the original analysis, regardless of microlensing treatment. Therefore, GausSN maintains the level of precision and accuracy achieved by existing time-delay extraction methods with fewer assumptions about the underlying shape of the light curve than template-based approaches, while incorporating microlensing into the statistical error budget rather than requiring post-processing to account for its systematic uncertainty. GausSN is scalable for time-delay cosmography analyses given current projections of glSNe discovery rates from Rubin-LSST and Roman.Comment: 18 pages, 12 figures, submitted to MNRA

Disentangling Time-series Spectra with Gaussian Processes: Applications to Radial Velocity Analysis

Measurements of radial velocity variations from the spectroscopic monitoring of stars and their companions are essential for a broad swath of astrophysics; these measurements provide access to the fundamental physical properties that dictate all phases of stellar evolution and facilitate the quantitative study of planetary systems. The conversion of those measurements into both constraints on the orbital architecture and individual component spectra can be a serious challenge, however, especially for extreme flux ratio systems and observations with relatively low sensitivity. Gaussian processes define sampling distributions of flexible, continuous functions that are well-motivated for modeling stellar spectra, enabling proficient searches for companion lines in time-series spectra. We introduce a new technique for spectral disentangling, where the posterior distributions of the orbital parameters and intrinsic, rest-frame stellar spectra are explored simultaneously without needing to invoke cross-correlation templates. To demonstrate its potential, this technique is deployed on red-optical time-series spectra of the mid-M-dwarf binary LP661-13. We report orbital parameters with improved precision compared to traditional radial velocity analysis and successfully reconstruct the primary and secondary spectra. We discuss potential applications for other stellar and exoplanet radial velocity techniques and extensions to time-variable spectra. The code used in this analysis is freely available as an open-source Python package

Disentangling time-series spectra with Gaussian processes : applications to radial velocity analysis

Funding: K.M. is supported at Harvard by NSF grants AST-1211196 and AST-156854. Work by B.T.M. was performed under contract with the Jet Propulsion Laboratory (JPL) funded by NASA through the Sagan Fellowship Program executed by the NASA Exoplanet Science Institute. This material was based upon work partially supported by the National Science Foundation under Grant DMS-1127914 to the Statistical and Applied Mathematical Sciences Institute.Measurements of radial velocity variations from the spectroscopic monitoring of stars and their companions are essential for a broad swath of astrophysics; these measurements provide access to the fundamental physical properties that dictate all phases of stellar evolution and facilitate the quantitative study of planetary systems. The conversion of those measurements into both constraints on the orbital architecture and individual component spectra can be a serious challenge, however, especially for extreme flux ratio systems and observations with relatively low sensitivity. Gaussian processes define sampling distributions of flexible, continuous functions that are well-motivated for modeling stellar spectra, enabling proficient searches for companion lines in time-series spectra. We introduce a new technique for spectral disentangling, where the posterior distributions of the orbital parameters and intrinsic, rest-frame stellar spectra are explored simultaneously without needing to invoke cross-correlation templates. To demonstrate its potential, this technique is deployed on red-optical time-series spectra of the mid-M-dwarf binary LP661-13. We report orbital parameters with improved precision compared to traditional radial velocity analysis and successfully reconstruct the primary and secondary spectra. We discuss potential applications for other stellar and exoplanet radial velocity techniques and extensions to time-variable spectra. The code used in this analysis is freely available as an open-source Python package.Publisher PDFPeer reviewe

Hubble Residuals of Nearby Type Ia Supernovae Are Correlated with Host Galaxy Masses

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 ~2.5{\sigma} 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 solar masses in a cosmology fit yields 1+w=0.22 +0.152/-0.143, while a combination where the 30 nearby SN instead have host masses greater than 10^10.8 solar masses yields 1+w=-0.03 +0.217/-0.108. 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.Comment: 16 pages, 6 figures, published in ApJ, minor change