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

Avoiding methane emission rate underestimates when using the divergence method

Methane is a powerful greenhouse gas, and a primary target for mitigating climate change in the short-term future due to its relatively short atmospheric lifetime and greater ability to trap heat in Earth's atmosphere compared to carbon dioxide. Top-down observations of atmospheric methane are possible via drone and aircraft surveys as well as satellites such as the TROPOspheric Monitoring Instrument (TROPOMI). Recent work has begun to apply the divergence method to produce regional methane emission rate estimates. Here we show that when the divergence method is applied to spatially incomplete observations of methane, it can result in negatively biased time-averaged regional emission rates. We show that this effect can be counteracted by adopting a procedure in which daily advective fluxes of methane are time-averaged before the divergence method is applied. Using such a procedure with TROPOMI methane observations, we calculate yearly Permian emission rates of 3.1, 2.4 and 2.7 million tonnes per year for the years 2019 through 2021. We also show that highly-resolved plumes of methane can have negatively biased estimated emission rates by the divergence method due to the presence of turbulent diffusion in the plume, but this is unlikely to affect regional methane emission budgets constructed from TROPOMI observations of methane. The results from this work are expected to provide useful guidance for future implementations of the divergence method for emission rate estimation from satellite data -- be it for methane or other gaseous species in the atmosphere.Comment: 19 pages, 10 figures, submitted to Environmental Research Letter

Evidence for Grain Growth in Molecular Clouds: A Bayesian Examination of the Extinction Law in Perseus

We investigate the shape of the extinction law in two $1^{\circ}$ square fields of the Perseus molecular cloud complex. We combine deep red-optical (r, i and z band) observations obtained using Megacam on the MMT with UKIRT (United Kingdom Infrared Telescope) Infrared Deep Sky Survey near-infrared (J, H and K band) data to measure the colours of background stars. We develop a new hierarchical Bayesian statistical model, including measurement error, intrinsic colour variation, spectral type and dust reddening, to simultaneously infer parameters for individual stars and characteristics of the population. We implement an efficient Markov chain Monte Carlo algorithm utilizing generalized Gibbs sampling to compute coherent probabilistic inferences. We find a strong correlation between the extinction $(A_V)$ and the slope of the extinction law (parametrized by $R_V)$. Because the majority of the extinction towards our stars comes from the Perseus molecular cloud, we interpret this correlation as evidence of grain growth at moderate optical depths. The extinction law changes from the ‘diffuse’ value of $R_V \sim 3$ to the 'dense cloud' value of $R_V \sim 5$ as the column density rises from $A_V = 2$ to 10 mag. This relationship is similar for the two regions in our study, despite their different physical conditions, suggesting that dust grain growth is a fairly universal process.Astronom