50 research outputs found
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 -band
spectrum of WASP-14, an F5 dwarf with a transiting exoplanet, and the moderate
resolution -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
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
Type Ia Supernova Light Curve Inference: Hierarchical Bayesian Analysis in the Near Infrared
We present a comprehensive statistical analysis of the properties of Type Ia
SN light curves in the near infrared using recent data from PAIRITEL and the
literature. We construct a hierarchical Bayesian framework, incorporating
several uncertainties including photometric error, peculiar velocities, dust
extinction and intrinsic variations, for coherent statistical inference. SN Ia
light curve inferences are drawn from the global posterior probability of
parameters describing both individual supernovae and the population conditioned
on the entire SN Ia NIR dataset. The logical structure of the hierarchical
model is represented by a directed acyclic graph. Fully Bayesian analysis of
the model and data is enabled by an efficient MCMC algorithm exploiting the
conditional structure using Gibbs sampling. We apply this framework to the
JHK_s SN Ia light curve data. A new light curve model captures the observed
J-band light curve shape variations. The intrinsic variances in peak absolute
magnitudes are: sigma(M_J) = 0.17 +/- 0.03, sigma(M_H) = 0.11 +/- 0.03, and
sigma(M_Ks) = 0.19 +/- 0.04. We describe the first quantitative evidence for
correlations between the NIR absolute magnitudes and J-band light curve shapes,
and demonstrate their utility for distance estimation. The average residual in
the Hubble diagram for the training set SN at cz > 2000 km/s is 0.10 mag. The
new application of bootstrap cross-validation to SN Ia light curve inference
tests the sensitivity of the model fit to the finite sample and estimates the
prediction error at 0.15 mag. These results demonstrate that SN Ia NIR light
curves are as effective as optical light curves, and, because they are less
vulnerable to dust absorption, they have great potential as precise and
accurate cosmological distance indicators.Comment: 24 pages, 15 figures, 4 tables. Accepted for publication in ApJ.
Corrected typo, added references, minor edit
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