Publications

In recent years, dedicated extreme precision radial velocity (RV) spectrographs have produced vast quantities of high-resolution, high-signal-to-noise (S/N) time-series spectra for bright stars. These data contain valuable information for the dual purposes of planet detection via the measured RVs and stellar characterization via the coadded spectra. However, considerable data analysis challenges exist in extracting these data products from the observed spectra at the highest possible precision, including the issue of poorly characterized telluric absorption features and the common use of an assumed stellar spectral template. In both of these examples, precision-limiting reliance on external information can be sidestepped using the data directly. Here we propose a data-driven method to simultaneously extract precise RVs and infer the underlying stellar and telluric spectra using a linear model (in the log of flux). The model employs a convex objective and convex regularization to keep the optimization of the spectral components fast. We implement this method in wobble, an open-source python package that uses TensorFlow in one of its first non-neural-network applications to astronomical data. In this work, we demonstrate the performance of wobble on archival High Accuracy Radial Velocity Planet Searcher (HARPS) spectra. We recover the canonical exoplanet 51 Pegasi b, detect the secular RV evolution of the M dwarf Barnard's Star, and retrieve the Rossiter–McLaughlin effect for the hot Jupiter HD 189733b. The method additionally produces extremely high-S/N composite stellar spectra and detailed time-variable telluric spectra, which we also present here.

A saddle point plus fluctuation analysis of the periodically driven half-filled two-dimensional Hubbard model is performed. For drive frequencies below the equilibrium gap, we find discontinuous transitions to time-dependent solutions. A highly excited, generically nonthermal distribution of magnons occurs even for drive frequencies far above the gap. Above a critical drive amplitude, the low-energy magnon distribution diverges as the frequency tends to zero and antiferromagnetism is destroyed, revealing the generic importance of collective mode excitations arising from a nonequilibrium drive.

The nonuniform fast Fourier transform (NUFFT) generalizes the FFT to off-grid data. Its many applications include image reconstruction, data analysis, and the numerical solution of differential equations. We present FINUFFT, an efficient parallel library for type 1 (nonuiform to uniform), type 2 (uniform to nonuniform), or type 3 (nonuniform to nonuniform) transforms, in dimensions 1, 2, or 3. It uses minimal RAM, requires no precomputation or plan steps, and has a simple interface to several languages. We perform the expensive spreading/interpolation between nonuniform points and the fine grid via a simple new kernel---the `exponential of semicircle' $e^{\beta \sqrt{1-x^2}}$ in $x\in[-1,1]$---in a cache-aware load-balanced multithreaded implementation. The deconvolution step requires the Fourier transform of the kernel, for which we propose efficient numerical quadrature. For types 1 and 2, rigorous error bounds asymptotic in the kernel width approach the fastest known exponential rate, namely that of the Kaiser--Bessel kernel. We benchmark against several popular CPU-based libraries, showing favorable speed and memory footprint, especially in three dimensions when high accuracy and/or clustered point distributions are desired.