# A Data-Driven Technique for Measuring Stellar Rotation

## TL;DR

This paper introduces a fast, data-driven method to measure stellar rotational velocities from high-resolution spectra by modeling spectral derivatives, enabling rapid analysis of large survey datasets with high accuracy.

## Contribution

It presents a novel approach adapting The Cannon framework to estimate $v\sin{i}$ by modeling spectral derivatives, improving efficiency and accuracy over traditional methods.

## Key findings

- Estimated $v\sin{i}$ for 27,000 spectra within 1.2 km/s accuracy.
- Achieved rapid computation, estimating $v\sin{i}$ in fractions of a second per spectrum.
- Validated method using SDSS APOGEE and California Kepler Survey data.

## Abstract

Measuring stellar rotational velocities is a powerful way to probe the many astrophysical phenomena that drive, or are driven by, the evolution of stellar angular momentum. In this paper, we present a novel data-driven approach to measuring the projected rotational velocity, $v\sin{i}$. Rather than directly measuring the broadening of spectral lines, we leverage the large information content of high-resolution spectral data to empirically estimate $v\sin{i}$. We adapt the framework laid down by The Cannon (Ness et al. 2015), which trains a generative model of the stellar flux as a function of wavelength using high-fidelity reference data, and can then produce estimates of stellar parameters and abundances for other stars directly from their spectra. Instead of modeling the flux as a function of wavelength, however, we model the first derivative of the spectra, as we expect the slopes of spectral lines to change as a function of $v\sin{i}$. This technique is computationally efficient and provides a means of rapidly estimating $v\sin{i}~$ for large numbers of stars in spectroscopic survey data. We analyze SDSS APOGEE spectra, constructing a model informed by high-fidelity stellar parameter estimates derived from high-resolution California Kepler Survey spectra of the same stars. We use the model to estimate $v\sin{i}~$ up to $15\,km\,s^{-1}$ for $27,000$ APOGEE spectra, in fractions of a second per spectrum. Our estimates agree with the APOGEE $v\sin{i}~$ estimates to within $1.2\,km\,s^{-1}$.