Faint Companions to Hot Stars. Spectroscopic Detection Sensitivity and Implications for Survey Design
Year: 2026
Type: preprint
Abstract: Searches for black holes in binaries must distinguish dark companions from faint luminous stars. This is challenging for hot stars, whose spectra contain few broad lines. We develop a Fourier-domain method that converts isolated, broadened lines into calibrated constraints on faint companions. Doppler shifts are encoded in the Fourier phase, while the line profile defines a smooth amplitude envelope. A faint secondary introduces an oscillatory perturbation to the log-amplitude. Expanding to first order in the secondary-to-primary line-depth ratio, $α$, yields a nearly linear model for a likelihood-ratio test against the single-star model. The method applies to single or multiple epochs without full spectral disentangling. At small velocity separation $v$, the companion signal becomes degenerate with the primary line profile, and the fractional uncertainty from the log-amplitude scales as $Δα/α\propto v^{-4}$. If the primary velocity is known, the Fourier phase provides a more favorable detection channel whose sensitivity scales as $v^{-1}$. We demonstrate the method on archival FEROS spectra of CPD$-41^\circ$7742, detecting the known secondary in He I 6678 Angstrom and obtaining a stringent non-detection in He II 5411 Angstrom, where its contribution is expected to be negligible. The framework yields detection efficiencies as functions of line-depth ratio, velocity separation, noise, and instrumental setup. These can be combined across lines, epochs, and targets to construct selection functions for spectroscopic black-hole searches, including those enabled by SDSS-V and Gaia.
Source: arXiv (Cornell University)
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223922163