Searching for Semi-relativistic Hypervelocity Stars with the Euclid and Roman Space Telescopes

Abstract — v1

In 2015 we predicted that mergers of massive black hole (MBH) binaries launch stars into intergalactic space at $10^4$–$10^5\ \mathrm{km\ s^{-1}}$ ($\approx 0.03$–$0.3c$), and that hundreds of these semi-relativistic hypervelocity stars (SHS) would be detectable in infrared surveys. No searches so far have revealed any such stars. We revisit the prediction in light of two developments. First, $e \gtrsim 0.5$ during hardening is now established by simulations: circumbinary disks settle at $e_{\rm eq} \simeq 0.45$–$0.5$ rather than circularizing, while retrograde disks pump toward $e \sim 1$. Pulsar timing arrays prefer a low-frequency turnover from environmental coupling, of which stellar slingshots are one leading interpretation. Second, the ejection speed depends almost entirely on the periapse, $v_\infty \propto (r_p/r_{g,1})^{-1/2}$, independent of primary mass except for tides. At fixed semimajor axis, $e = 0.5$ raises $v_\infty$ by $\sqrt{2}$; $e = 0.9$ by $\sqrt{10}$. Euclid and Roman both provide near-infrared imaging that yields photometric candidates, and slitless grism spectroscopy that verifies the bright tail. Euclid’s Wide Survey yields $\approx 140$ photometric detections at $H \simeq 24$ over $14{,}000\ \mathrm{deg}^2$; Roman’s High-Latitude Wide-Area Survey goes deeper, yielding $10^2$–$10^3$. Continuum detections in the two grisms are $\approx 0.3$ at Euclid $H = 19.5$ and $\approx 0.4$ at Roman $m_{\rm AB} \approx 21$; a velocity from bandheads is typically $0.5$–$1$ mag brighter, so the surveys yield of order $0.1$–$0.5$. A $5\sigma$ Rubin proper motion in $r$ with a Roman photometric distance reaches $\approx 0.4$ objects on the HLWAS footprint. A blueshifted photospheric spectrum would verify an SHS; a proper motion large for that distance, with no parallax, would solidify the identification.