Parameter Space, Realistic Matter, and Universal Relations in Bose--Einstein Condensate Dark Stars

Abstract

We study slowly rotating Bose--Einstein condensate (BEC) dark stars by solving the Tolman--Oppenheimer--Volkoff, Hartle dipole, and Postnikov--Hinderer equations together for a polytropic equation of state with a Lee--Huang--Yang correction of strength $ζ$~\citep{Panotopoulos2026}. A continuous scan of $ζ$ from 0 to 1.5 shows the mean-field-to-corrected transition is smooth, with no hidden structure at intermediate values. Scanning the underlying boson parameters $(m,a_s)$ more broadly, we find that a $2\,M_\odot$ maximum-mass bound and a GW170817-like tidal bound $Λ_{1.4}\lesssim800$ cannot be satisfied simultaneously anywhere in this equation-of-state class. The $I$-Love universal relation holds to $0.13\%$ across twelve $(m,a_s,ζ)$ models, and the $ζ=0$ and $ζ=1$ sequences sit on opposite sides of the master curve by a consistent, non-random offset. Applied without modification to realistic nuclear matter (SLy, APR4), the same solver reproduces published maximum masses to within $1\%$; applied to self-bound MIT-bag quark matter it gives the expected mass--radius shape; and once extended to a two-fluid baryon-plus-dark-matter formalism, it shows that the maximum mass of a hybrid star is not a monotonic function of the central dark-matter fraction. Pooling $I$-Love sequences across nuclear, hybrid, and BEC dark-star models, we find they collapse onto a single curve to within about $5\%$, while self-bound quark stars sit far off it, departing by up to $90\%$.