Iron Kα line of Kerr black holes with scalar hair

Abstract

Recently, a family of hairy black holes in 4-dimensional Einstein gravity\nminimally coupled to a complex, massive scalar field was discovered~\\cite{hbh}.\nBesides the mass $M$ and spin angular momentum $J$, these objects are\ncharacterized by a Noether charge $Q$, measuring the amount of scalar hair,\nwhich is not associated to a Gauss law and cannot be measured at spatial\ninfinity. Introducing a dimensionless scalar hair parameter $q$, ranging from 0\nto 1, we recover (a subset of) Kerr black holes for $q=0$ and a family of\nrotating boson stars for $q=1$. In the present paper, we explore the\npossibility of measuring $q$ for astrophysical black holes with current and\nfuture X-ray missions. We study the iron K$\\alpha$ line expected in the\nreflection spectrum of such hairy black holes and we simulate observations with\nSuzaku and eXTP. As a proof of concept, we point out, by analyzing a sample of\nhairy black holes, that current observations can already constrain the scalar\nhair parameter $q$, because black holes with $q$ close to 1 would have iron\nlines definitively different from those we observe in the available data. We\nconclude that a detailed scanning of the full space of solutions, together with\ndata from the future X-ray missions, like eXTP, will be able to put relevant\nconstraints on the astrophysical realization of Kerr black holes with scalar\nhair.\n