Spin and spectral properties of Cygnus X-1 observed with Insight-HXMT

Cygnus X-1 is a Galactic black hole X-ray binary with persistent X-ray emissions. We examine the spectral data from 2 – 22 keV gathered by Insight-HXMT observations conducted from 2020 to 2022. We use the continuum-fitting method to constrain three parameters of Cygnus X-1: the black hole spin $a^{⁎}$, the hydrogen column density $N_H$, and the photon index of the powerlaw component Γ. The fittings constrain $N_H=(1.1\pm 0.1)\times {10}^{22}$ atom cm⁻², and Γ evolving from ∼2.4 in 2020 to ∼1.9 in 2022. We find the dimensionless spin parameter $a^{⁎}>0.977$ $\left(3\sigma \right)$ assuming the distance of the source $D=2.22$ kpc, the mass of the black hole $M_{\mathrm{BH}}=21.4M_{\odot }$, and the inclination of the system $i={27.47}^{\circ }$. Furthermore, considering the uncertainty of D from 1.22 kpc to 3.22 kpc, $16M_{\odot }<M_{\mathrm{BH}}<25M_{\odot }$, ${22}^{\circ }<i<{31}^{\circ }$, the Monte Carlo analysis is performed and still confirms a large spin of the limitation $a^{⁎}>0.999\left(1\sigma \right)$ without the D, i, and $M_{\mathrm{BH}}$ bias for Cygnus X-1. We also try to use the limits of $a^{⁎}$ to reversely constrain the range of D, i, and $M_{\mathrm{BH}}$, and find that for the extreme situation ($a^{⁎}>0.99$), the derived distributions prefer a low i, large $M_{\mathrm{BH}}$, and a distance around 2 - 3 kpc. The effect of changing hardening factor on measuring $a^{⁎}$ is also discussed.