Thermal Spectra of Warped and Broken Accretion Disks

Black holes may accrete gas with angular momentum vectors misaligned with the black hole spin axis. The resulting accretion disks are subject to Lense-Thirring precession, and hence torque. Analytical calculations and simulations show that Lense-Thirring precession will warp, and, for large misalignments, fracture the disk. In GRMHD simulations, the warping or breaking occurs at $\lesssim10r_s$, where $r_s$ is the Schwarzschild radius. Considering that accretion disk spectra in the soft state of stellar-mass black holes are generally well modeled as multicolor blackbodies, the question arises as to how consistent warped and broken disks are with observations. Here, we analytically calculate thermal spectra of warped and broken disks with a warp or break radius at $10r_s$ for various disk inclinations. Due to self-irradiation and the projected area of the inclined disk regions, the spectra of inclined disks significantly deviate from multicolor blackbodies and do not follow the multicolor blackbody relation $\nu L_\nu\propto\nu^{\gamma}=\nu^{4/3}$ at low frequencies $\nu$. The power-law indices at low frequencies of the inclined disks vary with viewing angle; when viewed face-on, they vary between $\gamma\approx0.91-1.26$ for the warped disks and $\gamma\approx1.37-1.54$ for the broken disks depending on the inclination angle. The differences decrease when moving the location of the disk warp and break to larger radii; for inclined disks to emit as multicolor blackbodies, they must warp or break at radii $\geq50r_s$. Our results imply that accretion disks around black holes in the soft state warp or break at larger radii than suggested in GRHMD simulations.