Constraining the Spin and Inclination of the Maximal Kerr Black Hole 4U1957+11 Using Simultaneous NICER and NuSTAR Observations

4U 1957+11 is one of the few persistent black hole candidates (BHC), but in contrast to most of the other persistent BHC which are in high mass X-ray binaries (HMXB), it is in a low mass X-ray binary (LMXB) system. Furthermore, it has always been observed to be in a spectrally soft, disk-dominated state. The fact that the observed spectral energy distribution is dominated by the disk has made obtaining mass and distance estimates extremely difficult. On the other hand, the disk-dominated spectrum allows for estimates of the disk inclination and black hole spin using broad-band spectra that we have obtained with a series of simultaneous NICER and NuSTAR observations. The faintest of these observations remarkably is detected by NuSTAR at energies as high as 20 keV, despite exhibiting virtually no contribution from a hard X-ray powerlaw tail. The extremely high and broad range of temperatures detected with the NICER and NuSTAR observations places the spectrum in a minimally-degenerate region of physically motivated disk atmosphere models that strongly suggest that 4U 1957+11 is a maximally spinning black hole system viewed at high disk inclination. We further show that the spectra are consistent with the disk radius remaining constant as the system brightens, but the disk 'color-correction' factor decreasing with increasing Compton corona component. To place constraints on the system's mass and distance, we consider other sources of information, such as Gaia probability distributions for the distance and the fact that we have not observed a state transition to a spectrally hard state. We describe the remaining degeneracies in the spectral models and present probability distributions for the black hole distance and mass.