Final answer:
To determine if a black hole is spinning, telescopes like NuSTAR can observe the X-ray emissions from the accretion disk, analyzing the Doppler shifts and relativistic effects on the iron line in the X-ray spectra to infer the rotation speed and spin of the black hole.
Step-by-step explanation:
To determine if a black hole is spinning, we can look for signs of an accretion disk's rotation using observations from a telescope such as NuSTAR. The NuSTAR (Nuclear Spectroscopic Telescope Array) telescope is designed to observe high-energy X-rays, which are emitted from the regions around black holes. When a black hole has an accretion disk, the material in the disk moves at incredibly high speeds; part of this disk will be moving towards us and part will be moving away. This movement produces a distinct Doppler effect in the light emitted from the disk, similar to the blueshift and redshift observed in the NGC 4261 galaxy's accretion disk by the Hubble Space Telescope. The NuSTAR telescope is able to pick up the X-ray signatures of iron, which is often present in these accretion disks. The iron line can be broadened and skewed due to the relativistic effects close to the spinning black hole, allowing astronomers to infer the spin rate of the black hole. By analyzing the differences in the X-ray spectra from various parts of the disk, scientists can measure the rotation speed and hence the spin of the black hole.