Do we use transit photometry to look for a black hole star binary systems?

Question

What would a light curve look like for a black hole transiting a star? Initially I thought it would bend all light essentially blacking out a star but we would probably still detect some however the curve should look substantially different from a planet transiting.

Answer 1

A binary black hole that passes in front of its companion star when observed from Earth will produce a self-lensing flare once every orbit. Such flares are being searched for by TESS (The Transiting Exoplanet Survey Satellite), but none have been found so far (as of May 2024).

As discussed in "Prospects of Finding Detached Black Hole-Star Binaries with TESS" (Kento Masuda and Kenta Hotokezaka, Astrophysical Journal 883 (2019) 169), the light from the star in a black hole binary system varies because of:

• ellipsoidal variations caused by the black hole's gravity physically distorting the star,
• Doppler beaming (which includes relativistic aberration, time dilation, and Doppler shift) due to the star's motion relative to Earth, and
• self-lensing when the Black hole passes in front of the star and gravitionally focuses the light travelling towards the Earth.

For example (from Figure 2 of Masuda & Hotokezaka), here is a typical (idealized) light curve for a binary whose orbit is exactly edge on to Earth.

The narrow spike in the middle is the gravitational micro-lensing "flare" when the black hole is between the Earth and the star ("inferior conjunction"). Doppler beaming is modelled sinusoidally with a maximum when the star is in the part of its orbit when it is moving towards the Earth and an minimum when it is moving away. The ellipsoidal variations have minima when the star and black hole are aligned with the Earth, which happens twice each orbit at inferior and superior conjunction. (Note: The ellipsoidal variations in the figures in the paper – including the one reproduced above – seem a factor of 2 larger than I calculate from Equation 1 in the paper.)

You can search for black hole binary flares in TESS data yourself by joining the Black Hole Hunters citizen science project. TESS is looking at millions of stars and the expected black-hole-stellar-binary fraction is expected to be $10^{-5}$ to $10^{-6}$, so tens to hundreds are expected.

Although no black hole binary flares have yet been seen, the Kepler Space Telescope observed five self-lensing binary systems where a white dwarf gravitationally lenses a Sun-like star. Some of these also have since been observed by TESS.