What is the best planetary orbit around a black hole in order to support life?

1.Could any planetary orbit sustain life long-term without an imported energy source? I believe that black holes emit Hawking energy. Could that be of use to living creatures?

The power emitted by Hawking radiation (see Hawking (1974)) is $$P=\frac{\hbar c^6}{15360\pi G^2M^2}\tag{1}$$ For a black hole of ~1 M$_{\odot}$, that comes out to about 9.00$\times$10^-29 watts. We can use this to calculate the effective temperature on a planet orbiting the black hole. If we stuck Earth at 1 AU from this black hole, it would have an effective temperature of about 1 10^-55th of its current one (working off of solar luminosities).

What about the warmth generated by radioactive decay inside the planet or even from tidal forces?

Baumgardt et al. (2004) worked with tidal energy generated in stars orbiting black holes. They found that

The orbital energy at the tidal radius usually exceeds the binding energy of the star by several orders of magnitude, and some fraction of the orbital energy is dissipated at every new pericenter passage. As a result the star becomes very hot and expands.

Specifically, the calculation for $\Delta E$ is $$\Delta E=\frac{GM_*^2}{R_*}\left(\frac{M}{M_*}\right)^2\sum_{l=2}^{\infty}\left(\frac{R_*}{r_p}\right)^{2l+2}T_l(\eta)\tag{2}$$ However, this only becomes important at a radius $$r\approx\left(\frac{M}{M_*}\right) R_*$$ For a planet, though, this radius could be pretty large, given the enormous mass difference. However, the smaller radius might shrink the radius. For a planet like Earth, $r\approx 2.12\times 10^{12}$ meters . . . which is over 1 AU. So tidal heating would be important at orbital radii less than this.

2.What is the best and safest orbit for life when orbiting a black hole, what is the most dangerous? I am asking about distance and about whether to go around the equator or the poles - if that even makes sense with a black hole.

The safest orbital radius is as far away from the black hole as possible.

Orbiting in the rotational plane of the black hole could mean crossing paths with an accretion disk, while orbiting around the poles could hit astrophysical jets. Neither are too good for life.

posted over 8 years ago

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