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

Question

Note: I am aware of a previous question

Physiological effects of living on a world close to a black hole

As I understand it, that question refers specifically to a planet that is in a non-ideal orbit for life, i.e. it is 'close' to its sun. I'm asking for a description of the optimum orbit for life.

My question is this -

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

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.

I am asking this under the tag 'hard-science' as part of the fortnightly challenge.

Answer 1

1. Sustain life without imported energy source?

Well, there's nothing to say that the black hole cannot have a companion star. There are plenty of stable configurations possible. In a non-circumbinary planet, if a planet's distance to its primary is below about one fifth of the closest approach of the other star, the orbit can be assumed to be stable. So the world could still have an active sun.

That is a much more reliable source of energy than Hawking radiation, which is orders of magnitude smaller than the current levels of the cosmic microwave background. In other words, black holes are much, much 'colder' than an empty dark cosmic sky.

Radionuclei inside the planet can also help sustain life, but I strongly suspect that the amount of biomass the low concentrations of radionuclei would produce would not be very large. Still, you could look into natural nuclear reactors, which would be a pretty cool idea, assuming with some reason that orders of magnitude larger uranium deposits were generated in the original black hole collapse.

2. What is the best and safest orbit for life?

Orbiting a black hole (assuming it is a quiescent one, without a giant feeding accretion disk) is no different from orbiting a regular star of the same mass in terms of the gravitational effects on the orbiting body at moderately large distances such as the radius of Earth's orbit for a hypothetical sun-sized black hole. Orbit very close (a few tens of thousands of km) and the tidal forces caused by the gravitational gradient would probably tear the planet apart.

If the black hole is actively feeding, it will have deadly magnetic fields (these can die down if it is inactive, i think), and a horrible flattened accretion disk spewing radiation like there's no tomorrow. Any planet near the disk would be subjected to sterilizing radiation. Worse, if it's a captured world, it might be in high enough off the orbital plane (right ascension, was it?) to get into the path of the jets, which might even be strong enough to eventually liquefy the planet and blast the debris away.

Answer 2

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.