I Is Planet 9 Actually a Primordial Black Hole?

[Tom.G]

According to MIT Technology Review, the Solar System's conjectured 'ninth planet' might be a Black Hole.
https://www.technologyreview.com/s/614441/is-planet-9-actually-a-primordial-black-hole/

 

[anorlunda]

a superdense lump of matter about the size of a tennis ball.

I'm thinking about Hawking radiation.

What is the intensity of radiation from a BH that size?

Because of Hawking radiation, BHs evaporate, giving a lifetime proportional to radius. What is the lifetime of a BH that size?

Who can help us with those calculations?

 

[DrStupid]

What is the intensity of radiation from a BH that size?
[...]
What is the lifetime of a BH that size?

If my calculation is correct, the Hawking radiation of a black hole with the mass of Earth (just as an example) would have a power of 4.8·10^-13 W and the lifetime would be 4.7·10¹³ years. That would be possible in theory. However, it is highly speculaticve. I'm sure there are much better explanations but they are not worth a big headline.

 

[stefan r]

The radius is directly proportional to mass. A tennis ball has radius between 3.27 cm and 3.43 cm. A solar mass black hole has schwarschild radius 2.94 km. So 1.11 x 10^-5 to 1.16 x 10 ^-5 solar mass, 2.72 to 2.85 Earth mass.
Ping pong balls are nice because they have a 2 cm radius.

I'm thinking about Hawking radiation.

What is the intensity of radiation from a BH that size?

Because of Hawking radiation, BHs evaporate, giving a lifetime proportional to radius. What is the lifetime of a BH that size?

Who can help us with those calculations?

The Hawking radiation will be almost trivial. Particles hitting it should give off high energy radiation. Single protons falling in should give off 10^-11 Joules. A piece of dust would make a good flair.

The article claims there should be a dark matter halo and a steady supply of dark matter falling in. They calculated the dark matter halo will have around 15% of the black hole's mass (starting at 50%).

If my calculation is correct, the Hawking radiation of a black hole with the mass of Earth (just as an example) would have a power of 4.8·10^-13 W and the lifetime would be 4.7·10¹³ years. That would be possible in theory. However, it is highly speculaticve. I'm sure there are much better explanations but they are not worth a big headline.

If we have both rogue planets and primordial black holes the odds of capturing should be proportional to the population ratio of rogue planets and black holes.

 

[Janus]

I'm thinking about Hawking radiation.

What is the intensity of radiation from a BH that size?

Because of Hawking radiation, BHs evaporate, giving a lifetime proportional to radius. What is the lifetime of a BH that size?

Who can help us with those calculations?

If I recall correctly, you need a black hole to be something around the mass of the Moon for its Hawking temp to be higher than the cosmic background radiation. Any larger than that and even in the darkest of deep space it would be taking in mass in the form of energy faster than it could lose it via Hawking radiation. A tennis ball sized black hole would have a mass close to that of Uranus.

 

[ohwilleke]

The expected mass of the hypothetical object is about the same as the planet Neptune.

 

[mfb]

Here is a Hawking radiation calculator
Alternative if the first one goes down again

The temperature of the CMB is 2.7 K, plugging this into the calculator gives us 0.0076 Earth masses, or about half the mass of the Moon. It also gives us a lifetime of 2.5E44 years.

A lifetime of 20 billion years corresponds to 200 million tonnes initial mass (a small mountain) and an initial Hawking radiation of 9 GW at a temperature of 600 GK or 50 MeV. We would see such an intense source of gamma rays in the sky. Or maybe not. Poor photon statistics. 9 GW/(50 MeV * (100 AU)^2) * 1 m^2 = 5*10^-6/s.