B Can Dark Matter Explain Black Holes and the Mysterious Planet-Nine?

[BL4CKB0X97]

If it was a black hole, the radius would be relevant.

If they are estimating the mass in this range, then the answer to the question in the original post is no, it cannot be a black hole.

I believe the radius is estimated by mass, so it would be irrelevant should the mass match the model.

 

[Comeback City]

I believe the radius is estimated by mass, so it would be irrelevant should the mass match the model.

I think it can go either way. Mass and radius are related through the Schwarzschild radius equation,
r_s=2GM/c²
In my case, I used the estimated radius of "planet nine" to find the mass of this object if it was a black hole, like the OP predicted. That is why I thought the radius would be relevant, since I used it to find the mass in the first place.

 

[Bandersnatch]

The point that everybody here is trying to convey is that the radius of the object as given in one of the earlier posts is there for a particular reason other than observations, and as such comes burdened with certain assumptions.

The observations gave only the mass estimate.
Now, to get the radius, we have to make an informed guess as to what is the object made of. There are a few options:
1. It's made of normal matter (like planets and stars).
2. It's made of degenerate matter (like a white dwarf).
3. It's made of neutronium (like a neutron star).
4. It's a black hole.

Each of these options is in principle viable, in the sense that one can imagine objects made out of those materials. Each gives a different radius estimate for the same (observed) mass with identical gravitational effects.
But since we're making an informed guess, we can use our knowledge to eliminate some options. In particular, we can ask:
1) whether there is a way for either of the objects to form while having such low mass
2) whether such objects should produce additional observables that aren't there
...which eliminates all but the normal matter object, i.e. a planet. Plugging in a range of possible densities of normal matter (depending on possible compositions and using models for gravitational compression), you get a range of radii.

So, if you then take that radius and try to plug it into an equation for calculating a black hole mass, you're making two mistakes:
- you're ignoring the fact that the mass is what is already known and can't be anything else
- you're using the radius that was a guess based on the idea that the object is definitely not a black hole

 

[Comeback City]

The point that everybody here is trying to convey is that the radius of the object as given in one of the earlier posts is there for a particular reason other than observations, and as such comes burdened with certain assumptions.

The observations gave only the mass estimate.
Now, to get the radius, we have to make an informed guess as to what is the object made of. There are a few options:
1. It's made of normal matter (like planets and stars).
2. It's made of degenerate matter (like a white dwarf).
3. It's made of neutronium (like a neutron star).
4. It's a black hole.

Each of these options is in principle viable, in the sense that one can imagine objects made out of those materials. Each gives a different radius estimate for the same (observed) mass with identical gravitational effects.
But since we're making an informed guess, we can use our knowledge to eliminate some options. In particular, we can ask:
1) whether there is a way for either of the objects to form while having such low mass
2) whether such objects should produce additional observables that aren't there
...which eliminates all but the normal matter object, i.e. a planet. Plugging in a range of possible densities of normal matter (depending on possible compositions and using models for gravitational compression), you get a range of radii.

So, if you then take that radius and try to plug it into an equation for calculating a black hole mass, you're making two mistakes:
- you're ignoring the fact that the mass is what is already known and can't be anything else
- you're using the radius that was a guess based on the idea that the object is definitely not a black hole

If we only have observed the mass, it is around 7-10 Earth masses, and we are pretty sure there is no way for a black hole that small to form, then we have the answer to the original question: It cannot be a black hole. Thanks for pointing out the mistakes, though; I didn't realize that was the problem.

 

[Bandersnatch]

there is no way for a black hole that small to form, then we have the answer to the original question: It cannot be a black hole

There actually is a way for a black hole of just about that mass to form - it could have been formed at the very early stages in the evolution of the universe (cf: primordial black holes). But it would have a strong observable radiation signature - via accretion disc and Hawking radiation.

 

[Comeback City]

There actually is a way for a black hole of just about that mass to form - it could have been formed at the very early stages in the evolution of the universe (cf: primordial black holes). But it would have a strong observable radiation signature - via accretion disc and Hawking radiation.

And that is what @Chronos pointed in #15. We most likely would've detected its radiation emissions by this point in time.

 

[BL4CKB0X97]

I think it can go either way. Mass and radius are related through the Schwarzschild radius equation,
r_s=2GM/c²
In my case, I used the estimated radius of "planet nine" to find the mass of this object if it was a black hole, like the OP predicted. That is why I thought the radius would be relevant, since I used it to find the mass in the first place.

What Bandersnatch said. [emoji106]

 

[Physics_Kid]

this is awesome, my "simple" Q turns into a good discussion.

so, something i don't understand is, the planet-9 model makes the prediction of a mass & location based on the known things about the other orbiting objects in the solar system. so if a location is known then why can't they look there with Hubble or similar?

so, a BH = ~10 Earth's is possible, but we would have other observable things to identify such, but now i have to ask, if a BH is small, in the kuiper belt, would non-directional sensors be able to identify it, or would you need to have a sensor pointing right at it?

 

[Drakkith]

so, something i don't understand is, the planet-9 model makes the prediction of a mass & location based on the known things about the other orbiting objects in the solar system. so if a location is known then why can't they look there with Hubble or similar?

The model only gives a prediction of the orbit of the planet, not the location along the orbit. There's still a large area of sky to search and this hypothetical planet would be very dim.

 

[Physics_Kid]

i thought the prediction of the mass was based on all orbits, even the orbit of planet-9 mass. you would need an orbital location of a mass to be able to predict the affects of the other orbits, and vice-versa. so doesn't the model predict the mass required, and its orbit?

 

[Drakkith]

i thought the prediction of the mass was based on all orbits, even the orbit of planet-9 mass. you would need an orbital location of a mass to be able to predict the affects of the other orbits, and vice-versa. so doesn't the model predict the mass required, and its orbit?

It doesn't predict the current location of the planet, but it does predicts its orbit and mass. You don't need the exact position of a large mass to make predictions about what it can do to other objects nearby over time. Just having the orbital properties and the mass is good enough.

 

[DrK]

Firstly, a Black Hole can be of any size or mass.

Secondly, a BH that has the same solar mass as the Sun will have exactly the same gravitational pull as the Sun but will occupy a space relatively small.
If the Sun was replaced by a BH of the same mass, we would orbit it in exactly the same way as we do. We would not be sucked in

 

[Comeback City]

Firstly, a Black Hole can be of any size or mass.

See post #52.

We would not be sucked in

Even though I said this off a misconception, I wasn't referring to replacing our sun with a bh. I was referring to a bh with a huge mass in the place of planet 9.

 

[stoomart]

See post #52.

@Chronos adressed this more directly in post #27.