Friday, April 12, 2019

Black holes are Weird

On April 10th scientists from around the world came together to show the first ever picture of a blackhole.  This was really cool.  A strange thing to learn from all of the science tweets that came about as a result of the black hole news was a twitter thread where the author went into how the density of a black hole can be surprisingly low, like lower than the density of air at sea level.   This is because the radius of a black hole is proportional to the mass of a black hole (the thread I linked will do a better job of explaining why this is the case), accepting this fact means that when you double the mass of the blackhole, you've doubled the radius, but the volume of will have gone up 8X.  This then asks the question, is there a mass of a black hole that would be so massive that its density would be less than that of the interstellar void?
The goodnews is that there is already a solid starting point with the Wikipedia entry on the Schwarzschild radius, in this article there is a hand table that highlights the various densities of blackholes made from various amounts of stuff.

Observable universe[7]8.8×1052 kg1.3×1026 m (13.7 billion ly)9.5×1027 kg/m3
Milky Way1.6×1042 kg2.4×1015 m (~0.25 ly)0.000029 kg/m3
SMBH in NGC 48894.2×1040 kg6.2×1013 m0.042 kg/m3
SMBH in Messier 87[9]1.3×1040 kg1.9×1013 m0.44 kg/m3
SMBH in Andromeda Galaxy[10]3.4×1038 kg5.0×1011 m640 kg/m3
Sagittarius A* (SMBH)8.2×1036 kg1.2×1010 m1.1×106 kg/m3
Sun1.99×1030 kg2.95×103 m1.84×1019 kg/m3
Jupiter1.90×1027 kg2.82 meters2.02×1025 kg/m3
Earth5.97×1024 kg8.87×103 m2.04×1030 kg/m3
Moon7.35×1022 kg1.09×104 m1.35×1034 kg/m3
Human70 kilograms1.04×1025 m1.49×1076 kg/m3
Big Mac0.215 kilograms3.19×1028 m1.58×1081 kg/m3
Planck mass2.18×108 kg3.23×1035 m1.54×1095 kg/m3



With this starting point we now need to know what the density of the interstellar space is, this number  slightly varies from source to source, but seems to ballpark between 0.1 and 1 particle per cm^3, for sake of consistency (and the fact that its the most common element) we will assume that these particles are hydrogen atoms.  Therefore the average cubic meter of the interstellar void has between one hundred thousand and one million hydrogen atoms.  A single hydrogen atom has a mass of about 1.66 *10^-27 kg.  This gives a density of the interstallar medium of between 1.66*10^-22 kg/m^3 and 1.66*10^-21kg/m^3.
Now we need to determine how much mass our black hole needs to have to achieve this rather rarified density.  Right off the bat we know we can bound the mass somewhere between the Milky Way and the Observable universe.  As the Milky Way mass blackhole is too dense, and the Observable universe is roughly the density of 6 hydrogen atoms/cubic meter.
Plugging the Equation [3*C^3]/[32*π*G^3*M2] into Excel  (where C is the speed of light in meters/second, G is the gravitational constant, and M is the mass of the object)

We are able to determine that the blackhole would need to have a mass of 6.63*10^50 kilograms of mass to achieve our lower density of 1.66*10^-22 kilograms/m^3, and 2.10*10^50 kukigrams to get to 1.66*10-21 kilograms/m^3.

The radius of our blackhole would be between 3.11*10^23 and 9.84*10^23 meters in radius.  In light years that would be between 32.9 and 104 million light years.  Otherwise really effing big

Any questions/feedback are welcome. 

No comments:

Post a Comment