Interesting question. Assuming the figure of 10 million stars per cubic parsec is correct, there's still one missing piece of information to try getting a estimate: The size of this region with a very high concentration of stars. But at least we know it can't go very far, because at such densities (d), it would take a sphere with radius r = (3 10^11 / 4 * pi * d)^(1/3) ~= 6.2 parsecs to hold about 100 billion stars, on the order of the actual number of stars in the entire galaxy. So I will guess this region of high star density (r) holds only about 1% of that, corresponding to a radius of (3 10^9 / 4 * pi * d)^(1/3) ~= 1.34 parsecs.
To get a estimate of the brightness of the sky near the galactic center, I coded a simulation using Pharo 10 (a Smalltalk dialect):
This simulation just populates a spherical region of space randomly with points representing stars, assigning each of then a power output following the distribution of known stars near the solar system. Then it sums the luminance component of each star above a plane that passes through the center, and perpendicular to it. This is done 10 times and the average is taken, to average out the effect of a particular run where by chance we get a star very close to the center point, where we assume the planet of the observer is located. This estimate makes some assumptions:
* Stars near the core are randomly distributed in every direction;
* Stars don't obstruct each other. Probably mostly true, as the size of the stars is very small, when compared to the distances that separates them;
* The radiation has a path mostly free of dust, doubtful when talking about the Milkyway core;
* Luminance (total W/m^2) is a good proxy for what you would actually see with your eyes. 921
Probably not that realistic, as stars different of the sun radiate a lot of the energy outside the visible spectrum, as ultraviolet or infrared;
* We can take the known stars near the solar system as a representative sample of those near the galactic core. That's doubtful, as there's probably lots of still undiscovered brown and red dwarfs near us, and the near earth sample doesn't contain some kinds of stars that are surely present at the galact center, like red giants, outside the main sequence.
Given those disclaimer, here is the code for the simulation, as executed in <PERSON>'s playground:
| sunPowerOutput au moonAverageDistance moonRadius moonAlbedo sun radii t0 |
sunPowerOutput := 3.828e26. "In W/m^2"
au := 1.5e11. "In meters"
moonAverageDistance := 3.844e8. "In meters"
moonRadius := 1.7374e6. "In meters"
moonAlbedo := 0.1. "Dimensionless"
radii := #( 0.1675 0.335 0.67 1.34 ). "In parsecs"
sun := CelestialBody
withX: 0
withY: 0
withZ: 0
withPower: sunPowerOutput.
Transcript
clear;
show: 'Solar constant estimate (W/m^2): ';
show: (sun fluxDensity: au);
cr.
moon := CelestialBody
withX: 0
withY: 0
withZ: 0
withPower:
moonAlbedo * (sun fluxDensity: au) * Float pi
* moonRadius squared.
Transcript
show: 'Lunar constant estimate (W/m^2): ';
show: (moon fluxDensity: moonAverageDistance);
cr.
Transcript
show: 'Stellar constant estimate (W/m^2): ';
show:
(GalaxyCore withRadius: 150 withDensity: 0.14) centerPowerDensity;
cr.
Transcript
show: 'Radius';
show: ';';
show: 'W/m^2';
cr.
t0 := DateAndTime now.
radii do: [ :radius |
Transcript
show: radius;
show: ';';
show: (((1 to: 10) collect: [ :each |
(GalaxyCore withRadius: radius withDensity: 1e7)
centerPowerDensity ]) average round: 4);
cr ]. 371