Density of The Milky Way Galaxy

by 

lim ju boo



Student in Astronomy
University of Oxford




(This is a short forum discussions written regularly among dozens during the duration of the course in astronomy) 




The Milky Way is a barred spiral galaxy with a diameter between 150,000 and 200,000 light-years across (1), (2) (3) (4).



It is estimated to contain 100–400 billion stars (5), (6) and more than 100 billion planets (7), (8).


Its thickness on the average is approximately 1,000 light year (ly) or 0.3 kpc thick.



The galactic center is an intense radio source known as Sagittarius A, assumed to be a supermassive black hole of 4.100 (± 0.034) million solar masses.



About 90 percent of the stars in the universe, including the sun, are main sequence stars. These stars can range from about a tenth of the mass of the sun to up to 200 times as massive. Stars start their lives as clouds of dust and gas.



With so much variations, plus masses of gas clouds, dust, dark matter, baryonic and non-baryonic matter, black holes and super massive black holes, all not included, it is very hard to estimate the exact mass or even its exact size.



Nevertheless, let's make some approximation



Let us take its diameter as 150,000 ly across or a radius of 75,000 ly

Let us assume it is a disk 1,000 ly thick

Volume of the Milky Way (MY) disk = pi x r^(2) x thickness = pi x 75,0002 X 1,000

= 1.767 x 10^13 cubic light years (ly) 

Since 1 light year = 9.461 x 10^12 km = 9.461 x 10^15 metres

1 cubic light year = cube of 9.461 x 10^15 metres = 8.469 x 10^47    cubic metres

Hence the volume of the MY Galaxy = (1.767 x 10^13) cubic ly x (8.469 x 10^47) cubic metres

= 1.496 x 10^61 cubic metres …..(a)



Similarly, if it is 200,000 ly across, its volume will be 3.142 x 10^13 cubic ly



Hence, its estimated volume is between 1.767 x 10 ^13 to 3.142 x 10 ^13 cubic light years.



However the centre of the MY Galaxy where most of the stars are, may have a little elliptical bulge? If it is so, without knowing the semi-axis major and the semi-axis minor of the ellipse, and the thickness of the bulge, it is almost impossible to integrate its volume. But we shall assume it is somewhat a spiral circular disk.


Most of the stars lie in the compact centre of the MY, and becomes less dense towards the spiral periphery. But let us assume they are all uniformly spread out over the spiral disk for ease of calculations. 



Let us now calculate its mass.


It is estimated to contain 100–400 billion stars (5), (6) and more than 100 billion planets (7), (8).

(1 billion = one thousand million, or 10^9)



Since 90 % of the stars are main sequence stars like our Sun each with a solar mass of 2 x 10^30 kg we may roughly assume the total mass of all the 100 - 400 billion stars in the MY Galaxy would be:

2 x 10^41 kg – 8 x 10^41 kg

[Mass of the Sun = 1.989 × 10^33 g (approx. 2×10^30 kg)].

But the MY is estimated also to contain 100 billion planets (assuming they are all like those in our Solar System).

What I have done is to take the total mass of all the 9 planets in our Solar System plus our own moon (9) but leave out all the other moons and all the thousands of asteroids, and collectively I found them   to have a mass 2.67 x 10^27 kg. or a weighted average of 2.67 x 10^26 kg each



Hence the total mass of the 100 billion planets would be: 2.67 x 10^26 x kg x 10^11 = 2.67 x 10^37 kg.



Add this to the total mass of the stars = (2 x 10^41 kg to 8 x 10^41 kg) + 2.67 x 10^37 kg

= 2 x 10^41 kg – 8 x 10^41 kg ….(b)

Hence the density of the MY Galaxy = mass / volume = b/a = 2 x 10^41 kg / 1.496 x 10^61 cubic metres

= 1.34 x 10 ^ -20 kg per cubic metre (if it contains 100 billion stars across 150,000 ly in diameter)



Or If it contains 400 billion stars + 100 billion planets across 150,000 light years, then its density would be:

8 x 10^41 kg  / 1.497 x 10^61 cubic metres = 5.34 x 10 ^-20 kg /cubic metre

(Density of hydrogen = 0.0899 kg /cubic metre. The critical density for the Universe is approximately 10^-26 kg/m3), or 10 hydrogen atoms per cubic metre



The critical density for the Universe is approximately 10^-26 kg/m3 (or 10 hydrogen atoms per cubic metre)


Conclusion:


Hence we can see that the density of the Milky Way Galaxy is far below the critical density for the universe. . Suppose all the galaxies in the Universe has a density similar to our MY Galaxy, then we can expect the Universe will continue to expand forever


The 100 billion exoplanets in other stellar systems of the Milky Way with an estimated combined mass of 2.67 x 10^37 kg does not make any difference compared to the masses of 100 - 400 billion stars with an estimated combined mass of 2 x 10^41 kg to 8 x 10^41 kg


Hence, whether or not we add all the masses of 100 billion exoplanets to those found in the stars, the total density of the Milky Way Galaxy is still the same, and is still far too low than the critical density needed for Universe to slow down its expansion if we assume the Milky Way Galaxy represents the countless myriads of galaxies, clusters of galaxies and mega-clusters of galaxies that stretch out to 13.7 billion light years in radius (Hubble's Radius) of an Observable Universe




If all the matter, including baryonic and non- baryonic matter, gas
clouds, dusts, black holes, and unknown matter,  most of them not accounted for in the calculation were to be added, the density of the Milky Way probably will be at least 10 times higher than estimated here

Even then it is still far below the critical density estimated for the entire Universe 


References:

1.      M. López-Corredoira, C. Allende Prieto, F. Garzón, H. Wang, C. Liu and L. Deng (2018). "Disk stars in the Milky Way detected beyond 25 kpc from its center". Astronomy & Astrophysics. 612: L8. arXiv:1804.03064. Bibcode:2018A&A...612L...8L. doi:10.1051/0004-6361/201832880.

2.      David Freeman (May 25, 2018). "The Milky Way galaxy may be much bigger than we thought" (Press release). CNBC.

3.      Mary L. Martialay (March 11, 2015). "The Corrugated Galaxy—Milky Way May Be Much Larger Than Previously Estimated" (Press release). Rensselaer Polytechnic Institute. Archived from the original on March 13, 2015.

4.      Hall, Shannon (May 4, 2015). "Size of the Milky Way Upgraded, Solving Galaxy Puzzle". Space.com. Archived from the original on June 7, 2015. Retrieved June 9, 2015.

5.      Milky Way". BBC. Archived from the original on March 2, 2012.

6.      "How Many Stars in the Milky Way?". NASA Blueshift. Archived from the original on January 25, 2016.

7.      Cassan, A.; et al. (January 11, 2012). "One or more bound planets per Milky Way star from microlensing observations". Nature. 481 (7380): 167–169. arXiv:1202.0903. Bibcode:2012Natur.481..167C. doi:10.1038/nature10684. PMID 22237108.

8.      Staff (January 2, 2013). "100 Billion Alien Planets Fill Our Milky Way Galaxy: Study". Space.com. Archived from the original on January 3, 2013. Retrieved January 3,

9.      https://nssdc.gsfc.nasa.gov/planetary/factsheet/