# What's the energy of all the light/electromagnetic radiation in our galaxy?

I came upon this question while watching a pop-sci video on youtube about Dark Matter and thinking about all the things that could be contributing gravitational influence to a galaxy.

From relativity we know that mass and energy is more or less the same and and both bend spacetime (i.e. cause gravity). And given how much energy stars give off and how big galaxies are, there is a lot of light, a lot of photons whizzing around and altogether that adds up to a sizeable chunk of energy. Relatively speaking maybe negligible next to ordinary or dark matter, but should be a big number. Some bounded volume would have to be defined, but I have no idea if physicists have definition for the boundary of a galaxy or what it is.

## 2 Answers

We can easily see without a calculation that this mass-energy is negligible compared to the mass-energy of the stars. The galaxy is somewhere on the order of $$10^4$$ light years in size. That means that a star's light spends $$\sim10^4$$ years inside the galaxy before it's gone. So the ratio of the mass-energy of the light in our galaxy to the mass-energy of its stars is on the order of the fraction of the sun's mass that it loses by radiation over $$\sim10^4$$ years. This is a negligible fraction. (A calculation shows that it's $$\sim10^{-9}$$.)

There was an era when the universe's gravity was radiation-dominated, but that was in the very early universe.

• That was a much simpler and understandable answer than I anticipated. Thanks. – martixy Dec 9 '19 at 15:40
• The answer by @KeithMcCary includes photons from all stars and galaxies within the visible universe, but only yields a photon density about twice the value that Ben Crowell's gives. It's still "a negligible fraction" of the average mass density of our galaxy. – S. McGrew Dec 9 '19 at 16:28

You can calculate the flux from summing up the contribution from the blackbody spectrum. The answer is that there are about 400 CMB photons in every cubic centimeter of the Universe, all moving at the speed of light, and representing a flux of 3.14× 10-6W/m2 (at the surface of the Earth, and everywhere else!).
...
In terms of energy flux, the CMB is fairly similar to starlight within our Galaxy. http://www.astro.ubc.ca/people/scott/faq_email.html

CMB photon energy is about $$6.626 \times 10^{-4}$$ eV.

Volume of the Milky Way = $$6.7 \times 10^{51} km^3$$.

Taking "similar" to mean equal, the energy is

(CMB photon density)$$\times$$(CMB photon energy)$$\times$$(Volume of the Milky Way) $$\approxeq 2 \times 10^{65}$$ eV $$\approxeq 3 \times 10^{46}$$ J.

By $$E=mc^2$$ this corresponds to $$\approxeq 3 \times 10^{29}$$ kg. Dividing by the mass of MYG ($$\approxeq 6 \times 10^{42}$$ kg) gives $$\approxeq 5 \times 10^{-14}$$, five orders of magnitude less than Ben Crowell's estimate. The discrepancy could be due to:
1) My estimate of starlight seems to be for our location in the MWG. It is much higher in the center.
2) The thickness (1,000 ly) of the MWG might be a more appropriate estimate of size in Ben's calculation.
3) My bad arithmetic.

• Why CMB photons? OP seems to be interested in galactic photon content (ones generated by the stars in the galaxy, it looks) – Kyle Kanos Dec 9 '19 at 0:48
• @KyleKanos "In terms of energy flux, the CMB is fairly similar to starlight" Doesn't that mean the energy density is similar also? – Keith McClary Dec 9 '19 at 1:34
• Both? But if I'm reading this correctly, the CMB energy is 14 orders of magnitude more than the light from the stars...? – martixy Dec 9 '19 at 15:44
• @martixy Oops, CMB photon energy is $10^{-4}$, not $10^{4}$ (I knew that) so that reduces it by 8 orders of magnitude. – Keith McClary Dec 9 '19 at 17:49