What happens to energy of the stars?

[Whitefire]

Several days ago I started thinking about the mystery of dark matter (yup, it was after LIGO discovery, and we all do it from time to time, right?). Then I came up with a strange conclusion that within our galaxy, there should be an equivalent of about 24 000 stars that we just cannot see--in form of energy (light, heat).

Okay, just bear with me, please.

I assumed that our Sun burns about 1.5 mass of the Earth in 100 000 years (http://helios.gsfc.nasa.gov/qa_sun.html#consume)

I assumed 500 billion stars in Milky Way, all, on average, burning the same amount of energy (huuge approximation, I'm aware).

I also assumed, that even if all this energy was changed into light, in 100 000 years it wouldn't have the time to really leave the galaxy (which is also wrong, and by a lot, but it is also hard to define what it means to "leave" the galaxy so I let it be).

Well, I then did some calculations and viola, 24000 sun masses are there. Here. What a nice additional source of gravity (I understand that photons can, in themselves, be a source of gravity).

Now it is nowhere near the mass necessary to explain dark matter, but it made me wonder:

Are my assumptions even conceptually correct?

And, given that stars shine, and burn, and explode, an do whatever else it is they do, and yet the total energy should be preserved, what really happened to all that burned/spent energy since the beginning of time (or, say, last 13 billion years?) It should be still out there, right? As WHAT?

Thanks for answers.

 

[Orodruin]

24000 solar masses extra in the galaxy is essentially nothing in comparison to the matter density required to explain the dark matter observations.

 

[rootone]

And, given that stars shine, and burn, and explode, an do whatever else it is they do, and yet the total energy should be preserved, what really happened to all that burned/spent energy since the beginning of time (or, say, last 13 billion years?) It should be still out there, right? As WHAT?

Photons, or electromagnetic waves if you prefer, just keep on going forever unless they happen to interact with some matter which absorbs them.
Stars also release energy in other forms such as neutrinos and those don't interact very much at all.

 

[phinds]

... what really happened to all that burned/spent energy since the beginning of time

Well, among other things, a tiny amount of it has caused a lot of sunburns

 

[HallsofIvy]

"viola"? What does a musical instrument have to do with this?

 

[Nugatory]

Several days ago I started thinking about the mystery of dark matter (yup, it was after LIGO discovery, and we all do it from time to time, right?). Then I came up with a strange conclusion that within our galaxy, there should be an equivalent of about 24 000 stars that we just cannot see--in form of energy (light, heat).

Okay, just bear with me, please.

I assumed that our Sun burns about 1.5 mass of the Earth in 100 000 years (http://helios.gsfc.nasa.gov/qa_sun.html#consume)

I assumed 500 billion stars in Milky Way, all, on average, burning the same amount of energy (huuge approximation, I'm aware).

It's not that bad an approximation... It has the right number of digits. That's good enough for many problems, including this one. You conclude that

24000 sun masses are there... Now it is nowhere near the mass necessary to explain dark matter

24,000 against 500 billion is about one part in ten million so your conclusion looks good.

As for where this energy goes? It just spreads out as it moves away from its source, and it keeps on going.