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I was watching a Scott Manley video on youtube and he mentioned that the Sun was loosing 4 million tons of mass a second as it converts to energy.

With a few trillion trillion stars also converting mass to energy, I wonder if that would be a component to the missing "dark matter" mass?

I'm a complete layperson here, just very interested in astronomy and the physics involved.

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Well... the mass of the sun is $2 \times 10^{30} kg$. If it loses $4 \times 10^9 kg$ per second, it would take 160 billion years for it to lose 1% of its mass.

The dark matter content of the universe is theorized to be 26.8%. So, the total mass contribution from photons cannot possibly account for the missing dark matter.

Also, if light from stars really made such an enormous contribution to the mass-energy of the universe, then we would see this light. (i.e. it wouldn't be dark!)

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The cosmologically relevant light is the cosmic microwave background (CMB), not radiation from stars. The energy density of the CMB is about $10^{-13}$ J/m3. This is of the same order of magnitude as the energy density of starlight within our galaxy, but most of the universe is intergalactic space where the density of starlight is much lower. The average energy density of the universe is about $10^{-9}$ J/m3, so today the CMB is a very small component of the total. In the past, the universe was dominated by radiation rather than dark energy.

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Aside from the estimates of energy density that others have given you, it's worth pointing out that this energy is radiation in the form of massless photons. Dark matter is stuff that hangs around in galaxies for a long time, so it has to be made up of slow-moving massive particles. Photons fly off at the speed of light, and couldn't possibly play the role of dark matter.

Also, photons are pretty much the opposite of "dark."

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