# Could all the energy in all the photons in the universe account for dark matter? [duplicate]

I was hit with fridge logic, and I am curious:

Is it possible that the gravitational influence of photons inside of galaxies (And all throughout the universe) could account for dark matter?

Photons would be most concentrated close to the core and inner galaxy... And have a lessening concentration as they expanded away from galaxies due to the inverse square law..

I am struggling to understand the math involved, because I've not yet reached that level in my education.... But I'm really curious how the total photons stack up vs the measured dark matter in the universe?

• Dark matter moves relatively slowly; otherwise it wouldn't cluster around galaxies. Photons don't move slowly; they move at the speed of light. – Peter Shor Aug 3 '16 at 2:15
• Isn't the observation of dark matter kind of vicarious and indirect? How would we get an even remotely accurate measurement of the speed at which dark matter of traveling through the universe..? I am stating that it maybe instead that concentrations of photons may instead act as dark matter... not really the photons themselves... but the collective whole. – Daniel Drake Aug 3 '16 at 2:34
• The very word 'dark' in dark matter means that we can't see it. Photons are exactly what we can see. If there were enough to contribute significantly to mass, we would notice. – knzhou Aug 3 '16 at 3:20
• We can measure the distribution of dark matter due to its gravitation. No massless field can be confined in ways like that. If dark matter is matter, then it has to be massive and cold. If it isn't, then we simply don't have a model that works. – CuriousOne Aug 3 '16 at 3:37
• Possible duplicates: physics.stackexchange.com/q/45387/2451 , physics.stackexchange.com/q/34516/2451 and links therein. – Qmechanic Aug 3 '16 at 22:12

The problem here is the contrasting effects the two forms of matter have.

Photons are massless; they create negligible gravitational fields.

Dark matter, on the other hand, is about 85-90% of all mass in the universe. It's responsible for holding galaxies at constant rotation rates past certain radii (see Galactic Rotational Velocity Curves).

Photons, on the other hand, provide a repulsive force that we call radiation pressure.

In terms of contribution to the energy density of the universe:

Let the critical density $\Omega_c=1$. This is the energy density of flat space, and provides an accurate description of the large-scale universe by current measurements.

$\Omega_m$ is the energy density contribution of barionic matter. It's approximately equal to $0.3$. Of that $0.3$, visible matter contributes about $0.05$.

$\Omega_\Lambda$ is the energy density contribution attributed to the cosmological constant $\Lambda$, and is about $0.7$, or about 70% of the energy in the universe.

You might have noticed that $\Omega_m + \Omega_\Lambda \approx 1 = \Omega_c$. Where's the light/radiation?

$\Omega_r$, the energy density contribution of radiation, is $\approx 0.00001$.

• Photons have energy. Any energy/mass contributes to gravitation. – Peter Shor Aug 3 '16 at 2:12
• You're right, but not even close to the same magnitude. I'll edit. – hebetudinous Aug 3 '16 at 2:19
• As I understood, if all the light from all the stars in a 300 light year radius shone for ten years, it'd be enough mass to create a black hole. If all the light was in one spot, that is. Those stars have been shining for alot longer than 10 years.. The galaxy alone is 100,000 light years accross? Thats alot of "black holes" worth of gravitational influence that cannot be seen, floating around in the galaxy? – Daniel Drake Aug 3 '16 at 2:54
• "$Ω_m$ is the energy density contribution of barionic matter" : no, of the matter. We don't know its nature and cannot qualify it this way. You must remove barionic (and one the 2 another hand, do you have 2 other hands ? :) ). Then, be more clear on the density of photons : you said that its effect was neglictible but this needs details or a reference. Planck mission give a lot of values, including an evaluation of this one. – user46925 Aug 3 '16 at 3:01
• @DanielDrake: The energy density of light created by one star can be easily calculated and it is tiny. It doesn't even increase the total mass-energy: whatever mass-energy is in the radiation was lost by the star, so the total gravitational mass of the system is exactly the same. – CuriousOne Aug 3 '16 at 3:57