# How much mass does the Sun lose as light, neutrinos, and solar wind?

In this answer I estimate the loss of gravitational mass of the Sun to be about 1.3E+17 kilograms per year using $$E = m c^2$$ and 1360 W/m^2 at 1 AU.

While writing that answer I realized that solar neutrinos also carry away a lot of mass equivalence in the form of kinetic energy. The strongest component seems to be from the first step in the process; deuteron formation from proton–proton fusion.

Am I right so far?

Questions:

1. How much mass equivalent is lost per year by the sun via neutrinos?
2. Is my estimate of 1.3E+17 kg for loss per year via electromagnetic radiation close?
3. Are there any other comparable loss mechanisms? I'm assuming that the solar wind is lower, but I could be way wrong on that!

"bonus points:"

• Are these rates likely to have been at least similar 4.5 billion years ago? Or would there have been large changes over this time? ("large" = factors of 2 or so)
• solar wind has been answered here: astronomy.stackexchange.com/questions/13907/… Feb 25 '20 at 12:56
• @mao47 excellent, thank you for that! I was primarily worried about the neutrinos but I wanted to collect all loss mechanisms in one place. Hopefully an answer posted here can simply cite and quote results there.
– uhoh
Feb 25 '20 at 13:35

The solar neutrino luminosity is about 2.3% of its electromagnetic luminosity (i.e. light). So the extra mass lost in the form of neutrino energy is 2.3% of your original calculation.

The average mass loss in the form of a wind and coronal mass ejections is about $$4\times 10^{16}$$ kg/year, but varies with the solar cycle (and from cycle to cycle) (Mishra et al. 2019).

4.5 billion years ago? It depends how exact you want to be. The Sun is thought to be 4.57 billion years old, so 4.5 billion years ago it would have been 70 million years old.

A 70 million year old Sun would have been on the hydrogen burning main sequence and about 20% less luminous than it is now, so you can scale your luminosity-mass and neutrino mass loss rates by about 0.8.

However, the solar wind was probably much stronger than it is now. The observational constraints on this are weak, but theoretical models suggest the mass loss rate in the wind scales as rotation rate $$\Omega^{1.33}$$ (Johnstone et al. 2015). Unfortunately, we still don't know how fast the Sun rotated in its infancy; it could have been anything from about 10 to 100 times it's rotation rate now. That means the mass loss rate in the wind would have been 20-500 times what it is now. Thus mass loss from a wind would dominate.

But maybe you meant $$\sim 4.5$$ billion years ago, in the sense that you wanted an answer for before the Sun became a star. i.e. Before hydrogen fusion began at a few million years after the Sun's birth. In that case, the wind losses might have been as per the 70 million year old case (with similar uncertainties), but there would be no neutrino losses (no nuclear reactions) and the luminosity of the Sun could have been a factor of 10 higher as a contracting pre main sequence star. In that case, mass loss from a wind would probably still be the biggest contributor.

• This is great, exactly what I needed; thank you!
– uhoh
Feb 26 '20 at 0:10