Can LISA see stellar convection?

I sometimes have research ideas that I think are cool, but that don’t make sense for me to pursue. I generally just make a note of them and move on. This is the sixteenth post in a series describing some of the ideas I’ve accumulated.

Can LISA see stellar convection?

What’s the idea?

Convection in stars produces density fluctuations, resulting in a change in the quadrupole moment. This effect should be of order the square of the convective Mach number (which controls density fluctuations). Any individual star will definitely not produce an observable effect, but I wonder if this could contribute to the LISA noise floor (or the noise floor of future missions) when added up across all of the stars in the galaxy.

Why is this important?

This is a bet that has low odds of working, where it should be easy to tell if it’ll work within a day of checking, and that would be extremely cool if it worked.

If stellar convection contributes to the noise floor it is probably the case that there is some structure in its frequency variations, which could be informative about convection in stars of different masses. Also, if this contributes to the noise floor of future missions it could matter in their design.

Again, my guess is this won’t work, and will be easy to show won’t work, but it seems worth a look.

How can I get started?

• Estimate the time-varying quadrupole moment of a convective star. This is something like $M R^2 \mathrm{Ma}^2$, though there’s a question about where you want to take the Mach number from and there are probably with geometric factors accounting for where the convection produces the strongest quadrupole fluctuations.
• Convert that estimate into a LISA signal, then add it up over all the stars in the galaxy. I suspect solar-like stars dominate this calculation by having higher density-weighted Mach numbers, but I’m not sure.
• Compare the total signal to other sources of noise in LISA and future missions.