# Is there a way to estimate the age of M dwarf stars?

Wolf 1061 (only 13.8 ly away) was recently found to have three rocky planets one of which is in the habitable zone. It was stated on the english wikipedia site that it has a very stable light curve and was not found to have "any significant activity such as sunspots or flares." Would this imply that this star is very old? The expected lifetime of this M dwarf with a mass estimated to be 0.25 solar mass could potentially reach a trillion years.

## 1 Answer

Really difficult.

Very young ($<50$ Myr) M dwarfs may still exhibit lithium in their photospheres. Any older and it will have been depleted.

For older dwarfs you then move on to looking at rotation and activity. Both decline with age, but in an M dwarf as cool as this, the decay timescale is many Gyr, so it is only weakly constraining and not very well calibrated for such low mass stars. A very slow rotation rate or very low level of magnetic activity might indicate it was older than 5 Gyr.

The lack of flares and the lack of light curve modulation by starspots may indicate that it has spun down, is magnetically inactive and is therefore older than 5 Gyr ( I cannot immediately locate the source of this Wikipedia claim). The ratio of X-ray to bolometric luminosity would be more definitive and could probably be derived from the ROSAT all-sky survey (or a constraining upper limit would be found).

A useful paper is by Stelzer et al. (2013). http://arxiv.org/abs/1302.1061 She finds various activity diagnostics for nearby stars, including this one. Its projected rotation velocity is 1.5 km/s, which suggests a rotation period of $\sim 10$ days for a star of this size. This could not be less constraining on the age! The X-ray to bolometric flux ratio is $10^{-4.45}$ which suggests it is neither very young or very old - say between 1 and 5 Gyr for a star of this mass.

Another possibility is to look at the Galactic space motion and position. Older stars tend to have higher velocities, especially perpendicular to the Galactic plane, and also tend to be found further from the Galactic plane. The velocities for this object do not look large, suggesting it is not very old, ie younger than perhaps 10 Gyr and likely a young disk object with age of $<5$ Gyr.

You can also look at the metallicity. This is difficult to measure in M-dwarfs. Maldonado et al. (2015) give [Fe/H]$=-0.05 \pm 0.03$. This is very close to the solar value and does not constrain the age beyond suggesting the star is younger than 10Gyr.

Beyond this, it is basically impossible. Even if you had a very precise distance and could place the star on a HR diagram, low mass M dwarfs evolve so little in luminosity and temperature over many Gyr that this offers no constraint.

So my conclusion - the age is between 1 and 5 Gyr, with the probability peaking somewhere in the middle.