# What is the characteristic time of the evaporation of the galaxies?

For a star, to leave its galaxy, it requires probably a 3-body near-collision at the edge of the galaxy. It is unlikely, but possible. And, if a star once somehow got the required velocity to escape the galaxy, then it will escape and never comes back.

Thus, galaxies should have a characteristic time of their evaporation, what could be calculated. I suspect, this time is probably longer, than other related processes (expansion of the Universe, end of the age of the stars, etc), but it exists can it can be probably calculated (most likely, by numeric simulations).

It probably also depends on the size and star density of the galaxy.

Was it calculated? How big is it?

• Supermassive blackholes and "puny" blackholes can eject stars (not at the edge) from a galaxy (newscientist.com/article/…), so doesn't that need to be figured into the answer? Also, what are you asking with the question "Did it happen?" Are you asking if a galaxy has already evaporated? Feb 22 '20 at 18:37
• @Bob516 I understand this on the "characteristic time of the evaporation of a galaxy": how long would the galaxy disappear, if the evaporation rate (in star/year) would not change due to other processes. Feb 22 '20 at 18:58

The overall timescale for galactic evaporation is $$\tau_{evap}= 100\tau_{relax}\sim 10^{19}$$ years.
The relaxation timescale $$\tau_{relax}=\frac{R}{v}\frac{N}{12 \ln(N/2)},$$ where $$R$$ is the size of the system, $$v$$ is the typical random velocity, and $$N$$ is the total number of stars. This corresponds to the time it takes to completely randomize the velocity of a star by interactions with other stars.
• Does this assume that \$N\$ is constant (i.e. the same number of stars are born as die)? Feb 23 '20 at 9:30
• @Graipher - Yes, it assumes $N$ stays constant. In practice this does not matter much since star formation declines from the early stelliferous era, so the error is at most a small multiplicative factor totally swamped by other uncertainties like the velocity dispersion. Feb 23 '20 at 16:20
• Funny thing is, the evaporation of the galaxy is surprisingly low. We have $\approx 10^{11}$ stars in our galaxy, leading to an evaporation rate of 1 star per 100million years. WIth other words, $\approx$ 140 stars ejected our galaxy until now. Feb 23 '20 at 18:19
• @AndersSandberg (after much more reading) yes, it's a dark and lonely future! In fact all the stars in our merged Milkomeda galaxy are expected to have exhausted their fuels after ~$10^{14}$ years, leaving just stellar remnants and brown dwarfs. If that's the case, our galaxy's stelliferous period represents just the first 0.001% of the timescale for galactic evaporation. Feb 25 '20 at 3:41