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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?

peterh
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    Supermassive blackholes and "puny" blackholes can eject stars (not at the edge) from a galaxy (https://www.newscientist.com/article/dn10020-puny-black-holes-can-eject-milky-ways-stars/), 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? – Bob516 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. – peterh Feb 22 '20 at 18:58

1 Answers1

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The standard treatment can be found in (Binney & Tremaine 2008), but see also (Adams & Laughlin 1997) for a good treatment.

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.

Anders Sandberg
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  • This matches very closely the estimated time given here: https://en.wikipedia.org/wiki/Timeline_of_the_far_future – Michael Feb 23 '20 at 05:06
  • Does this assume that $N$ is constant (i.e. the same number of stars are born as die)? – Graipher Feb 23 '20 at 09:30
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    @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. – Anders Sandberg 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. – peterh Feb 23 '20 at 18:19
  • @peterh-ReinstateMonica - ~140 ejected by this kind of random event. There are a few more hypervelocity stars due to close encounters with the central black hole. – Anders Sandberg Feb 23 '20 at 18:26
  • @AndersSandberg It looks the central black hole is a far more effective "evaporator". (Sorry for the unaccept, it looks this question is popular and I would like to attract attention. I will again accept in some days.) – peterh Feb 23 '20 at 18:48
  • @peterh-ReinstateMonica - There are several processes discussed in Binney & Tremaine, with different efficiencies over time (could bring them into the answer, but it would not be very concise). The eventual dissolution is more due to the slow statistical effects than "hard encounters", but there is a fair bit of calculation involved. – Anders Sandberg Feb 23 '20 at 20:32
  • @AndersSandberg $10^{19}$ years is about a billion times the current age of the Universe. Does that evaporation timescale take into account the accelerating expansion of space due to dark energy? – Chappo Hasn't Forgotten Feb 25 '20 at 00:59
  • @ChappoSaysSEDuddedMonica - Accelerated expansion does not strongly affect dynamics inside galactic systems (lots of other answers about that here). Long before the evaporation happens each galaxy will be in its own little island universe, and ejected stars soon (after a few billion years) will be alone in intergalactic space with nothing visible. – Anders Sandberg Feb 25 '20 at 02:14
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    @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. – Chappo Hasn't Forgotten Feb 25 '20 at 03:41
  • @ChappoSaysSEDuddedMonica I think a galaxy of stellar remnants evaporate roughly with the same intensity. More interesting question: after this $10^{20}$ years, the stars will be dispersed in the Universe. Where is their gravitational potential energy is coming from? (What is "dudded"?) – peterh Feb 28 '20 at 18:01
  • @peterh-ReinstateMonica Dudded is Australian slang for tricked, robbed, left in the lurch. – Chappo Hasn't Forgotten Feb 29 '20 at 05:16