Tiny galaxies with exoplanets

Question

Segue 2 is a galaxy with only about 1000 stars and is 111 light years in radius. It has a light output only 900 times that of our sun. (This is a real galaxy in our universe)

However, I want my fictional galaxy to be small but have many habitable planets.

Is it plausible for a galaxy like this to be comprised mostly of solar systems with Earth-like planets? I'm looking for at least 100 Earth-like planets in the galaxy. And any galaxy under 3000 stars is ok.

Assume an exact duplicate of our universe's physics but not an exact duplicate a.k.a. I want probabilities, not statements of "there isn't one in our universe"

If only 1 thing is stopping this from happening e.g. Size/Age of the Universe please state so I can consider changing it.

Answer 1

Galaxy size

The first question is whether such a galaxy (less than 3000 stars) is possible. The clear answer is yes; Segue II already satisfies those requirements. Segue I and Willman I appear quite similar in terms of size, mass, and mass-to-light ratio; they're small and likely contain a lot of dark matter. With populations of a few times $10^3$ stars, you're venturing into globular cluster territory, to be honest, but the large amounts of dark matter are more indicative of low-mass galaxies. I therefore agree with Mark's assessment; this much is possible.

Frequency of planets

You're looking to have approximately 10% of your stars host planets. This doesn't seem too far-fetched. Estimates of the number of planets in the Milky Way vary, but it's possible that there's up to 1 planet per star (according to optimistic microlensing measurements). I wouldn't expect a dwarf galaxy to be substantially less conducive to planet formation, so 100 planets is absolutely achievable in a Segue II-sized dwarf galaxy.

Stability from encounters

The main thing I'm worried about isn't the formation of these planetary systems, but their survival. Globular clusters are often thought to be poor places for planets because close encounters between stars are common, and dwarf spheroidals often aren't great, either.¹ We can calculate the mean time between encounters in a globular cluster to get an idea of the timescales a planet can survive on. Beer et al. (2004) give a formula for the expected time before a star passes a distance $b_{\text{min}}$ from a star of mass $M$: $$\tau=7\times10^8\left(\frac{n}{10^5\text{ pc}^{-3}}\right)^{-1}\left(\frac{b_{\text{min}}}{\text{AU}}\right)^{-1}\left(\frac{M}{M_{\odot}}\right)^{-1}\frac{v_{\infty}}{10\text{ km s}^{-1}}\text{ years}$$ where $n$ is the stellar number density and $v_{\infty}$ is the velocity dispersion. Say we want to compare Segue II to a typical globular cluster. We're looking at an approach to the same star with mass $M$, at the same distance $b_{\text{min}}$. Then the ratio of encounter times is $$\frac{\tau_{\text{Seg}}}{\tau_{\text{GC}}}=\frac{n_{\text{GC}}}{n_{\text{Seg}}}\frac{v_{\infty,\text{Seg}}}{v_{\infty,\text{GC}}}$$ We can make a rough estimate of the mean stellar number density near the center of Segue II: $$n\approx\frac{\mathcal{M}/2}{r_l^3\Upsilon}$$ where $\mathcal{M}$ is the total mass of the galaxy, $r_l$ is the half-light radius, and $\Upsilon$ is the mass-to-light ratio. I've assumed that half of the stars are within the half-light radius. Substituting this in, we get another expression: $$\frac{\tau_{\text{Seg}}}{\tau_{\text{GC}}}=\frac{\mathcal{M}_{\text{GC}}}{\mathcal{M}_{\text{Seg}}}\left(\frac{r_{l,\text{Seg}}}{r_{l,\text{GC}}}\right)^3\frac{\Upsilon_{\text{Seg}}}{\Upsilon_{\text{GC}}}\frac{v_{\infty,\text{Seg}}}{v_{\infty,\text{GC}}}$$ The discovery paper, Belokurov et al. (2009), measured $\mathcal{M}=5\times10^5M_{\odot}$, $r_l=34\text{ pc}$, $\Upsilon=650$ and $v_{\infty}=3.4\text{ km s}^{-1}$, although Kirby et al. (2013) say $v_{\infty}=2.2\text{ km s}^{-1}$ at the most, using a larger sample of stars. A typical globular cluster might have $\mathcal{M}=10^4M_{\odot}$, $r_l=10\text{ pc}$, and $v_{\infty}=13\text{ km s}^{-1}$, along with $\Upsilon=2$. Plugging this all in gives me $\tau_{\text{Seg}}/\tau_{\text{GC}}=67$, or $\tau_{\text{Seg}}/\tau_{\text{GC}}=43$ using the Kirby figures. In other words, planets should only survive for an order of magnitude or so longer in Segue II than in a globular cluster - which still isn't a long time.

Stability from tidal interactions

I would argue that encounters with other stars are the main threat to system stability, at least near the center of Segue II, but I agree with Mark that encounters with another galaxy and subsequent tidal interactions could be problematic. Indeed, it's possible that some dwarf galaxies could be the results of more massive galaxies that were subsequently torn apart by neighbors (!). Today's Astrobites article, in fact, looks at D'Souza & Bell (2018), who argue that M32 is the remains of a larger galaxy that was ripped apart by Andromeda.

It's also been suggested that a number of stellar streams around the Milky Way were once dwarf satellite galaxies. Candidates include:

• The Helmi Stream
• The Virgo Stream
• The Aquarius Stream
• The Monoceros Ring

It's unclear whether planetary systems could survive this sort of catastrophic tidal encounter. I would think they wouldn't, but it's always possible. At any rate, it's yet another possible danger to face.

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¹ The one planet we know of is PSR B1620-26 b, in the globular cluster M4.

Answer 2

That's a very interesting question! It breaks into two parts: Can you have a galaxy of only a thousand stars and, if so, how likely is it that most of its stars would have an Earth-like planet.

First the question of galaxy size. The answer is a clear "maybe." The current theory of the formation of galaxies has them forming in parts of the universe where the dark matter was more dense and formed a gravity well for the ordinary matter to collect in. (AKA, the Cosmic Web.)

As far as I know, we have never observed galaxies as small as a thousand stars, and I don't think our simulations of the interaction of dark matter and ordinary matter are fine-grained enough to demonstrate that such small galaxies are likely, but it's difficult to see what would prevent them.

Perhaps the biggest issue is whether they'd be stable once formed. Galaxies are very close together compared with stars or solar systems and their peculiar motion is enough to mean they interact more than once in their lifetimes. (In fact, there's a lot of evidence that big galaxies like the Milky Way grow by consuming smaller galaxies which pass too close.) Because a tiny galaxy's gravity well is so shallow, I'd expect that if they form, nearly all of them get disrupted by tidal forces long before the present.

So 1000-star galaxies are possible, but very rare.

As people have commented, there is no reason to think that the distribution of planet-bearing stars would be different in a 1000-star galaxy than in the Solar neighborhood, so you'd expect the fraction with Earth-like planets to be similar also. The fraction of stars which have Earth sized planets seems to be around 10% or 15%. At this point we don't have a good idea what fraction of them are Earth-like, but our own Solar systems gives a hint: We have two or three Earth-sized planets, and one is Earthlike. Given the anthropic principle is in play here (there had to be at least one since we're here) that has to be a strong upper bound on the fraction.

So the fraction of stars with Earthlike planets is probably in the 1% to 10% range.

Bottom line: Your scenario is possible but rather unlikely.