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 $M$: $$\tau =7\times {10}^8{\left(\frac{n}{{10}^5{\text{ pc}}^{-3}}\right)}^{-1}{\left(\frac{b_{\text{min}}}{\text{AU}}\right)}^{-1}{\left(\frac{M}{M_{\odot }}\right)}^{-1}\frac{v_{\mathrm{\infty }}}{10{\text{ km s}}^{-1}}\text{ years}$$ where $n$ is the stellar number density and $v_{\mathrm{\infty }}$ 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 $$\frac{{\tau }_{\text{Seg}}}{{\tau }_{\text{GC}}}=\frac{n_{\text{GC}}}{n_{\text{Seg}}}\frac{v_{\mathrm{\infty },\text{Seg}}}{v_{\mathrm{\infty },\text{GC}}}$$ We can make a rough estimate of the mean stellar number density near the center of Segue II: $$n\approx \frac{\mathcal{M}/2}{r_l^3\mathrm{{\rm Y}}}$$ where $\mathcal{M}$ is the total mass of the galaxy, $r_l$ is the half-light radius, and $\mathrm{{\rm Y}}$ 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: $$\frac{{\tau }_{\text{Seg}}}{{\tau }_{\text{GC}}}=\frac{{\mathcal{M}}_{\text{GC}}}{{\mathcal{M}}_{\text{Seg}}}{\left(\frac{r_{l,\text{Seg}}}{r_{l,\text{GC}}}\right)}^3\frac{{\mathrm{{\rm Y}}}_{\text{Seg}}}{{\mathrm{{\rm Y}}}_{\text{GC}}}\frac{v_{\mathrm{\infty },\text{Seg}}}{v_{\mathrm{\infty },\text{GC}}}$$ The discovery paper, Belokurov et al. (2009), measured $\mathcal{M}=5\times {10}^5{M}_{\odot }$, $r_l=34\text{ pc}$, $\mathrm{{\rm Y}}=650$ and $v_{\mathrm{\infty }}=3.4{\text{ km s}}^{-1}$, although Kirby et al. (2013) say $v_{\mathrm{\infty }}=2.2{\text{ km s}}^{-1}$ at the most, using a larger sample of stars. A typical globular cluster might have $\mathcal{M}={10}^4{M}_{\odot }$, $r_l=10\text{ pc}$, and $v_{\mathrm{\infty }}=13{\text{ km s}}^{-1}$, along with $\mathrm{{\rm Y}}=2$. 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.

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

posted over 6 years ago

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