# Could a dwarf galaxy host a star at the center instead of a SMBH?

I don't think this would be possible, but I'm curious, and as what ever query I googled I only found posts about black holes indeed existing, what black holes are, that even the Milky Way has a black hole in its center or that We can't know if dwarf galaxies have non-SMBH at their center.

So sorry if it is a stupid question but I didn't want to go on with assuming something without knowing: So is it theoretically possible for a Galaxy to have a star at its gravitational center of mass?

• The smaller the mass, the less an object will dominate the kinematics of the galaxy. Even SMBHs are not exactly at the gravitational center of a galaxy. Stars are millions to billions of times less massive than SMBHs, so even if at some point it's at the center, it will not maintain that position. – pela Oct 6 '17 at 10:11
• @pela Im aware of that but my intention to ask was more of a star as massive as possible before collapsing, could such a thing theoretically dominate the ather stars around it? Quite sure, as soon this tiny galaxy collides with another galaxy it wont stay for it self anylonger, but as long this doesnt happens, could it work? and at least to a riny degree realistically occur? – Zaibis Oct 6 '17 at 10:16
• A very massive star would have a mass of 100 $M_\odot$. Even the hypothetical PopIII stars are thought to have masses of only $10^3 M_\odot$. A dwarf galaxy typically has $10^8$ stars, but even if you take one of the smallest known dwarf with $10^3$ stars, a PopIII star won't dominate the kinematics. Such small galaxies ar even more dark matter-dominated. And for a given star, a 10 $M_\odot$ star at distance $x$ will exert the same gravitational pull as the $10^3 M_\odot$ at distance $x/10$. – pela Oct 6 '17 at 10:30
• What I'm trying to say is, that yes, it's theoretically possible to have a star at the gravitational center of a galaxy, but it won't stay there. It will, however, have a higher probability than stars farther away from the center, to have a low energy, and thus stay near the center. But it will not dominate the gravitational field. – pela Oct 6 '17 at 10:34
• @pela so that that star would more behave kind of like a star in a twin system(not that violent of course)? Like it would be the most dominant thing in the galaxy but would have no consistant orbit to what ever it orbits it self? conclusional one can sayin theory this could exist, but to dominate a galaxy, a black hole to be you have?^^ mind posting that as answer?:) – Zaibis Oct 6 '17 at 10:51

The region within which a BH dominates over that of the stars (the "sphere of influence"$^\dagger$) is given by (e.g. Peebles 1972) $$r = \frac{G M_\mathrm{BH}}{\sigma^2},$$ where $G$ is the gravitational constant, $M_\mathrm{BH}$ is the mass of the black hole, and $\sigma$ is the velocity dispersion.
In the Milky Way (MW), there's a SMBH (Sagittarius A*) of roughly $M_\mathrm{BH} \simeq 4\times10^6\,M_\odot$. In that region, the stellar velocity dispersion is roughly $50$–$100\,\mathrm{km}\,\mathrm{s}^{-1}$ (e.g. Genzel et al. 2010). Plugging in those values, you'll find that Sgr A* dominates the kinematic out to roughly 3 pc, or 10 lightyears, which is nothing compared to MW's radius of $\sim10^5$ lightyears.
If you take the most massive conceivable stars (a hypothesized Pop III star of $M\sim10^3\,M_\odot$) in Willman 1, the smallest known dwarf galaxy — which has stellar velocity dispersion of the order $5$–$10\,\mathrm{km}\,\mathrm{s}^{-1}$ — you'll find that such a star will dominate the gravitational potential out to a distance of only $\lesssim0.1\,\mathrm{pc}$, again completely negligible compared to the galaxy's radius of $\sim25\,\mathrm{pc}$.
$^\dagger$Not to be confused with the event horizon which is even smaller.