If our solar system were to somehow be created outside of a galaxy as a single star in the vast nothingness between galaxies, would life on Earth change any?
Does being a member of a galaxy actually provide some kind of benefit to our solar system or the creation/sustaining of life?
I've had my eye on this question for some time, but I haven't had the time to answer it. Sorry for not getting to it sooner.
As zibadawa timmy said, you'd be hard-pressed to find the materials necessary for a star system if you're outside a galaxy. For one thing, there aren't any stellar nurseries in the intergalactic void (well, none that we know of. But I'd guess it's highly unlikely that they exist plentifully). So you have no hydrogen or helium, or dust, or other elements - in fact, you have nothing that you could use. That's a wee bit of a problem.
There is a way you could get around this, though - if your star system is in a globular cluster. They're groups of stars that orbit a galaxy. We don't know just how they got out there. They could be from dwarf galaxies, which then lost them, or they could have been partially chucked out of the larger galaxy but stayed in an orbit. The trouble is, as Wikipedia says,
However, they are not thought to be favorable locations for the survival of planetary systems. Planetary orbits are dynamically unstable within the cores of dense clusters because of the perturbations of passing stars. A planet orbiting at 1 astronomical unit around a star that is within the core of a dense cluster such as 47 Tucanae would only survive on the order of $10^8$ years.
Yep. Not a great place to live.
But I take it you didn't intend for our solar system to be in a globular cluster, so I'll go back into intergalactic space. It's not actually a vacuum - not that most parts of outer space are. There's a lot of plasma and hot gas there (the intergalactic medium), sometimes getting to a toasty $10^5$ or $10^7 \text { K}$. Could it harbor a stellar system? That depends on just what material the star brings with it. If planets haven't formed around it yet, and the star has a protplanetary disk, then perhaps that disk could dominate over the intergalactic medium. Remove the ICM and maybe planetary formation could proceed normally.
What happens then? Well, there would be some interesting effects. For example, the Oort Cloud might not have become spherical, because it was partly deformed by the galactic tide. Here, tidal forces probably wouldn't be as strong (although this depends in part on just how far away we are from the galaxy). We probably wouldn't have a lot of negative effects, because we don't have a lot of extreme benefits here in the Milky Way. Our galaxy does not appear to have an AGN, there aren't any monstrous black holes nearby, and we aren't undergoing any catastrophic galactic collisions. And the Milky Way-Andromeda collision won't be too bad.
We probably wouldn't be in too bad of a position if we were in intergalactic space. There's not a lot of benefits from being in a galaxy - well, no significant ones, at least. Well, besides star formation depositing all the materials we need for the solar system to form. That's a biggie.
