I have an Earth analog that is nearly completely covered in ice and glaciers. I want to have oases of warmth scattered across the planet. These oases aren't tropical by any means, having just enough heat to support soil temperatures warm enough to allow tree growth. However, geothermal heat often seems dangerous due to poisonous gas releases, sulfur compounds, and other dangers. Are there any other possible ways to warm these oases?
So, first of all, there's no particular reason that geothermal heat has to be dangerous. Scandanavia makes VERY extensive use of it and always has. The use of geothermal heating for exactly the kind of purposes you're describing goes back to the paleolithic era.
Ultimately, there are only two sources of thermal energy available to a planet. Radiant energy from the sun, and Geothermal energy from the molten core (assuming it has one). An ice planet can only be that way because it's not getting enough radiant energy to keep water liquid at the surface, so I'm really not sure what other alternative you have BESIDES geothermal.
Telluric iron fires.
I was thinking about the underground coal fires, which are natural occurrences, can burn a long time, and produce a lot of heat. And also a lot of poison: the landscapes over these fires are spectacularly dead. Plus it has been done.
But what else could be underground, gradually oxidize and give off heat? What about metallic iron? Native non-meteoric iron is super rare. I did not think there was any in the crust until I researched this question.
Metallic iron exists. The oxidation of iron is what makes those pocked hand warmers heat up. Your world has underground places where metallic iron has become exposed to air - maybe by the action of glaciers, or some sort of crustal upwelling. Or maybe these are ancient meteorites, not telluric iron. In any case: iron, and oxygen loves it. In your world, underground caves of iron breathe the air and gradually oxidize, exhaling warm and and heating up the crust - without a lot of tar and sulfur as part of the reaction.
I made this up as far as I know. Maybe it happened long ago during the Great Oxidizing. Not currently as far as can tell.
Use Earth crust and volcanoes as an analog
Just having a hot core would do it. If there is liquid water under the ice (or slush under the ice), convection can occur. That would make areas where the warm, deep water is brought to specific areas under the ice crust. Those would slowly melt the ice in those areas providing a route to the surface.
Also, the pressure of the warm water convection may push the ice crust around. That may form cracks and other weak spots that allow the up welling warm water to push through to the surface.
The hot crust can come from an Earth like core or it can come from tidal stress like happens in several of Jupiter's and Saturn's moons.
Geothermal heat does not have to be dangerous there are many places where springs exist that provide warm water that is not dangerous only a few are in active volcanic zones like Yellowstone.
One example are the hot springs that provide the waters for the Roman Baths in the city of Bath in England. https://en.m.wikipedia.org/wiki/Roman_Baths_(Bath) Water percolates through limestone aquifers to a depth of upto 4km in the Earths crust and returns to the surface through faults and fissures under pressure. Whilst the water is mineral rich it is safe to drink, I have it does have a slightly strange taste.
Other similar springs exist in many other places England has several Droitwich Spa, Matlock are just two others, Baden Baden in Germany is another famous example.
Option 1: Giant Rings: The planet has huge sunlight blocking rings. Except, at a few specific angles and specific times of day, some spots get direct sunlight, creating warm habitable zones.
Option 2: Global warming: The planet is warming up, over the next 200,000 years the glacier will be gone. But right now, only small patches are visible.
While this is certainly a plausable option at least if we tweak some some basic planetary parameters, unless your planet has been terraformed by low tech humans the native flora and fauna will have successfully adepted to the dangers of life near geothermal oasis. Adaption to a radiation and heavy metal poisened environment might be more difficult. Biological radiation resistance can be found in the Tardigrades have evolved an natural radiation resistance by shielding their cells, having az lot of redundant information and repairing their DNA. Adaption to heavy metal poisened environments might be mor difficult, but as some guy said; life always finds a way.
In the former colony of France, Gabon in Africa,
uranium deposits with a lower than expected U235 (the fissile isotope which reactors require) fraction where found. This lead to an investigation which discovered that the special geological setup of the region had created a number of natural nuclear reactors.
At the time when the reactors where active groundwater filled the uranium ore veins. Since the the fissible U235 made up 3% of the Uranium 1.7 billion years ago when the reactors where active the water acted as a moderator and the setup became critical, i.e. produced energy.
Water was needed as a neutron moderator, because while neutrons are given off by every U235 fission event, they are usually too fast to be absorbed by other U235 nuclei. Only hen they are slow they can be absorbed and cause further fission.
In the Oklo setup ground-water flowed into the vein and was cooked by the heat its fission produced. After 3 hours all the water had been cooked out of the vein, escaped into the rock and possibly to the surface and the cycle started again. Your oases would essentially be the places with the highest uranium concentration on the surface. This would also create the possibility of huge glacier lake caverns where the fission does not produce enough heat to break the ice shild. To be fair this setup could also be found with geothermal vents.
Uranium is generated almost exclusively in neutron star mergers.
Having a few of these occur in the region your solar system formed would be a plsusible statistical fluke. This and having complex life develope faster than on Earth will ensure that there will be enough U235 to keep natural reactors running fpr a long time.
A few things must be considered in this setup. Firstly natural nuclear bombs might be an option in the early history of the planet. I'm not 100 % certain about that, asking a nuclear physicist is the best way to clear this up. Secondly the planet will have a lot radiogenic heat, so it might transitioned into a plate tectonic setups from its original lid tectonic setup much later than Earth, which did it about 0.5 byr after its formation. The planet will also jave a very thin crust and a lot of vulcanism due to this. Thirdly the abundance of U235 will not come in isolation, just look at the other elements formed by neutron star mergers. The system and the planet will be incredibly valuble mining worlds.