Is it possible for stable Neutron Stars or White Dwarfs to have habitable planets?
Fascinating topic!
Your answer has been adressed by researchers at least in these cases I have found.
Habitability in White Dwarf systems:
https://arxiv.org/pdf/1207.6210.pdf
Habitability in Neutron Star systems:
https://arxiv.org/pdf/1705.07688.pdf
White Dwarfs
Every sufficiently hot object has an habitable zone (in terms of temperature strictly). White dwarfs reach hundreds of thousands of Kelvins at their surfaces, so they are adequate to harbour a circumstellar habitable zone (where water could be found in liquid state).
When an object has a high temperature with respect to its surroundings it loses heat to the environment (very rapidly at the beginning and slower when there is less energy left). Cool white dwarfs (cool means with temperatures similar to that of our Sun) are loosing heat slowly (and because there is a phase transition under 6000K where the star literally crystallizes the heat loss is even slower). That means that the habitable zone is going to change position in the time span of, maybe, billions of years. Any planet located there has plenty of time until it freezes and gets uninhabitable due to the slow drifting of the habitable zone to the insides of the system as the white dwarf slowly radiates the heat.
White dwarfs are also very constant in terms of luminosity. Their variability tends to be even smaller than our Sun's, so the climate would be stable for eons and any catastrophic flaring event can be discarded.
It's also true that 10% of white dwarfs have huge magnetic fields that could make the planet unsuitable for life (radiation belts and other complex issues), but still 90% are... let's say... OK.
So far so good. Now comes the tricky thing. White dwarfs as an evolutionary stage of a late type star, are preceded by a red giant phase, in which
the inner planets are generally engulfed by the expanding star. Far away planets could survive this stage but the inner ones would probably fall apart while spiraling inwards inside the extremely tenuous outer layers of the red giant. Thus, we wouldn't expect planets close to the white dwarf, the only survivors should be the outer ones. And here comes the problem,
the habitable zone of a cool white dwarf with temperatures in the range of 4000K and 6000K (solar-like temperatures) is just 0.01 AU away from the star. A hotter white dwarf would push the habitable zone farther away, but remember, we need a cool white dwarf to sustain habitability for large periods of time (life needs time to appear and time to evolve and with little time the probability of finding life there diminishes). With a cool white dwarf a planet in the habitable zone would retain Earth-like temperatures for 8 billion years!. Therefore we need our planet at the 2,5% of Mercury's distance to our Sun. But how can we archive this if the inner planets were destroyed in the red giant phase of the star?
Well we have some possible scenarios for that. Maybe planetary migration (for example due to pure friction of the planet as it moves through stellar wind or the interplanetary residuals of the red giant phase) takes some outer planets sufficiently close to make the deal. But this is improbable since the process of planetary migration would have to be precisely tuned as to stop the inspiraling planet just face-to-face with the stellar corpse. A jupiter-like planet orbiting inside the red giant (
this can actually happen) could survive the entire phase while loosing a lot of its atmospheric content until, finally, a small rocky body remains in a close orbit around the residual white dwarf.
This is what is thought to happened with Kepler-70b and Kepler-70c, both small rocky planets that
have survived the red giant stage of their host star (their star is
not yet a white dwarf but this is just a matter of time). We don't know of any exoplanets around white dwarfs yet (except perhaps for these
circumbinary planets around a red dwarf - white dwarf binary system) but, as It turns out, having planets close to them
could be quite common in fact as we have detected the chemical pollution of a terrestrial planet that recently was cannibalized by one.
So, yeah habitability around white dwarfs sounds promising. There are even good news in terms of ultraviolet radiation as the dose in these conditions would be inferior to that needed for DNA disruption,
again as explained in this paper. Photosynthesis would be particularly benefited by the white dwarf's electromagnetic radiation. We are not accounting for problems like tidal locking (a probable situation at such distances) and the maybe poor chemical diversity of the planet (that would make nutrients and biochemical reactions much more improbable) as the red giant could have sublimated and dissociated many interesting compounds (or even ripped apart the entire atmosphere).
Detectability is in our current capabilities. The constancy of white dwarf's luminosity allows for any planetary transit to be easily confirmed. White dwarfs have small radii and so the transit would be quite abrupt while the planet eclipses a huge part of the stellar disk. The fact that we should search for a planet so close to its star makes the probability of seen the particular alignment needed for a transit even greater (transits are more frequent for inner planets because the orbital period is small and also because a wide range of orbital inclinations can yield those transits).
Campaigns are being undertaken to search for them. And there is also the fact that polarization of light from the atmospheres of these white dwarf exoplanet's would be very easy to detect in relative terms.
Another interesting question would be if there can be life
on white dwarfs themselves. We can't forget that white dwarfs could eventually be so cold as to become
habitable carbonaceous planets. Would life evolve on the surface of
a diamond planet (an extinct white dwarf) or the
chemical environment would be inherently sterile and devoid of water?
Neutron stars
Planets around Neutron stars are known. In fact the first exoplanets discovered where around a neutron star (the pulsar PSR B1257+12). At the moment
there are 4 pulsar planets confirmed.
Neutron stars environment is extreme and harsh; Energetic flares, high X-ray flux, large magnetic fields and in the case of pulsars you even have a particle accelerator beam of dead.
But these guys proposed a possible scenario were a Super-Earth with a dense atmosphere could retain it against the pulsar winds, gamma and X-ray flux for even billions of years and at the same time protect a possible biosphere below the thick fog.
If the planet is far away radiation could be less damaging. And there, where the thermal radiation of their neutron stars is low (thus the corresponding heating is less important)
the X-ray heating of the atmosphere takes the lead and can be sufficient to create life-sustaining conditions on the distant planet. In this way the habitable zone has to be redefined for these exotic systems as the place where heat transferred by X-rays reacting with the atmosphere can be sufficient to allow for liquid water.
I want to quote two particularly inspiring notes from them:
Imagine what would be life on such planets: a huge pressure on the surface (due to the large atmospheric mass) able to crush anything we are familiar with. And completely dark. A very thick, black, warm fog. Indeed since gamma and X-rays cannot penetrate the whole atmosphere and reach the surface, neither will ultraviolet, optical or infrared light. It must vaguely look (and feel) like the deepest regions of the sea here on Earth with the difference that you have a whole planet at your disposal.
and
What would it be for an intelligent organism to communicate in this immensely thick fog. And if they would manage to make it outside their enormous atmosphere what would they see? A neutron star spinning hundreds of times per second and emitting beacons of radiation. They would learn with little effort things which are incredibly complex for us. They would witness the effects of general relativity in front of their eyes. Neutron stars do indeed bend space and time in a way that is second only to black holes. They could learn about
ultra-dense matter and the behavior of the strong force if they could measure the mass and radius of their neutron star. They would witness the effects of strong magnetic fields and complex electromagnetism by looking at the pulsar. And perhaps they would then look at the other stars, the “normal” stars, like the Sun, and wonder whether life would be possible around those large distant objects, whether such poor emitters of X-ray radiation could sustain life. Whether it would be even conceivable to have life around such pale, cold, weak stars
As before another interesting question would be if there can be life
on neutron stars themselves. According to
this source,
Martin Rees once said that neutron stars could hypothetically harbor
"hyper-dense microscopic organisms controlled by nuclear forces with a metabolism faster than ordinary chemical-based life". An idea explored in the science-fiction novel "
Dragon's egg", where a microscopic civilization rises in a matter of months on the surface of a neutron star and overcomes natural catastrophes such as
starquakes and magnetic field anomalies just to start an exponential technological growth that surpasses that of the human visitors that study the phenomena.
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And as always, sorry for my English. I just writted this in the metro and had no time to be as vigilant as I should with grammar.
EDIT: I edited some parts (my spelling was terrible) and added some links to interesting readings. Thanks for the feedback also