How to use the James Webb Space Telescope to hunt for life around white dwarfs

The paper cited in the space.com, A New Method for Finding Nearby White Dwarf Exoplanets and Detecting Biosignatures, [2209.12914] A New Method for Finding Nearby White Dwarf Exoplanets and Detecting Biosignatures (arxiv.org) , 26-Sep-2022. I note from the abstract, "we find that the detection of the biosignature pair O3+CH4 is possible for all habitable-zone Earths (within 6.5 pc; six white dwarf systems) or super-Earths (within 10 pc; 17 systems) orbiting white dwarfs with only 5-36 hrs of integration using MIRI's Low Resolution Spectrometer (LRS)."

An ambitious project here :) The exoplanet.eu site shows 21 confirmed pulsars with exoplanets and 7 listed with WD or white dwarfs. The space.com article states, "Because sunlike stars are very common, and sunlike stars evolve into white dwarfs, there should also be a lot of planets around white dwarfs. And yet observations there have come up short, with only a handful of exotic examples. One is WD 0806-661b, a gas giant planet nearly eight times more massive than Jupiter that orbits at a distance of over 2,500 astronomical units, or 232.5 billion miles (373.7 billion kilometers), from its white dwarf star, meaning it takes more than 158,840 Earth years to complete one orbit. Another is PSR B1620-26 (AB) b, a gas giant that orbits a white dwarf-pulsar pair. There are two challenges for anyone interested in finding exoplanets around white dwarfs. One, they're very small and relatively dim, so the commonly used transit method, in which we stare at a star and wait for the exoplanet to cross in front of it, doesn't work. Two, white dwarfs don't have a lot of standout features in their spectra, so the other popular method, which involves watching the redshift and blueshift of spectral features as an orbiting planet tugs on its parent star, doesn't work either."

Properties for WD 0806-661 b listed, The Extrasolar Planet Encyclopaedia — WD 0806-661 B b (exoplanet.eu)
and PSR B1620-26 (AB) b, The Extrasolar Planet Encyclopaedia — PSR B1620-26 (AB) b (exoplanet.eu) , shows the semi-major axis 23 AU from the PSR. Defining the conservative habitable zone (CHZ) and optimistic habitable zone (OHZ) must be challenging to show :) Some of the masses for exoplanets at WD are 56 or 8 Mjup. PSR 1257 12 b shows 0.022 earth mass planet. PSR J2055+3829 b shows a 39 Mjup planet.
 
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It's hard to have much expectation of any advanced forms of life on a planet orbiting a star that once turned the planet into toast. The super smart ones would have left long before that happened, which will be our game plan, no doubt, if we are around 4 billion years from now.

Then there is the problem of young WDs having a surface temperature of around 150,000K. This smaller but much hotter object is about 35x more luminous than the Sun. Earth would need to have moved past Jupiter to maintain the same level of luminosity.

This exoplanet would then need to migrate inward as the WD cooled. But the WD cools very fast until it reaches, say, about ~ 6,000K where the next 500K drop in temp. takes over 1 billion years.

Because the size of a WD is tiny compared to the Sun, it would need to be around 60,000K to be as luminous (wattage) as the Sun for a planet at 1 AU. But, as mentioned, this high temperature drops quickly, so the HZ moves quickly as well. [My math could use some scrutiny, perhaps, since I'm still rushing around these days trying to finalize a move to a new house.]

As for locating the exoplanets of WDs, I would assume it is far less likely that transits would be seen given how small the disk are for WDs. But, radial spectroscopy is likely a little easier given their smaller mass.
 

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