In about five billion years' time, the Sun will grow into a red giant, probably swallowing the Earth and putting an end to any and all life that's still kicking then. As this material is shed off, the Sun itself will become a small, dim, white dwarf star, and the Earth will be blasted into a dead core of a planet. But according to a new study, any aliens out there might still be able to pick up radio waves from this planetary core – for up to a billion years.

It's long been hypothesized that planetary cores should exist around white dwarfs, left behind after the red giants blast away their atmosphere and mantle. So far only one possible fragment is believed to have been spotted, just a few months ago around a white dwarf some 40 light-years from Earth. But generally, it hasn't been known how easily these cores would be to detect, or how we can detect them.

So for the new study, researchers from the University of Warwick set out to determine how long they may be detectable for, and which white dwarfs are the best candidates to start the search.

The team says that these planetary cores could be detectable through the radio waves they give off. The magnetic field of a white dwarf can actually interact with the planetary core if it's metallic enough, creating a unipolar inductor circuit. Radiation from that circuit can then be detected by radio telescopes here on Earth, in the form of radio waves.

But would these cores survive long enough to be detectable at all? According to the researchers, yes. They ran models of different scenarios and found that some cores would survive for more than 100 million years, and in some cases maybe as long as a billion years. That gives us plenty of time to notice them.

The researchers identified under which scenarios the cores would be most likely to survive, a finding that can give them a clue as to where to start looking.

"There is a sweet spot for detecting these planetary cores: a core too close to the white dwarf would be destroyed by tidal forces, and a core too far away would not be detectable," says Dimitri Veras, lead author of the study. "Also, if the magnetic field is too strong, it would push the core into the white dwarf, destroying it. Hence, we should only look for planets around those white dwarfs with weaker magnetic fields at a separation between about 3 solar radii and the Mercury-Sun distance."

With this research under their belts, the astronomers hope to begin using radio telescopes to search for planetary cores – and possibly even still-living planets – around white dwarfs.

The research was published in the journal Monthly Notices of the Royal Astronomical Society.