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Abstract

We explore the prospects for the detection of giant circumbinary exoplanets
and brown dwarfs (BDs) orbiting Galactic double white dwarfs binaries (DWDs)
with the Laser Interferometer Space Antenna (LISA). By assuming an occurrence
rate of 50%, motivated by white dwarf pollution observations, we built a
Galactic synthetic population of P-type giant exoplanets and BDs orbiting DWDs.
We carried this out by injecting different sub-stellar populations, with
various mass and orbital separation characteristics, into the DWD population
used in the LISA mission proposal. We then performed a Fisher matrix analysis
to measure how many of these three-body systems show a periodic Doppler-shifted
gravitational wave perturbation detectable by LISA. We report the number of
circumbinary planets (CBPs) and (BDs) that can be detected by LISA for various
combinations of mass and semi-major axis distributions. We identify pessimistic
and optimistic scenarios corresponding, respectively, to 3 and 83 (14 and 2218)
detections of CBPs (BDs), observed during the length of the nominal LISA
mission. These detections are distributed all over the Galaxy following the
underlying DWD distribution, and they are biased towards DWDs with higher LISA
signal-to-noise ratio and shorter orbital period. Finally, we show that if LISA
were to be extended for four more years, the number of systems detected will be
more than doubled in both the optimistic and pessimistic scenarios. Our results
present promising prospects for the detection of post-main sequence exoplanets
and BDs, showing that gravitational waves can prove the existence of these
populations over the totality of the Milky Way. Detections by LISA will deepen
our knowledge on the life of exoplanets subsequent to the most extreme
evolution phases of their hosts, clarifying whether new phases of planetary
formation take place later in the life of the stars.