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Abstract

We present simultaneous, multi-colour optical light curves of the companion
star to the black-widow pulsar PSR J2051-0827, obtained approximately 10 years
apart using ULTRACAM and HiPERCAM, respectively. The ULTRACAM light curves
confirm the previously reported asymmetry in which the leading hemisphere of
the companion star appears to be brighter than the trailing hemisphere. The
HiPERCAM light curves, however, do not show this asymmetry, demonstrating that
whatever mechanism is responsible for it varies on timescales of a decade or
less. We fit the symmetrical HiPERCAM light curves with a direct-heating model
to derive the system parameters, finding an orbital inclination of
$55.9^{+4.8}_{-4.1}$ degrees, in good agreement with radio-eclipse constraints.
We find that approximately half of the pulsar's spin-down energy is converted
to optical luminosity, resulting in temperatures ranging from approximately
$5150^{+190}_{-190}$ K on the day side to $2750^{+130}_{-150}$ K on the night
side of the companion star. The companion star is close to filling its Roche
lobe ($f_{\rm RL} =0.88^{+0.02}_{-0.02}$) and has a mass of
$0.039^{+0.010}_{-0.011}$ M$_{\odot}$, giving a mean density of
$20.24^{+0.59}_{-0.44}$ g cm$^{-3}$ and an apsidal motion constant in the range
$0.0036 < k_2 < 0.0047$. The companion mass and mean density values are
consistent with those of brown dwarfs, but the apsidal motion constant implies
a significantly more centrally-condensed internal structure than is typical for
such objects.