  We analyse emission spectra of WASP-12b from a partial phase curve observed
over three epochs with the Hubble Space Telescope, covering eclipse,
quadrature, and transit, respectively. As the 1.1-day period phase curve was
only partially covered over three epochs, traditional methods to extract the
planet flux and instrument systematic errors cannot recover the thermal
emission away from the secondary eclipse. To analyse this partial phase curve,
we introduce a new method, which corrects for the wavelength-independent
component of the systematic errors. Our new method removes the achromatic
instrument and stellar variability, and uses the measured stellar spectrum in
eclipse to then retrieve a relative planetary spectrum in wavelength at each
phase. We are able to extract the emission spectrum of an exoplanet at
quadrature outside of a phase curve for the first time; we recover the
quadrature spectrum of WASP-12b up to an additive constant. The dayside
emission spectrum is extracted in a similar manner, and in both cases we are
able to estimate the brightness temperature, albeit at a greatly reduced
precision. We estimate the brightness temperature from the dayside
(Tday=3186+-677 K) and from the quadrature spectrum (Tquad=2124+-417 K) and
combine them to constrain the energy budget of the planet. We compare our
extracted relative spectra to global circulation models of this planet, which
are generally found to be a good match. However, we do see tentative evidence
of a steeper spectral slope in the measured dayside spectrum compared to our
models. We find that we cannot match this increased slope by increasing optical
opacities in our models. We also find that this spectral slope is unlikely to
be explained by a non-equilibrium water abundance, as water advected from the
nightside is quickly dissociated on the dayside.
