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.
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