Magellan Adaptive Optics first-light observations of the exoplanet beta Pic b. II. 3-5 micron direct imaging with MagAO+Clio, and the empirical bolometric luminosity of a self-luminous giant planet

Young giant exoplanets are a unique laboratory for understanding cool, low-gravity atmospheres. A quintessential example is the massive extrasolar planet \(\beta\) Pic b, which is 9 AU from and embedded in the debris disk of the young nearby A6V star \(\beta\) Pictoris. We observed the system with first light of the Magellan Adaptive Optics (MagAO) system. In Paper I we presented the first CCD detection of this planet with MagAO+VisAO. Here we present four MagAO+Clio images of \(\beta\) Pic b at 3.1 \(\mu\)m, 3.3 \(\mu\)m, \(L^\prime\), and \(M^\prime\), including the first observation in the fundamental CH\(_4\) band. To remove systematic errors from the spectral energy distribution (SED), we re-calibrate the literature photometry and combine it with our own data, for a total of 22 independent measurements at 16 passbands from 0.99--4.8 \(\mu\)m. Atmosphere models demonstrate the planet is cloudy but are degenerate in effective temperature and radius. The measured SED now covers \(>\)80\% of the planet's energy, so we approach the bolometric luminosity empirically. We calculate the luminosity by extending the measured SED with a blackbody and integrating to find log(\(L_{bol}\)/\(L_{Sun}\)) \(= -3.78\pm0.03\). From our bolometric luminosity and an age of 23\(\pm\)3 Myr, hot-start evolutionary tracks give a mass of 12.7\(\pm\)0.3 \(M_{Jup}\), radius of 1.45\(\pm\)0.02 \(R_{Jup}\), and \(T_{eff}\) of 1708\(\pm\)23 K (model-dependent errors not included). Our empirically-determined luminosity is in agreement with values from atmospheric models (typically \(-3.8\) dex), but brighter than values from the field-dwarf bolometric correction (typically \(-3.9\) dex), illustrating the limitations in comparing young exoplanets to old brown dwarfs.