Future space--based telescopes, such as the Wide--Field Infrared Survey Telescope (WFIRST), will observe the reflected--light spectra of directly imaged extrasolar planets. Interpretation of such data presents a number of novel challenges, including accounting for unknown planet radius and uncertain stellar illumination phase angle. Here we report on our continued development of Markov Chain Monte Carlo retrieval methods for addressing these issues in the interpretation of such data. Specifically we explore how the unknown planet radius and potentially poorly known observer--planet--star phase angle impacts retrievals of parameters of interest such as atmospheric methane abundance, cloud properties and surface gravity. As expected, the uncertainty in retrieved values is a strong function of signal--to--noise ratio (SNR) of the observed spectra, particularly for low metallicity atmospheres, which lack deep absorption signatures. Meaningful results may only be possible above certain SNR thresholds; for cases across a metallicity range of 1--50 times solar, we find that only an SNR of 20 systematically reproduces close to the correct methane abundance at all phase angles. However, even in cases where the phase angle is poorly known we find that the planet radius can be constrained to within a factor of two. We find that uncertainty in planet radius decreases at phase angles past quadrature, as the highly forward scattering nature of the atmosphere at these geometries limits the possible volume of phase space that relevant parameters can occupy. Finally, we present an estimation of possible improvement that can result from combining retrievals against observations at multiple phase angles. 2

A number of magnetic anomalies are present along the northern edge of the lunar South Pole-Aitken (SPA) basin. A variety of hypotheses for their formation have been proposed, but an in-depth study of their properties has not been performed. Here we use two different methods to invert for their source body characteristics: one that completely searches a small parameter space of less than ten uniform-strength dipoles per anomaly, and another that uses grids of hundreds of dipoles with variable magnetization strengths. Both methods assume uniform magnetization directions at each anomaly and with one exception, produce nearly the same results. We introduce new Monte Carlo methods to quantify errors in our inversions arising from Gaussian time-dependent changes in the external field and the uncertain geometry of the source bodies. We find the errors from uncertainty in source body geometry are almost always higher. We also find a diverse set of magnetization directions around SPA, which we combine with other physical arguments to conclude that the source bodies were likely magnetized in a dynamo field. Igneous intrusions are a reasonable explanation (Purucker et al., 2012) for the directional variability, since they could be intruded over different magnetic epochs. However the directional variability also implies either surprisingly large amounts of true polar wander or non-axially aligned dynamo fields. We also explore the possibility that true polar wander caused by the SPA impact could allow iron-rich SPA ejecta to record a diverse set of magnetic field directions. Some of this material may have also become "sesquinary" ejecta and re-impacted across the Moon on 10 4-10 6 year timescales to capture such changes. No completely satisfactory answer emerges, except that the dipoleaxis of the lunar dynamo may have been variable in direction. the vector magnetic field at up to 18 Hz and transmitted its measurements at a reduced 87 resolution of 9 Hz. Level 1B LP-MAG data are obtained from the NASA Planetary Data 88 System (ppi.pds.nasa.gov). The SELENE/Kaguya spacecraft used a tri-axial fluxgate 89 magnetometer with a sampling rate up to 32 Hz. K-MAG magnetometer data are obtained 90 from the SELENE data archives (l2db.selene.darts.isas.jaxa.jp). The cadence of 91 measurements used in this study is 0.2 Hz for LP-MAG and 0.25 Hz for K-MAG. 92 Topography data are from the Lunar Orbiter Laser Altimeter (LOLA) (Smith et al., 2010) 93 (pds-geosciences.wustl.edu). 94 95 To best capture the Moon's crustal field, all data used for analysis were collected in either 96 the lunar wake or while the Moon was in the Earth's magnetotail (wake/tail), avoiding 97 distortions caused by the solar wind noted by (Halekas et al., 2008; Kurata et al., 2005). 98 Tail datasets specifically exclude epochs during which plasma sheet disturbances were 99 noted (Halekas et al., 2012). Consecutive orbits are ~1° in longitude apart. At 0.2 Hz, 100 successive magnetometer measurements are separated by ~8 km in the latitudinal 101 direction. All data used...