The dominant theory for the formation of planets is the core accretion theory, and in this theory, the most massive planets are thought to form beyond the snow line where ices have condensed to maximize the solid material available for the formation of planet cores. There are only 7 known exoplanets with likely masses of less than 50 Earth-masses located beyond the snow line, and all of them been found by gravitational microlensing. Statistical analyses of the early microlensing results indicate that planets with mass ratios in the Neptune-Saturn range are quite common beyond the snow line and that planets with smaller mass ratios are more common. This appears to be in accord with the predictions of the core accretion theory, but precise tests of the theory are hampered by the fact that the mass of only one of these 7 cold, low-mass planets is known. We propose to remedy this difficulty by determining the masses of 4 additional low-mass microlens planets located beyond the snow line to bring the total number of low-mass planets beyond the snow-line to 5. We will apply innovative techniques that rely upon the high angular resolution of HST images and the unique stability of the HST point spread function. The proposed observations will provide individual planet and host star masses and distances for each of the microlensing planetary systems that we observe, and they will allow us to make a first estimate of the exoplanet mass function beyond the snow line. The propose observations will also demonstrate the primary planetary mass measurement method of the WFIRST mission. Our observing program aims to identify and characterize the host stars for 4 low-mass planetary microlensing events using the two methods that will be used by the WFIRST mission to determine the masses of planetary microlenses and their host stars. These methods determine the lens properties even though host and source stars are not individually resolved. These methods, the color dependent centroid shift (Bennett et al. 2006) and image elongation (Bennett, Anderson & Gaudi 2007) both require multiple dithered exposures. For most targets, the optimal exposure times are less than the minimum 348 second exposures that allow parallel, full-frame buffer dumps. But fortunately, even a 512 × 512 WFC3/UVIS sub-array will contain >∼ 400 bulge G and K-dwarfs, similar to the source stars, which can be used to measure the PSF. One of the main goals of our observations is to measure the relative proper motion of the lens and source stars. The magnitude of this proper motion is generally predicted by the light curve, but the direction is unknown. But, it is possible for a companion to the source or an unrelated to mimic the signal of a bright lens star. Therefore, we must observe each target in a second epoch to confirm that the motion of the apparent lens is following the microlensing model prediction, so all WFC3/UVIS observations will be repeated in cycle 21. Two of our targets, OGLE-2007-BLG-368 (Sumi et al. 2010) and MOA-2008-BLG-310 (Janczak et al. 2010), are relatively bright at I = 19.51 and 19.28, respectively, so we request only a single orbit of WFC3/UVIS observations for each of these target. Each orbit will contain 8 dithered exposures in each of the F814W and F555W passbands, so most of the observations will use 512 × 512 sub-arrays in order to avoid serial buffer dumps. These will be sufficient to measure both the color dependent centroid shift and the image elongation to better than 8-σ for both of these events if the excess flux seen in the ground-based AO images is indeed due to the planetary host star. The one target without ground-based AO images is OGLE-2005-BLG-169 (Gould et al. 2006). However, the microlensing model parameters for this even imply that the lens star will be at least 10% as bright as the source in the I band if the lens is a main sequence star (see the left panel of Fig. 1). This guarantees that the color dependent centroid shift and the image elongation will be detected at better than 20-σ with a single orbit of observations in the F555W and F814W passbands, with the same strategy as for OGLE-2007-BLG-368 and MOA-2008-BLG-310. However, as the left panel of Fig. 3 shows, the detection of these effects does not necessarily mean that the host star mass can be determined. In particular, the mass-magnitude relation for this event, as well as the V − I centroid shift distributions are flat for 0.2M⊙ <∼ ML <∼ 0.4M⊙. This is a consequence of the fact that the I−band mass- luminosity relation increases with the same slope that the luminosity is decreasing due to distance for this particular event, and the other events in our sample do not have this effect. It implies that we will also need to make measurements in the F438W-band so that we can determine the lens star mass in this range with the B − V centroid shift measurement. Since the target is faint in this band, we will use a series of 6 dithered 350 sec full 4096 × 4096 frame exposures. Perhaps the most interesting event in our sample is MOA-2007-BLG-192. The original analysis of this event (Bennett et al. 2008) indicated that the planetary host star is near or below the bottom of the main sequence based on a microlensing parallax measurement. However, the microlensing parallax signal is not strong enough to give a precise mass because the direction of relative motion is not tightly constrained by the light curve. In addition, although the planetary signal is quite strong, the time coverage of the planetary signal is rather sparse. This means the the effects of the finite source is also not strongly constrained. Furthermore, the color of the source star is only weakly constrained by the difference between two very similar passbands (Gould et al. 2010a). However, ground-based AO images from the VLT/NACO instrument have detected a very red star superimposed upon the source star (Kubas et al. 2011). This implies that the lens star is likely to be a star at the bottom of the main sequence instead of a brown dwarf, but we will need to detect the color dependent centroid shift and image elongation to confirm this. These events will also yield the direction of lens-source relative motion, which will resolve the uncertainty in the microlensing parallax measurement. The uncertainties in the light curve of this event lead to uncertainties in the mass ratio, so that unlike most events, the mass of the planet is not precisely determined even when the mass of the host star is precisely determined. Fortunately, it is possible to improve this situation by measuring the lens-source relative proper motion, μ, with the color dependent centroid shift and image elongation, but to reduce the uncertainty in the planet mass, we also need to measure the color of the source star. This is complicated by the fact that the source is blended with the lens star, but with the addition of WFC3/IR observations in the F125W, and F160W observations, we should have enough information to constrain both the color of the planet host star and the source star. This will require one additional orbit for both IR passbands. Because this star is quite faint, we will require one orbit each for the WFC3/UVIS F814W and F555W observations. For maximum S/N for both photometry and astrometry, we request 4×348 second full frame box-dithered exposures with parallel buffer dumps, then 4 × 185 second box dithered exposures, using a 512 × 512 sub-frame to minimize readout time and avoid buffer dump overheads.. The last exposure of each WFC3/UVIS orbit will be a full frame 30 sec exposure that will allow cross-calibration with relatively bright stars that are well observed with the microlensing survey telescopes. The uncertainty in the planetary mass determined by this procedure will depend on the results of the actual measurements, but it should reduce the uncertainty in the mass of the planet from a factor of ∼ 2.5 (Kubas et al. 2011) to about 25%. EXTRA-SOLAR PLANETS 12 false 0.0 0.0 false false false false SUPPORTED STAR G V-IV J2000 J2000 I = 20.3 +/- 0.3 STAR K V-IV M V-IV J2000 J2000 I = 21.44 +/- 0.08 STAR G V-IV J2000 J2000 I = 19.51 STAR G V-IV J2000 J2000 I = 19.28, H = 17.46 WFC3/UVIS Imaging No No F814W WFC3/UVIS Imaging No No F555W WFC3/UVIS Imaging No No F438W WFC3/UVIS Imaging No No F814W WFC3/UVIS Imaging No No F555W WFC3/IR Imaging No No F125W WFC3/IR Imaging No No F160W WFC3/UVIS Imaging No No F814W WFC3/UVIS Imaging No No F555W WFC3/UVIS Imaging No No F814W WFC3/UVIS Imaging No No F555W WFC3/UVIS Imaging No No F814W WFC3/UVIS Imaging No No F555W WFC3/UVIS Imaging No No F438W WFC3/UVIS Imaging No No F814W WFC3/UVIS Imaging No No F555W WFC3/UVIS Imaging No No F814W WFC3/UVIS Imaging No No F555W WFC3/UVIS Imaging No No F814W WFC3/UVIS Imaging No No F555W POS-TARG DITHER 0.173 LINE 0.112 false false 81.785 4 23.884 WFC3-UVIS-DITHER-BOX 1 false POS-TARG DITHER 0.135 LINE false false 3 46.84 WFC3-UVIS-DITHER-LINE-3PT 2 false POS-TARG DITHER 0.572 LINE 0.365 false false 74.653 4 18.528 WFC3-IR-DITHER-BOX-MIN 3 false POS-TARG DITHER 0.636 LINE false false 3 41.788 WFC3-IR-DITHER-LINE 4 false POS-TARG DITHER 0.145 LINE false false 2 46.84 WFC3-UVIS-DITHER-LINE 5 false The scheduling data was generated by CASM 19.3. CASM was run in Phase II mode. We request early observations of OGLE-2005-BLG-169L because this target has a large lens-source relative proper motion and because the microlensing event occurred more than 6 years ago. This implies that maximizing the time interval between the cycle 19 and cycle 21 observing epochs will yield the most precise mass determination for this event. 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