# Unveiling MOA-2007-BLG-192: An M Dwarf Hosting a Likely Super-Earth

Sean K. Terry Department of Astronomy, University of Maryland, College Park,
MD 20742, USA  Code 667, NASA Goddard Space Flight Center, Greenbelt, MD
20771, USA  Jean-Philippe Beaulieu Sorbonne Université, CNRS, Institut
d’Astrophysique de Paris, IAP, F-75014 Paris, France  School of Natural
Sciences, University of Tasmania, Private Bag 37 Hobart, Tasmania, 70001,
Australia  David P. Bennett Department of Astronomy, University of Maryland,
College Park, MD 20742, USA  Code 667, NASA Goddard Space Flight Center,
Greenbelt, MD 20771, USA  Euan Hamdorf  School of Natural Sciences, University
of Tasmania, Private Bag 37 Hobart, Tasmania, 70001, Australia  Aparna
Bhattacharya  Department of Astronomy, University of Maryland, College Park,
MD 20742, USA  Code 667, NASA Goddard Space Flight Center, Greenbelt, MD
20771, USA  Viveka Chaudhry  Sidwell Friends School, Washington, DC 20016, USA
Andrew A. Cole School of Natural Sciences, University of Tasmania, Private Bag
37 Hobart, Tasmania, 70001, Australia  Naoki Koshimoto Department of Earth and
Space Science, Graduate School of Science, Osaka University, Toyonaka,
560-0043, Japan  Jay Anderson Space Telescope Science Institute, 3700 San
Martin Drive, Baltimore, MD 21218, USA  Etienne Bachelet  IPAC, Caltech,
Pasadena, CA 91125, USA  Joshua W. Blackman Physikalisches Institut,
Universität Bern, Gessellschaftsstrasse 6, CH-3012 Bern, Switzerland  Ian A.
Bond School of Mathematical and Computational Sciences, Massey University,
Auckland 0745, New Zealand  Jessica R. Lu Department of Astronomy, University
of California Berkeley, Berkeley, CA 94701, USA  Jean Baptiste Marquette
Laboratoire d’Astrophysique de Bordeaux, CNRS, B18N, allée Geoffroy Saint-
Hilaire, Pessac, France  Sorbonne Université, CNRS, Institut d’Astrophysique
de Paris, IAP, F-75014 Paris, France  Clément Ranc Sorbonne Université, CNRS,
Institut d’Astrophysique de Paris, IAP, F-75014 Paris, France  Natalia E.
Rektsini School of Natural Sciences, University of Tasmania, Private Bag 37
Hobart, Tasmania, 70001, Australia  Sorbonne Université, CNRS, Institut
d’Astrophysique de Paris, IAP, F-75014 Paris, France  Kailash Sahu Space
Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
Aikaterini Vandorou Department of Astronomy, University of Maryland, College
Park, MD 20742, USA  Code 667, NASA Goddard Space Flight Center, Greenbelt, MD
20771, USA S. K. Terry<EMAIL_ADDRESS>
###### Abstract

We present an analysis of high angular resolution images of the microlensing
target MOA-2007-BLG-192 using Keck adaptive optics and the Hubble Space
Telescope. The planetary host star is robustly detected as it separates from
the background source star in nearly all of the Keck and Hubble data. The
amplitude and direction of the lens-source separation allows us to break a
degeneracy related to the microlensing parallax and source radius crossing
time. Thus, we are able to reduce the number of possible solutions by a factor
of ${\sim}2$, demonstrating the power of high angular resolution follow-up
imaging for events with sparse light curve coverage. Following (Bennett et
al., 2023), we apply constraints from the high resolution imaging on the light
curve modeling to find host star and planet masses of $M_{\rm host}=0.28\pm
0.04M_{\sun}$ and $m_{p}=12.49^{+65.47}_{-8.03}M_{\earth}$ at a distance from
Earth of $D_{L}=2.16\pm 0.30\,$kpc. This work illustrates the necessity for
the Nancy Grace Roman Galactic Exoplanet Survey (RGES) to use its own high
resolution imaging to inform light curve modeling for microlensing planets
that the mission discovers.

gravitational lensing: micro, planetary systems

##  1 Introduction

Since the early 1990’s, surveys of the galactic bulge have searched for
variations in the brightness of background stars (sources) induced by the
gravitational field of foreground objects (lenses). The number of lensing
events detected has dramatically increased from a few dozen per year in the
1990’s (Udalski et al., 1994; Alcock et al., 1996) to thousands per year
currently. At present there are three primary ground-based surveys that
contribute to these lensing event detections: OGLE (Udalski et al., 2015), MOA
(Bond et al., 2001), and KMTNet (Kim et al., 2016). NASA’s Nancy Grace Roman
Space Telescope (Roman) is scheduled to launch in the next several years and
will conduct the Roman Galactic Bulge Time Domain Survey (GBTDS). As part of
this bulge survey, the Roman Galactic Exoplanet Survey (RGES) will be the
first dedicated space-based gravitational microlensing survey and is expected
to detect over 30,000 microlensing events and over 1400 bound exoplanets
during its five-year survey (Penny et al., 2019). This mission will complement
previous large statistical studies of transiting planets from missions like
Kepler/TESS and radial velocity planets from many ground-based RV surveys. The
GBTDS is also expected to discover free-floating planets that do not orbit any
host star (Johnson et al. (2020); Koshimoto et al. (2023); Sumi et al. (2023),
Johnson et al. in prep).
As of this writing, microlensing has detected $\sim$200 planets at distances
up to the Galactic Bulge. As for most transient phenomena, one limitation of
this method for fully characterizing microlensing systems is the cadence at
which the photometric data is obtained by the dedicated ground-based surveys.
An effective way to increase the sampling for a given microlensing event is to
issue a public alert so that observatories around the world can observe
ongoing events as a ‘follow-up’ network of telescopes. MOA-2007-BLG-192 was
the first planetary microlensing event detected without follow-up observations
from other observatories. The initial analysis reported a low-mass planet
orbiting a very-low mass host star or brown dwarf (Bennett et al., 2008). Due
to the lack of follow-up network data for this microlensing event, there are
significant gaps in the photometric light curve coverage, which leads to
uncertainties in the derived lens system parameters. There are also additional
degeneracies in the interpretation of this lens system that arise from the
possible planet-star separations and microlensing parallax. The details of
these degeneracies are discussed further in Section 2.1.
One way to mitigate some of these degeneracies is by resolving the source and
lens independently with high angular resolution imaging (i.e. Hubble Space
Telescope (HST), Keck AO, Subaru AO) several years after peak magnification
(Bennett et al., 2006, 2007). This high angular resolution imaging can enable
measurements of the lens-source separation, relative proper motion, and lens
flux which can then be used with mass-luminosity relations (Henry & McCarthy,
1993; Henry et al., 1999; Delfosse et al., 2000) to calculate a direct mass
for the host.
This current analysis is part of the NASA Keck Key Strategic Mission Support
(KSMS) program, “Development of the WFIRST Exoplanet Mass Measurement Method”
(Bennett, 2018), which is a pathfinder project for the Nancy Grace Roman Space
Telescope (formerly known as WFIRST) (Spergel et al., 2015). For several years
now, the KSMS program has measured the masses of many microlensing host stars
and their companions (Bhattacharya et al., 2018; Vandorou et al., 2020;
Bennett et al., 2020; Blackman et al., 2021; Terry et al., 2021, 2022), all of
which are included in one of the most complete statistical studies of the
microlensing exoplanet mass ratio function (Suzuki et al., 2016, 2018). This
statistical study shows a break and likely peak in the mass-ratio function for
wide-orbit planets at about a Neptune mass which is at odds with the runaway
gas accretion scenario of the leading core accretion theory of planet
formation (Lissauer, 1993; Pollack et al., 1996), which predicts a planet
desert at sub-Saturn masses (Ida & Lin, 2004) for gas giants at wide orbits.
This paper is organized as follows: In Section 2 we present the light curve
re-analysis of MOA-2007-BLG-192 and explain the challenges in the modeling
posed by lack of photometric coverage and degeneracies. In Section 3, we
describe the high angular resolution HST and Keck adaptive optics (AO)
observations and analysis. Section 4 details our direct measurement of the
lens system flux and lens-source separation in the Keck and HST data which
allows us to reduce the total number of solutions. Section 5 describes the
newly derived lens system properties from the light curve modeling that
incorporates the high resolution imaging results. Finally, we discuss the
overall results and conclude the paper in Section 6.

##  2 Prior Studies of the Microlensing Event MOA-2007-BLG-192

###  2.1 Fitting the microlensing light curve

MOA-2007-BLG-192 (hereafter MB07192), located at RA (J2000) $=$ 18:08:03.80,
DEC (J2000) $=$ $-$27:09:00.27 and Galactic coordinates ($l,b=(4.03,-3.39)$)
was first alerted by MOA on May 24, 2007. Due to the faintness of the source
and poor weather at the MOA telescope, the event was not alerted until the day
that the planetary deviation was observed in the light curve.

Figure 1 shows the observed light curve with OGLE (blue) and MOA (red) data as
well as the best-fit planetary model (2L1S) from our re-analysis of the light
curve modeling. The original light curve analysis for this event was presented
by Bennett et al. (2008) (hereafter B08). The only photometric monitoring of
the target during magnification was conducted in OGLE-I and MOA-R bands. Due
to the faintness of the source, there is no direct $V$-band measurement of the
target from OGLE or MOA. In order to get a source color estimate, earlier
studies used the photometric measurements from these two data sets and
converted to (V-I) color following Gould et al. (2010). As apparent in Figure
1, there are significant gaps in the photometric coverage for this event. Due
to this incomplete coverage, there are multiple binary lens solutions, with
similar mass-ratio that can equally explain the deviations in the light curve
due to a binary lens system.

This lack of coverage also resulted in large uncertainties in the measurement
of the angular source size and a poorly determined angular Einstein radius,
$\theta_{E}$. However, these various solutions all gave a low mass planetary
system with a mass ratio of $q\sim 2\times 10^{-4}$, and with quite large
errors on the reported $q$’s. Using the constraints from microlensing parallax
and the source star size, B08 concluded that the system was composed of a
$0.06^{+0.028}_{-0.021}M_{\odot}$ object orbited by a
$3.3^{+4.9}_{-1.6}~{}M_{\oplus}$ super-Earth. We note at the time of the B08
publication the MOA team was unaware of systematics in their photometry due to
chromatic differential refraction effects (Bennett et al., 2012a). This led to
an erroneous measurement of microlensing parallax ($\pi_{E}$) reported in
their study. Further, the caustic-crossing models presented in B08 contributed
to relatively small error bars on the derived planet mass (see Figure 5 in
B08). These caustic-crossing models have now been largely ruled out by this
study, therefore the planet mass error bars have increased (e.g. Section 5).

###  2.2 Constraining the lensing system with adaptive optics

Kubas et al. (2012) (hereafter K12) obtained two epochs with NACO AO imaging
on the Very Large Telescope (VLT) shortly after the peak of the microlensing
event when the target was still magnified by a factor of 1.23, as well as 18
months later at baseline. They observed in three bands, $J,~{}H,~{}K_{S}$,
this was the first microlensing event for which a fairly large AO data set had
been obtained. The AO data was reduced with the Eclipse package (Devillard,
1997) and the authors performed PSF photometry using the Starfinder tool
(Diolaiti et al., 2000). The absolute calibration was performed by a two-stage
process using 2MASS and data collected by the IRSF telescope in South Africa.
Knowing the source flux from the microlensing fit, they detected excess flux
in all three near-IR bands. Assuming that all the excess flux comes from the
lens, they obtained new constraints on the lensing system. Combining the
results of the two epochs, they derived that the lens has the following
magnitudes: $J_{L}=20.73\pm 0.32,~{}H_{L}=19.94\pm 0.35,~{}K_{L}=19.16\pm
0.20$. Using these constraints, and the (erroneous) microlensing parallax fit
by B08, they concluded that the lensing system is a
$0.084^{+0.015}_{-0.012}M_{\odot}$ M dwarf at a distance of $660^{+100}_{-70}$
pc orbited by a $3.2^{+5.2}_{-1.8}~{}M_{\oplus}$ super-Earth at
$0.66^{+0.51}_{-0.22}$ AU.

###  2.3 Why revisiting this system?

MB07192 is an important event from the Suzuki et al. (2016) sample of cold
planets. Its mass ratio is in the region where a change of slope has been
observed in the mass-ratio function. Also MOA have recently improved their
photometry methods, so we have re-reduced the MOA photometry following Bond et
al. (2017). This re-reduction includes corrections for systematic errors due
to chromatic differential refraction (Bennett et al., 2012a). This has direct
consequences on the microlensing model compared to the initial studies, which
affects the fitting parameters like microlensing parallax, finite size of the
source star, and other higher order effects. Additionally, over the years we
have refined our procedures to process, analyze, and calibrate AO data as well
as update extinction correction calculations. We will therefore adopt our
standard method described by (Beaulieu et al., 2018) and re-analyze the
$K_{S}$ NACO data.

Finally, we have obtained recent Keck-NIRC2 and HST observations in 2018 and
2023, which should give us the opportunity to independently resolve the source
and lens and measure the magnitude and direction of their relative proper
motion.

Figure 1: Best fit light curve with constraints from the high resolution
follow-up data as described in section 3. The 2L1S model shown is from the
second column of Table 5 with $u_{0}<0$ and $s<1$.  Table 1: New HST and Keck
observations in this work

Epoch (UT) | Instrument | PA | Filter | $T_{\textrm{exp}}$ | $N_{\textrm{exp}}$ | $\Delta t$ | Reference
---|---|---|---|---|---|---|---
(yyyy-mm-dd) |  | (deg) |  | (sec) |  | (yr) |
2012-03-30 | WFC3$-$UVIS | 131.8 | F606W (V) | 1760 | 8 | 4.85 | (a)
|  |  | F814W (I) | 1640 | 8 |  |
2014-03-30 | WFC3$-$UVIS | 131.8 | F606W (V) | 1760 | 8 | 6.85 | (b)
|  |  | F814W (I) | 1640 | 8 |  |
2018-08-06∗ | NIRC2 | 0.0 | $K_{S}$ | 900 | 15 | 11.20 | (c)
2023-08-06 | WFC3$-$UVIS | 309.5 | F814W (I) | 600 | 2 | 16.20 |

††footnotetext: Note: $\Delta t$ gives the amount of time (in years) since the
peak of the microlensing event. ∗ The 2018 epoch is from Keck, all other
epochs are from HST. References. (a) Bennett et al. (2012b), (b) Bennett et
al. (2014), (c) Bennett (2018), (d) Sahu et al. (2023)

##  3 High angular resolution follow-up with HST and KECK

###  3.1 Preparing the absolute calibration data set

We use our own re-reduction of data from the VVV survey (Minniti et al., 2010)
obtained with the 4m VISTA telescope at Paranal (see Beaulieu et al. (2018)).
We cross identified these $JHK_{S}$ catalogues with the VI OGLE-III map
(Udalski et al., 2015). We then obtain an OGLE-VVV catalogue of 8500 objects
with $VIJHK_{S}$ measurements, covering the footprint of the HST and KECK
observations. We subsequently used this catalog to calibrate HST and KECK
data, and we also revisit the VLT/NACO data.

###  3.2 Keck NIRC2

The target MB07192 was observed with the NIRC2 instrument on Keck-II in the
$K_{\textrm{short}}$ band ($\lambda_{c}=2.146\mu m$, hereafter Ks) on August 5
and 6, 2018. The two nights of data were combined using the KAI reduction
pipeline (Lu, 2022). The pipeline registers the images together, applies flat
field correction, dark subtraction, as well as bad pixel and cosmic ray
masking before producing the final combined image that we analyze. The data
from both nights are of similar quality, with an average point spread function
(PSF) full width at half maximum (FWHM) of 66.2 mas for the August 5 data, and
67.5 mas for the August 6 data.

Figure 2: Top Left: The co-added sum of 15 Keck NIRC2 narrow camera images,
each with an exposure time of 60 seconds. The target is indicated with a
square outline. Top Right: Zoomed image of the MB07192 blended source and lens
stars. The magnitude of the separation in this epoch is $29.3\pm 1.1$ mas.
Bottom Left: The residual image from a single-star PSF fit with DAOPHOT. A
clear signal is seen due to the blended stellar profiles. Bottom Right: The
residual image for a simultaneous two-star PSF fit, showing a significantly
improved subtraction. The color bar represents the pixel intensity (or counts)
in the bottom panel residual images.

For the 2018 Ks band observations, both the NIRC2 wide and narrow cameras were
used. The pixel scales for the wide and narrow cameras are 39.69 mas/pixel and
9.94 mas/pixel, respectively. All of the images were taken using the Keck-II
laser guide star adaptive optics (LGSAO) system. For the narrow data, we
combined 15 flat-field frames, six dark frames, and 15 sky frames for
calibrating the science frames. A total of 15 Ks band science frames with an
integration time of 60 seconds per frame were reduced using KAI which corrects
instrumental aberrations and geometric distortion (Ghez et al., 2008; Lu et
al., 2008; Yelda et al., 2010; Service et al., 2016).

Because of the potentially significant effects of a spatially varying PSF in
ground-based AO imaging (Terry et al., 2023), we made a careful selection of
bright and isolated reference stars that were used to build the empirical PSF
model. Each of the eight selected PSF reference stars has magnitude
$-0.7<m<0.7$ and separations $-4\arcsec<r<4\arcsec$ from the target. The
resulting PSF model has a FWHM in the x and y directions of 6.8 pixels and 6.5
pixels, respectively.

Further, a co-add of 4 wide camera images were used for photometric
calibration using the catalogue prepared in section 3.1. The wide camera
images were flat-fielded, dark current corrected, and stacked using the SWarp
software (Bertin, 2010). We performed astrometry and photometry on the co-
added wide camera image using SExtractor (Bertin & Arnouts, 1996), and
subsequently calibrated the narrow camera images to the wide camera image by
matching 80 bright isolated stars in the frames. The uncertainty resulting
from this procedure is 0.05 magnitudes.

HST, VLT NACO, and Keck single-star PSF photometry  Data set $V$ $I$ $J$ $H$
$K_{S}$ HST 2012 $23.88\pm 0.02$ $20.93\pm 0.01$ $19.04\pm 0.01$ $18.28\pm
0.01$ HST 2014 $23.83\pm 0.02$ $20.90\pm 0.01$ K12 NACO ep.1 $19.21\pm 0.04$
$18.28\pm 0.04$ $17.95\pm 0.04$ K12 NACO ep.2 $19.32\pm 0.07$ $18.55\pm 0.11$
$17.99\pm 0.04$ NACO ep.1 $17.80\pm 0.05$ NACO ep.2 $17.92\pm 0.05$ KECK 2018
$17.88\pm 0.05$ HST 2023 $21.01\pm 0.04$ ††footnotetext: Note: We provide the
magnitudes measured at the source position for MB07192. We recall the measured
magnitudes from K12 for the two epochs. We underline that the time of the
first epoch, the source was still amplified by $\sim 0.15$ mag. We re-analyzed
the NACO $K_{S}$ images and calibrated against VVV for the two epochs.
Finally, we provide our flux calibration in $K_{S}$ with Keck-NIRC2.

###  3.3 Resolving the Source and Lens in Keck/NIRC 2

Given the lens detections from HST 2012 and 2014 data, the lens and source
stars have a predicted separation of $0.65\times$FWHM in 2018, we expect the
stars to be partially resolved, so it is necessary to use a PSF fitting
routine to measure both targets separately. Following the methods of
Bhattacharya et al. (2018) and Terry et al. (2021), we use a modified version
of the DAOPHOT-II package (Stetson, 1987), that we call DAOPHOT_MCMC, to run
Markov Chain Monte Carlo (MCMC) sampling on the pixel grid encompassing the
blended targets. Further details of the MCMC routine are given in Terry et al.
(2021) and Terry et al. (2022). The stellar profile does not appear to be
significantly extended in the NIRC2 data, as seen in the top-right panel of
Figure 2. However, using DAOPHOT_MCMC to fit a single-star PSF to the target
produces the residual seen in the lower-left panel of Figure 2, which shows a
strong signal due to extended flux from the blended star (presumed lens). Re-
running the routine in the two-star fitting mode (e.g. simultaneously fit two
PSF models) produces a significantly better fit as expected, with a $\chi^{2}$
improvement of $\Delta\chi^{2}\sim 784$. The two-star residual is nearly
featureless, as can be seen in the lower-right panel of Figure 2. Table 3.7
shows the calibrated magnitudes for the two stars of $K_{1}=18.94\pm 0.10$ and
$K_{2}=18.39\pm 0.09$.

The final error bars on the Keck photometry and astrometry that we report in
Tables 3.7 and 4 are determined with a combination of MCMC and jackknife
errors. The jackknife method (Quenouille, 1949, 1956; Tierney & Mira, 1999)
allows us to determine uncertainties due to PSF variations between individual
Keck images. From the total of 15 Keck images, we construct $N=14$ co-added
jackknife images, with each combined image containing all but one successive
image in each iteration. This method is also sometimes called the “drop-one”
or “leave-one-out” method. The jackknife errors are then calculated via the
equation:

$\sigma_{x}=\sqrt{\frac{N-1}{N}\sum(x_{i}-\bar{x})^{2}},$ (1)

where $x_{i}$ is a given value for the $i$th jackknife image, and $\bar{x}$ is
the mean value for the jackknife images. See Bhattacharya et al. (2021) and
Terry et al. (2022) for further details on the jackknife method.

From the dual-star PSF fitting in Keck, we find a difference in $K$-band
magnitude between the two blended stars of $K_{S1}-K_{S2}=-0.55\pm 0.13$.
Since the two stars are similar enough magnitude in $K$, at this point we
simply apply arbitrary labels of ‘star 1’ and ‘star 2’ to the two stars in
Keck. However, our subsequent analysis of the HST data will allow us to
confidently determine which star is the source and which is the lens (Section
3.7).

###  3.4 HST WFC3/UVIS: 2012-2014-2023 Data

The target MB07192 was observed a total of three times with the WFC3/UVIS
camera on the Hubble Space Telescope (HST). The first observation took place
on 23 February 2012 in the F555W, F814W, F125W and F160W filters. A second
epoch of observations were obtained on 30 March 2014 with the same four
filters, and finally a third epoch was obtained on 06 August 2023 with just
two exposures in the F814W filter. The datasets are from proposals GO-12541,
GO-13417 (PI: Bennett), and GO-16716 (PI: Sahu), and were obtained from the
Mikulski Archive for Space Telescopes (MAST). We flat-fielded, stacked,
corrected for distortions and performed PSF photometry with the program
DOLPHOT (Dolphin, 2000). Because of the disparate sensitivities, the visible
images obtained with the UVIS module (F555W and F814W) and the near-IR images
obtained with the IR module (F125W and F160W) were reduced separately.

The drizzled, stacked frames with the astrometric solutions from STScI were
used as the reference image for source finding. We used Dolphot to correct for
pixel area distortions, remove cosmic rays, and perform PSF fitting photometry
of the individual frames. Because of the crowded nature of the field, the sky
background was determined iteratively and many artifacts due to bright stars
were rejected. Dolphot uses a library of reference PSFs for each filter and
applies corrections to these during photometry to minimize the residuals when
the photometered stars are subtracted. The PSF-fit magnitudes are aperture
corrected to a standard circular aperture of radius 0$\farcs$5 and matched
across all filters. In order to eliminate marginal detections and stars badly
impacted by bright neighbors, we rejected stars with signal-to-noise ratio
$<$5 and crowding parameter $>$0.75 as well as any objects flagged by the
software as too sharp or too extended to be stellar. The output magnitudes are
given in the STScI Vegamag system (m555, m814, m125, m160). Note that we used
only main sequence stars for calibration, and ignore color terms between VVV
and the STSCI Vegamag system.

###  3.5 HST Multiple Star PSF Fitting

In addition to the photometry obtained using Dolphot, we performed multi-star
PSF fitting on the target in all three of the HST epochs. Since the 2012 and
2014 epochs are approximately 6.4 and 4.4 years before the Keck observations,
we expect the separation between the source and lens star to be $0.619\times$
and $0.734\times$ smaller in these HST images compared to Keck. The 2023 HST
images were taken approximately 5.0 years after the Keck observations, so we
expect the lens and source separation to be $1.445\times$ larger in this epoch
than the Keck images. Because each HST observation is separated by at least
several years and some epochs were taken at different position angles (PA), we
performed coordinate transformations between the Keck observation and each of
the HST observations independently. We do this by cross-matching ${\sim}$two
dozen isolated and bright (but not saturated) stars in each dataset, and then
calculate the linear (i.e. first order) transformation between the pixel
positions in the HST and Keck catalogs. The transformations are listed as
follows:

$\begin{split}\textrm{2012:}\hskip
28.45274ptx_{hst}=-0.170x_{keck}+0.186y_{keck}+804.011\\\
y_{hst}=-0.184x_{keck}-0.169y_{keck}+1175.664\\\ \\\ \textrm{2014:}\hskip
28.45274ptx_{hst}=-0.169x_{keck}+0.186y_{keck}+802.920\\\
y_{hst}=-0.185x_{keck}-0.169y_{keck}+1175.561\\\ \\\ \textrm{2023:}\hskip
28.45274ptx_{hst}=0.164x_{keck}-0.188y_{keck}+283.268\\\
y_{hst}=0.187x_{keck}+0.166y_{keck}+225.342\end{split}$

The average RMS scatter for these relations is $\sigma_{x}\sim 0.25$ and
$\sigma_{y}\sim 0.20$ HST/UVIS pixels for the same 16 stars used in each
transformation. Given the varying baseline between the earliest and latest HST
epochs and the 2018 Keck epoch, this scatter of ${\sim}13$ mas can be at least
mostly explained by an average proper motion of $\sim$2.5 mas/yr in each
direction. We note the 2012 and 2014 data were taken with the larger sub-array
chip, UVIS2-2K2C-SUB, while the recent 2023 data were taken with the smaller
chip, UVIS2-C1K1C-SUB. Using the smaller sub-array chip allows for CTE losses
to be minimized as the detector has measurably degraded since the 2012 and
2014 epochs were obtained.

This HST analysis was performed using a modified version of the codes
developed in Bennett et al. (2015) and Bhattacharya et al. (2018), which
analyzes the original individual images with no resampling. This avoids any
loss in resolution that can occur when dithered, undersampled images are
combined. The top-left panel of Figure 3 shows the target and surrounding HST
stars from the combined I-band image in 2014. A zoom on the target is shown in
the top-right panel, which also shows an unrelated star to the North of
MB07192. The lower panels of Figure 3 show the residual images after fitting a
single PSF model and simultaneously fitting two PSF models to the blended
stars. The single-star residual shows the typical signal that we would expect
for two highly blended stars, the direction and amplitude of the measured
separation here is consistent with the 2018 detection in Keck (Table 4). The
$V$-band detection is at a lower confidence than the $I$-band detection
(${\sim}2\sigma$ vs. $>5\sigma$), this leads to a larger error on the measured
$V$-band lens magnitude (Table 3.7) and significantly larger error on the
measured lens-source separations in HST $V$-band (see Table 4).

Given the strong detection in the Keck data, we impose separation constraints
when analyzing the earlier HST epochs, particularly the 2012 epoch in
$V$-band, where the lens detection is most marginal. We convert the Keck
relative proper motion value ($\mu_{\textrm{rel,H}}=2.63\pm 0.13$ mas/yr) to
constraints on the position of the lens and source in the 2012 HST images,
while taking into account the 4.8520 years between the microlensing event peak
and the 2012 Hubble observations. We note that in all of our HST PSF fitting
procedures we include the unrelated faint nearby neighbor as a third star to
avoid any interference of its PSF with our measurement of lens-source
separation. Between the 2012 and 2023 epochs, the unrelated neighbor star
moves ${\sim}1$ HST pixel closer to MB07192.

For all three HST epochs (2012, 2014, 2023), the F814W fits converge to a
consistent solution with ‘star 1’, to the North as the slightly brighter star
($\Delta m_{\textrm{F814W}}\,{\sim}\,$0.1). For the two epochs of F555W data
(2012, 2014), the PSF fit converged to a unique solution in the 2014 data
without requiring any separation constraint but the 2012 fit required a
separation constraint to be imposed, as mentioned previously. In all HST F814W
fits, ‘star 2’, to the South is slightly fainter than ‘star 1’. Our reduction
and fitting code places the star coordinates from both filters into the same
reference system, so all stars have positions that are consistent between both
passbands. The best-fit magnitudes (calibrated to OGLE $V$ and $I$) from the
2014 HST epoch are given in Table 3.7, and the best-fit positions in all
epochs and filters are given in Table 4.

The HST data were calibrated to the OGLE-III catalog (Szymański et al., 2011)
using eight relatively bright isolated OGLE-III stars that were matched to HST
stars. The same eight stars were used in each epoch. For the best quality HST
data in both filters (i.e. 2014 epoch), the calibrations yielded
$I_{1}=21.56\pm 0.15$, $V_{1}=24.93\pm 0.32$, $I_{2}=21.68\pm 0.16$, and
$V_{2}=24.25\pm 0.18$. The magnitude of both lens and source stars combined is
measured to significantly higher precision, $I_{12}=20.87\pm 0.02$ and
$V_{12}=23.79\pm 0.04$. This combined magnitude allows us to place a stronger
constraint when re-evaluating the light curve photometry. During our PSF
fitting, the two blended stars can trade flux back and forth which results in
larger errors on the individual stars’ magnitude.

Extinction estimates towards the source  Ext. map $E(V-I)$ $E(J-K_{s}$)
$A_{V}$ $A_{I}$ $A_{J}$ $A_{H}$ $A_{K_{S}}$ B08 $1.12\pm 0.09$ $2.73\pm 0.13$
$1.61\pm 0.10$ K12 $0.43\pm 0.14$ $0.72\pm 0.10$ $0.46\pm 0.10$ $0.29\pm 0.10$
ext. calc $1.10\pm 0.13$ $2.43\pm 0.16$ $1.33\pm 0.1$ this study $\bf 1.10\pm
0.06$ $\bf 0.33\pm 0.02$ $\bf 2.45\pm 0.15$ $\bf 1.35\pm 0.07$ $\bf 0.44\pm
0.02$ $\bf 0.24\pm 0.01$ $\bf 0.11\pm 0.01$ ††footnotetext: Note. We summarize
here the different estimates for the extinction towards the source, in the
initial study (B08), the follow up work with NACO data (K12), and this study.
Extinction values are derived from a combination of the methods described in
Nishiyama et al. (2009), Bennett et al. (2010), Nataf et al. (2013), and Surot
et al. (2020) (see section 3.6).

Figure 3: Similar to Figure 2, but for the 2014 HST data (eight exposures).
The zoomed inset and residual image panels show 100 $\times$ 100 super-sampled
pixels where the observed dither offsets are accurate to 0.01 pixels. The
color bar represents the pixel intensity (counts) seen in the top-right and
lower-left/right panels.

###  3.6 The Extinction Towards the Source star

The OGLE extinction calculator111https://ogle.astrouw.edu.pl/cgi-
ogle/getext.py is a standard way to estimate the extinction for a galactic
bulge field, and it has been commonly used for many years. The calculator is
derived from the reddening and extinction study of Nataf et al. (2013). For
MB07192, the calculator gives $E(V-I)=1.10\pm 0.127$ and an extinction
$A_{I}=1.3$. These standard extinction maps have recently been superseded by
the Surot et al. (2020) analysis of the VVV survey and give $E(J-Ks)=0.329\pm
0.018$ at the location of the target. We then follow Nataf et al. (2013) in
adopting $E(J-K_{S})/E(V-I)=0.3433$, and
$A_{I}=0.7465E(V-I)+1.37E(J_{K_{S}}),$ with which we derive the extinctions.
Following Nishiyama et al. (2009), we obtain the extinctions summarized in
Table 3.5 along with prior estimates from the literature. For our subsequent
analysis, we adopt the numbers from the last row of Table 3.5 (i.e. this
work).

###  3.7 Identifying the Source and Lens Stars

With the HST $V$ and $I$-band measurements described in Section 3.5, we can
now attempt to determine which star is the source and which is the lens. As
mentioned previously, since the original discovery paper of Bennett (2008),
the MOA group has begun detrending its photometry to remove systematic errors
caused by differential atmospheric refraction (Bennett & Rhie, 2002; Bond et
al., 2017). Following Bond et al. (2017), we correct the MOA photometric data
and perform re-modeling of the MOA + OGLE photometry. This re-analysis yields
an estimate of the source star $I$-band magnitude of $I_{S}=21.8\pm 0.05$ with
a color of $V_{S}-I_{S}=2.7\pm 0.2$. This source $I$-band magnitude is within
$1\sigma$ of the HST $I$-band magnitude for ‘star 2’, and just over $1\sigma$
fainter than the HST $I$-band magnitude for ‘star 1’. Additionally, this
estimated source color is a closer match to the measured HST $V-I$ color of
‘star 2’ ($2.57\pm 0.24$) as can be seen in Figure 4. These results support
the identification of ‘star 2’ as the true source star. However, since the
ground-based $V$-band estimate of the source comes from a relatively weak
relationship (OGLE I $-$ MOA R), we conduct a further verification of the
source and lens using their relative proper motions as measured in HST and
Keck.

We calculate the 2D prior probability distribution of the lens-source relative
proper motion using the Koshimoto et al. (2021) Galactic model to determine
which stars are the preferred lens and source. Figure 5 shows this proper
motion distribution for MB07192, with two locations for the possible lens
(North and South lens). We calculate these $\mu_{\textrm{rel}}$ priors from
the distribution of single lens stars that reproduces the Einstein radius
crossing time that accounts for the host star mass, i.e., $t_{E}/\sqrt{1+q}$.
The results show that there is a preference for the North star to be the lens
star considering the stellar distribution along this sight-line. The relative
probability is $P_{N}/P_{S}=25.88/12.43=2.08$; this means the North star is
$>2\times$ more likely to be the lens than the South star. So, using the
locations of ‘star 1’ and ‘star 2’ on the CMD (Figure 4) and the relative
proper motion prior probability distribution (Figure 5), we identify star 2 to
be the source star and star 1 to be the lens star which hosts the planet. We
therefore label the source and lens on the CMD in Figure 4 as well as the
stars in Table 3.7.

Figure 4: The observed color-magnitude diagram (CMD) for the MB07192 field.
The OGLE-3 stars within 90 arcseconds of MB07192 are shown in black, with the
HST CMD of all detected sources from the 2014 epoch shown in green. The red
point indicates the location of the red clump centroid, and the purple and
orange points show the source and lens colors and magnitudes from the 2014 HST
observations.  Figure 5: The probability distribution for the north and east
components of lens-source relative proper motion ($\mu_{\textrm{rel}}$) using
the Galactic model from Koshimoto et al. (2021) and genulens (Koshimoto &
Ranc, 2021). The possible lens positions (North and South) are plotted in
black and given by the relative motion of the two stars detected in the HST
and Keck data. Importantly, this distribution uses $t_{E}$ values that are
close to the measured $t_{E}$ value from the light curve modeling
($t_{E}\,{\sim}\,99.5$ days). This implies that the North star is $>2\times$
more likely to be the lens than the South star.

HST and Keck multi-star PSF photometry  Star $V$ Mag $I$ Mag $K$ Mag Star 1
(Lens) $24.93\pm 0.32$ $21.56\pm 0.15$ $18.39\pm 0.09$ Star 2 (source)
$24.25\pm 0.18$ $21.68\pm 0.16$ $18.94\pm 0.10$ Lens $+$ Source $23.79\pm
0.04$ $20.87\pm 0.02$ $17.88\pm 0.05$ ††footnotetext: Note. $V$ and $I$
magnitudes are calibrated to the OGLE-3 system and $K$ magnitudes are
calibrated to the 2MASS system as described in section 3.

##  4 Lens-Source Relative Proper Motion

The Keck (2018) and HST (2012, 2014, 2023) follow up observations were taken
between 4.85 and 16.20 years after the peak magnification which occurred in
May 2007. The motion of the source and lens on the sky is the primary cause
for their apparent separation, however there is also a small component that
can be attributed to the orbital motion of Earth. As this effect is of order
$\leq 0.10$ mas for a lens at a distance of $D_{L}\geq 2$ kpc, we are safe to
ignore this contribution in our analysis as it is much smaller than the error
bars on the stellar position measurements. The mean lens-source relative
proper motion is measured to be
$\mu_{\textrm{rel},H}=(\mu_{\textrm{rel,H,E}},\mu_{\textrm{rel,H,N}})=(0.653\pm
0.291,2.790\pm 0.274)$ mas yr-1, where ‘H’ indications that these measurements
were made in the heliocentric reference frame, and the ‘E’ and ‘N’ subscripts
represent the East and North on-sky directions respectively.

Our light curve modeling is performed in the geocentric reference frame that
moves with the Earth at the time of the event peak. Thus, we must convert
between the geocentric and heliocentric frames by using the relation given by
Dong et al. (2009):

$\mu_{\textrm{rel,H}}=\mu_{\textrm{rel,G}}+\frac{{\nu_{\earth}}{\pi_{\textrm{rel}}}}{AU}\
,$ (2)

where $\nu_{\earth}$ is Earth’s projected velocity relative to the Sun at the
time of peak magnification. For MB07192 this value is
$\nu_{\earth\textrm{E,N}}=(25.772,1.237)$ km/sec = $(5.433,0.261)$ AU yr-1 at
HJD${}^{\prime}=4245.45$. With this information and the relative parallax
relation $\pi_{\rm{rel}}\equiv AU(1/D_{L}-1/D_{S})$, we can express equation 2
in a more convenient form:

$\mu_{\textrm{rel,G}}=\mu_{\textrm{rel,H}}-(5.433,0.261)\times(1/D_{L}-1/D_{S})\,\textrm{mas/yr},$
(3)

where $D_{L}$ and $D_{S}$ are the lens and source distance, respectively,
given in kpc. We have directly measured $\mu_{\textrm{rel,H}}$ from the HST
and Keck data, so this gives us the relative proper motion in the geocentric
frame of $\mu_{\textrm{rel,G}}=3.10\pm 0.19\,$mas/yr. As a reminder, the lens
and source distance we use in Equation 2 are inferred by the best-fit light
curve results which include constraints from the high-resolution imaging.

Figure 6: Left: The MCMC distribution for $\pi_{E}$ from the light curve
modeling without any constraint from the high-resolution imaging. Right: The
MCMC distribution for $\pi_{E}$ from the light curve modeling with the
inclusion of high-resolution imaging constraints. The color bar represents the
$\chi^{2}$ differences from the best-fit light curve model: red represents
$\Delta\chi^{2}<1$, orange represents $\Delta\chi^{2}<4$, green represents
$\Delta\chi^{2}<16$, and purple represents $\Delta\chi^{2}<25$. The two
components of the relative proper motion that were measured by HST and Keck
allow the north component, $\pi_{E,N}$ to be tightly constrained.

Measured Lens-Source Separations from HST and Keck Separation (mas) Year East
North Total $2012\,(HST\,\,V)$ $2.28\pm 4.60$ $15.58\pm 4.96$ $15.75\pm 6.78$
$(HST\,\,I)$ $1.01\pm 1.39$ $18.17\pm 1.71$ $18.20\pm 2.23$ $2014\,(HST\,\,V)$
$9.84\pm 4.74$ $22.17\pm 4.01$ $24.26\pm 6.22$ $(HST\,\,I)$ $3.12\pm 1.23$
$21.62\pm 1.03$ $21.84\pm 1.63$ $2018\,(Keck\,\,K)$ $-0.34\pm 1.03$ $29.37\pm
1.01$ $29.38\pm 1.46$ $2023\,(HST\,\,I)$ $-1.97\pm 1.49$ $43.13\pm 1.68$
$43.17\pm 2.26$ $\mu_{\textrm{rel,H,E}}$(mas/yr)
$\mu_{\textrm{rel,H,N}}$(mas/yr) $\mu_{\textrm{rel,H}}$(mas/yr) weighted mean
$0.63\pm 0.29$ $2.76\pm 0.27$ $2.83\pm 0.37$

##  5 Lens System Properties

As has been shown in prior work (Bhattacharya et al., 2018; Bennett et al.,
2020; Terry et al., 2021; Rektsini et al., 2024), we find it particularly
useful to apply constraints from the high resolution follow-up observations to
the light curve models (we deem this “image-constrained modeling”). This can
help prevent the light curve modeling from exploring areas in the parameter
space that are excluded by the high resolution follow-up observations. We
refer the reader to Bennett et al. (2023) for a full description of the
methodology for applying these constraints to the modeling and an exhaustive
list of the light curve + high-res imaging parameters that are important for
obtaining full solutions for planetary lens systems in this context.

We use a modified version of the light curve modeling code eesunhong (Bennett
& Rhie, 1996; Bennett, 2010) to incorporate constraints on the brightness and
separation of the lens and source stars from the high resolution imaging via
HST and Keck (Bennett et al., 2023). Ideally, we want to use a mass-distance
relation coupled with empirical mass-luminosity relations to infer the mass
and distance of the host star. In order to do this, we need to know the
distance to the source star, $D_{S}$. Thus we are required to include the
source distance as a fitting parameter in the re-modeling of the light curve
with imaging constraints. We include a weighting from the Koshimoto et al.
(2021) Galactic model as a prior for $D_{S}$, and we also use the same
Galactic model to obtain a prior on the lens distance for a given value of
$D_{S}$. This prior is not used directly in the light curve modeling, but
instead is used to weight the entries in a sum of Markov chain values.

The angular Einstein radius, $\theta_{E}$, and the microlensing parallax
vector, $\pi_{E}$, give relations that connect the lens system mass to the
source and lens distances, $D_{S}$ and $D_{L}$ (B08, Gaudi (2012)). The
relations are given by:

$M_{L}=\frac{c^{2}}{4G}\theta_{E}^{2}\frac{D_{S}D_{L}}{D_{S}-D_{L}},$ (4)

and

$M_{L}=\frac{c^{2}}{4G}\frac{\textrm{AU}}{{\pi_{E}}^{2}}\frac{D_{S}-D_{L}}{D_{S}D_{L}},$
(5)

where $M_{L}$ is the lens mass, $G$ and $c$ are the gravitational constant and
speed of light. $D_{L}$ and $D_{S}$ are the distance to the lens and source,
respectively. As mentioned previously, the measurement of
$\mu_{\textrm{rel,H}}$ from the high resolution imaging allows us to measure
$\mu_{\textrm{rel,G}}$ to high precision, which ultimately lets us determine
$\theta_{E}$. Additionally, the two components of the $\mu_{\textrm{rel}}$
measurement enables a much tighter constraint on the possible values of
$\pi_{E,N}$. The north direction in particular is usually only weakly
constrained because it is typically perpendicular to the orbital acceleration
of the observer for microlensing events towards the Galactic bulge. The
geocentric relative proper motion and the microlensing parallax are related
by:

$\boldsymbol{\pi}_{E}=\frac{\pi_{\textrm{rel}}}{t_{E}}\frac{\boldsymbol{\mu}_{\textrm{rel,G}}}{|\mu_{\textrm{rel,G}}|^{2}},$
(6)

so with the measurement of $\pi_{E,E}$ and $\mu_{\textrm{rel,H}}$, we can use
equations 2 and 6 to solve for $\pi_{E,N}$. This tight constraint on the north
component of the microlensing parallax can be seen in Figure 6, where the left
panel shows the distribution in $\pi_{E,N}$ largely unconstrained. When the
constraint from the high resolution measurement of $\mu_{\textrm{rel}}$ is
applied, the distribution collapses to a relatively small region centered on
$\pi_{E,N}\,{\sim}\,0.3$.

Best Fit Model Parameters with $\mu_{\textrm{rel}}$ and Magnitude Constraints
$u_{0}<0$ $u_{0}>0$ Parameter $s<1$ $s>1$ $s<1$ $s>1$ MCMC Averages $t_{E}$
(days) $99.469$ $98.722$ $100.111$ $99.262$ $99.577\pm 3.919$ $t_{0}$ (HJD′)
$4245.446$ $4245.448$ $4245.431$ $4245.436$ $4245.440\pm 0.0070$ $u_{0}$
$-0.0027$ $-0.0029$ $0.0035$ $0.0004$ $-0.0027\pm 0.0012$ ($u_{0}>0$)
$0.00195\pm 0.00155$ $s$ $0.9102$ $1.0311$ $0.8780$ $1.1441$ $0.8728\pm
0.0667$ ($s>1$) $1.0951\pm 0.0938$ $\alpha$ (rad) $2.1061$ $1.9288$ $4.5473$
$3.2862$ $2.4364\pm 0.5075$ ($u_{0}>0$) $3.9167\pm 0.6305$ $log(q)$ $-3.9751$
$-3.9975$ $-3.6017$ $-3.7937$ $-3.8690\pm 0.5253$ $t_{*}{}$ (days) $0.0562$
$0.0539$ $0.0567$ $0.0547$ $0.0551\pm 0.0044$ $\pi_{\textrm{E,N}}$ $0.3161$
$0.3152$ $0.3119$ $0.3133$ $0.3154\pm 0.0218$ $\pi_{\textrm{E,E}}$ $-0.2364$
$-0.2308$ $-0.2338$ $-0.2300$ $-0.2359\pm 0.0474$ $D_{\textrm{s}}$ (kpc)
$7.8423$ $7.1562$ $6.9687$ $7.1156$ $7.049\pm 1.163$ Fit $\chi^{2}$ $4760.94$
$4760.97$ $4761.45$ $4761.53$

Additionally, since we have a direct measurement of lens flux in the $V$, $I$,
and $K$-bands, we utilize the Delfosse et al. (2000) empirical mass-luminosity
relations in each of these passbands as described by Bennett et al. (2018). We
consider the foreground extinction in each passband (i.e. Table 3.5) and
generate the relations in conjunction with the mass-distance relations given
by equations 4 and 5. Figure 7 shows the measured mass and distance of the
MB07192 lens. The blue (HST V), green (HST I), and red (Keck K) curves
represent the mass-distance relations obtained from the empirical mass-
luminosity relations with lens flux measurements given in Table 3.7. The
dashed lines represent the $1\sigma$ error from the Keck and HST measurements.
Further, the mass-distance relation obtained from the measurement of
$\theta_{E}$ (i.e. equation 4) is shown in solid brown. Considering only these
two relations (empirical mass-luminosity and $\theta_{E}$), there is overlap
for a significant amount of mass and distance space. This is sometimes
referred to as the “continuous degeneracy” (Gould, 2022). Fortunately this
degeneracy is broken when we include the constraint from the microlensing
parallax measurement, $\pi_{E}$, shown as the solid teal curve in Figure 7.

Table 5 shows the results of the four degenerate light curve models and the
Markov chain average for all four models. Although we are able to successfully
reduce the number of possible solutions presented in K12 by a factor of two,
the close/wide and $u_{0}$ degeneracies still remain. Further, the host star
mass is very precisely measured now, however the best-fit mass ratio, $q$,
remains largely uncertain because of poor sampling of the light curve. This
also results in a large error in the inferred planet mass (see Table 5).

Figure 7: The mass-distance relation for MB07192L with constraints from the
lens flux measurement in blue (HST V), green (HST I), and red (Keck K). Dashed
lines show the 1$\sigma$ error bars for each passband. The solid teal region
shows the mass-distance relation calculated using the microlensing parallax
measurement ($\pi_{E}$), and the solid brown region shows the mass-distance
relation calculated using the angular Einstein radius measurement
($\theta_{E}$).

The MB07192 lens system is located at a distance of ${\sim}2.2$ kpc and has a
log mass ratio of $log_{10}(q)=-3.87\pm 0.53$. The host star is directly
detected in several high resolution imaging passbands, enabling us to
precisely measure its mass to be $M_{\textrm{host}}=0.28\pm 0.04M_{\sun}$ with
a less-precisely measured mass of the planet to be
$m_{\textrm{planet}}=12.49^{+65.47}_{-8.03}M_{\oplus}$. These masses are
consistent with a planet with mass between a super-Earth and sub-Saturn
orbiting an M dwarf star near the bottom of the main sequence. We note the
most likely mass for the planet is in the super-Earth regime
(${\sim}3-12M_{\oplus}$), as given by the top-left panel in Figure 8. The
best-fit solution gives a 2D projected separation of $a_{\perp}=2.02\pm
0.44\,$AU. These physical parameters are calculated from the best-fit solution
which takes a combined weighting of several models along with a Galactic model
prior based on Koshimoto et al. (2021). Table 5 gives the derived lens system
physical parameters along with their 2$\sigma$ ranges. Lastly, Figure 8 shows
the final posterior probability distributions for the planetary companion
mass, host star mass, 2D projected separation, and lens system distance.

Lens System Properties with Lens Flux Constraints  Parameter Units Values &
RMS 2-$\sigma$ range Angular Einstein Radius ($\theta_{E}$) mas $0.854\pm
0.043$ $0.775-0.947$ Geocentric lens-source relative proper motion
($\mu_{\textrm{rel,G}}$) mas/yr $3.14\pm 0.15$ $2.84-3.44$ Host Mass ($M_{\rm
host}$) $M_{\sun}$ $0.28\pm 0.04$ $0.23-0.37$ Planet Mass ($m_{\rm p}$)
$M_{\earth}$ $12.49^{+65.47}_{-8.03}$ $2.75-105.06$ 2D Separation
($a_{\perp}$) AU $2.02\pm 0.44$ $1.26-2.86$ 3D Separation ($a_{3\textrm{d}}$)
AU $2.44^{+1.39}_{-0.68}$ $1.38-9.65$ Lens Distance (DL) kpc $2.16\pm 0.30$
$1.75-2.76$ Source Distance (DS) kpc $7.05\pm 1.17$ $4.83-9.38$

##  6 Discussion & Conclusion

Our high resolution follow up observations of the microlensing target MB07192
have allowed us to make a direct measurement of the lens system flux in
multiple passbands ($V$, $I$, $K$) as well as a precise determination of the
amplitude and direction of the lens-source relative proper motion
$\mu_{\textrm{rel}}$. We perform simultaneous multiple-star PSF fitting to
obtain best-fit positions and fluxes for both stars across two independent
platforms (HST and Keck). The lens flux measurements we make enable us to use
mass-luminosity relations and new constraints on higher order light curve
effects ($\pi_{E}$, $\theta_{E}$) to measure a precise mass and distance for
the lens system.

Further, we demonstrate the importance of applying constraints from high
resolution follow up imaging on the microlensing light curve modeling.
Particularly, the microlensing parallax effect, which is present in all
microlensing events observed from a heliocentric reference frame, is tightly
constrained when the direction of $\mu_{\textrm{rel}}$ can be measured through
high resolution imaging. This measurement is critically important for several
reasons; poor light curve sampling (i.e. for MB07192) can result in a lack of
a microlensing parallax signal from the light curve alone, even for long
timescale events. Second, the mass-distance relation that results from a
direct measurement of $\pi_{E}$ (via lens-source separation) allows for the
“continuous degeneracy” to be completely broken.

Figure 8: The posterior probability distributions for the lens system physical
parameters: planetary companion mass (upper-left), host mass (upper-right), 2D
projected separation (lower-left), and lens distance (lower-right). The
vertical black line shows the median of the probability distribution for each
parameter. The central 68% of the distributions are shown in dark blue with
the remaining central 95% shown in light blue.

Although the host mass and lens system distance have now been precisely
measured as a result of the direct detection in HST and Keck, the sampling of
the light curve photometry during the microlensing event remains poor. This
means that the large uncertainty in the mass ratio parameter, ($q$ in Table
5), results in a large error in the inferred mass of the planetary companion
($m_{\rm p}$ in Table 5). As previously mentioned in Section 2, the large
uncertainty in the planetary companion mass comes from a combination of
factors; the event is located in a MOA field with a relatively low cadence
which leads to poor sampling of the light curve, and the planetary signal was
not detected in real time. It was several days after the photometric peak that
the anomaly in the light curve was alerted. In conclusion, the distance to the
MB07192 lens system is ${\sim}3\times$ larger than previously reported, now at
a distance of approximately 2 kpc. Both the mass of the host star and
planetary companion are also $2-5\times$ larger than previously reported,
which now extends the possible mass range for the planet to a possible sub-
Saturn class planet. However, as the top-left panel of Figure 8 shows, the
most likely mass for the planetary companion remains in the super-Earth range
(${\sim}3-12M_{\oplus}$). The previous studies reported a smaller planet mass
and also underestimated the error bars on the planet mass for several reasons.
All of the B08 models report a too-large microlensing parallax value, which
led to a smaller derived planet mass than the median value of the planet mass
that we report here. Further, the B08 and K12 caustic-crossing models
contributed significant weighting to the combined results which gave much
smaller error bars on the derived planet mass. Our new results have ruled out
the caustic crossing models, which now gives larger error bars on the derived
planet mass, particularly the upper 1$\sigma$ error. The results of this work
have several implications for the upcoming RGES. If Roman is expected to
employ lens flux measurement methods similar to those described in this work,
then a careful selection of secondary observing filters must be made to avoid
or minimize instances of the “continuous degeneracy”. For example, the mass-
luminosity relation given by a bluer Roman passband would have a smaller
overlap with the mass-distance relation given by $\theta_{E}$ compared to
other redder Roman filters. This effect is more severe for nearby M dwarf
lenses (i.e. Figure 7). Also, for Roman detected events with very faint
sources or very short Einstein timescales that don’t have a measurable
microlensing parallax signal, a successful lens-source flux measurement by
Roman itself will be important for breaking possible degeneracies like those
discussed in this work. This paper is based in part on observations made with
the NASA/ESA Hubble Space Telescope, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.
The Keck Telescope observations and data analysis were supported by a NASA
Keck PI Data Award, 80NSSC18K0793, administered by the NASA Exoplanet Science
Institute. Data presented herein were obtained at the W. M. Keck Observatory
from telescope time allocated to the National Aeronautics and Space
Administration through the agency’s scientific partnership with the California
Institute of Technology and the University of California. The Observatory was
made possible by the generous financial support of the W. M. Keck Foundation.
The authors wish to recognize and acknowledge the very significant cultural
role and reverence that the summit of Maunakea has always had within the
indigenous Hawaiian community. We are most fortunate to have the opportunity
to conduct observations from this mountain. The material presented here is
also based upon work supported by NASA under award number 80GSFC21M0002. This
work was supported by the University of Tasmania through the UTAS Foundation
and the endowed Warren Chair in Astronomy and the ANR COLD-WORLDS
(ANR-18-CE31-0002). This research was also supported in part by the Australian
Government through the Australian Research Council Discovery Program (project
number 200101909) grant awarded to Cole and Beaulieu. Some of this research
has made use of the NASA Exoplanet Archive, which is operated by the
California Institute of Technology, under the Exoplanet Exploration Program.
Software: DAOPHOT-II (Stetson, 1987), daophot$\\_$mcmc (Terry et al., 2021),
eesunhong (Bennett & Rhie, 1996), genulens (Koshimoto & Ranc, 2021), hst1pass
(Anderson, 2022), KAI (Lu, 2022), Matplotlib (Hunter, 2007), Numpy (Oliphant,
2006).

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## 2023 HST Snapshot Images

We show the four-panel figure created from the two exposures taken during the
August 2023 Snapshot Program (Sahu et al., 2023). The stacked frame has
noticeably larger Poisson noise than the previous HST epochs which have
4$\times$ more exposures. The longer time baseline between the peak of the
microlensing event and the 2023 HST data helps to mitigate the lack of
exposures, as the larger separation between source and lens can be clearly
detected in this epoch.

Figure 9: Top Left: The 2023 HST I band stack image created from two
individual exposures from the Snapshot Program. The target is indicated with a
yellow box. Top Right: Zoomed image of the target, with the two points
indicating the best-fit positions for the two stars from the multi-star PSF
fitting. We note the unrelated neighbor star has moved closer to the target(s)
by ${\sim}1$ pixel between the 2012 and 2023 HST data. Bottom Left: The
residual image from a single-star PSF fit, showing a strong signal of the
blended lens(source). Bottom Right: Residual image for the simultaneous two-
star PSF fit, showing a smoother subtraction with Poisson noise remaining as
well as systematics due to the less-characterized PSF model. The color bar
represents the pixel intensity (counts) seen in the top-right and lower-
left/right panels.

This 2023 data, in conjunction with the previous HST epochs, largely confirm
that the two stars we detect are the true source and lens separating from each
other with their expected relative proper motions. This multi-epoch tracking
rules out the scenarios in which we are detecting an unrelated blend or a
bound stellar companion to either the source or lens.

## Full Light Curve Modeling Comparison

We show in Figure 10 the comparison of the fitting parameters between the
light curve modeling from photometry only and from photometry plus HST/Keck AO
imaging. In Sections 3 and 5 we explained one of the strongest high-res
imaging constraints is that of the microlensing parallax vectors, particularly
the North component, $\pi_{\textrm{E,N}}$. Additionally, the tighter
constraint on the source radius crossing time, $t_{*}$, comes primarily from
the $\mu_{\textrm{rel,H}}$ measurement derived from the Keck data via the
following equation:

$t_{*}=\frac{\theta_{*}}{\mu_{\textrm{rel}}}$ (1)

where $\theta_{*}$ is the angular size of the source star, which we estimate
using surface brightness relations from Boyajian et al. (2014), considering
only stars spanning the range in colors that are relevant for microlensing
targets. And $\mu_{\textrm{rel}}$ in equation 1 comes from the best-fit lens-
source separation measurement in Keck.

The caustic crossing models given in the prior studies (B08, K12) are ruled
out by this Keck data, and the models with a close approach to a caustic cusp
do not strongly constrain $t_{*}$ very well. Ultimately, we can further reduce
the total number of possible solutions from K12 (8 solutions) by a factor of
2, which leaves a four-fold degeneracy remaining (i.e. $s\rightarrow 1/s$ and
$u_{0}<0$, $u_{0}>0$).

Figure 10: Comparison of model parameter distributions from the light curve
photometry only (light grey) and light curve photometry plus HST/Keck imaging
constraints (black). The two cases shown are for the $s<1,u_{0}<0$ model. The
constraints from the high-resolution imaging are tightened most for the North
and East components of the microlensing parallax ($\pi_{E,N}$, $\pi_{E,E}$) as
well as the source radius crossing time ($t_{*}$). The median values given in
the title headings (above each histogram) are for the constrained light curve
$+$ imaging model. All other model parameters give consistent distributions
between the two cases.