KMT-2017-BLG-2820 and the Nature of the Free-Floating Planet Population

Formally, free-floating planets (FFPs) are planetary mass ($M<13\,M_{J}$) objects that are not bound to any star. However, from a theoretical viewpoint, one would like to distinguish between objects that formed in situ, as stars do via gravitational collapse, and those that formed in protoplanetary disks, like planets, and were subsequently ejected. This can only be done statistically, and only by a method that is sensitive to a broad range of masses that extends well below $M\lesssim M_{J}$, i.e., objects that are non-luminous given current technology. That is, gravitational microlensing is the only current technique by which such studies can be carried out.

Because it is increasingly difficult to form low-mass objects by gravitational collapse, and also increasingly difficult to form high-mass objects in protoplanetary disks (and even more difficult to then eject them), one expects a “gap” (more accurately, a strong minimum) between these two regimes, which is analogous to the so-called “brown dwarf desert”. The appearance of such a “gap” would allow one to individually identify the objects that likely formed within the protoplanetary disk, thus enabling further study.

In fact, the short-timescale, single-lens/single-source (1L1S) events that are the expected signature of FFPs can also be generated by planets in wide orbits. For example, if a doppelganger of our own solar system were oriented face-on and lay half way to the Galactic center, then its “Neptune” would lie about 7.5 Einstein radii from its “Sun”. Hence, for most trajectories of the lens system relative to a background source, a microlensing event due to the “Neptune” would be indistinguishable from 1L1S, even though the planet is bound. Therefore, to distinguish between wide-orbit planets (which are themselves quite interesting) and FFPs, one must wait for the source and lens to be sufficiently displaced that they can be separately imaged. Because a putative host might be very faint, while sources range from upper main-sequence stars to giants, this means waiting until the separation is adequate to resolve at severe to extreme contrast ratios. We adopt a range of 1.2 – 1.5 FWHM from main-sequence to giant sources. With diffraction limited imaging, this requires waiting

where $\lambda$ is the wavelength of the observations, $D$ is the diameter of the mirror, $\mu_{\rm rel}$ is the lens-source relative proper motion, and 1.25 = 1.5/1.2. For most FFP candidates discovered to date, and also for those that will be discovered in data from the next few years, this means waiting until the end of this decade, when the separations become accessible to current telescopes and when adaptive optics (AO) imaging on 30m class telescopes becomes available (thereby reducing the pre-factor in Equation (1) by a factor $\sim 3$).

Thus, the study of FFPs is intrinsically a long-term project.

The first approach to the study of FFPs was based on the distribution of Einstein timescales,

of 1L1S events. Here, $\theta_{\rm E}$ is the Einstein radius and $\pi_{\rm rel}$ is the lens-source relative parallax. Sumi et al. (2011) found a strong excess of $t_{\rm E}\sim 1\,$day events, which they interpreted as due to a population of roughly Jupiter-mass planets, with about twice the frequency of stars. However, using an independent and superior data set, Mróz et al. (2017) ruled out such an excess. Nevertheless, Mróz et al. (2017) found an excess of few-hour events, which they suggested is consistent with a population of Earth- or super-Earth-mass objects.

Of particular note in the present context, the Mróz et al. (2017) excess was separated from the main distribution by a clear gap¹¹1The gap appears despite the fact that the timescale errors are fairly large, with typical $1\,\sigma$ confidence intervals spanning a factor of two in $t_{\rm E}$, whereas the Sumi et al. (2011) excess was not. This difference is not due to the different qualities of the two data sets, but is simply the result of the respective ratios of the mean timescale of the putative planets to that of the bulge lenses from the bottom of the stellar and brown dwarf population (say $0.01\,M_{\odot}$), i.e., $\langle t_{\rm E}\rangle\sim\sqrt{\kappa(0.01\,M_{\odot})(16\,\mu{\rm as})}/(5\,{\rm mas}\,{\rm yr}^{-1})=2.6\,$days. For the putative Sumi et al. (2011) planets, this ratio was about 0.4. Hence, the short-timescale tail of the brown-dwarf (BD) distribution strongly overlaps the peak of the FFP distribution due to the wide range of values of $\pi_{\rm rel}$ and $\mu_{\rm rel}$ entering Equation (2). However, the corresponding ratio for the Mróz et al. (2017) excess is only about 0.08, implying that the BD-tail is negligibly small.

Given that the Jupiter FFP population is at least 8 times smaller than suggested by Sumi et al. (2011), it can hardly be studied at all using the global $t_{\rm E}$ distribution. That is, the Jupiter FFP events result in a small excess of $t_{\rm E}\sim 1\,$day events, relative to the higher-mass “background”, which is difficult to detect even statistically. Moreover, such a small excess could in principle be due to imperfect modeling of the BD population, or even to the long-timescale tail of lower-mass FFPs. By contrast, there is essentially no “background” of unrelated microlensing events for the few-hour events found by Mróz et al. (2017): the only real issues are whether these brief “bumps” in the light curve are really due to microlensing, and if so, whether these “isolated” low-mass objects are due to FFPs rather than wide-separation bound planets. Regarding the first question, Mróz et al. (2017) argued that these events are likely due to microlensing.

Regarding the second question, as mentioned above, one can in principle wait for the lens and source to separate and then conduct AO imaging. However, because these are point-source (PSPL) rather than finite-source (FSPL) single lens events, there is no measurement of $\mu_{\rm rel}$, and therefore Equation (1) does not give a definite estimate of how long one must wait. If one sets a “reasonably conservative” lower limit²²2 For the adequate approximation that bulge stars have an isotropic Gaussian proper motion distribution with standard deviation $\sigma=2.9\,{\rm mas}\,{\rm yr}^{-1}$, events with $\mu_{\rm rel}<\mu_{{\rm rel},\rm lim}\rightarrow 1.5\,{\rm mas}\,{\rm yr}^{-1}$ constitute a fraction $f=(2/\sqrt{\pi})\int_{0}^{(\mu_{{\rm rel},\rm lim/2\sigma})^{2}}dx\,\sqrt{x}e^{-x}\simeq(4/3\sqrt{\pi})(\mu_{{\rm rel},\rm lim/2\sigma})^{3}\rightarrow 1.3\%$ of all bulge-bulge microlensing events. That is, in this regime, $f\propto\mu_{{\rm rel},\rm lim}^{3}$ $\mu_{\rm rel}>1.5\,{\rm mas}\,{\rm yr}^{-1}$, then with the fiducial parameters, one should wait 43 years. However, this still implies that most of the Mróz et al. (2017) FFP candidates can be vetted at, or soon after, first AO light on 30m telescopes.

If some or all of the FFP candidates prove to be wide-orbit planets, then they can be subjected to further study. For each case, the planet-host separation can be measured with a precision of about $10\,{\rm au}$ as we discuss in Section 9. Then, they can be classified into either true analogs of Uranus and Neptune, which appear to have been “ejected” from their Jupiter/Saturn-like orbits but remaining in the same region of the Solar System, or those that have been ejected into Kuiper-like or even Oort-like orbits (Gould, 2016).

A second approach to the investigation of FFPs was pioneered by Mróz et al. (2018), who searched for OGLE light curves that were consistent with being due to short 1L1S microlensing events, but often with incomplete coverage. Then they checked whether the event could be characterized using other survey data. Although not specifically intended, this approach tends to select FSPL events with source crossing times $t_{*}\equiv\rho t_{\rm E}$ of about half a day or so. Here, $\rho=\theta_{*}/\theta_{\rm E}$ is the ratio of the source-star angular radius to the Einstein radius. Substantially longer events would be adequately covered by OGLE itself and would therefore not require this hybrid approach. Substantially shorter events would either fall mostly inside or mostly outside a single night of OGLE data and therefore either would not require this approach or would not be detected by it at all. PSPL events of similar effective duration have sufficient longer-term structure to characterize them from several nights of data. To date, this approach has yielded two FSPL FFP candidates: OGLE-2016-BLG-1540 and OGLE-2012-BLG-1323 (Mróz et al., 2018, 2019), with $t_{*}=0.53\,$days and $t_{*}=0.78\,$days respectively. In both cases, OGLE data covered regions near the peak of the box-like light curve, and these data had to be supplemented by data from other time zones to be properly interpreted. These were from Australia and South Africa in the first case, and from Israel and New Zealand in the second.

OGLE discovered one other FSPL FFP directly from its Early Warning System (EWS, Udalski et al. 1994; Udalski 2003), OGLE-2019-BLG-0551 (Mróz et al., 2020). Because its self-crossing time was much longer, $t_{*}=1.7\,$days, this event did not require any other data for full characterization, although KMTNet (Kim et al., 2016) data were included in the fit. And a special OGLE search yielded the very short FFP event, OGLE-2016-BLG-1928 (Mróz et al., 2020), which had not been alerted by OGLE EWS. With $t_{*}=0.10\,$days, the event was almost completely contained within only one night of OGLE data, although the post-event (completely flat) KMTNet data from South Africa were helpful in ruling out 2L1S alternative solutions. Thus, these two FFP candidates tend to confirm that the hybrid approach of Mróz et al. (2018) tends to select FSPL events with $t_{*}\sim 0.5\,$days. The source stars for such events are essentially all giants.

In the course of their 2019 annual review of microlensing events found by their EventFinder system (Kim et al., 2018), KMTNet identified KMT-2019-BLG-2073 as a likely FFP candidate. Kim et al. (2020) then showed that, like the previous three³³3OGLE-2016-BLG-1928 had not yet been discovered. FSPL FFP events (defined as having $\theta_{\rm E}\lesssim 10\,\mu{\rm as}$), KMT-2019-BLG-2073 had a giant-star source and $\rho\gtrsim 1$. In order of discovery, these four events had $\theta_{*}=(12,15,20,5.4)\,\mu{\rm as}$ and $\rho=(5.0,1.6,4.5,1.1)$. This led Kim et al. (2020) to suggest a systematic search for such giant-source FSPL FFP events. Moreover, they immediately recognized that if such a search were extended to all giant-source FSPL events, it would have substantially greater scientific value. They developed an automated algorithm for searching the KMT EventFinder list for FSPL candidates, as well as procedures to vet these. They carried out an additional special search for giant-source events based on a variant of EventFinder that would be more forgiving of FSPL light curve distortions and more inclusive of giant sources than the standard EventFinder. In addition, more representations of the light curve were shown to the operator than in the general search to enable easier recognition of non-standard light curves. Kim et al. (2020) showed concretely that these searches and procedures were tractable by applying them to the 2019 KMT data. And they demonstrated that the results were statistically well behaved.

Kim et al. (2020) found a total of 13 FSPL events, of which two were “planetary” ($\theta_{\rm E}<10\,\mu{\rm as}$). There was a “gap” of $\Delta\log\theta_{\rm E}=0.82$ between the two FFPs and the next smallest $\theta_{\rm E}$, while all of the 11 other increments in the cumulative distribution function had $\Delta\log\theta_{\rm E}<0.28$.

While cautioning that no statistical conclusions could be drawn about FFP frequency from the 2019 sample (due to publication bias), Kim et al. (2020) argued that the gap was likely real and, in any case, could be tested by carrying out similar searches on other seasons of KMT data. This illustrates one of the powerful advantages of FSPL studies of FFPs: the corresponding gap in the underlying $t_{\rm E}$ distribution of 1L1S events would be substantially weaker. There are two reasons for the difference. First, from Equation (2), the $\theta_{\rm E}$ distribution is less “smeared out” relative to the mass distribution because there is only one degenerate variable $(\pi_{\rm rel})$, rather than two $(\pi_{\rm rel},\mu_{\rm rel})$ for the $t_{\rm E}$ distribution. Second, the cross section for 1L1S microlensing events is $\theta_{\rm E}\propto\sqrt{M}$, whereas the cross section for FSPL events is $\theta_{*}$, which is independent of lens mass. Hence, the population of BD events that can “scatter down” to the planetary regime is suppressed for the FSPL ($\theta_{\rm E}$) distribution relative to the 1L1S ($t_{\rm E}$) distribution.

A second advantage is that the independent measurement of $\mu_{\rm rel}$ can in some cases constrain the location of the lens. Mróz et al. (2020) combined the high value of $\mu_{\rm rel}$ for OGLE-2016-BLG-1928 with the Gaia source proper motion to argue that the lens was almost certainly in the disk. Given the low value $\theta_{\rm E}=0.84\,\mu{\rm as}$, this implied a very low lens mass $M=0.23\,M_{\oplus}(\pi_{\rm rel}/125\,\mu{\rm as})^{-1}$.

Third, by measuring the proper motion, one obtains a definite estimate of the wait time until AO observations can distinguish between FFP and 2L1S interpretations. For example, using the fiducial parameters of Equation (1), and keeping in mind that giant sources require 1.5 FWHM separation, the six FSPL FFP candidates found to date have first observation epochs of OGLE-2012-BLG-1323 (2027), OGLE-2016-BLG-1540 (2024), OGLE-2016-BLG-1928 (2024), KMT-2017-BLG-2820 (2028), OGLE-2019-BLG-0551 (2039), and KMT-2019-BLG-2073 (2032).

The launch of the Nancy Grace Roman (f.k.a. WFIRST) satellite will provide another path to FFPs. Johnson et al. (2020) estimate that FFP population models consistent with the Mróz et al. (2017) short-$t_{\rm E}$ events would lead to several hundred Roman detections (see their Figure 7). For the events among these that are generated by wide-separation planets (as opposed to genuine FFPs), a substantial fraction of the hosts will be directly detected as blended flux. This is because most of the sources are M dwarfs, and hence have comparable flux to the lens hosts, while the fields are relatively sparse at Roman ($\sim 100\,{\rm mas}$) resolution. However, for those events without measurable blended flux $f_{b}$ (either because $f_{b}$ is small or the errors in $f_{b}$ are large due to the faintness of the source and the small number of magnified points), then ground-based 30m AO will still be required to confirm that these are FFPs. Because the sources are small, most will not have $\mu_{\rm rel}$ estimates. Thus, adopting a relatively conservative $\mu_{\rm rel}>1.5\,{\rm mas}\,{\rm yr}^{-1}$ limit, and using the scaling of Equation (1), one should wait $\sim 15\,$yr after the mission, i.e., circa 2045 before vetting these candidate FFPs. Nevertheless, a fraction $\sim\rho=\theta_{*}/\theta_{\rm E}\sim(0.25\,\mu{\rm as})/(5\,\mu{\rm as})=5\%$ will have $\mu_{\rm rel}$ measurements, meaning that of order a dozen FFP candidates can be vetted by 2035. Thus, space-based and ground-based FFP surveys will remain complementary for several decades.

Finally, we note that the frequency of wide orbit planets can be studied by looking for short “bumps” in the long-term light curves of archival microlensing events (Poleski et al., 2018, 2020). One could then check whether this population of wide-orbit planets was large enough to account for the rate of FFP candidates. If we assume that the source must come within $u_{0}<u_{0,\rm lim}$ planetary Einstein radii to be detected, and that a fraction $\xi$ of a given microlensing light curve is covered, then the probability of detection is

Here, we have scaled to the planet-host mass ratio $q$ that would be appropriate if the FFP candidates turn out to be bound and to the light-curve coverage factor that would be appropriate for such short events that are observed from a single site. If we consider only the $N_{\rm ev}\sim 5000$ OGLE-IV events in fields with the necessary $\Gamma\geq 1\,{\rm hr}^{-1}$ cadence, and assume $N_{\rm pl}=5$ planets per star, then the expected number of detections $N_{\rm ev}N_{\rm pl}p=2.5/(s/5)$, which could provide marginal evidence for the wide-orbit hypothesis (if detected). Note that for Jupiter-mass planets ($q\sim 2\times 10^{-3}$, $\xi\sim 0.7$) the expectation is much higher: $N_{\rm ev}N_{\rm pl}p=14\,N_{\rm pl}/(s/5)$. Moreover, events in lower-cadence fields could also be probed. To date, four wide ($s>3$) bound planets have been found by microlensing, with $(s,\log q)=[(4.7,-1.5),(4.4,-1.8),(4.6,-3.3),(5.3,-3.6)]$ (Han et al., 2017; Poleski et al., 2017, 2018, 2014). As noted by Poleski et al. (2018), there is a 1.5 dex gap in $q$ between the first two and last two, although one should keep in mind that the sample is not homogeneously selected.

Here we report on a new FSPL FFP candidate, which was discovered by applying the above-described supplemental giant-source search to the 2017 KMT light-curve data base. This search returned 232 microlensing candidates, of which 15 had not previously been identified in the EventFinder search, which had yielded 2817 candidates. Being the third on this list of 15, we designate it KMT-2017-BLG-2820, following the convention introduced by Mróz et al. (2020) for OGLE-2016-BLG-1928. We also discuss the broader implications of the accumulating set of FSPL FFP discoveries.

KMT-2017-BLG-2820 occurred at (R.A., Decl)${}_{J2000}=$ (17:34:58.25, $-28$:32:51.22), corresponding to $(l,b)=(-0.91,+2.18)$. It therefore lies in KMT field BLG14, which was observed at the time of the event at nominal cadences of $\Gamma=(1.0,0.75,0.75)\,{\rm hr}^{-1}$ from KMT’s three observatories at the Cerro Tololo Interamerican Observatory (KMTC), South African Astronomical Observatory (KMTS), and Siding Springs Observatory (KMTA), respectively. Each facility has a 1.6m telescope equipped with a $2^{\circ}\times 2^{\circ}$ camera. Most observations were in Cousins $I$. In 2017, every tenth $I$-band observation from KMTC was complemented by an observation in Johnson $V$ band, while this applied to only every twentieth observation from KMTS and KMTA.

The event also lies in OGLE field BLG653, which was observed in Cousins $I$ band with a cadence of $\Gamma=0.17\,{\rm hr}^{-1}$ from OGLE’s 1.3m telescope at Las Campanas Observatory, which is equipped with a $1.4\,{\rm deg}^{2}$ camera. OGLE also took occasional $V$-band images. Unfortunately, neither KMT nor OGLE took such images when the source was sufficiently magnified to measure its color.

Neither KMT nor OGLE alerted the event in real time, so there was no possibility of follow-up observations. We checked and found that the UKIRT microlensing survey (Shvartzvald et al., 2017) was taking observations close to the peak of the event. Unfortunately, however, while this field was in their 2016 footprint, it was not in their 2017 footprint. Because UKIRT observes in $H$ and $K$, even a single such observation would have yielded a very good color measurement.

Data reductions were carried out using specific implementations of difference image analysis (Tomaney & Crotts, 1996; Alard & Lupton, 1998), by Albrow et al. (2009) for KMT and Woźniak (2000) for OGLE.

Figure 1 shows the color-coded data from the four observatories together with the best-fit zero-blending FSPL model, which has four parameters (apart from the flux parameters). These are the three Paczyński (1986) parameters $(t_{0},u_{0},t_{\rm E})$ and $\rho$, where $t_{0}$ is the time of closest approach and $u_{0}$ is the impact parameter in units of $\theta_{\rm E}$. The fit parameters are given in Table 1. This will be our preferred solution. However, in contrast to the cases of some other FSPL FFP candidates, there is no compelling reason from the light curve data themselves to conclude that the source is unblended. For example, for OGLE-2019-BLG-0551, the blending was poorly constrained, but the source color was well measured to be similar to that of the baseline object. This implied that strong blending was unlikely. But, more importantly, it implied that the $\theta_{\rm E}$ determination was independent of the blending (Mróz et al., 2020). The current case is closer to that of KMT-2019-BLG-2073, for which the source color was not measured and the blending fraction $\epsilon\equiv f_{b}/f_{\rm base}$ was measured to only about $\sigma(\epsilon)\sim 20\%$ at the $1\,\sigma$ level (Kim et al., 2020). However, in the present case, while there is also no color measurement and the $1\,\sigma$ limit on $\epsilon$ is similar, there is a strong $3\,\sigma$ limit $\epsilon<0.4$ that implies that the source definitely dominates the light from the baseline object. This fact will play an important role in the argument given in Section 6 that the source is most likely not blended.

Before continuing, we remark on the technical point that we implement “zero blending” by fixing $f_{s,\rm KMTA}=f_{\rm base,KMTA}$ i.e., we equate the source and baseline fluxes at KMTA. We find in Section 4 that the color and magnitude offsets of the source from the clump are nearly identical for KMTA and OGLE (and indeed are similar for all four observatories). So, from this standpoint, either (or really, any) observatory could be used. However, the $\rho$ measurement depends primarily on the KMTA data, and $\theta_{\rm E}$ is directly proportional to the square root of the normalized surface brightness $\hat{S}\equiv f_{s}/\rho^{2}$ (Mróz et al., 2020; Kim et al., 2020). Therefore, it is really only the fixing of $f_{s,\rm KMTA}$ that directly impacts the result. We considered fixing some or all of the other source fluxes, but this does not significantly change the values of the other parameters compared to just fixing $f_{s,\rm KMTA}$.

Table 1 also shows the parameters for the case of free blending. The estimate of the blended flux is consistent with zero, and the remaining parameters have similar values to the zero-blending fit. However, the errors are much larger. Nevertheless, the normalized surface brightness $\hat{S}$ has a fractional error of only 3.6%, implying that this measurement contributes only 1.8% to the uncertainty in $\theta_{\rm E}=\sqrt{\hat{S}}\times$[color term]. That is, as discussed in some detail by Kim et al. (2020), as regards the crucial measurement of $\theta_{\rm E}$, the real uncertainty introduced by unknown blending is the degree to which it implies that the source color differs from that of the baseline object, which is used in the analysis as a proxy for the source color. To address this issue further requires the analysis of two types of auxiliary data: photometric and astrometric.

Figures 2 and 3 show color-magnitude diagrams (CMDs) within a $2^{\prime}\times 2^{\prime}$ box centered on the event for OGLE and KMTA, respectively. In each case, the “baseline object” is shown in black, while the clump centroid is shown in red. The OGLE CMD is calibrated, and the KMTA CMD has been shifted by offsets derived from relatively bright comparison stars, $14<I_{\rm OGLE}<16.9$. We need to compare these two CMDs because, while the OGLE photometry is unquestionably better (see, e.g., the lower giant branches in the respective figures), the normalized surface brightness $\hat{S}\equiv f_{s}/\rho^{2}$ is best constrained from the KMTA data.

We measure the offset from the clump $\Delta[(V-I),I]=[(V-I),I]_{\rm base}-[(V-I),I]_{\rm clump}$, finding $(+0.07,-0.19)$ and $(+0.07,-0.18)$ for OGLE and KMTA, respectively. That is, even though the OGLE photometry is substantially better, the KMTA photometry is adequate for measuring this offset.

In the zero-blending model, the “baseline object” is the source. Then, using the known dereddened position of the clump $[(V-I),I]_{\rm clump,0}=(1.06,14.50)$ (Bensby et al., 2013; Nataf et al., 2013), we obtain $[(V-I),I]_{s,0}=(1.13,14.31)\pm(0.03,0.05)$, where the principal source of error is from centroiding the clump. We cannot use a substantially larger area because of differential reddening. Then employing the standard procedure of Yoo et al. (2004), we convert to $[(V-K),K]$ using the color-color relations of Bessell & Brett (1988) and apply the color/surface-brightness relation of Kervella et al. (2004) to obtain,

where we have added 5% to the error, in quadrature, to account for systematic errors in the overall method. Using the zero-blending parameters from Table 1, we then obtain

We re-emphasize that Equations (4) and (5) only apply under the assumption of zero blending. However, from the standpoint of measuring $\theta_{\rm E}$, it is equally important to emphasize that this measurement is affected by blending only to the extent that the blend color differs from that of the baseline object. As discussed in Section 3, $\theta_{\rm E}=\sqrt{\hat{S}}\times$[color term]. Because $\hat{S}$ is nearly invariant, $\theta_{\rm E}$ is unaffected by blending, provided that it does not change the estimated color of the source.

If there is blended light that is displaced from the source by $\Delta{\mbox{\boldmath$\theta$}}_{b}$, then the source position (measured from difference images near peak) will be displaced from the baseline object by

where $\epsilon=f_{b}/f_{\rm base}$ is the fraction of the baseline-object flux that is due to the blend. Using the three good seeing images near peak, we measure, in $0.4^{\prime\prime}$ pixels, and in the (West,North) coordinate system of the detector, ${\mbox{\boldmath$\theta$}}_{s}=(156.005,145.177)\pm(0.014,0.016)$, where the error bars are the standard errors of the mean of the three measurements. The baseline object position is ${\mbox{\boldmath$\theta$}}_{\rm base}=(155.990,145.210)$. While we do not have an independent way to estimate the error bars of this latter measurement, we judge them to be of the same order as those of ${\mbox{\boldmath$\theta$}}_{s}$ because the baseline object is bright and isolated and because the baseline flux is similar to the difference flux at peak. Together, these yield

Even assuming Gaussian statistics (which would be somewhat optimistic), this has a probability of $p=26\%$ under the hypothesis that the true value is zero (i.e., either $f_{b}=0$ or $\Delta\theta_{b}=0$). Hence, the astrometric measurement does not provide positive evidence in favor of blended light, and it is consistent with zero blended light. We now turn to the limits and constraints on blended light.

As discussed in Section 3, we have adopted the parameters of the zero-blend fit, even though the light curve permits 20% blending at $1\,\sigma$ and 40% at $3\,\sigma$. In this section, we justify this choice.

Logically, there are only three possible sources of blended light: a companion of the source, a companion of the lens, and an ambient star that is unrelated to the event. We consider these in turn.

It is possible in principle to distinguish between bulge and disk lenses by combining the scalar lens-source relative proper motion $\mu_{\rm rel}$ (derived from the microlensing analysis) with the vector source proper motion ${\mbox{\boldmath$\mu$}}_{s}$ derived from external sources. For example, Mróz et al. (2020) found that the source star for OGLE-2016-BLG-1928 had a proper motion almost identical to the centroid of the neighboring bulge field stars. Because $\mu_{\rm rel}\sim 10\,{\rm mas}\,{\rm yr}^{-1}$ in that case, the lens had to be moving at $10\,{\rm mas}\,{\rm yr}^{-1}$ relative to the mean bulge motion. However, the Gaia proper motion diagram showed that there are few, if any, bulge stars with such proper motions.

We pursue a similar investigation here. We use 10 years of OGLE-IV data, which we align to Gaia using a technique that is described by Udalski et al. (2020). We find that the proper motion of the baseline object is

where we have doubled the formal errors derived from the scatter of the fit, based on tests performed by Udalski et al. (2020) in regions where overlapping OGLE fields provide two independent measurements. This measurement agrees with Gaia within the errors, but is more precise. Note that Gaia errors in bulge fields are also underestimated by a factor of about two. In view of the small probability of significant blended light found in Section 6, we identify the source with the baseline object, ${\mbox{\boldmath$\mu$}}_{s}={\mbox{\boldmath$\mu$}}_{\rm base}$.

Figure 4 shows this measurement (red), together with the proper motions of bulge field stars (black). The figure is rotated to Galactic coordinates. In addition, for the first time, we show all proper motions in the geocentric frame at the time of the peak of the event, when Earth was moving ${\bf v}_{\oplus,\perp}(E,N)=(+28.90,-0.79)\,{\rm km}\,{\rm s}^{-1}$ relative to the Sun. Thus, before rotating the OGLE-IV heliocentric proper motions to Galactic coordinates we first subtract ${\mbox{\boldmath$\mu$}}_{\oplus,R_{0}}={\bf v}_{\oplus,\perp}/R_{0}=(+0.74,-0.02)\,{\rm mas}\,{\rm yr}^{-1}$, where $R_{0}=8.2\,{\rm kpc}$.

In this way, we ensure that the magenta circle that is centered on the geocentric source proper motion, and represents the $7.95\pm 0.73\,{\rm mas}\,{\rm yr}^{-1}$ geocentric lens-source relative proper motion, accurately predicts the range of allowed geocentric lens proper motions. Note that to obtain the $1\,\sigma$ range of the predicted ${\mbox{\boldmath$\mu$}}_{l}={\mbox{\boldmath$\mu$}}_{s}+{\mbox{\boldmath$\mu$}}_{\rm rel}$ we have added in quadrature the errors for $|{\mbox{\boldmath$\mu$}}_{s}|$ and $\mu_{\rm rel}$. As can be seen, this range is quite consistent with the lens lying in the bulge (black points).

We now ask whether this annulus is also consistent with the lens lying in the disk. The blue circles represent the mean geocentric lens proper motion for disk lenses lying at 2 kpc (right) and 5 kpc (left). The error bars reflect the velocity dispersions of stars at each distance. The blue curve connecting the blue circles shows the mean proper motions at $2<D_{L}/{\rm kpc}<5$. We have assumed dispersions of $\zeta^{1/2}\times(28,18)\,{\rm km}\,{\rm s}^{-1}$ where $\zeta=\exp(D_{L}/2.5)\,{\rm kpc}$ is the ratio of the local surface density to the one in the solar neighborhood. We also assume an asymmetric drift of $v_{\rm rot}-\sqrt{v_{\rm rot}^{2}-\zeta(47\,{\rm km}\,{\rm s}^{-1})^{2}}$, where $v_{\rm rot}=235\,{\rm km}\,{\rm s}^{-1}$ is the local rotation speed. We take account of the motion of the Sun relative to the local standard of rest (LSR), $v_{\odot,\perp}(l,b)=(12,7)\,{\rm km}\,{\rm s}^{-1}$, as well as the instantaneous motion of Earth. The mean estimates for each distance are well displaced toward lower $\mu(l)$ from the origin. Three factors contribute to this. First, the Sun is moving at $+12\,{\rm km}\,{\rm s}^{-1}$ relative to the LSR in this direction. Second, Earth’s instantaneous motion is $+15\,{\rm km}\,{\rm s}^{-1}$ relative to the Sun in this direction. Third, the asymmetric drift of stars at these distances is in the opposite direction. In the latitude direction, Earth’s strong motion toward Galactic south overwhelms the small northerly motion of the Sun.

Hence, the mean expected motion is displaced from the origin, though which the magenta annulus directly passes. Nevertheless, after taking account of the velocity dispersions of the lens (error bars), the lens is consistent with being in the disk at the $1\,\sigma$ level and at any distance from us. Thus, the proper-motion analysis is quite consistent with the lens lying in either the bulge or the disk.

If the lens has a host, then it may leave its signature on the (seemingly) 1L1S event, either by generating a second, much longer, bump in the light curve or by creating caustic structures on the main, short timescale, event. To search for such host signatures, we follow the procedures described by Kim et al. (2020) for KMT-2019-BLG-2073. In particular, we add three parameters to the fit $(s,q,\alpha)$, i.e., the planet-host separation in units of the total-mass (i.e., host+planet) Einstein radius, the ratio of the host and planet masses, and the angle of the host-planet axis with respect to the lens-source relative motion. We center the coordinate system on the planetary caustic. We conduct a grid search in these variables, seeding the remaining four at their values implied by the 1L1S solution. Figure 5 shows the result of this search, with a clear minimum at about $(s,q)\sim(6,100)$, which is favored over the 1L1S solution by $\Delta\chi^{2}=-22$. Figure 6 shows the corresponding light curve for the best fit.

To understand the origin of this $\chi^{2}$ improvement, we plot the cumulative distribution of $\Delta\chi^{2}$ in Figure 7. This shows that the net $\chi^{2}$ improvement comes entirely from KMTA, with the other three observatories canceling each other out. Hence, the most likely explanation for the improvement is low-level systematics in the KMTA data.

Returning to Figure 5, we see that all models with $s<3$ and $q>100$ have $\Delta\chi^{2}>36$ relative to the minimum, and so $\Delta\chi^{2}>14$ relative to 1L1S. The same applies to models with $s<2.5$ and $q>10$. We regard such models as ruled out. Thus, if future AO observations identify a host, yielding estimates of $M_{\rm host}$ and $D_{L}$, and if second-epoch observations measure the projected planet-host separation $a_{\perp}$ (see Section 9.3), then $a_{\perp}>3\,\theta_{{\rm E},\rm host}D_{L}$. For example, if $M_{\rm host}=0.8\,M_{\odot}$ and $D_{L}=6\,{\rm kpc}$, then $q\simeq 90$, and we predict $a_{\perp}>9\,{\rm au}$. As we discuss in Section 9.3, this threshold is near the limit with current instrumentation (and modest efforts), but plausibly could be achieved with 30m AO.

We have discovered a new FSPL FFP candidate, KMT-2017-BLG-2820, with Einstein radius $\theta=5.94\pm 0.37\,\mu{\rm as}$ and lens-source relative proper motion $\mu_{\rm rel}=7.95\pm 0.52\,{\rm mas}\,{\rm yr}^{-1}$. Whether this is truly a “free-floating planet” or is simply a very wide-separation planet can can be determined with excellent (though not perfect) confidence by AO followup observations made before the end of the current decade. If the latter, then the planet-host projected separation can be measured with roughly $10\,{\rm au}$ precision from a second AO epoch.

KMT-2017-BLG-2820 was discovered in an ongoing systematic search for giant-source FSPL events within 2016–2019 KMT data (Kim et al., 2020). It is the third FFP candidate in this developing homogeneous sample and the sixth FSPL FFP candidate overall. Five of these six FSPL FFP candidates have a very similar Einstein timescale distribution as the six PSPL FFP candidates found by Mróz et al. (2017) in their study of 1L1S events found in the OGLE-IV database. Moreover, the detection rates of the Mróz et al. (2017) PSPL sample and the sample being collected under the Kim et al. (2020) protocols are comparable (see Appendix). We therefore argue that the five FSPL FFP candidates and six PSPL FFP candidates are drawn from the same population. Based on the measured Einstein radii $\theta_{\rm E}\sim 5\,\mu{\rm as}$ of the former, these could be either sub-Jovian FFPs in the bulge or super-Earth FFPs in the disk. We argue that, if the Einstein desert in the $\theta_{\rm E}$ distribution of giant-source FSPL events tentatively found by Kim et al. (2020) is confirmed, then it argues for the latter scenario, which was already suggested by (Mróz et al., 2017) on different grounds.

In making our parameter estimates, we have adopted the zero-blending model. First, while the blending parameter $\epsilon=f_{b}/f_{\rm base}$ is relatively weakly constrained by the light curve at the $1\,\sigma$ level, $\epsilon=0.12\pm 0.10$, it has a firm upper limit $\epsilon<0.4$ at the $3\,\sigma$ level. Thus, the source dominates the baseline object, which sits on the upper giant-branch track. Hence, the probability for $\epsilon>0.1$ from a source companion is less than 1% due to rarity of lower giant-branch stars. The probability for $\epsilon>0.1$ from an ambient star is similarly restricted by the close astrometric alignment between the source and the baseline object. If the lens has a host, then this would supply blended light at some level. However, essentially all potential hosts at $D_{L}>4\,{\rm kpc}$ generate $\epsilon\ll 0.1$ and this applies to most potential hosts at $D_{L}<4\,{\rm kpc}$ as well. In any case, we showed that ignoring such possible blended light from the host would not cause one to overestimate $\mu_{\rm rel}$ and thereby underestimate the wait time for AO followup observations.