KMT-2018-BLG-1025Lb: microlensing super-Earth planet orbiting a low-mass star
Cheongho Han, Andrzej Udalski, Chung-Uk Lee, Michael D. Albrow, Sun-Ju Chung, Andrew Gould, Kyu-Ha Hwang, Youn Kil Jung, Doeon Kim, Hyoun-Woo Kim, Yoon-Hyun Ryu, In-Gu Shin, Yossi Shvartzvald, Jennifer C. Yee, Weicheng Zang, Sang-Mok Cha, Dong-Jin Kim, Seung-Lee Kim, Dong-Joo Lee, Yongseok Lee, Byeong-Gon Park, Richard W. Pogge, Chun-Hwey Kim, Woong-Tae Kim, Przemek Mróz, Micha? K. Szyma?ski, Jan Skowron, Rados?aw Poleski, Igor Soszy?ski, Pawe? Pietrukowicz, Szymon Koz?owski, Krzysztof Ulaczyk, Krzysztof A. Rybicki, Patryk Iwanek, Marcin Wrona
aa r X i v : . [ a s t r o - ph . E P ] F e b Astronomy & Astrophysicsmanuscript no. ms © ESO 2021February 4, 2021
KMT-2018-BLG-1025Lb: microlensing super-Earth planet orbiting alow-mass star
Cheongho Han , Andrzej Udalski , Chung-Uk Lee (Leading authors)Michael D. Albrow , Sun-Ju Chung , , Andrew Gould , , Kyu-Ha Hwang , Youn Kil Jung , Doeon Kim ,Hyoun-Woo Kim , Yoon-Hyun Ryu , In-Gu Shin , Yossi Shvartzvald , Jennifer C. Yee , Weicheng Zang ,Sang-Mok Cha , , Dong-Jin Kim , Seung-Lee Kim , , Dong-Joo Lee , Yongseok Lee , , Byeong-Gon Park , ,Richard W. Pogge , Chun-Hwey Kim , Woong-Tae Kim (The KMTNet Collaboration),Przemek Mróz , , Michał K. Szyma´nski , Jan Skowron , Radosław Poleski , Igor Soszy´nski , Paweł Pietrukowicz ,Szymon Kozłowski , Krzysztof Ulaczyk , Krzysztof A. Rybicki , Patryk Iwanek , and Marcin Wrona (The OGLE Collaboration) Department of Physics, Chungbuk National University, Cheongju 28644, Republic of Koreae-mail: [email protected] Astronomical Observatory, University of Warsaw, Al. Ujazdowskie 4, 00-478 Warszawa, Poland Korea Astronomy and Space Science Institute, Daejon 34055, Republic of Korea University of Canterbury, Department of Physics and Astronomy, Private Bag 4800, Christchurch 8020, New Zealand Korea University of Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon, 34113, Republic of Korea Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany Department of Astronomy, The Ohio State University, 140 W. 18th Ave., Columbus, OH 43210, USA Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 76100, Israel Center for Astrophysics | Harvard & Smithsonian 60 Garden St., Cambridge, MA 02138, USA Department of Astronomy and Tsinghua Centre for Astrophysics, Tsinghua University, Beijing 100084, China School of Space Research, Kyung Hee University, Yongin, Kyeonggi 17104, Republic of Korea Department of Astronomy & Space Science, Chungbuk National University, Cheongju 28644, Republic of Korea Department of Physics & Astronomy, Seoul National University, Seoul 08826, Republic of Korea Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA 91125, USA Department of Physics, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UKReceived ; accepted
ABSTRACT
Aims.
We aim to find missing microlensing planets hidden in the unanalyzed lensing events of previous survey data.
Methods.
For this purpose, we conduct a systematic inspection of high-magnification microlensing events, with peak magnifications A peak &
30, in the data collected from high-cadence surveys in and before the 2018 season. From this investigation, we identify ananomaly in the lensing light curve of the event KMT-2018-BLG-1025. The analysis of the light curve indicates that the anomaly iscaused by a very low mass-ratio companion to the lens.
Results.
We identify three degenerate solutions, in which the ambiguity between a pair of solutions (solutions B) is caused by thepreviously known close–wide degeneracy, and the degeneracy between these and the other solution (solution A) is a new type that hasnot been reported before. The estimated mass ratio between the planet and host is q ∼ . × − for the solution A and q ∼ . × − for the solutions B. From the Bayesian analysis conducted with measured observables, we estimate that the masses of the planet andhost and the distance to the lens are ( M p , M h , D L ) ∼ (6 . M ⊕ , . M ⊙ , . ∼ (4 . M ⊕ , . M ⊙ , . Key words. gravitational microlensing – planets and satellites: detection
1. Introduction
The microlensing method has unique advantages in detectingsome specific populations of planets. It enables one to detectplanets orbiting very faint low-mass stars, which are the mostcommon populations of stars in the Galaxy, because of the lens-ing characteristic that does not depend on the luminosity of theplanet host. Another very important advantage of the method is that its detection e ffi ciency extends to very low-mass planets be-cause of the slow decrease of the e ffi ciency with the decreaseof the planet / host mass ratio q . The microlensing e ffi ciency de-creases as √ q , while the e ffi ciency of other methods, for exam-ple, the radial-velocity method, decreases in direct proportion to q . See Gaudi (2012) for a review on various advantages of themicrolensing method. With the sensitivity to planets that are dif- Article number, page 1 of 10 & Aproofs: manuscript no. ms ficult to be detected by other methods, microlensing plays animportant role to complement other methods not only for thecomplete demographic census of planets but also for the com-prehensive understanding of the planet formation process.However, these advantages of the microlensing method, es-pecially the latter one, i.e., the high sensitivity to low-massplanets, were di ffi cult to be fully realized during the earlygeneration of microlensing experiments, for example MACHO(Alcock et al 1997) and OGLE (Udalski et al. 1994). A planetarymicrolensing signal, in general, appears as a short-term anomalyto the smooth and symmetric lensing light curve generated bythe host of the planet (Mao & Paczy´nski 1991; Gould & Loeb1992). For this reason, a microlensing planet search shouldbe carried out in two steps: first by detecting lensing events,and second by inspecting planet-induced anomalies in the lightcurves of detected lensing events. The probability for a star to begravitationally lensed is very low, on the order of 10 − for starslocated in the Galactic bulge field, toward which microlensingsurveys have been and are being carried out (Paczy´nski 1991;Griest et al. 1991; Sumi & Penny 2016; Mróz et al. 2019), andthus a lensing survey should cover a large area of sky to increasethe number of lensing events by maximizing the number of mon-itored stars. This requirement had limited the cadence of lensingsurveys, and subsequently the rate of planet detections, espe-cially that of very low-mass planets. Gould & Loeb (1992) pro-posed to overcome this problem by conducting intensive follow-up observations of survey-detected events, which led to the firstdetections of low mass planets (Beaulieu et al. 2006; Gould et al.2006). However, this approach is necessarily restricted by tele-scope resources to a small number of events.The planet detection rate has rapidly increased with theoperation of high-cadence lensing surveys including MOA II(Bond et al. 2001), OGLE-IV (Udalski et al. 2015), and KMT-Net (Kim et al. 2016). By employing multiple telescopesequipped with large-format cameras, these surveys achieve anobservation cadence reaching down to 15 min for dense bulgefields. This cadence is shorter than those of the first-generationMACHO and OGLE surveys, that had been carried out with a ∼ In Table 1, we list the microlensing super-Earth planets,along with the masses of the planets and their hosts, that havebeen detected from the last 28 year operation of lensing surveyssince 1992. Among the total ten super-Earth planets, seven weredetected during the last four years since the full operation of theKMTNet survey in 2016, and for all of these events, the KMTNetdata played key roles in detecting and characterizing the planets.In this paper, we report the detection of a new microlensingsuper-Earth planet. The planet was found from a project that hasbeen conducted to search for unrecognized planets in the pre-vious KMTNet data collected in and before the 2018 season.In the first part of this project, Han et al. (2020b) investigatedlensing events with faint source stars, considering the possibil-ity that planetary signals might be missed due to the noise orscatter of data. From the investigation, they found four plane- We note that the term "super-Earth" refers only to the mass of theplanet, and so does not imply anything about the atmosphere structure,surface conditions, or size of the planet.
Fig. 1.
Light curve of KMT-2018-BLG-1025. The upper and lowerpanels show the whole view and the zoomed-in view of the peak re-gion, respectively. The colors of data points indicate the observatories,as given in the legend. The curve plotted over the data points is the 1L1Smodel, for which the residuals in the peak region are presented in thebottom panel. The dotted vertical lines at t ∼ .
38 and t ∼ . tary events that had not been reported before. The new plane-tary system that we report in this work is found from the secondpart of the project that has been carried out by inspecting subtleplanetary signals in the light curves of high-magnification lens-ing events with peak magnifications A peak &
30. In this project,high-magnification events are selected as targets for reinspec-tion because the sensitivity to planets for these events is high(Griest & Safizadeh 1998). Despite the high chance of planetperturbations, some planetary signals produced by a non-caustic-crossing channel may not be noticed due to their weak signals(Zhu et al. 2014).For the presentation of the work, we organize the paper asfollows. The acquisition and reduction processes of the data usedin the analysis are discussed in Sect. 2. We describe the charac-teristics of the anomaly in the lensing light curve in Sect. 3. Weexplain various models tested to explain the observed anomaly,and show that the anomaly is of a planetary origin in Sect. 4. Theprocedure to estimate the angular Einstein radius is discussed inSect. 5. We estimate the physical parameters of the planetary sys-tem, including the mass and distance, in Sect. 6. We summarizethe results and conclude in Sect. 7.
2. Observations and data
The planet is found from the analysis of the microlensingevent KMT-2018-BLG-1075. The source star of the event liesin the Galactic bulge field with the equatorial coordinates of(R . A ., decl . ) = (17 : 59 : 27 . , −
27 : 52 : 41 . l , b ) = (2 ◦ . , − ◦ . Article number, page 2 of 10heongho Han et al.: KMT-2018-BLG-1025Lb: microlensing super-Earth planet orbiting a low-mass star
Table 1.
Microlensing super-Earth planetsEvent M p ( M ⊕ ) M host ( M ⊙ ) ReferenceOGLE-2005-BLG-390Lb ∼ . ∼ .
22 Beaulieu et al. (2006)MOA-2007-BLG-192Lb ∼ . ∼ .
06 Bennett et al. (2008)OGLE-2013-BLG-0341Lb ∼ ∼ . ∼ . ∼ .
067 Bond et al. (2017), Shvartzvald et al. (2017)OGLE-2016-BLG-1928L ∼ . ∼ . ∼ .
23 Udalski et al. (2018)KMT-2018-BLG-0029Lb ∼ . ∼ . ∼ ∼ .
25 Ryu et al. (2019)OGLE-2018-BLG-0677Lb ∼ . ∼ .
12 Herrera-Martín et al. (2020)KMT-2019-BLG-0842Lb ∼ . ∼ .
76 Jung et al. (2020)
Notes.
The sample is selected with a planet mass limit of M p . M ⊕ . OGLE-2016-BLG-1928L is a free-floating planet, and thus the host massis not included. Table 2.
Data readjustment factorsData set N data k σ min KMTA (BLG03) 1423 1.562 0.005KMTA (BLG43) 1246 1.483 0.010KMTC (BLG03) 1563 1.183 0.010KMTC (BLG43) 1790 1.225 0.010KMTS (BLG03) 1357 1.208 0.005KMTS (BLG43) 1249 1.483 0.005OGLE 1457 1.575 0.005
Notes. N data indicates the number of each data set. lensing-induced magnification with an apparent baseline bright-ness of I ∼ .
65, was highly magnified during about 10 dayscentered at HJD ′ ≡ HJD − ∼ .
85. The event wasfound from the post-season inspection of the 2018 season datausing the KMTNet Event Finder System (Kim et al. 2018). Atthe time of finding, the event drew little attention due to the sim-ilarity of the lensing light curve to that of a regular single-sourcesingle-lens (1L1S) event. See more detailed discussion in the fol-lowing section.Observations of the event by the KMTNet survey wereconducted using three telescopes that are located in Australia(KMTA), Chile (KMTC), and South Africa (KMTS). Each tele-scope has a 1.6m aperture and is equipped with a camera yield-ing 4 deg field of view. The event is located in the two over-lapping survey fields of “BLG03” and “BLG43”, which are dis-placed with a slight o ff set to fill the gaps between the chips of thecamera. Observations in each field were conducted with a 30 mincadence, resulting in a combined cadence of 15 min. Thanks tothe high-cadence coverage of the event using the globally dis-tributed multiple telescopes, the peak region of the event wascontinuously and densely covered.Images of the source were obtained mostly in the I band, anda fraction of images were acquired in the V band for the measure-ment of the source color. Reduction of the data was done usingthe KMTNet pipeline (Albrow et al. 2009) based on the di ff er-ence imaging method (Tomaney & Crotts 1996; Alard & Lupton1998), that is developed for the optimal photometry of stars ly-ing in very dense star fields. For a subset of the KMTC data, anadditional photometry was conducted using the pyDIA software(Albrow 2017) to construct a color-magnitude diagram (CMD)of stars and to measure the color of the source star. The de-tailed procedure of determining the source color is describedin Sect. 5. Error bars of the data estimated from the automa-tized photometric pipeline were readjusted using the method ofYee et al. (2012). In this method, the error bars are renormalized Fig. 2. ∆ χ map in the s – q plane. The color coding is set to representpoints with < n σ (red), < n σ (yellow), < n σ (green), < n σ (cyan), < n σ (blue), and < n σ (purple), where n =
4. The three encircledregions indicate the positions of the three degenerate local solutions A,B c , and B w . by σ = [ σ + ( k σ ) ] / , where σ denotes the error estimatedfrom the pipeline, σ min is a scatter of data, and k is a factor usedto make χ per degree of freedom (dof) unity. In Table 2, we listthe numbers and the data readjustment factors for the individualdata sets.Although not alerted at the time of the lensing magnifica-tion, the source star of the event lies in the field covered bythe OGLE survey. We, therefore, checked the OGLE imagescontaining the source and conducted photometry for the sourceidentified by the KMTNet survey. From this, we recover theOGLE photometry data, among which seven data points coverthe peak of the light curve. OGLE observations were done us-ing the 1.3m telescope of the Las Campanas Observatory inChile, and reduction is carried out using the OGLE photome-try pipeline (Udalski 2003). We publish the photometry data toensure reproducibility of the analysis. The data are available athttp: // astroph.chungbuk.ac.kr / ∼ cheongho / data.html. Article number, page 3 of 10 & Aproofs: manuscript no. ms
Fig. 3.
Zoomed-in view of the light curve in the peak region and the residuals from five tested models including 1L1S, 1L2S, and three 2L1Smodels (solutions A, B c , and B w ). Although three 2L1S model curves are drawn over the data points in the top panel, it is di ffi cult to distinguishthem within the line width due to the severity of the degeneracy among the solutions.
3. Characteristics of the anomaly
The light curve of KMT-2018-BLG-1025 is shown in Figure 1.At the first glance, it appears to have the smooth and sym-metric form of a 1L1S event. A 1L1S modeling yields an im-pact parameter (scaled to the angular Einstein radius θ E ) ofthe lens-source approach and an event timescale of ( u , t E ) ∼ (0 . , . A peak ∼ / u ∼ t indicates the time of theclosest lens-source approach. We note that finite-source e ff ectsare considered in the 1L1S model, but the e ff ects are negligible,and thus the value of the normalized source radius ρ is not pre-sented in the table. The normalized source radius is defined asthe ratio of the angular source radius θ ∗ to θ E , that is, ρ = θ ∗ /θ E .The event was reanalyzed because it was selected in the listof high-magnification events for close examinations among theKMTNet events detected in and before the 2018 season in searchfor planetary signals that had not been noticed previously. Fromthis analysis, we find that the light curve exhibits a subtle butnoticeable deviation from a 1L1S model.In the lower two panels of Figure 1, we present a zoomed-inview of the light curve and residuals from the 1L1S model in thepeak region, which shows a slight bump in the residuals centeredat t ∼ .
38 and a dip centered at t ∼ .
66. Although mi- nor, with ∆ I . .
05 magnitude, the deviation drew our attentionfor two major reasons. The first reason is that the deviation oc-curred in the central magnification region, in which the chance ofa planet-induced perturbation is high (Griest & Safizadeh 1998).The second reason is that di ff erent data sets exhibit a consistentpattern of deviation. The data sets obtained using the KMTC, lo-cated in Chile, and KMTS, located in South Africa, telescopesshow consistent deviations. Considering that the two telescopesare remotely located, it is di ffi cult to explain the consistency witha coincidental systematics in the data such as changes in trans-parency. Furthermore, the OGLE data in the deviation region ex-hibit a consistent anomaly pattern with that of the KMTC data,although their coverage is not very dense. Therefore, the devia-tion is very likely to be real.
4. Interpretation of the anomaly
The fact that the anomaly occurred in the peak region of a high-magnification event suggests the possibility that the anomalymay be produced by a planetary companion, M , to the primarylens, M . In order to check this possibility, we conduct an addi-tional modeling under a binary-lens (2L1S) interpretation.The modeling is carried out to find a set of lensing param-eters that best explain the observed anomaly in the light curve.In addition to the 1L1S lensing parameters ( t , u , t E , ρ ), a 2L1Smodeling requires one to add three extra lensing parameters of( s , q , α ), which represent the projected separation (normalized Article number, page 4 of 10heongho Han et al.: KMT-2018-BLG-1025Lb: microlensing super-Earth planet orbiting a low-mass star
Fig. 4.
Lens system configurations of the three degenerate 2L1S so-lutions: A, B c , and B w . In each panel, the blue dots, marked by M (host) and M (planet), are the lens positions, the line with an arrow isthe source trajectory, and the cuspy closed curves are the caustics. Thedashed circle centered at M represents the Einstein ring. The enlargedviews in the central magnification regions for the individual solutionsare presented in Fig. 5. to θ E ) and mass ratio between the binary lens components, andthe angle between the source trajectory and the M – M axis(source trajectory angle), respectively. The parameter ρ is in-cluded to account for potential finite-source e ff ects in the lens-ing curve caused by a source approach close to or a crossingover lensing caustics induced by a lens companion. The 2L1Smodeling is done in two steps. In the first step, we conduct gridsearches for the binary lensing parameters s and q , while theother parameters are found using a downhill approach based onthe Markov Chain Monte Carlo (MCMC) algorithm. Consider-ing that central anomalies can also be produced by a very wideor a close binary companion with a mass roughly equal to theprimary (Han 2009a), we set the ranges of ( s , q ) wide enoughto check the binary origin of the anomaly: − . ≤ log s ≤ . − . ≤ log q ≤ .
0. In the second step, the individual lo-cal solutions found from the first step are refined by allowing allparameters (including s and q ) to vary.From the 2L1S modeling, we identify three degenerate localsolutions. Figure 2 shows the locations of the local solutions inthe ∆ χ map on the s – q plane obtained from the grid search. Theindividual locals lie at ( s , q ) ∼ (0 . , . × − ), solution “A”,(0 . , . × − ), solution “B c ”, and (1 . , . × − ), solu-tion “B w ”. Here the subscripts “c”, standing for close, and “w”,standing for wide, imply that the normalized binary separationis less ( s < .
0, close solution) and greater ( s > .
0, wide solu-tion) than unity, respectively. The model curves of the individual2L1S solutions and the residuals from the models in the regionaround the peak of the light curve are shown in Figure 3. In Ta-ble 3, we also list the lensing parameters of the solutions alongwith the values of χ / dof for the individual models. The uncer-tainty of each lensing parameter is estimated as the standard de-viation of the distribution of points in the MCMC chain under Fig. 5.
Lens system configurations in the central magnification regionfor the three 2L1S solutions. Notations are same as those in Fig. 4. Thetwo orange circles represent the source positions at the times of themajor anomalies at t and t that are marked in Figs. 1 and 3. The sizeof the circle is scaled to the source size. In the case of the solution A,for which the source size cannot be securely measured, the radius of thecircle is set to that of the best-fit value. the assumption that the distribution is gaussian. The ∆ χ = . ff erence between the A solution and the minimum of the twoB solutions is not big enough to confidently distinguish betweenthem. To be noted among the parameters is that the mass ratios,which are q ∼ . × − for the solution A and ∼ . × − forthe solutions B, are very low, indicating that the primary lensis accompanied by a very low-mass planetary companion ac-cording to the models. From an additional modeling consideringmicrolens-parallax e ff ects (Gould 1992), we find that it is di ffi -cult to securely constrain the microlens parallax π E due to therelatively short timescale, ∼ ff erenttypes of degeneracy. The ambiguity between the pair of the solu-tions B c and B w is caused by the well-known close–wide degen-eracy (Griest & Safizadeh 1998; Dominik 1999; An 2005). Thesolution A is not subject to this type of degeneracy because thesource trajectory of the corresponding wide solution passes overthe planetary caustic located at a position with a separation from M of ∼ s − / s ∼ .
12 on the planet side, and this causes a poorfit of the wide solution to the observed data.We note that the degeneracy between the A and B solu-tions is a new type that has not been reported before. The de-generacy is accidental in the sense that it is caused by the un-expected combination of multiple lens parameters instead ofbeing rooted in the lensing physics, for example, the close–wide degeneracy that is originated in the invariance of the bi-nary lens equations with s and s − . For such accidental de-generacies, it is di ffi cult to identify them from the explo-ration of the numerous combinations of lensing parameters andthe simulations of various observational conditions, and thusthey are mostly identified from the analyses of actual lensing Article number, page 5 of 10 & Aproofs: manuscript no. ms
Table 3.
Lensing parameters of various tested modelsParameter 1L1S 1L2S 2L1SSolution A Solution B c Solution B w χ / dof 10251 . / . / . / . / . / t (HJD ′ ) 8274 . ± .
001 8274 . ± .
001 8274 . ± .
001 8274 . ± .
001 8274 . ± . u (10 − ) 6 . ± .
177 7 . ± .
532 7 . ± .
237 8 . ± .
319 8 . ± . t E (days) 10 . ± . . ± .
262 9 . ± .
258 8 . ± .
234 8 . ± . s – – 0 . ± .
021 0 . ± .
025 1 . ± . q (10 − ) – – 0 . ± .
270 1 . ± .
499 1 . ± . α (rad) – – 6 . ± .
009 2 . ± .
023 2 . ± . ρ (10 − ) – – . . . ± .
645 7 . ± . t , (HJD ′ ) – 8274 . ± .
017 – – – u , (10 − ) – 7 . ± .
793 – – – ρ (10 − ) – – – – – q F – 0 . ± .
004 – – –
Notes.
HJD ′ ≡ HJD − events, as illustrated in the cases of the events OGLE-2011-BLG-0526 and OGLE-2011-BLG-0950 / MOA-2011-BLG-336(Choi et al. 2012), OGLE-2012-BLG-0455 / MOA-2012-BLG-206 (Park et al. 2014), and MOA-2016-BLG-319 (Han et al.2018). Although the o ff sets of the source trajectory from the cen-tral caustic for both solutions, ξ ∼ u / cos α ∼ . × − for thesolution A and ξ ∼ . × − for the solution B, are similar toeach other, this degeneracy is di ff erent from the caustic-chiralitydegeneracy reported by Skowron et al. (2018) and Hwang et al.(2018) for two reasons. First, the source stars of the two solutionsA and B move in almost opposite directions, while the source di-rections of the two solutions subject to the caustic-chirality de-generacy are nearly identical. Second, while the caustic-chiralitydegeneracy, in general, occurs when the source passes a plane-tary caustic, around which the magnification pattern on the leftand right sides are approximately symmetric (Gaudi & Gould1997), the magnification pattern around the central caustic in-ducing the observed anomaly is not symmetric (Chung et al.2005).The lens system configurations of the individual 2L1S lo-cal solutions are shown in Figure 4. In each panel of the figure,the blue dots marked by M and M denote the positions of thelens components, the line with an arrow represents the sourcetrajectory, and the red closed curves are caustics. The planet in-duces two sets of caustics, one lying near the position of M (central caustic) and the other lying at a position with a separa-tion from M of ∼ s − / s (planetary caustic). For all solutions,the anomaly is explained by the passage of the source close tothe central caustic, but the source incidence angles of the solu-tions A and B di ff er from one another: α ∼ − ◦ . α ∼ ◦ for the solutions B c and B w .Figure 5 shows the enlarged views of the configuration in thecentral magnification region for the individual solutions. In eachpanel, we mark the source positions corresponding to the times t and t (two orange circles), and draw equi-magnification con-tours (grey curves around the caustic). Around a central caustic,the magnification excess, defined by ǫ = ( A − A ) / A ,varies depending on the region. Here A and A denotethe 2L1S and 1L1S lensing magnifications, respectively. Positiveanomalies occur in the regions around the cusps of the caustic,and negative anomalies arise in the outer region of the fold caus-tic and the back end region of the wedge-shaped caustic. Seeexample maps of magnification excess around central causticspresented in Han (2009a) and Han (2009b). According to thesolution A, the bump at t is produced when the source passesthrough the positive excess region extending from the protrudent Fig. 6.
Cumulative distributions of ∆ χ for the three degenerate 2L1S(solutions A, B c , and B w ) models and 1L2S model with respect to the1L1S model. The dotted vertical lines denote the times of the majoranomalies at t and t that are marked in Fig. 1. cusp of the central caustic, and the dip at t is produced when thesource moves through the negative excess region formed alongthe caustic fold. According to the solutions B, on the other hand,the bump and dip are produced by the successive passage of thepositive and negative excess regions formed in the back end re-gion of the caustic, respectively.Models with the addition of a planetary companion to thelens improves the fit by ∆ χ ∼
158 – 170 with respect to the1L1S solution. To show the region of the fit improvement, wepresent the cumulative distributions of ∆ χ for the three 2L1Ssolutions in Figure 6. The distributions show that the major fitimprovement occurs at around t and t , that are the times of themajor anomalies from the 1L1S model. This can also be seen inthe residuals of the 2L1S solutions, shown in Figure 3, whichshows that the major residuals from the 1L1S model at around t and t disappear in the residuals of the 2L1S solutions. Article number, page 6 of 10heongho Han et al.: KMT-2018-BLG-1025Lb: microlensing super-Earth planet orbiting a low-mass star
Fig. 7.
Distributions of points in the MCMC chains for the three de-generate 2L1S solutions. The red, yellow, green, cyan, and blue colorsrepresent points within 1 σ , 2 σ , 3 σ , 4 σ , and 5 σ , respectively. The sig-nificance level is determined so that n σ corresponds to ∆ χ = n withrescaled uncertainties. We also check the possibility that the anomaly was producedby a companion to the source: 1L2S model. Similar to the caseof a 2L1S modeling, extra parameters in addition to those ofthe 1L1S modeling are needed for a 1L2S modeling. Followingthe parameterization of Hwang et al. (2013), these extra param-eters are ( t , , u , , ρ , q F ), which denote the time of the closestapproach of the second source to the lens, the companion-lensseparation at that time, the normalized radius of the source com-panion, and the flux ratio between the source stars, respectively.Considering the possibility that source stars approach very closeto the lens, we consider finite-source e ff ects in the 1L2S model-ing by including two parameters ( ρ , ρ ), which denote the nor-malized source radii of the first and second source stars, respec-tively. In the 1L2S modeling, we use the parameters of the 1L1Smodel as initial parameters, and set the other parameters consid-ering the anomaly features of the light curve. We list the best-fitlensing parameters of the 1L2S model in Table 3, present theresiduals from the model in Figure 3, and show the cumulative ∆ χ distribution with respect to the 1L1S model in Figure 6. Wenote that the normalized source radii of both source stars are notmeasurable due to very week finite-source e ff ects, and thus thevalues of ρ and ρ are not listed in Table 3. It is found that the1L2S model reduces the residuals at around t , but the model stillleaves noticeable residuals near the peak of the lightcurve. The fitof the 1L2S model is better than the 1L1S model by ∆ χ ∼ ∆ χ ∼
35 – 46. We,therefore, conclude that the anomaly in the lensing light curvewas generated by a companion to the lens rather than a compan-ion to the source.
5. Angular Einstein radius
In general cases of lensing events, the angular Einstein radius isestimated from the combination of the angular source radius θ ∗ and the normalized source radius ρ by θ E = θ ∗ ρ . (1) Fig. 8.
The source (cross mark) position with respect to the centroid ofthe red giant clump (RGC, red dot) in the instrumental color-magnitudediagram of stars lying in the vicinity of the source. We mark sourcepositions corresponding to the three degenerate solutions, which yieldvery similar source locations. Also marked is the position of the blend(green dot).
The value of θ ∗ can be derived from the color and brightness ofthe source, and the value of ρ is decided from the analysis of thelight curve a ff ected by finite-source e ff ects. Then, the prerequi-site for the measurement of θ E is that a lensing light curve shouldbe a ff ected by finite-source e ff ects to yield the normalized sourceradius ρ . In the case of KMT-2018-BLG-1025, the feasibility of mea-suring ρ varies depending on the solution. We find that finite-source e ff ects are securely detected according to the solutions B c and B w , but according to the solution A, the e ff ects are not firmlydetected and the model is consistent with a point-source modelwithin 3 σ . This is shown in Figure 7, in which we present the ∆ χ distributions of points in the MCMC chain obtained fromthe modeling runs of the three degenerate 2L1S solutions. Thesescatter plots show that the normalized source radii of the B so-lutions, ρ ∼ × − , are well determined, but only a upperlimit, ρ max ∼ . × − , can be placed for the solution A. As aresult, the angular Einstein radius is determined for the solutionsB c and B w , but only a lower limit can be placed for the solu- The angular Einstein radius can also be measured by separately imag-ing the lens and source. By resolving the images, one can measure thevector separation ∆ θ between the lens and source and hence their helio-centric relative proper motion by µ hel = ∆ θ / ∆ t , where ∆ t representsthe time elapsed since the event. Then, the Einstein radius is deter-mined by θ E = µ geo t E . Here the geocentric relative proper motion isrelated to µ hel by µ geo = µ hel − v ⊕ , ⊥ π rel / au, where v ⊕ , ⊥ is Earth’s ve-locity projected on the plane of the sky at t . Due to the long timespan ∆ t required for the lens–source resolution together with the lim-ited access to high-resolution instrument, there exist just five casesof planetary lens events for which the values of θ E are measured bythis method: OGLE-2005-BLG-071 (Bennett et al. 2020), OGLE-2005-BLG-169 (Batista et al. 2015; Bennett et al. 2015), OGLE-2012-BLG-0950 (Bhattacharya et al. 2018), MOA 2013 BLG-220 (Vandorou et al.2020), and MOA-2007-BLG-400 (Bhattacharya et al. 2020).Article number, page 7 of 10 & Aproofs: manuscript no. ms tion A. Below, we describe the procedure of θ E estimation forthe individual solutions.The angular source radius and the resulting Einstein radiusfor each solution is estimated following the routine procedureoutlined in Yoo et al. (2004). In the first step of the procedure,we specify the source type by placing the positions of the sourceand the centroid of the red giant clump (RGC) in the CMD ofstars lying in the vicinity of the source. Figure 8 shows the po-sitions of the source, marked by a black cross at ( V − I , I ) = (2 . ± . , . ± . V − I , I ) RGC = (2 . , . I - and V -band images. We note that thesource color and brightness estimated from the other solutions,marked by grey crosses and listed in Table 4, result in similarvalues. Also marked is the position of the blend, green dot. Aswe will show in the following section, the lens is a very low-mass M dwarf, while the color and brightness of the blend corre-spond to an early main-sequence star or a subgiant. This impliesthat the contribution of the lens flux to the blended flux is neg-ligible. We calibrate the source color and brightness using theknown de-reddened values of the RGC centroid, ( V − I , I ) = (1 . , . ff sets in the color ∆ ( V − I ) and bright-ness ∆ I between the source and RGC centroid, the reddening andextinction corrected values of the source color and brightness areestimated by( V − I , I ) = ( V − I , I ) RGC , + ∆ ( V − I , I ) . (2)The values of ( V − I , I ) corresponding to the individual solu-tions are listed in Table 4. The estimated color and brightness are( V − I , I ) ∼ (1 . , . V − I color into V − K color using the color-color relation of Bessell & Brett (1988),and estimate the angular source radius using the ( V − K ) – θ ∗ re-lation of Kervella et al. (2004). The measured source radii are inthe range of 0 . . θ ∗ /µ as . .
70. Finally, the angular Einsteinradius and the relative lens-source proper motion are estimatedby the relations θ E = θ ∗ /ρ and µ = θ E / t E , respectively.In Table 4, we list the values of θ ∗ , θ E , and µ correspondingto the individual solutions. We note that the lower limits of θ E and µ are presented for the solution A, for which only the upperlimit of ρ is constrained. We note that the Einstein radius esti-mated from the solutions B, θ E = .
091 for the solution B c and0.094 mas B w , is substantially smaller than ∼ . ∼ . M ⊙ located roughly halfway between the lens and source. The an-gular Einstein radius is related to the lens mass and distance by θ E = ( κ M π rel ) / ; π rel = au D L − D S ! , (3)where κ = G / ( c au) and D S is the distance to the source. Then,the small value of θ E for the solutions B suggests that the lenshas a low mass or it is located close to the source.
6. Physical lens parameters
The lens mass and distance are unambiguously determined bysimultaneously measuring θ E and π E , which are related to thephysical lens parameters by M = θ E κπ E , D L = au π E θ E + π S . (4) Fig. 9.
Bayesian posteriors of the host mass for the three degenerate2L1S solutions. The three curves in each panel represent contributionsby the disk (blue), bulge (red), and total (black) lens populations. Thesolid vertical line represents the median, and the two dotted verticallines indicate 1 σ range of the distribution. Here π S = au / D S denotes the parallax of the source. In the caseof KMT-2018-BLG-1025, only θ E is measured for the solutionsB c and B w , and neither of θ E and π E is measured for the solu-tion A. Although this makes it di ffi cult to uniquely determine M and D L , these parameters can be statistically constrained from aBayesian analysis with the priors of a lens mass function and aGalactic model.In the Bayesian analysis, we conduct a Monte Carlo sim-ulation to produce artificial lensing events. For the productionof events, we use priors of a mass function, to assign lensmasses, and a Galactic model, to assign lens locations and rel-ative lens-source transverse velocities. For the mass function,we use a model constructed by combining those of Zhang et al.(2019) and Gould (2000) mass functions, and the model con-siders not only stellar lenses but also substellar brown dwarfsand stellar remnants. For the physical lens distribution, we usethe modified version of Han & Gould (2003) model, in whichthe original double-exponential disk model is replaced with theBennett et al. (2014) model. We note that the distance to thesource, D S , is allowed to vary by choosing D S from the physicaldistribution model of the bulge instead of using a fixed value.For the dynamical distribution of the lens and source motion,we adopt the Han & Gould (1995) model. A detailed descriptionof the adopted priors is given in Han et al. (2020a). The num-ber of events produced by the simulation for each solution is10 . With the events produced by the simulation, posteriors of M and D L are obtained by constructing the probability distributionsof events that are consistent with the measured observables. Al-though the ρ value is not tightly constrained for the solution A,we use its distribution obtained based on the MCMC links toweight the posteriors of the M and D L .The posteriors for the host mass, M h , and distance to the lensare shown in Figures 9 and 10, respectively. For each posterior, Article number, page 8 of 10heongho Han et al.: KMT-2018-BLG-1025Lb: microlensing super-Earth planet orbiting a low-mass star
Table 4.
Source color, brightness, Einstein radius, and proper motionValue Solution A Solution B c Solution B w ( V − I , I ) (2 . ± . , . ± . . ± . , . ± . . ± . , . ± . V − I , I ) RGC (2 . , . ← ← ( V − I , I ) RGC , (1 . , . ← ← ( V − I , I ) (1 . ± . , . ± . . ± . , . ± . . ± . , . ± . θ ∗ (uas) 0 . ± .
05 0 . ± .
05 0 . ± . θ E (mas) ≥ .
12 0 . ± .
007 0 . ± . µ (mas yr − ) ≥ . . ± .
28 3 . ± . Notes.
The notation “ ← ” indicates that the value is same as that presented in the left column. Table 5.
Physical lens parametersParameter Solution A Solution B c Solution B w M h ( M ⊙ ) 0 . + . − . . + . − . . + . − . M p ( M ⊕ ) 6 . + . − . . + . − . . + . − . D L (kpc) 6 . + . − . . + . − . . + . − . a ⊥ (au) 1 . + . − . . + . − . . + . − . we present three distributions, in which the red and blue distri-butions are contributions by the bulge and disk lens populations,respectively, and the black distribution is the sum of contribu-tions by the both lens populations. In Table 5, we list the esti-mated physical parameters of the host and planet ( M p ) masses,distance, and projected physical separation ( a ⊥ ) of the planetfrom its host. For each physical parameter, we choose a medianof the probability distribution as a representative value, and theupper and lower limits are estimated as the 16% and 84% rangesof the distributions. The estimated masses of the planet and hostare( M p , M h ) ∼ ( (6 . M ⊕ , . M ⊙ ) for solution A , (4 . M ⊕ , . M ⊙ ) for solution B. (5)The planet mass is in the category of a super-Earth regardlessof the solutions, and thus the planet is the eleventh super-Earthplanet discovered by microlensing. The host mass varies depend-ing on the solutions: a mid-M dwarf for the solution A and a verylate M dwarf or possibly a substellar brown dwarf for the solu-tions B. The estimated distance to the lens is D L ∼ ( . , . t E ∼ . θ E ∼ .
09 mas.For the same reason, the distance to the lens predicted by the so-lutions B, ∼ . ∼ . ρ Sol A < . × − and ρ Sol B > . × − , both at 3 σ , while from Tables 3 and 4,the quantity θ ∗ / t E is about 10% larger for solution A than so-lutions B c and B w . Therefore, the 3 σ limits for µ = θ ∗ / ( ρ t E ) Fig. 10.
Bayesian posteriors of the lens distance for the three 2L1Ssolutions. Notations are same as those of in Fig. 9. barely overlap. Most likely, the actual proper motion measure-ment will be well away from this boundary, e.g., near the bestfits µ ≃ . − (for solutions B) or µ ≃ . − (forsolution A). Only if the measured value is about half way be-tween will the correct solution remain undetermined. Note thatthe long tail in the solution A distribution, which prevented aprecise estimate of θ E and µ for this case, does not a ff ect the res-olution of the degeneracy: if the true value of ρ is in this tail, thenthe proper motion will be high, and solution A will be unambigu-ously favored. To be confident of detecting the lens, one shouldallow for proper motions as low as µ ∼ − , which arepermitted by solutions B. However, even at this slow pace, thesource and lens will be separated by 30 mas in 2028, the earli-est possible date for first AO light 30m class telescopes. At thatpoint the source and lens can be easily resolved. By contrast, theclose–wide degeneracy between the solutions B c and B w cannotbe resolved because the relative proper motions expected fromthe degenerate solutions are similar to one another.
7. Conclusion
We reported the discovery of a super-Earth planet that was foundfrom the analysis of the lensing event KMT-2018-BLG-1025.
Article number, page 9 of 10 & Aproofs: manuscript no. ms
The planetary signal in the lensing light curve had not been no-ticed during the season of the event discovery, and was foundfrom the systematic inspection of high-magnification events inthe KMTNet data collected in and before the 2018 season. Weidentified three degenerate solutions, in which the ambiguity be-tween a pair of solutions was caused by the previously knownclose–wide degeneracy, and the degeneracy between these andthe other solution was a new type that had not been reportedbefore. The estimated mass ratio between the planet and hostwas q ∼ . × − for one solution and ∼ . × − forthe other pair of solutions. From the Bayesian analysis car-ried out with the measured observables, we estimated that themasses of the planet and host and the distance to the lens were( M p , M h , D L ) ∼ (6 . M ⊕ , . M ⊙ , . ∼ (4 . M ⊕ , . M ⊙ , . ff erence betweenthe relative lens-source proper motions expected from the twosets of solutions, the degeneracy between the solutions can belifted by resolving the lens and source from future high resolu-tion imaging observations. These observations will also yield themass and distance of the lens, and so the mass of the planet. Acknowledgements.
Work by CH was supported by the grants of National Re-search Foundation of Korea (2020R1A4A2002885 and 2019R1A2C2085965).Work by AG was supported by JPL grant 1500811. This research has madeuse of the KMTNet system operated by the Korea Astronomy and Space Sci-ence Institute (KASI) and the data were obtained at three host sites of CTIOin Chile, SAAO in South Africa, and SSO in Australia. The OGLE project hasreceived funding from the National Science Centre, Poland, grant MAESTRO2014 / / A / ST9 / References
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