# MagAO Observations of the Binary Microlens OGLE-2014-BLG-1050 Prefer the Higher-mass Solution

Xiaojia Xie, Subo Dong, Wei Zhu, A. Gould, A. Udalski, J.-P. Beaulieu, L.

Close, J. Males, J.-B. Marquette, K. Morzinski, et al.

► To cite this version:

Xiaojia Xie, Subo Dong, Wei Zhu, A. Gould, A. Udalski, et al. MagAO Observations of the Binary Microlens OGLE-2014-BLG-1050 Prefer the Higher-mass Solution. The Astronomical Journal, 2021, 161 (3), pp.113. 10.3847/1538-3881/abd6c0. hal-03430357

HAL Id: hal-03430357

https://hal.science/hal-03430357v1

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# MagAO Observations of the Binary Microlens OGLE-2014-BLG-1050 Prefer the Higher-mass Solution*

Xiaojia Xie¹,², Subo Dong¹,<fnref n="14" />, Wei Zhu³, A. Gould⁴,⁵, A. Udalski⁶, J.-P. Beaulieu⁷,⁸, L. M. Close⁹, J. R. Males⁹, J.-B. Marquette¹⁰,<fnref n="13" />, K. M. Morzinski⁹, R. W. Pogge⁴,¹¹, and J. C. Yee¹²

¹ Kavli Institute for Astronomy and Astrophysics, Peking University, Yi He Yuan Road 5, Hai Dian District, Beijing 100871, People's Republic of China
dongsubo@pku.edu.cn

² Department of Astronomy, Peking University, Yi He Yuan Road 5, Hai Dian District, Beijing 100871, People's Republic of China

³ Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada

⁴ Department of Astronomy, Ohio State University, 140 W. 18th Avenue, Columbus, OH 43210, USA

⁵ Max-Planck-Institute for Astronomy, Köigstuhl 17, D-69117 Heidelberg, Germany

⁶ Astronomical Observatory, University of Warsaw, Al. Ujazdowskie 4, 00-478 Warszawa, Poland

⁷ School of Natural Sciences, University of Tasmania, Private Bag 37 Hobart, Tasmania 7001 Australia

⁸ Sorbonne Université, UPMC Université Paris 6 et CNRS, UMR 7095, Institut d'Astrophysique de Paris, 98 bis Bd Arago, F-75014 Paris, France
⁹ Steward Observatory, University of Arizona, Tucson, AZ 85721, USA

¹⁰ Laboratoire d'Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, F-33615 Pessac, France

¹¹ Center for Cosmology and AstroParticle Physics, The Ohio State University, 191 West Woodru Avenue, Columbus, OH 43210, USA
¹² Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA

Received 2020 October 30; revised 2020 December 16; accepted 2020 December 22; published 2021 February 11

## Abstract

We report adaptive optics (AO) follow-up imaging of OGLE-2014-BLG-1050, which is the second binary microlensing event with space-based parallax measurements. The degeneracy in microlens parallax $\pi_E$ led to two sets of solutions, either a $\sim (0.9, 0.35) M_\odot$ binary at $\sim 3.5$ kpc or a $\sim (0.2, 0.07) M_\odot$ binary at $\sim 1.1$ kpc. We measure the flux blended with the microlensed source by conducting Magellan AO observations, and find that the blending is consistent with the predicted lens flux from the higher-mass solution. From the combination of the AO flux measurement together with previous lensing constraints, it is estimated that the lens system consists of a $1.05_{-0.07}^{+0.08} M_\odot$ primary and a $0.38_{-0.06}^{+0.07} M_\odot$ secondary at $3.43_{-0.21}^{+0.19}$ kpc.

Unified Astronomy Thesaurus concepts: Binary lens microlensing (2136); Gravitational microlensing (672); High-resolution microlensing event imaging (2138)

## 1. Background

Microlensing is sensitive to stellar binaries over a relatively broad range of masses and separations, and the sensitivity peaks when the projected separation is near the Einstein radius (Mao & Paczynski 1991). Usually, the physical parameters including the lens mass $M_L$, the relative lens-source parallax $\pi_{rel}$, and relative lens-source proper motion $\mu_{rel}$ are degenerate. Gould (1992) showed that the degeneracy can be broken by measuring microlens parallax $\pi_E$ and angular Einstein ring radius $\theta_E$, and the lens mass can then be determined as

$$M_L = \frac{\theta_E}{\kappa\pi_E}, \qquad (1)$$

where $\kappa = 8.14 \text{ mas}/M_\odot$ is a constant. Using the Spitzer space telescope, OGLE-2014-BLG-1050 (Zhu et al. 2015, Z2015 hereafter) was the second binary microlensing event with measured space-based microlens parallax (Refsdal 1966; Gould 1994), after the binary microlensing event OGLE-2005-SMC-001 (Dong et al. 2007). Unlike OGLE-2005-SMC-001, OGLE-2014-BLG-1050 showed caustic crossing features, which allowed for measuring $\theta_E$ via finite-source effects. However, because Spitzer did not capture the caustic entrance,

there were two degenerate solutions of $\pi_E$ and therefore two solutions of the mass and distance for the lens system inferred by Z2015.

The lens flux values expected from the two degenerate solutions (a binary with $\sim (0.9, 0.35) M_\odot$ stars at $\sim 3.5$ kpc versus a $\sim (0.2, 0.07) M_\odot$ binary at $\sim 1.1$ kpc) are different, and thus measuring the lens flux allows one to distinguish one solution from the other. The lens flux measurement also provides one with a relation between lens mass and distance (e.g., Dong et al. 2009; Beaulieu et al. 2018). In the crowded bulge field, the microlens target is usually blended with ambient stars on seeing-limited images. Diffraction-limited imaging with a space telescope such as the Hubble Space Telescope (e.g., Dong et al. 2009) or a large ground-based telescope with an adaptive optics (AO) system (e.g., Janczak et al. 2010) are needed to constrain the lens flux.

In this paper we present the observations of OGLE-2014-BLG-1050 using Magellan adaptive optics (MagAO; Close et al. 2012; Males et al. 2014; Morzinski et al. 2014) conducted for the lens flux measurement that leads to the resolution of the degeneracy in lensing solutions and accurate measurements of the lens parameters.

## 2. MagAO Observations

We observed the field of OGLE-2014-BLG-1050 (J2000 equatorial coordinates: $\alpha = 17^h45^m07^s83$, $\delta = -22^\circ54'20''0$) using MagAO mounted on the 6.5 m Magellan Clay telescope on UT 2015 May 19 in the H band. We used the Clio Wide camera with a pixel size of 27.5 mas and a field of view

<footnote>* This paper includes data gathered with the 6.5m Magellan Clay Telescope at Las Campanas Observatory, Chile.</footnote>

<footnote n="13">¹³ Associated with the Sorbonne Université, UPMC Université Paris 6 et CNRS, UMR 7095, Institut d'Astrophysique de Paris, 98 bis Bd Arago, F-75014 Paris, France.</footnote>

<footnote n="14">¹⁴ Corresponding author.</footnote>
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Left: the *I*-band OGLE image with OGLE-2014-BLG-1050 at the center. Right: the *H*-band MagAO image of the same field, and the upper-right inset is a zoomed view centered on the microlens baseline object, which is indicated using a half cross.</figcaption></figure>

of ~28" × 14" (Morzinski et al. 2015). We used an *H* = 10.24 mag AO guide star (J2000 equatorial coordinates: α = 17h45m08s80, δ = −22°54′33″3), which was 19" from the microlens. We took 5 frames at each of the 10 dithering positions, and the integration time for each science exposure was 30 s. The processing of raw images includes correcting for detector nonlinearity (Morzinski et al. 2015), dark currents, and flat-fielding. Then we align the frames using the *geomap* and *geotran* tasks of IRAF, which utilizes the positions of isolated bright stars as references for the alignment. The detailed processing procedures follow X. Xie et al. (2021, in preparation). The right panel of Figure 1 shows our processed MagAO image.

We use SExtractor (Bertin & Arnouts 1996) for astrometry and aperture photometry on the MagAO images. We perform astrometry calibration of the MagAO images mainly following Janczak et al. (2010). We first measure the position of the microlensed source on the subtracted Optical Gravitational Lensing Experiment (OGLE) images. Then we compute a linear coordinate transformation relation between OGLE and MagAO using the positions of seven bright and isolated stars on both sets of frames. The point source shown in the right panel of Figure 1 is identified as the microlens on the MagAO image, and its offset from the transformed OGLE source position is (Δα cos δ, Δδ) = (5 ± 14, −5 ± 10)mas. The relative proper motion of the source and lens is μrel ≈ 7 mas yr⁻¹ (Z2015), and at the time of MagAO observations (~310 days after the peak), the expected separation between source and lens is ≈6 mas, which is much smaller than its FWHM of 250 mas on the MagAO image. The nearest detected neighbor star of the target on the MagAO image is about 900 mas away. Hence, the MagAO microlens identification is secure.

We first estimate the internal photometric uncertainties using the multiple MagAO dithers, and then we make external calibrations. We set an aperture that is 1.5 FWHM to perform photometry of each MagAO dither and estimate the internal

photometric errors by comparing the results of all dithers. The internal error of the microlens is 0.015 mag. Due to the lack of common stars between MagAO and Two Micron All Sky Survey (2MASS), we calibrate the MagAO magnitudes using VISTA Variables in the Via Lactea (VVV) survey (Minniti et al. 2010) as a bridge. We use DoPhot (Schechter et al. 1993) to perform point-spread function photometry on the extracted VVV images and then calibrate to the 2MASS magnitude system using common isolated stars within 3' of the target. Only stars with *H* > 13.6 are used to avoid detector nonlinearity for VVV. We calculate the magnitude zero-point of MagAO by cross-matching five common isolated stars between the MagAO and VVV images and find that the standard error of the zero-point calibration is 0.04 mag. We also use a second method to estimate the calibration error by performing photometry on a combined image by coadding all MagAO dithers. For this method, we find a calibration error of 0.02 mag. The resulting photometric estimates from the two methods are consistent, although the associated uncertainties are different. Taking a conservative approach, we adopt the larger estimate. The final calibrated *H*-band flux of the microlens baseline object is *H*<sub>base</sub> = 15.78 ± 0.05.

OGLE-2014-BLG-1050 was observed by the Small & Moderate Aperture Research Telescope System (SMARTS) A Novel Dual Imaging CAMera (ANDICAM; DePoy et al. 2003), which took *H*-band and *I*-band images simultaneously. We obtained the instrumental *H*-band source flux using the *I* − *H* color from linear regression and the reported best-fit *I*-band source flux from Z2015. Then we calibrate the *H*-band source flux using VVV and find that *H*<sub>s</sub> = 17.98 ± 0.02. Subtracting the source flux from the baseline object, we derive the blend flux *H*<sub>b</sub> = 15.93 ± 0.06.

## 3. Constraints on Lens Parameters

We first estimate the expected *H*-band fluxes of the lens system from the two physical solutions in Z2015. We assume
<figure><img src="image_4.png" /><figcaption>**Figure 2.** The left panel shows the constraints on the lens primary mass and distance. The blue and cyan lines show the constraint from the $\pi_E$ of (+, +) and (-, +) solutions, respectively. The black lines show the constraint from $\theta_E$ and the red line shows the constraint from the lens H-band flux. The dotted lines show the 1$\sigma$ error of each constraint. The right panel is a zoom-in of the black dashed rectangle in left panel, with each constraint shown by the dashed lines. The contours enclose the region with likelihoods of 68% and 95%. The blue contours show the likelihood considering constraints of $\theta_E$ and $\pi_E$, while the dark red contours show the likelihood combining all of the three constraints $\theta_E$, $\pi_E$ in the ($u_0$, $u_0$) solution, and lens flux.</figcaption></figure>

<figure><img src="image_5.png" /></figure>

that both components of the binary lens are main-sequence stars, and estimate their luminosities using isochrones from the Dartmouth Stellar Evolution Database (Dotter et al. 2008) by adopting uniform priors of [Fe/H] between -0.2 and 0.2 and age between 1 and 10 Gyr. Following Bennett et al. (2015), we model extinction as a function of lens distance $D_L$ by

$$A_L = (1 - \exp(-D_L/\tau_{\text{dust}}))/(1 - \exp(-D_S/\tau_{\text{dust}}))A_S, \quad (2)$$

where $\tau_{\text{dust}} = 0.1 \text{ kpc}/\sin(b)$ is the scale height of the dust toward the galactic bulge. There is a four-fold degeneracy of light-curve parameters (Refsdal 1966), depending on which side the observed source trajectory lies on the lens as seen from Earth/Spitzer (i.e., the sign of impact parameters $u_0$). The four solutions are ($u_{0,\oplus}$+, $u_{0,\text{Spitzer}+}$), ($u_{0,\oplus}$+, $u_{0,\text{Spitzer}-}$), ($u_{0,\oplus}$-, $u_{0,\text{Spitzer}+}$), and ($u_{0,\oplus}$-, $u_{0,\text{Spitzer}-}$), which we denote as (+, +), (+, -), (-, +), and (-, -) below. In the case of OGLE-2014-BLG-1050, the degenerate solutions correspond to two different sets of physical lens parameters. The best-fit higher- and lower-mass solutions in Z2015 predict $H_{L,(+,+)} = 16.70 \pm 0.89$ and $H_{L,(-,+)} = 18.51 \pm 0.49$, respectively. We note that $H_{L,(+,+)}$ is consistent with the observed blend brightness within a $1\sigma$ error under the assumption that the blended light comes from the lens, but $H_{L,(-,+)}$ is inconsistent with the observed blend brightness.

In Figure 2, we present the constraints on the lens mass and distance given by the measured observables, including $\pi_E$, $\theta_E$, and $H_L$. It is found that the intersections between the $\pi_E$ and $\theta_E$ constraints are consistent with the intersection between the $\pi_E$ and $H_L$ constraints for the higher-mass solution. In contrast, the $\pi_E - \theta_E$ and $\pi_E - H_L$ intersections for the lower-mass solution show a considerable difference in the $M_{\text{primary}} - D_L$ parameter space. The right panel of Figure 2 shows the zoomed-in view in the higher-mass region, and the likelihood contours for the higher-mass solution with and without the lens flux constraint are shown in blue and dark red, respectively.

Combining all the available constraints, including $\theta_E$, $\pi_E$, and the lens flux, we estimate the physical properties of the lens system. We note that there exist two sets of higher-mass solutions, in which both source trajectories seen from Earth and the satellite pass on the upper, (+, +) solution and lower, (-, -) solution sides with respect to the lens. We, therefore, estimate the lens parameters by weighting the relative likelihood $\exp(-\Delta\chi^2/2)$, where $\Delta\chi^2$ is the $\chi^2$ difference between the two solutions. The posterior distributions of the physical parameters are shown in Figure 3, showing that the binary lens system consisting of a $M_{\text{primary}} = 1.05_{-0.07}^{+0.08} M_\odot$ primary star orbited by a $M_{\text{secondary}} = 0.38_{-0.06}^{+0.07} M_\odot$ secondary star at a projected separation $5.40_{-0.22}^{+0.23} \text{ au}$. The binary system is at a distance of $3.43_{-0.21}^{+0.19} \text{ kpc}$.

## 4. Discussion

There is no other star detected between the baseline object and its nearest neighbor on the MagAO frame, and both stars were detected on OGLE images according to Z2015. Z2015 suggested that the OGLE blend at $I_b = 17.95$ is the lens, which is expected to $I_L \sim 17.9$ from the higher-mass solution, and our data provide additional support to this interpretation.

The most straightforward interpretation is that the most of the blended flux comes from the lens. However, we note that it is difficult to completely rule out (some) contributions from possible additional lens companions, source companions, or ambient stars. Given the lens-source proper motion of ~7 mas yr$^{-1}$, the lens can be separately resolved from the source using AO on 6–10 m telescopes in several years, like in the cases of Batista et al. (2015) and Bennett et al. (2020). Such observations will further constrain the lens system. Moreover, because the primary is bright, further spectroscopic observations will better constrain the lens parameters (e.g., Han et al. 2019). The expected radial velocity (RV) signals are on the order of ~10 km s$^{-1}$ with a period on the order of a decade, and future RV monitoring can definitively verify the lens solution
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Red lines show the posterior distribution of (a) the primary mass, (b) the secondary mass, (c) the lens distance, and (d) the projected binary separation, respectively. The black lines are distributions without the constraint of lens flux for comparison.</figcaption></figure>

and constrain its orbital properties (Skowron et al. 2011; Boisse et al. 2015; Santerne et al. 2016; Yee et al. 2016).

X.X. and S.D. acknowledge the support of National Key R&D Program of China No. 2019YFA0405100 and Project 11573003 supported by NSFC. The authors acknowledge the Telescope Access Program (TAP) funded by NAOC, CAS, and the Special Fund for Astronomy from the Ministry of Finance. The OGLE project has received funding from the National Science Centre, Poland, grant MAESTRO 2014/14/A/ST9/00121 to A.U. The work of K.M.M. is supported by the NASA Exoplanets Research Program (XRP) by cooperative agreement NNX16AD44G. J.P.B. is supported by the University of Tasmania through the UTAS Foundation and the endowed Warren Chair in Astronomy. J.P.B. and J.B.M. acknowledge the financial support of the ANR COLD WORLDS (ANR-18-CE31-0002).

## ORCID iDs

Subo Dong https://orcid.org/0000-0002-1027-0990

A. Udalski https://orcid.org/0000-0001-5207-5619

J.-P. Beaulieu https://orcid.org/0000-0003-0014-3354

L. M. Close https://orcid.org/0000-0002-2167-8246

K. M. Morzinski https://orcid.org/0000-0002-1384-0063

R. W. Pogge https://orcid.org/0000-0003-1435-3053

## References

Batista, V., Beaulieu, J.-P., Bennett, D. P., et al. 2015, ApJ, 808, 170

Beaulieu, J.-P., Batista, V., Bennett, D. P., et al. 2018, AJ, 155, 78

Bennett, D. P., Bhattacharya, A., Anderson, J., et al. 2015, ApJ, 808, 169

Bennett, D. P., Bhattacharya, A., Beaulieu, J.-P., et al. 2020, AJ, 159, 68

Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393

Boisse, I., Santerne, A., Beaulieu, J. P., et al. 2015, A&A, 582, L11

Close, L. M., Males, J. R., Kopon, D. A., et al. 2012, Proc. SPIE, 8447, 84470X

DePoy, D. L., Atwood, B., Belville, S. R., et al. 2003, Proc. SPIE, 4841, 827

Dong, S., Gould, A., Udalski, A., et al. 2009, ApJ, 695, 970

Dong, S., Udalski, A., Gould, A., et al. 2007, ApJ, 664, 862

Dotter, A., Chaboyer, B., Jevremović, D., et al. 2008, ApJS, 178, 89

Gould, A. 1992, ApJ, 392, 442

Gould, A. 1994, ApJL, 421, L75

Han, C., Yee, J. C., Udalski, A., et al. 2019, AJ, 158, 102

Janczak, J., Fukui, A., Dong, S., et al. 2010, ApJ, 711, 731

Males, J. R., Close, L. M., Morzinski, K. M., et al. 2014, ApJ, 786, 32

Mao, S., & Paczynski, B. 1991, ApJL, 374, L37

Minniti, D., Lucas, P. W., Emerson, J. P., et al. 2010, NewA, 15, 433

Morzinski, K. M., Close, L. M., Males, J. R., et al. 2014, Proc. SPIE, 9148, 914804

Morzinski, K. M., Males, J. R., Skemer, A. J., et al. 2015, ApJ, 815, 108

Refsdal, S. 1966, MNRAS, 134, 315

Santerne, A., Beaulieu, J. P., Rojas Ayala, B., et al. 2016, A&A, 595, L11

Schechter, P. L., Mateo, M., & Saha, A. 1993, PASP, 105, 1342

Skowron, J., Udalski, A., Gould, A., et al. 2011, ApJ, 738, 87

Yee, J. C., Johnson, J. A., Skowron, J., et al. 2016, ApJ, 821, 121

Zhu, W., Udalski, A., Gould, A., et al. 2015, ApJ, 805, 8