Full orbital solution for the binary system in the northern Galactic disc microlensing event Gaia16aye

TL;DR

This paper presents a comprehensive orbital solution for the binary system in the Gaia16aye microlensing event, including detailed modeling, detection of space-parallax, and implications for dark object studies.

Contribution

It provides the first full orbital solution for a binary microlensing event using Gaia data and detailed follow-up, including space-parallax detection and system property predictions.

Findings

Derived complete orbital parameters of the binary system.

Detected the first microlensing space-parallax between Earth and Gaia.

Predicted astrometric and radial velocity signals for the binary system.

Abstract

Gaia16aye was a binary microlensing event discovered in the direction towards the northern Galactic disc and was one of the first microlensing events detected and alerted to by the Gaia space mission. Its light curve exhibited five distinct brightening episodes, reaching up to I=12 mag, and it was covered in great detail with almost 25,000 data points gathered by a network of telescopes. We present the photometric and spectroscopic follow-up covering 500 days of the event evolution. We employed a full Keplerian binary orbit microlensing model combined with the motion of Earth and Gaia around the Sun to reproduce the complex light curve. The photometric data allowed us to solve the microlensing event entirely and to derive the complete and unique set of orbital parameters of the binary lensing system. We also report on the detection of the first-ever microlensing space-parallax between the Earth and Gaia located at L2. The properties of the binary system were derived from microlensing parameters, and we found that the system is composed of two main-sequence stars with masses 0.57$\pm$0.05 $M_\odot$ and 0.36$\pm$0.03 $M_\odot$ at 780 pc, with an orbital period of 2.88 years and an eccentricity of 0.30. We also predict the astrometric microlensing signal for this binary lens as it will be seen by Gaia as well as the radial velocity curve for the binary system. Events such as Gaia16aye indicate the potential for the microlensing method of probing the mass function of dark objects, including black holes, in directions other than that of the Galactic bulge. This case also emphasises the importance of long-term time-domain coordinated observations that can be made with a network of heterogeneous telescopes.

Figures

Tables

Table 1. Table 1: Telescopes used in the photometric follow-up observations of Gaia16aye.

Telescope code	Telescope/observatory name	Location	Longitude [deg]	Latitude [deg]	Reference
AAVSO	American Association of Variable Star Observers	world-wide network, MA, USA	–	–	-
Akeno50	50-cm telescope, Akeno Observatory	Asao, Akeno-mura, Japan	138.30	35.47	-
APT2	Automatic Photometric Telescope 2,	Serra La Nave, Mt. Etna, Italy	14.97	37.69	-
	Catania Astrophysical Observatory
Aries130	1.30-m telescope,	Manora Peak, Nainital, India	79.45	29.37	-
	Aryabhatta Research Institute of Observational Sciences
Aristarchos	Aristarchos Telescope, Helmos Observatory	Mt. Helmos, Peloponnese	22.20	37.99	Goudis et al. (2010)
ASASSN	All-Sky Automated Survey for Supernovae	world-wide network of 20 telescopes	–	–	Kochanek et al. (2017b)
ASV1	Astronomical Station Vidojevica 0.6 m	Vidojevica, near Prokuplje, Serbia	21.56	43.14	-
ASV2	Astronomical Station Vidojevica 1.4 m	Vidojevica, near Prokuplje, Serbia	21.56	43.14	-
AUT25	25-cm telescope, Akdeniz University	Antalya, Turkey	30.66	36.90	-
BAS2	Rozhen 2 m, National Astronomical Observatory,	Rozhen, Bulgaria	24.74	41.70	-
	Bulgarian Academy of Sciences
BAS50/70	Schmidt-camera 50/70 cm, National Astronomical	Rozhen, Bulgaria	24.74	41.70	-
	Observatory, Bulgarian Academy of Sciences
Bialkow	Białków Observatory,	Białków, Poland	16.66	51.48	-
	Astronomical Institute of the University of Wrocław
C2PU	C2PU-Omicron,	OCA, Calern Plateau, France	6.92	43.75	-
	Center for Pedagogy in Planet and Universe sciences
Conti	Conti Private Observatory	MD, USA	-76.49	38.93	-
CrAO	Crimean Astrophysical Observatory	Nauchnyi, Crimea	34.01	44.73	-
DEMONEXT	DEdicated MONitor of EXotransits and Transients,	AZ, USA	-110.60	31.67	Villanueva et al. (2018)
	Winer Observatory
Foligno	Foligno Observatory	Perugia Province, Italy	12.70	42.96	-
HAO50	Horten Astronomical Telescope	Nykirke, Horten, Norway	10.39	59.43	-
Krakow50	50-cm Cassegrain telescope,	Kraków, Poland	19.82	50.05	-
	Astronomical Observatory of Jagiellonian University
Kryoneri	1.2-m Kryoneri telescope, Kryoneri Observatory	Mt. Kyllini, Peloponnese, Greece	22.63	38.07	Xilouris et al. (2018)
LCO-Texas	Las Cumbres Observatory	McDonald Observatory, TX, USA	-104.02	30.67	Brown et al. (2013)
LCO-Hawaii	Las Cumbres Observatory	Haleakala, HI, USA	-156.26	20.71	Brown et al. (2013)
Leicester	University of Leicester Observatory	Oadby, UK	-1.07	52.61	-
Loiano	1.52 m Cassini Telescope,	INAF-Bologna, Loiano, Italy	11.33	44.26	-
	INAF - Bologna Observatory of Astrophysics and Space Science
LOT1m	Lulin One-meter Telescope	Lulin Observatory, Taiwan	120.87	23.47	-
LT	Liverpool Telescope,	La Palma, Spain	-17.88	28.76	Steele et al. (2004)
	Roque de Los Muchachos Observatory
MAO165	1.65-m Ritchey–Chretien telescope,	Molėtai, Kulionys, Lithuania	25.56	55.32	-
	Molėtai Astronomical Observatory
Mercator	Mercator Telescope,	La Palma, Spain	-17.88	28.76	-
	Roque de Los Muchachos Observatory
Montarrenti	Montarrenti Observatory	Siena, Italy	11.18	43.23	-
OHP	T120, L’Observatoire de Haute-Provence	St. Michel, France	5.71	43.93	-
OndrejovD50	D50 telescope, Astronomical Institute	Ondrejov, Czech Rep.	14.78	49.91	-
	of Academy of Sciences of the Czech Republic
Ostrowik	Cassegrain telescope,	Ostrowik, Poland	21.42	52.09	-
	Warsaw University Astronomical Observatory
PIRATE	Physics Innovations Robotic Astronomical	Tenerife, Spain	-16.51	28.30	-
	Telescope Explorer Mark-III, Teide Observatory				Kolb et al. (2018)
pt5m	0.5m robotic telescope,	La Palma, Spain	-17.88	28.76	Hardy et al. (2015)
	Roque de Los Muchachos Observatory
RTT150	1.5-m Russian-Turkish Telescope,	Mt. Bakirlitepe, Antalya, Turkey	30.33	36.83	-
	TUBITAK National Observatory
SAI	60-cm Zeiss-2 telescope, Moscow State Univercity	Nauchnyi, Crimea	34.01	44.73	-
	observational station of Sternberg Astronomical Institute
Salerno	Salerno University Observatory	Fisciano, Italy	14.79	40.78	-
SKAS-KFU28	C28 CGEM-1100 telescope,	Zelenchukskaya, Caucasus, Russia	41.43	43.65	-
	Zelenchukskaya Station of Kazan Federal University
Skinakas	1.3-m telescope, Skinakas Observatory	Skinakas, Crete, Greece	24.90	35.21	-
SKYNET	Skynet Robotic Telescope Network,	WI, USA	-88.56	42.57	-
	41-inch telescope, Yerkes Observatory
Swarthmore24	24-inch telescope, Peter van de Kamp Observatory	Swarthmore College, PA, USA	-75.36	39.91	-
T60	60-cm telescope, TUBITAK National Observatory	Mt. Bakirlitepe, Antalya, Turkey	30.33	36.83	-
T100	1.0-m telescope, TUBITAK National Observatory	Mt. Bakirlitepe, Antalya, Turkey	30.33	36.83	-
TJO	Joan Oró Telescope, Montsec Observatory	Sant Esteve de la Sarga, Lleida, Spain	0.73	42.03	-
TRT-GAO	Thai Robotic Telescope GAO, Yunnan Observatory	Phoenix Mountain, Kunming, China	105.03	26.70	-
TRT-TNO	Thai Robotic Telescope TNO,	Doi Inthanon, Chiang Mai, Thailand	98.48	18.57	-
	Thai National Observatory
UCLO-C14E	University College London Observatory, C14 East	Mill Hill, London, UK	-0.24	51.61	-
UCLO-C14W	University College London Observatory, C14 West	Mill Hill, London, UK	-0.24	51.61	-
UBT60	Akdeniz University Telescope,	Mt. Bakirlitepe, Antalya, Turkey	30.33	36.83	-
	TUBITAK National Observatory
Watcher	40-cm telescope, Boyden Observatory	Orange Free State, South Africa	26.40	-29.04	French et al. (2004)
WHT-ACAM	William Herschel Telescope,	La Palma, Spain	-17.88	28.76	-
	Roque de Los Muchachos Observatory
Wise1m	1.0-m telescope, Wise Observatory	Mitzpe Ramon, Israel	34.76	30.60	-
WiseC28	C28 Jay Baum Rich telescope, Wise Observatory	Mitzpe Ramon, Israel	34.76	30.60	-

Table 2. Table 3: Summary of the spectroscopic observations of Gaia16aye.

Spectrum	Observation date	Wavelength range	Telescope – Instrument
ID	HJD	(Å)
LT 1	2457612.900668	4200 – 7994	Liverpool Telescope – SPRAT
LT 2	2457617.940097	4200 – 7994	Liverpool Telescope – SPRAT
LT 3	2457643.845837	4200 – 7994	Liverpool Telescope – SPRAT
WHT 1	2457701.3045827	4303 – 9500	William Herschel Telescope – ACAM
Palomar 1	2457662.1047682	3100 – 10200	Palomar Hale Telescope – DBSP
Palomar 2	2457932.6881373	3800 – 10000	Palomar Hale Telescope – DBSP
INT 1	2457703.4230518	7550 – 9000	Isaac Newton Telescope – IDS; R831R grating
INT 2	2457706.3547417	7550 – 9000	Isaac Newton Telescope – IDS; R831R grating
INT 3	2457712.2970278	7500 – 8795	Isaac Newton Telescope – IDS; R1200Y grating
INT 4	2457713.2967616	7500 – 8795	Isaac Newton Telescope – IDS; R1200Y grating
INT 5	2457714.2949097	7500 – 8795	Isaac Newton Telescope – IDS; R1200Y grating
Asiago 1	2457612.430953	3320 – 7880	1.22m Reflector – DU440A-BU2
Asiago 2	2457623.364186	4160 – 6530	1.82m Reflector – AFOSC; GR07 grating
Asiago 3a	2457700.264730	8200 – 9210	1.82m Reflector – AFOSC; VPH5 grating
Asiago 3b	2457700.275567	5000 – 9280	1.82m Reflector – AFOSC; VPH6 grating
Asiago 4a	2457700.260113	8200 – 9210	1.82m Reflector – AFOSC; VPH5 grating
Asiago 4b	2457700.270951	5000 – 9280	1.82m Reflector – AFOSC; VPH6 grating
Asiago 5a	2457722.263836	8200 – 9210	1.82m Reflector – AFOSC; VPH5 grating
Asiago 5b	2457722.235417	5000 – 9280	1.82m Reflector – AFOSC; VPH6 grating
Asiago 6a	2457723.246689	8200 – 9210	1.82m Reflector – AFOSC; VPH5 grating
Asiago 6b	2457723.204078	5000 – 9280	1.82m Reflector – AFOSC; VPH6 grating

Table 3. Table 4: Data sets used in the modelling

Observatory	Filter	Number	$\gamma$	$ϵ$
Gaia	$G$	53	1.4	0.0
Bialkow	$I$	72	1.15	0.005
APT2	$I$	156	1.70	0.01
LT	$i$	94	1.15	0.005
DEMONEXT	$I$	110	1.35	0.005
Swarthmore	$I$	19	1.00	0.00
UBT60	$I$	18	1.00	0.005
ASAS-SN	$V$	68	1.45	0.01

Table 4. Table 5: Best-fit microlensing model parameters of the Gaia16aye binary event.

Parameter	Value
$t_0$ (HJD′)	$7674.738\pm 0.057$
$u_0$	$0.0400\pm 0.0014$
$t_E$ (d)	$111.09\pm 0.41$
${\pi }_{E,N}$	$-0.373\pm 0.002$
${\pi }_{E,E}$	$-0.145\pm 0.001$
$\log \rho$	$-2.519\pm 0.003$
$q$	$0.639\pm 0.004$
$s_0$	$1.007\pm 0.002$
$\alpha$ (rad)	$5.339\pm 0.002$
$s_z$	$0.404\pm 0.028$
${\gamma }_x$ (yr-1)	$0.384\pm 0.009$
${\gamma }_y$ (yr-1)	$0.591\pm 0.012$
${\gamma }_z$ (yr-1)	$-1.121\pm 0.032$
$I_s$ (mag)	$14.70\pm 0.02$
$I_{\mathrm{blend}}$ (mag)	$16.09\pm 0.02$
$R_s$ (mag)	$15.62\pm 0.02$
$R_{\mathrm{blend}}$ (mag)	$17.05\pm 0.02$
$V_s$ (mag)	$16.61\pm 0.02$
$V_{\mathrm{blend}}$ (mag)	$17.98\pm 0.02$

Table 5. Table 6: Physical parameters of the binary lens system.

Parameter	Value
${\theta }_E$ (mas)	$3.04\pm 0.24$
${\mu }_{\mathrm{rel}}$ (mas/yr)	$10.1\pm 0.8$
$M_1$ ($M_{\odot }$)	$0.57\pm 0.05$
$M_2$ ($M_{\odot }$)	$0.36\pm 0.03$
$D_l$ (pc)	$780\pm 60$
$a$ (au)	$1.98\pm 0.03$
$P$ (yr)	$2.88\pm 0.05$
$e$	$0.30\pm 0.03$
$i$ (deg)	$65.5\pm 0.7$
$\Omega$ (deg)	$-169.4\pm 0.9$
$\omega$ (deg)	$-30.5\pm 3.8$
$t_{\mathrm{peri}}$ (HJD′)	$8170\pm 14$

Table 6. Table 8: Gaia photometric measurements of the Gaia16aye microlensing event. The full table is available in the electronic form of the article. TCB is the barycentric coordinate time.

Observation date		average
TCB	JD	G mag
2014-10-30 20:50:59	2456961.369	15.48
2014-10-30 22:37:33	2456961.443	15.48
2015-02-15 09:54:03	2457068.913	15.44
2015-02-15 14:07:43	2457069.089	15.44
2015-02-15 15:54:18	2457069.163	15.45
2015-03-09 08:16:20	2457090.845	15.45
2015-03-09 10:02:55	2457090.919	15.43
2015-03-09 14:16:35	2457091.095	15.45
2015-03-09 16:03:10	2457091.169	15.45
2015-05-20 19:20:37	2457163.306	15.45
2015-06-10 03:08:39	2457183.631	15.47
2015-07-25 13:45:22	2457229.073	15.45
2015-08-04 00:05:24	2457238.504	15.45
2015-08-04 01:51:58	2457238.578	15.46
2015-10-08 06:23:08	2457303.766	15.40
2015-11-11 05:44:30	2457337.739	15.35
2015-12-18 09:29:34	2457374.896	15.35
2015-12-18 11:16:08	2457374.970	15.35
2016-01-08 03:37:06	2457395.651	15.35
2016-01-08 05:23:40	2457395.725	15.35
2016-01-08 09:37:20	2457395.901	15.39
2016-01-08 11:23:54	2457395.975	15.34
2016-02-27 21:18:55	2457446.388	15.48
2016-02-27 23:05:29	2457446.462	15.38
2016-02-28 03:19:09	2457446.638	15.39
2016-03-23 23:08:54	2457471.465	15.40
2016-04-25 22:50:35	2457504.452	15.39
2016-06-02 20:18:57	2457542.346	15.52
2016-06-20 04:10:13	2457559.674	15.23
2016-08-05 00:53:51	2457605.537	14.18
2016-08-05 02:40:25	2457605.611	14.19
2016-08-05 06:54:05	2457605.788	14.40
2016-08-05 08:40:39	2457605.862	14.25
2016-08-15 13:00:28	2457616.042	15.26
2016-08-15 14:47:02	2457616.116	15.05
2016-09-27 13:28:36	2457659.062	13.67
2016-10-21 05:33:20	2457682.731	14.09
2016-11-21 17:05:46	2457714.212	12.81
2016-11-21 18:52:20	2457714.286	13.00
2017-01-02 12:24:22	2457756.017	14.91
2017-01-02 16:38:01	2457756.193	14.94
2017-01-02 18:24:35	2457756.267	14.91
2017-01-20 10:48:21	2457773.950	14.75
2017-01-20 12:34:55	2457774.024	14.77
2017-01-20 16:48:35	2457774.200	14.75
2017-01-20 18:35:09	2457774.274	14.78
2017-03-10 23:52:28	2457823.495	14.53
2017-03-11 01:39:02	2457823.569	14.56
2017-04-07 23:48:22	2457851.492	14.45
2017-04-08 01:34:57	2457851.566	14.47
2017-05-07 11:34:44	2457880.982	13.96
2017-05-07 13:21:19	2457881.056	13.98
2017-06-16 16:39:01	2457921.194	14.87
2017-08-16 09:12:15	2457981.884	15.26
2017-08-16 10:58:49	2457981.958	15.27
2017-08-28 17:04:45	2457994.212	15.32
2017-08-28 21:18:24	2457994.388	15.29
2017-10-08 14:08:21	2458035.089	15.4
2017-10-08 15:54:55	2458035.163	15.41
2017-11-04 03:39:50	2458061.653	15.55
2017-12-03 09:23:18	2458090.891	15.53
2018-01-18 19:12:05	2458137.300	15.53
2018-01-18 20:58:40	2458137.374	15.53
2018-01-19 01:12:20	2458137.550	15.52
2018-01-19 07:12:33	2458137.800	15.54
2018-02-04 19:23:34	2458154.308	15.52
2018-02-04 21:10:08	2458154.382	15.51
2018-02-05 01:23:49	2458154.558	15.51
2018-02-05 03:10:23	2458154.632	15.51
2018-03-23 01:03:21	2458200.544	15.54
2018-04-22 12:49:53	2458231.035	15.54
2018-04-22 14:36:27	2458231.109	15.56
2018-05-19 00:41:48	2458257.529	15.53
2018-06-30 07:22:25	2458299.807	15.56
2018-07-12 01:29:24	2458311.562	15.58
…	…

Table 7. Table 9: Photometric follow-up observations of Gaia16aye. ID denotes the unique id of the observation in the Calibration Server.

ID	MJD	Magnitude	Error	Filter	Observatory/Observer
	[d]	[mag]	[mag]
41329	57609.74664	16.635	0.052	B	UBT60 V.Bakis
41348	57609.74742	14.914	0.012	V	UBT60 V.Bakis
41367	57609.74819	14.108	0.006	r	UBT60 V.Bakis
41386	57609.74897	13.375	0.005	i	UBT60 V.Bakis
41330	57609.74978	16.548	0.037	B	UBT60 V.Bakis
41349	57609.75055	14.907	0.010	V	UBT60 V.Bakis
41368	57609.75133	14.102	0.005	r	UBT60 V.Bakis
41387	57609.75210	13.378	0.005	i	UBT60 V.Bakis
41331	57609.75281	16.600	0.037	B	UBT60 V.Bakis
41350	57609.75359	14.897	0.010	V	UBT60 V.Bakis
41369	57609.75436	14.117	0.005	r	UBT60 V.Bakis
41388	57609.75514	13.374	0.005	i	UBT60 V.Bakis
41332	57609.75588	16.504	0.035	B	UBT60 V.Bakis
41351	57609.75665	14.902	0.010	V	UBT60 V.Bakis
41370	57609.75743	14.105	0.005	r	UBT60 V.Bakis
41389	57609.75820	13.399	0.005	i	UBT60 V.Bakis
41333	57609.75896	16.538	0.035	B	UBT60 V.Bakis
41352	57609.75973	14.904	0.010	V	UBT60 V.Bakis
41371	57609.76051	14.117	0.006	r	UBT60 V.Bakis
41390	57609.76128	13.403	0.005	i	UBT60 V.Bakis
54690	57609.78240	14.202	0.009	r	SAI A.Zubareva
54689	57609.78569	16.528	0.024	B	SAI A.Zubareva
54680	57609.78902	16.544	0.016	B	SAI A.Zubareva
54663	57609.79078	14.974	0.007	V	SAI A.Zubareva
54681	57609.79218	14.148	0.005	r	SAI A.Zubareva
54682	57609.79395	16.539	0.019	B	SAI A.Zubareva
41334	57609.79522	16.599	0.024	B	UBT60 V.Bakis
54664	57609.79569	14.971	0.008	V	SAI A.Zubareva
41353	57609.79600	14.884	0.008	V	UBT60 V.Bakis
41372	57609.79677	14.082	0.005	r	UBT60 V.Bakis
54683	57609.79711	14.167	0.005	r	SAI A.Zubareva
41391	57609.79755	13.355	0.005	i	UBT60 V.Bakis
54684	57609.79888	16.583	0.020	B	SAI A.Zubareva
54665	57609.80063	15.014	0.009	V	SAI A.Zubareva
54685	57609.80202	14.168	0.005	r	SAI A.Zubareva
54686	57609.80373	14.178	0.005	r	SAI A.Zubareva
41335	57609.80477	16.605	0.026	B	UBT60 V.Bakis
41354	57609.80554	14.876	0.008	V	UBT60 V.Bakis
41373	57609.80632	14.102	0.005	r	UBT60 V.Bakis
41392	57609.80709	13.374	0.005	i	UBT60 V.Bakis
41336	57609.80787	16.549	0.025	B	UBT60 V.Bakis
41355	57609.80864	14.864	0.008	V	UBT60 V.Bakis
41374	57609.80942	14.106	0.005	r	UBT60 V.Bakis
41393	57609.81019	13.380	0.005	i	UBT60 V.Bakis
41337	57609.81094	16.488	0.025	B	UBT60 V.Bakis
41356	57609.81171	14.884	0.008	V	UBT60 V.Bakis
41375	57609.81249	14.102	0.005	r	UBT60 V.Bakis
41394	57609.81326	13.382	0.005	i	UBT60 V.Bakis
41338	57609.81405	16.492	0.027	B	UBT60 V.Bakis
41357	57609.81483	14.879	0.008	V	UBT60 V.Bakis
41376	57609.81560	14.101	0.005	r	UBT60 V.Bakis
41395	57609.81638	13.374	0.005	i	UBT60 V.Bakis
40186	57609.90821	17.158	0.134	B	pt5m L.Hardy
40187	57609.90927	16.939	0.116	B	pt5m L.Hardy
40188	57609.91009	16.548	0.098	B	pt5m L.Hardy
40189	57609.91092	14.917	0.022	V	pt5m L.Hardy
40190	57609.91181	14.964	0.021	V	pt5m L.Hardy
40191	57609.91263	14.958	0.022	V	pt5m L.Hardy
40192	57609.91346	14.132	0.009	r	pt5m L.Hardy
40193	57609.91457	14.188	0.011	r	pt5m L.Hardy
40194	57609.91540	14.106	0.010	r	pt5m L.Hardy
40195	57609.91640	13.439	0.010	i	pt5m L.Hardy
40196	57609.91751	13.448	0.009	i	pt5m L.Hardy
40197	57609.91834	13.453	0.010	i	pt5m L.Hardy
40268	57610.00399	16.522	0.014	B	TJO U.Burgaz
40271	57610.01489	15.002	0.006	V	TJO U.Burgaz
40272	57610.01842	14.956	0.020	V	TJO U.Burgaz
40274	57610.03669	13.107	0.055	i	TJO U.Burgaz
40275	57610.04022	13.293	0.011	i	TJO U.Burgaz
40276	57610.04375	13.388	0.004	i	TJO U.Burgaz
54687	57610.05719	16.491	0.057	B	SAI A.Zubareva
54666	57610.05894	14.977	0.018	V	SAI A.Zubareva
54688	57610.06035	14.192	0.009	r	SAI A.Zubareva
41339	57610.76348	16.499	0.029	B	UBT60 V.Bakis
41358	57610.76424	14.805	0.009	V	UBT60 V.Bakis
41377	57610.76499	14.009	0.005	r	UBT60 V.Bakis
41396	57610.76576	13.285	0.005	i	UBT60 V.Bakis
…	…	…	…	.	…

Table 8. Table 10: Photometric follow-up observations of Gaia16aye used in the model. Observatory codes: 1 Gaia (G), 2 Bialkow (I), 3 APT2 (I), 4 LT (i), 5 DEMONEXT (I), 6 Swarthmore (I), 7 UBT60 (I), and 8 ASAS-SN (V). The full data set is available in the on-line version of the paper.

HJD [d]	Magnitude [mag]	Error [mag]	Observatory code
2456961.36775	15.480	0.010	1
2456961.44175	15.480	0.010	1
2457068.91154	15.440	0.010	1
…	…	…	…
2457619.36442	14.350	0.009	2
2457623.42542	14.323	0.006	2
2457625.43582	14.320	0.006	2
…	…	…	…
2457612.33545	13.127	0.013	3
2457613.46778	12.894	0.003	3
2457614.40174	12.293	0.003	3
…	…	…	…
2457647.43662	14.256	0.007	4
2457648.33147	14.245	0.009	4
2457649.33125	12.208	0.004	4
…	…	…	…
2457690.67443	13.433	0.007	5
2457691.65978	13.433	0.006	5
2457692.59705	13.428	0.006	5
…	…	…	…
2457714.45266	12.246	0.003	6
2457714.46433	12.261	0.004	6
2457714.47873	12.280	0.005	6
…	…	…	…
2457610.28565	13.379	0.007	7
2457611.30428	13.286	0.005	7
2457616.35217	14.400	0.010	7
…	…	…	…
2457467.10912	17.020	0.170	8
2457489.03978	17.940	0.330	8
2457512.02932	18.110	0.290	8
…	…	…	…

Equations

$${\theta }_E=\sqrt{\kappa M_L({\pi }_{\mathrm{l}}-{\pi }_{\mathrm{s}})},\text{leavevmode}\text{leavevmode}\text{leavevmode}\kappa \equiv \frac{4G}{c^2}\approx 8.144\text{leavevmode}\mathrm{mas}\text{leavevmode}{\mathrm{M}}_{\odot }^{-1},$$

Full text

1 Introduction

Measuring the masses of stars or stellar remnants is one of the most challenging tasks in modern astronomy. Binary systems were the first to facilitate mass measurement through the Doppler effect in radial velocity measurements (e.g. Popper, 1967), leading to the mass-luminosity relation and an advancement in the understanding of stellar evolution (e.g. Paczyński, 1971; Pietrzyński et al., 2010). However, these techniques require the binary components to emit detectable amounts of light, often demanding large-aperture telescopes and sensitive instruments. In order to study the invisible objects, in particular stellar remnants such as neutron stars or black holes, other means of mass measurement are necessary. Recently, the masses of black holes were measured when a close binary system tightened its orbit and emitted gravitational waves (e.g. Abbott et al., 2016), yielding unexpectedly high masses that were not observed before (e.g. Abbott et al., 2017; Belczynski et al., 2016; Bird et al., 2016). Because of the low merger rates, gravitational wave experiment detections are limited to very distant galaxies. Other means of mass measurement are therefore required to probe the faint and invisible populations in the Milky Way and its vicinity.

Gravitational microlensing allows for detection and study of binary systems regardless of the amount of light they emit and regardless of the radial velocities of the components, as long as the binary crosses the line of sight to a star that is bright enough to be observed. Therefore, this method offers an opportunity to detect binary systems that contain planets (e.g. Gould & Loeb, 1992; Albrow et al., 1998; Bond et al., 2004; Udalski et al., 2005), planets orbiting a binary system of stars (e.g. Poleski et al., 2014; Bennett et al., 2016), and black holes or other dark stellar remnants (e.g. Shvartzvald et al., 2015).

Typically, searches for microlensing events are conducted in the direction of the Galactic bulge because of the high stellar density, potential sources and lenses, and the high microlensing optical depth (e.g. Kiraga & Paczynski, 1994; Udalski et al., 1994b; Paczynski, 1996; Wozniak et al., 2001; Sumi et al., 2013; Udalski et al., 2015a; Wyrzykowski et al., 2015; Mróz et al., 2017). The regions of the Galactic plane outside of the bulge have occasionally also been monitored in the past for microlensing events, however, even though the predicted rates of events were orders of magnitude lower (e.g. Han, 2008; Gaudi et al., 2008). Derue et al. (2001) first published microlensing events that were detected during the long-term monitoring of the selected disc fields. Two serendipitous discoveries of bright microlensing events outside of the bulge were reported by amateur observers, the Tago event (Fukui et al., 2007; Gaudi et al., 2008), and the Kojima-1 event (Nucita et al., 2018; Dong et al., 2019; Fukui et al., 2019), which has a signature of a planet next to the lens. The first binary microlensing event in the Galactic disc was reported in Rahal et al. (2009) (GSA14), but its light curve was too poorly sampled in order to conclude on the parameters of the binary lens.

The best-sampled light curves come from bulge surveys, such as MACHO (Alcock et al., 1997; Popowski et al., 2001), the Expérience pour la Recherche d’Objets Sombres (EROS) (Hamadache et al., 2006), the Optical Gravitational Lensing Experiment (OGLE) (Udalski et al., 1994b, 2000, 2015a), the Microlensing Observations in Astrophysics (MOA) (Yock, 1998; Sumi et al., 2013), and the Korean Microlensing Telescope Network (KMNet) (Kim et al., 2016). In particular, the OGLE project has been monitoring the Galactic bulge regularly since 1992 and was the first to report on a binary microlensing event in 1993 (Udalski et al., 1994a). Binary microlensing events constitute about 10% of all events reported by the microlensing surveys of the bulge. The binary lens differs from a single lens when the component separation on the sky is of order of their Einstein radius Paczynski (1996); Gould (2000), which is computed as

[TABLE]

where $M_{L}$ is the total mass of the binary and $\pi_{\rm l}$ and $\pi_{\rm s}$ are parallaxes of the lens and the source, respectively. For the conditions in the Galaxy and a typical mass of the lens, the size of the Einstein ring is about 1 milliarcsecond (1 mas). Instead of a circular Einstein ring as in the case of a single lens (or very tight binary system), two (or more) lensing objects produce a complex curve on the sky, shaped by the mass ratio and projected separation of the components. This is called the critical curve. In the source plane this curve turns into a caustic curve (as opposed to a point in the case of a single lens), which denotes the places where the source is infinitely amplificated (e.g. Bozza, 2001; Rattenbury, 2009). As the source and the binary lens move, their relative proper motion changes the position of the source with respect to the caustics. Depending on this position, there are three (when the source is outside of the caustic) or five (inside the caustic) images of the source. Images also change their location as well as their size, therefore the combined light of the images we observe changes the observed amplification, with the most dramatic changes at the caustic crossings. In a typical binary lensing event the source–lens trajectory can be approximated with a straight line (e.g. Jaroszynski et al., 2004; Skowron et al., 2007). If the line crosses the caustic, it produces a characteristic U-shaped light curve because the amplification increases steeply as the source approaches the caustic and remains high inside the caustic (e.g. Witt & Mao, 1995). If the source approaches one of the caustic cusps, the light curve shows a smooth increase, similar to a single lensing event. Identifying all these features in the light curve helps constrain the shape of the caustic and hence the parameters of the binary. An additional annual parallax effect causes the trajectory of the source to curve, which probes the caustic shape at multiple locations (e.g. An & Gould, 2001; Skowron et al., 2009; Udalski et al., 2018) and thus helps constrain the solution of the binary system better.

The situation becomes more complex when a binary system rotates while lensing, which causes the binary configuration on the sky to change. This in turn changes the shape and size of the caustic (Albrow et al., 2000). In the case of most binary microlensing events the effect of the orbital motion can be neglected because the orbital periods are often much longer (typically years) than the duration of the event (typically weeks). However, in longer events the orbital motion has to be taken into account in the model. Together with the source–lens relative motion and the parallax effect, this causes the observed amplification to vary significantly during the event and may generate multiple crossings of the caustic and amplification due to cusp approach (e.g. Skowron et al., 2009). However, in rare cases, such a complex event allows us not only to measure the mass and distance of the lens, but also to derive all orbital parameters of the binary. The first such case was found by the OGLE survey in the event OGLE-2009-BLG-020 (Skowron et al., 2011), and its orbital parameters found in the model were verified with radial velocity measurement (Yee et al., 2016). The orbital motion was also modelled in the MOA-2011-BLG-090 and OGLE-2011-BLG-0417 events (Shin et al., 2012), but the former was too faint and the latter was not confirmed with radial velocity data (Boisse et al., 2015; Bachelet et al., 2018).

Additional information that helps constrain the parameters of the system may also come from space parallax (e.g. Refsdal, 1966; Gould, 1992; Gould et al., 2009). This is now being routinely done by observing microlensing events from the Earth and Spitzer or Kepler, separated by more than 1 au (e.g. Udalski et al., 2015b; Yee et al., 2015; Calchi Novati & Scarpetta, 2016; Shvartzvald et al., 2016; Zhu et al., 2016; Poleski et al., 2016).

The most difficult parameter to measure, however, is the size of the Einstein radius. It can be found when the finite source effects are detected, when the angular source size is large enough to experience a significant gradient in the magnification near the centre of the Einstein ring or the binary lens caustic (e.g. Yoo et al., 2004; Zub et al., 2011). The measurement of the angular separation between the luminous lens and the source years or decades after the event also directly leads to calculation of $\theta_{E}$ (e.g. Kozłowski et al., 2007). Otherwise, for dark lenses, the measurement of $\theta_{E}$ can only come from astrometric microlensing (Dominik & Sahu, 2000; Belokurov & Evans, 2002; Lu et al., 2016; Kains et al., 2017; Sahu et al., 2017). As shown in Rybicki et al. (2018), Gaia will soon provide precise astrometric observations for microlensing events, which will allow us to measure $\theta_{E}$, but only for events brighter than about $V<15$ mag.

Here we present Gaia16aye, a unique event from the Galactic disc, far from the Galactic bulge, which lasted almost two years and exhibited effects of binary lens rotation, an annual and space parallax, and a finite source. The very densely sampled light curve was obtained solely thanks to an early alert from Gaia and a dedicated ground-based follow-up of tens of observers, including amateurs and school pupils. The wealth of photometric data allowed us to find the unique solution for the binary system parameters.

The paper is organised as follows. Sections 2 and 3 describe the history of the detection and the photometric and spectroscopic data collected during the follow-up of Gaia16aye. In Section 4 we describe the microlensing model we used to reproduce the data. We then discuss the results in Section 5.

2 Discovery and follow-up of Gaia16aye

Gaia16aye was found during the regular examination of the photometric data collected by the Gaia mission. Gaia is a space mission of the European Space Agency (ESA) in science operation since 2014. Its main goal is to collect high-precision astrometric data, that is, positions, proper motions, and parallaxes, of all stars on the sky down to about 20.7 mag in Gaia G band (Gaia Collaboration et al., 2016; Evans et al., 2018). While Gaia scans the sky multiple times, it provides near-real-time photometric data, which can be used to detect unexpected changes in the brightness or appearance of new objects from all over the sky. This is dealt with by the Gaia Science Alerts system (Wyrzykowski & Hodgkin, 2012; Hodgkin et al., 2013; Wyrzykowski et al., 2014), which processes daily portions of the spacecraft data and produces alerts on potentially interesting transients. The main purpose of the publication of the alerts from Gaia is to enable the astronomical community to study the unexpected and temporary events. Photometric follow-up is necessary in particular in the case of microlensing events in order to fill the gaps between Gaia observations and subsequently construct a densely sampled light curve, sensitive to short-lived anomalies and deviations to the standard microlensing evolution (e.g. Wyrzykowski et al., 2012).

Gaia16aye was identified as an alert in the data chunk from 5 August 2016, processed on 8 August by the Gaia Science Alerts pipeline (AlertPipe), and published on Gaia Science Alerts webpages222http://gsaweb.ast.cam.ac.uk/alerts/alert/Gaia16aye on 9 August 2016, 10:45 GMT. The full Gaia photometry of Gaia16aye is listed in Table 8.

The alert was triggered by a significant change in brightness of an otherwise constant-brightness star with G=15.51 mag. The star has a counterpart in the 2MASS catalogue as 2MASS19400112+3007533 at RA,Dec (J2000.0) = 19:40:01.14, 30:07:53.36, and its source Id in Gaia DR2 is 2032454944878107008 (Gaia Collaboration et al., 2018). Its Galactic coordinates are $l$,$b$ = 64.999872, 3.839052 deg, which locates Gaia16aye well in the northern part of the Galactic Plane towards the Cygnus constellation (see Fig. 1).

Gaia collected its first observation of this star in October 2014, and until the alert in August 2016, there were no significant brightness variation in its light curve. Additionally, this part of the sky was observed prior to Gaia in 2011–2013 as part of a Nova Patrol (Sokolovsky et al., 2014), and no previous brightenings were detected at a limiting magnitude of V$\approx$14.2.

In the case of Gaia16aye the follow-up was initiated because the source at its baseline was relatively bright and easily accessible for a broad range of telescopes with smaller apertures. Moreover, microlensing events brighter than about G=16 mag will have Gaia astrometric data of sufficient accuracy in order to detect the astrometric microlensing signal (Rybicki et al., 2018). For this purpose, we have organised a network of volunteering telescopes and observers who respond to Gaia alerts, in particular to microlensing event candidates, and invest their observing time to provide dense coverage of the light curve. The network is arranged under the Time-Domain work package of the European Commission’s Optical Infrared Coordination Network for Astronomy (OPTICON) grant333https://www.astro-opticon.org/h2020/network/na4.html.

The follow-up observations started immediately after the announcement of the alert (the list of telescopes and their acronyms is provided in Tab.2.1), with the first data points taken on the night 9/10 Aug 2016 with the 0.6m Akdeniz Univ. UBT60 telescope in the TUBITAK National Observatory, Antalya, the SAI Southern Station in Crimea, the pt5m telescope at the Roque de los Muchachos Observatory on La Palma (Hardy et al., 2015), the 0.8m Telescopi Joan Oro (TJO) at l’Observatori Astronomic del Montsec, and the 0.8m robotic APT2 telescope in Serra La Nave (Catania). The data showed a curious evolution and a gradual rise (0.1 mag/day) in the light curve without change in colour, which is atypical for many known types of variable and cataclysmic variable stars. On the night 13/14 Aug 2016 (HJD${}^{\prime}\equiv$ HJD-2450000.0 $\sim$ 7614.5) the object reached a peak V=13.8 mag (B-V=1.6 mag, I=12.2 mag), as detected by ATP2 and TJO, which was followed by a sudden drop by about 2 magnitudes. Alerted by the unusual shape of the light curve, we obtained spectra of Gaia16aye with the 1.22m Asiago telescope on 11 August and with the 2.0m Liverpool Telescope (LT, La Palma) on 12 August, which were consistent with a normal K8-M2 type star (Bakis et al., 2016). The stellar spectra along with the shape of the light curve implied that Gaia16aye was a binary microlensing event, which was detected by Gaia at its plateau between the two caustic crossings, and we have observed the caustic exit with clear signatures of the finite source effects.

The continued follow-up after the first caustic exit revealed a very slow gradual rise in brightness (around 0.1 mag in a month). On 17 September 2016, it increased sharply by 2 mag (first spotted by the APT2 telescope), indicating the second caustic entry. The caustic crossing again showed a broad and long-lasting effect of finite source size (flattened peak), lasting for nearly 48 hours between HJD*′*=7649.4 and 7651.4 and reaching about V=13.6 mag and I=12 mag. The caustic crossing was densely covered by the Liverpool Telescope and the 0.6m Ostrowik Observatory near Warsaw, Poland.

Following the second caustic entry, the object remained very bright (I$\sim$12-14 mag) and was observed by multiple telescopes from around the globe, both photometrically and spectroscopically. The complete list of telescopes and instruments involved in the follow-up observations of Gaia16aye is shown in Table 2.1, and their parameters are gathered in Table A in the appendix. In total, more than 25,000 photometric and more than 20 spectroscopic observations were taken over the period of about two years. In early November 2016, the brightness trend changed from falling to rising, as expected for binary events during the caustic crossing (Nesci, 2016; Khamitov et al., 2016b). A simple preliminary model for the binary microlensing event predicted the caustic exit to occur around November 20.8 UT (HJD*′*=7713.3) and the caustic crossing to last about seven hours (Mroz et al., 2016). In order to catch and cover the caustic exit well, an intensive observing campaign was begun, involving also amateur astronomical associations (including the British Astronomical Association and the German Haus der Astronomie) and school pupils. The observations were also reported live on Twitter (hashtag #Gaia16aye). A DDT observing time was allocated at the William Herschel Telescope (WHT/ACAM) and the Telescopio Nazionale Galileo (TNG/DOLORES) to provide low- and high-resolution spectroscopy at times close to the peak. However, the actual peak occurred about 20 hours later than expected, on 21 November 16 UT (7714.17), and was followed by TRT-GAO, Aries130, CrAO, AUT25, T60, T100, RTT150 (detection of the fourth caustic was reported in Khamitov et al. 2016a), Montarrenti, Bialkow, Ostrowik, Krakow50, OndrejovD50, LT, pt5m, Salerno, and UCLO, spanning the whole globe, which provided 24-hour coverage of the caustic exit. The sequence of spectroscopic observations before and at the very peak was taken with the IDS instrument on the Isaac Newton Telescope (INT). After the peak at 11.85 mag in I band, the event brightness smoothly declined, as caught by Swarthmore24, DEMONEXT, and AAVSO. The first datapoint taken on the next night from India (Aries130 telescope) showed I=14.33 mag, indicating the complete exit from the caustic. The event then again began to rise very slowly, with a rate of 1 mag over four months, and it exhibited a smooth peak on 5 May 2017 (HJD’=7878), reaching I=13.3 mag (G$\sim$14 mag) (Wyrzykowski et al., 2017). After this, the light curve declined slowly and reached the pre-alert level in November 2017, at G=15.5 mag. We continued our photometric follow-up for another year to confirm that there was no further re-brightening. Throughout the event, the All-Sky Automated Survey for SuperNovae (ASAS-SN) (Shappee et al., 2014; Kochanek et al., 2017a) observed Gaia16aye serendipitously with a typical cadence of between two and five days. Its data cover various parts of the light curve of the event, including the part before the Gaia alert, where a smooth rise and the first caustic entry occurred.

2.1 Ground-based photometry calibrations

Each observatory processed the raw data with their own standard data reduction procedures to create bias, dark-subtracted, and flat-fielded images. Then, the images were solved astrometrically, most often with the use of Astrometry.net code (Hogg et al. 2008; Lang et al. 2010), and the instrumental photometry for all objects within the field of view was derived with a variety of tools, including Source EXtractor (Bertin & Arnouts, 1996) and Daophot (Stetson, 1987). The lists of detected sources with their measured instrumental magnitudes were uploaded to the Cambridge Photometric Calibration Server (CPCS)444http://gsaweb.ast.cam.ac.uk/followup, designed and maintained by Sergey Koposov and Lukasz Wyrzykowski. The CPCS matches the field stars to a reference catalogue, identifies the target source, and determines which filter was used for observations. This tool acted as a central repository for all the data, but primarily, it standardised the data into a homogenous photometric system. It relied on available archival catalogues of this patch of the sky (primarily the AAVSO Photometric All-Sky Survey, APASS, and the Pan-STARRS1 Surveys, PS1) and derived zero-points for each of the observations. The use of a common repository allowed for near-real-time tracking of the evolution of the event, which is particularly important near the caustic entry and exit. Photometric data were uploaded by the observers within minutes of the observation, which facilitated detailed planning of the spectroscopic follow-up.

The list of all the ground-based photometric observations is summarised in Table 2.1 and the photometric observations are listed in Table 9 that is available in the appendix. The full table contains 23,730 entries and is available in the electronic version of the paper. Figure 2 shows all follow-up measurements collected for Gaia16aye over a period of about one and a half years.