J/MNRAS/506/2482 Microlensing events in VVV light curves (Husseiniova+, 2021)
A microlensing search of 700 million VVV light curves.
Husseiniova A., McGill P., Smith L.C., Evans N.W.
<Mon. Not. R. Astron. Soc., 506, 2482-2502 (2021)>
=2021MNRAS.506.2482H 2021MNRAS.506.2482H (SIMBAD/NED BibCode)
ADC_Keywords: Milky Way ; Gravitational lensing ; Infrared sources ;
Photometry, infrared
Keywords: gravitational lensing: micro - Galaxy: bulge - Galaxy: structure
Abstract:
The VISTA Variables in the Via Lactea (VVV) survey and its extension
have been monitoring about 560 deg2 of sky centred on the Galactic
bulge and inner disc for nearly a decade. The photometric catalogue
contains of order 109 sources monitored in the Ks band down to 18
mag over hundreds of epochs from 2010 to 2019. Using these data we
develop a decision tree classifier to identify microlensing events. As
inputs to the tree, we extract a few physically motivated features as
well as simple statistics ensuring a good fit to a microlensing model
both on and off the event amplification. This produces a fast and
efficient classifier trained on a set of simulated microlensing events
and catacylsmic variables, together with flat baseline light curves
randomly chosen from the VVV data. The classifier achieves 97 per cent
accuracy in identifying simulated microlensing events in a validation
set. We run the classifier over the VVV data set and then visually
inspect the results, which produces a catalogue of 1959 microlensing
events. For these events, we provide the Einstein radius crossing time
via a Bayesian analysis. The spatial dependence on recovery efficiency
of our classifier is well characterized, and this allows us to compute
spatially resolved completeness maps as a function of Einstein
crossing time over the VVV footprint. We compare our approach to
previous microlensing searches of the VVV. We highlight the importance
of Bayesian fitting to determine the microlensing parameters for
events with surveys like VVV with sparse data.
Description:
We observing the light curves in order to produce the version two of
the VVV Infrared Astrometric Catalogue (see Smith et al.
2018MNRAS.474.1826S 2018MNRAS.474.1826S, Cat. II/364 for details of version one)
which has yielded a time series photometry data base of order 109
stars in the VVV area (approx. 560 deg2) using VVV and VVVX data.
We proceed to data reduction via VIRCAM stacked pawprint images which
uses a modified version of the dophot profile fit image reduction
software (Schechter, Mateo & Saha 1993PASP..105.1342S 1993PASP..105.1342S;
Alonso-Garcia et al. 2012AJ....143...70A 2012AJ....143...70A).
Photometric measurements were coarsely calibrated using a globally
optimized zero-point plus illumination map model.
In our search algorithm, we opt for a feature extraction based
approach to distinguish microlensing events from other light curves
However, instead of computing many general summary statistics of the
light curve, we focus on a few interpretable features based on
microlensing model fitting and checking. This first feature captures
how well a microlensing model fits the data compared to a constant
magnitude model. Bayesian analysis of this problem obtaining posterior
samples using the maximum likelihood (MLE) fits, which are much
cheaper to compute (typically 0.1 seconds per source for PSPL
microlensing models), (see equation 5 section 3.1 Maximum likelihood
estimates).
Hereafter, we compare the MLE of PSPL models for every sources to
check quality of their fits to the data with the help of the Akaike
information criterion (AIC; Akaike H., 1981, J. Econometrics, 16, 3)
as an estimator of the in-sample predictive performance (equation 8
and 9 section 3.2 Model comparison). We complete this estimator with a
lists of quality cuts resumed in the section 3.3.1 Quality cuts. Next,
we compute the standardized residual for a given data point (i.e
equation 10 section 3.3.2 Features) and the von Neumann ratio (i.e the
ratio of the mean square of adjacent differences of data points to the
variance of all the data points on the light curve, see equation 11
section 3.4 The von Neumann ratio).
Consequently, with the helps of the above features, we train a a
decision tree classifier to extract microlensing events from the VVV
survey. Decision trees are non-parametric supervised machine learning
algorithms that classify objects based on computed features. We use a
training algorithm similar to C4.4, which is implemented in the
scikit-learn python package (namely decisiontreeclassifier; Pedregosa
et al. 2011, J. Mach. Learn. Res., 12, 2825), (see 3.5 Decision Tree
Classifier). We finally validate the performance of the classifier
(see 3.6 Validation).
Once the classifier has been trained, it is applied to the 217 317
VVV light curves that passed the quality cuts. This yields
microlensing candidates with a decision tree microlensing class
probability up to 0.5. Here (i.e section 5), we compare our recovered
sample of microlensing events to the three catalogues of previously
found microlensing events in the VVV 'Navarro smaples'.
In this work, we instead opt for a Bayesian approach to determine the
PSPL parameters. We wish to sample the posterior distribution of the
PSPL parameters θ = [t0,tE,u0,m0,fbl] for each event,
(see equation 18 section 5.2 Bayesian inference of PSPL parameters).
Leading us to our VVV light curves sample which pass the quality cuts
(1959 light curves) we fit the PSPL model by the above bayesian method
to obtain posterior distributions. The tablea1.dat contains the 16th,
50th, and 84th posterior percentiles of the θ PSPL parameters.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
tablea1.dat 203 1959 *Posterior inferences on the PSPL microlensing
model parameters for all found microlensing
events
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Note on tablea1.dat: For the 1959 microlensing events in our catalogue,
we fit the PSPL (point source and point lens) model by the Bayesian method
described in Section 5.2 Bayesian inference of PSPL parameters.
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See also:
II/376 : VISTA Variable in the Via Lactea Survey (VVV) DR4.2
(Minniti+, 2023)
J/ApJ/889/56 : VVV survey microlensing events; -3.7<b<-3.9°
(Navarro+, 2020)
J/ApJ/893/65 : VVV Survey microlensing events in the Gal. Bulge
(Navarro+, 2020)
II/364 : VIRAC. The VVV Infrared Astrometric Catalogue (Smith+, 2019)
J/ApJS/244/29 : Microlensing events toward the Galactic bulge (Mroz+, 2019)
J/ApJS/216/12 : OGLE-III Galactic bulge microlensing events
(Wyrzykowski+, 2015)
Byte-by-byte Description of file: tablea1.dat
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Bytes Format Units Label Explanations
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1- 17 A17 --- ID Event designation name (Event_ID) (1)
19- 29 F11.7 deg RAdeg Barycentric right ascension (ICRS)
at Ep=2015.5 (ra) (2)
31- 41 F11.7 deg DEdeg Barycentric declination (ICRS)
at Ep=2015.5 (dec) (2)
43- 51 F9.6 mag m016mag 16th posterior percentile of m0 baseline
magnitude in the infrared Ks band
at 2.15 µm (m0_16) (7)
53- 61 F9.6 mag m050mag 50th posterior percentile of m0 baseline
magnitude in the infrared Ks band
at 2.15 µm (m0_50) (7)
63- 71 F9.6 mag m084mag 84th posterior percentile of m0 baseline
magnitude in the infrared Ks band
at 2.15 µm (m0_84) (7)
73- 80 F8.6 --- u016 16th posterior percentile of u0
impact parameter (u0_16) (3)
82- 89 F8.6 --- u050 50th posterior percentile of u0
impact parameter (u0_50) (3)
91- 98 F8.6 --- u084 84th posterior percentile of u0
impact parameter (u0_84) (3)
100-110 F11.6 d tE16 16th posterior percentile of tE Einstein
time (tE_16) (4)
112-122 F11.6 d tE50 50th posterior percentile of tE Einstein
time (tE_50) (4)
124-134 F11.6 d tE84 84th posterior percentile of tE Einstein
time (tE_84) (4)
136-147 F12.6 d t016 16th posterior percentile of closest approach
time in modified julian date (t0_16) (5)
149-160 F12.6 d t050 50th posterior percentile of closest approach
time in modified julian date (t0_50) (5)
162-173 F12.6 d t084 84th posterior percentile of closest approach
time in modified julian date (t0_84) (5)
175-182 F8.6 --- fbl16 16th posterior percentile of blending fraction
(fbl_16) (6)
184-191 F8.6 --- fbl50 50th posterior percentile of blending fraction
(fbl_50) (6)
193-200 F8.6 --- fbl84 84th posterior percentile of blending fraction
(fbl_84) (6)
202-203 A2 --- DET Event detected in previous search (8)
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Note (1): Event are labelled in the standard format VVV-date-DSC-Number or
VVV-date-BLG-Number. The data gives the year in which the maximum of
the event occurs, whilst disc (DSC) or bulge (BLG) refers to the
VVV field in which the event is located according to whether the
absolute value of the Galactic longitude |l| is greater or less
than 10 degrees. Of course, this does not necessarily mean that the
source or lens lie in the disc or bulge.
Note (2): From preliminary results of the VVV Infrared Astrometric Catalogue
version 2 (see Smith et al. 2018MNRAS.474.1826S 2018MNRAS.474.1826S, Cat. II/364
for version 1). Positions are on the International Celestial
Reference Frame at epoch 2015.5 Julian years, and were calculated
using references stars from Gaia Data Release 2
(Gaia Collaboration 2018A&A...616A...1G 2018A&A...616A...1G, Cat. I/345).
Note (3): As explained by Paczynski (1986ApJ...301..503P 1986ApJ...301..503P, and also equation 1),
here u0 is the impact parameter normalized by the angular Einstein
radius RE/D1 where RE is the Einstein Radius of the Einstein
ring and D1 is the distance from the observer to the lens,
(to more explanations on equations and microlensing effect please see
section 1 Introduction).
Note (4): tE is the Einstein crossing time containing physical information,
as it is related to the mass of the lens M and the relative source
lens transverse velocity v by the equation 3,
(to more explanations on equations and microlensing effect please see
section 1 Introduction).
Note (5): t0 is the time of the event peak,
(to more explanations on equations and microlensing effect please see
section 1 Introduction).
Note (6): fbl is the fraction of lensed source flux to the total blend flux
as used in the equation 2,
(to more explanations on equations and microlensing effect please see
section 1 Introduction).
Note (7): As explained in the section 3 Search algorithm, the PSPL model
inducing some non-zero amount of blended light not from source,
then the magnitude is modelled like :
mPSPL = m0 -2.5*log[Aobs(t)]; with Aobs(t) written in
equation 2 section 1 Introduction,
(to more explanations please see section 3 Search Algorithm).
Note (8): Found in previous sample encoded as follows:
-N = Navarro samples from Navarro et al.
2020ApJ...889...56N 2020ApJ...889...56N, Cat. J/ApJ/889/56;
2020ApJ...893...65N 2020ApJ...893...65N, Cat. J/ApJ/893/65;
2020ApJ...902...35N 2020ApJ...902...35N
O- = OGLE samples from Mroz et al.
2019ApJS..244...29M 2019ApJS..244...29M, Cat. J/ApJS/244/29;
2020ApJS..249...16M 2020ApJS..249...16M, Cat. J/ApJS/249/16
ON = Boths
-- = Neither
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History:
From electronic version of the journal
(End) Luc Trabelsi [CDS] 21-Jun-2024