10.9.4 Processing steps
The Microlensing detection pipeline was divided into two parts. The first part (Extractor, unpublished) aimed at a very crude detection of outbursting events in the light curve, while the second part (SOS, published) used Microlensing models to fine-tune the classification of candidate events. Such data were then filtered and validated by humans.
The main role of the Extractor is to check if the light curve has a Microlensing-like outburst, flag it, and associate it with a membership score. However, because it has to sieve through hundreds of millions of time series data, it has to work quickly. The Extractor studies , , and data as well as statistical parameters derived on the time series. The Extractor runs a series of simple tests, executed consecutively:
bright event selection in -band, to verify if the event has a sufficient number of FoV measurements brighter than the median of the whole time series:
where denotes the -th element of the time series;
achromaticity, to verify if the brightening also appears in and for the time interval identified in -band data;
unique rise and fall, to verify if there is only one rise and one fall in the light curve and if the variability is sufficiently significant by comparing pairs of consecutive points;
baseline constancy, to verify if the light curve outside of identified candidate microlensing event is constant, by analysing the weighted standard deviation.
A source has to pass all of these tests to be identified as a candidate event.
The (unpublished) information gathered for each source passing through all tests of the identified candidate microlensing event include the time of the peak and its duration, the values related to the tests mentioned above, a membership score, the total duration of the event, and the number of measurements in the light curve during the event.
In the subsequent stage of the processing, the candidates that passed the Extractor criteria and were above some minimum membership score were analysed by the SOS pipeline, where three levels of Microlensing models were fitted to -, - and -band light curves for each source, with the number of fitted parameters increasing at higher levels.
Model fitting: Level 0
The simplest Microlensing model assumes no microlensing parallax and no blending. Such model is a good approximation for most of the microlensing events, especially in the less crowded regions of the sky and for faint or dark lenses. This model is also the most stable mathematically. It contains three parameters in common with all bands (paczynski0_u0, paczynski0_te, paczynski0_tmax) and an additional parameter for each band (paczynski0_g0, paczynski0_bp0, paczynski0_rp0).
The parameters of the model fit were initialized with the values from the Extractor. The fitting algorithm employed Java Simplex with a maximum number of evaluations of 15 000. This model is symmetric and the best-fitting parameters could in principle return negative values (e.g., for a lens moving in the opposite direction) for paczynski0_u0 or paczynski0_te. For clarity, the code returns the absolute value of those parameters.
Model fitting: Level 1
This model includes blending parameters for , , and bands, when enough measurements are available for all bands (see 10.9.2). The blended model fitting is less stable; in particular, the blending parameter(s) can be unconstrained in case of events with sparsely sampled wings in the Microlensing curve. The model parameters of the event for Level 1 (paczynski1_u0, paczynski1_te, paczynski1_tmax), as well as baselines in each band (paczynski1_g0, paczynski1_bp0, paczynski1_rp0) were initialized with the values obtained at Level 0. Each band had also additional blending parameter initialized at one (paczynski1_fs_g, paczynski1_fs_bp, paczynski1_fs_rp). The fitting algorithm employed Java Simplex with a maximum number of evaluations of 5000. Similarly as in Level 0, the model is symmetric, hence the absolute values of paczynski1_u0 and paczynski1_te are returned.
Model fitting: Level 2
This model includes the effect of microlensing parallax, but does not include blending. Both blending and microlensing parallax cause modification to the standard Microlensing light curve, particularly in the wings of the curve. For the sparse sampling of Gaia light curves, the degeneracy between these two effects can be severe and can prevent the quick convergence of the minimisation procedure. This model contained the standard Microlensing parameters, among which the baseline magnitudes for each of the bands and the reduced (paczynski2_chi2_dof) of the best fitting model, and two additional ones describing the parallax vector in North and East directions (paczynski2_parallax_north and paczynski2_parallax_east). More in-depth information about parameter description and fitting procedure can be found in Wyrzykowski et al. (2023).
The Level-2 parameters are not part of Gaia DR3 and were used only for the selection of candidate events.
A membership score (unpublished) was calculated based on various tests. The initial score was set to one and then:
if the amplitude in was smaller than 0.25 mag, the score was multiplied by 0.6;
if the amplitude in was between 0.25 and 0.5 mag, the score was multiplied by 0.9;
if the reduced of all fitting Levels was larger than 10, the score was multiplied by 0.5;
if the lowest reduced of all fitting Levels was between 3 and 10, the score was multiplied by 0.9;
if the time at maximum brightness, including the uncertainty of the model with the lowest reduced , was not between the beginning and the end of the light curve in , the score was multiplied by 0.9;
if the absolute value of the impact parameter, including the uncertainty of the model with the lowest reduced , was not between 0 and 1.5, the score was multiplied by 0.7;
if the absolute value of the impact parameter, including the uncertainty of the model with the lowest reduced , was between 0 and 0.001, the score was multiplied by 0.9;
if the model with the lowest reduced had a baseline magnitude in (paczynski0_g0) below 20 mag, the score was multiplied by 0.8;
if the Einstein time, including its uncertainty, was not within 2 and 500 days, the score was multiplied by 0.2;
if one of the parallax vector components was between 1.0 and the maximum value of a double type variable, the score was multiplied by 0.95;
if both of the parallax vector components were between 1.0 and the maximum value of a double type variable, the score was multiplied by 0.9.
Cuts and selections
In total, 98 750 637 sources passed the Extractor filters and the SOS pipeline, among which 11 344 530 had a membership score 0.75 (and 227 666 with a baseline magnitude brighter than 17 mag). Such a vast sample required further filtering. We have used some of the Microlensing parameters and other parameters derived by the variability processing pipeline to derive a series of cuts, which produced a small number of possible candidates. These conditions and their thresholds were achieved in an iterative way, involving visual inspections of the candidates while preserving the largest number of known microlensing events.
Table 10.2 gathers all the conditions applied, which returned 324 candidate events (set A). Visual inspections of those candidates, performed by three independent experienced researchers, yielded 164 events (set A1), described in more detail in Section 10.9.5.
|membership score||Membership score from the pipeline|
|paczynski0_u0||Only high amplification events|
|paczynski0_te||Timescale should be realistic and reasonable for Gaia DR3 duration|
|skewness_mag_g_fov||Only events getting brighter above the baseline|
|median_mag_bp median_mag_rp||Colour cut to remove blue outbursts and very red variables|
|median_mag_g_fov and||Amplitude cut as a function of magnitude|
|std_dev_mag_g_fov std_dev_mag_rp or||light curve robustness|
|paczynski0_tmax paczynski0_te||At least one timescale within the data, where tminforfit is the (unpublished) time at the beginning of the light curve used for fitting|
|ExtractorNumPointsInEvent||More than three outlying points identified by the Extractor|
|Duration||Duration in days between outlying points from the Extractor|
|MaxNumSigmaInEvent||‘Strength’ of the event from the Extractor|
|paczynski0_u0 / paczynski0_u0_error||Only fits with robust paczynski0_u0 determination selected|
|paczynski0_u0_error and paczynski0_te_error||Only fits with robust paczynski0_u0 and paczynski0_te selected|
|paczynski2_chi2_dof||Goodness of the parallax fit|
|paczynski2_parallax_east and||Only reasonable parallax vector selected|
|paczynski0_tmax or paczynski0_tmax and||Stricter skewness-Abbe selection for events|
|abbe_mag_g_fovskewness_mag_g_fov||in a period of times with more photometric|
Events from literature
Microlensing events known from literature were selected based on the papers with OGLE-IV events from the Galactic bulge and disc (Mróz et al. 2019, 2020), as well as events known in the Gaia Science Alerts (Hodgkin et al. 2021) that occurred during the Gaia DR3 time span: Gaia16aua, Gaia16aye, Gaia16bnn, Gaia17ahl, Gaia17aqu, Gaia17bbi, and Gaia17bej. We have also added two events found by the ASAS-SN survey (Shappee et al. 2014) within the same time interval: ASASSN-16oe and ASASSN-V J044558.57+081444.6 (Jayasinghe et al. 2017).
From the OGLE-IV sample, we have selected events that had timescales larger than 20 days and with maximum brightness between JD=2 456 863.9375 and JD=2 457 901.86458 (denoting the beginning and the end of Gaia DR3, respectively). We have cross-matched selected events with Gaia DR3 in order to obtain their Gaia source_id and in total 1074 sources have been identified, of which 404 (set B) passed through the Extractor and SOS pipeline (i.e., bright enough and with sufficient data points). After visual inspection, 233 events were selected (set B1).