# ASASSN-19cq: a gravitational microlensing event

## Observed: 23 sessions in Feb-Mar 2019

###### Michel Bonnardeau

28 Feb, 1, 8, 10, 12, 17, 20, 27 Mar, 5, 7, 11 Apr 2019

### Abstract

*Photometric observations of this microlensing event are presented
and interpreted. *

### Introduction

The discovery of the candidate microlensing event ASASSN-19cq was reported
by Sokolovsky et al (2019), on Feb 12. I observed this event from Feb
13 until Mar 27, 2019.

### Observations

The observations were carried out with a 203mm f/6.3 Schmidt-Cassegrain
telescope, a V filter and a ST7E camera (KAF-401E CCD). The duration of
each exposure is 200 s. A total of 471 valid images were obtained over
23 sessions.

For the differential aperture photometry, the comparison star is UCAC4
383-92972 (RA=17:46:48.98 DEC=-13:30:30.1) with an APASS magnitude V=12.227,
and the check star is UCAC4 383-93080 (RA=17:46:58.07 DEC=-13:30:43.9).

The light curves:

*The individual measurements of ASASSN-19cq (red) and of the check star
shifted by +3.1 mag (blue).*

*Each dot is the average of one session, and the error bars are ±1
standard deviation.*

### Analysis

**The theory**

The theory of the gravitational microlensing is explained in Wikipedia.

According to the GAIA DR2 catalog, the parallax to the lensed object
is 0.0914±0.0389 mas so the distance is d_{S}=10941±4656
pc. Let be d_{L} the distance to the lensing object and M its
mass. The Einstein angle is then:

The angular distance u(t) from the lensing object to the lensed star
is, in unit of θ_{E}, with t_{E} the Einstein time:

(u_{min}, the impact parameter, is the minimum distance, at t=t_{0}).

The amplification A of the flux from the lensed object is:

In the CMC14 catalog, the lensed star has the magnitudes r'=14.766, J=12.269,
H=11.539 and K=11.325. Owing to the transformation formula of Bilir et
al (2008) and Smith et al (2002) it can be computed that it has the magnitudes
V_{0}=15.389 and g_{0}=16.217 in the V and g bands respectively
(when not lensed).

The magnitude with the lensing effect is then:

V(t)=-2.5*log A(t)+V_{0}

**A Monte Carlo fit**

The V(t) function is fitted to the observations using a Monte Carlo method.
There are 4 parameters to be adjusted: u_{min}, t_{0},
t_{E} and also V_{0}. V_{0} needs to be adjusted
because it is determined by transformations formulas, which are only approximate,
and also to allow for a possible shift with the different photometry setups.

The 4 parameters are allowed to vary in the following ranges:

u_{min} around 0.15 ± 0.1

t_{0} around the time of my first observation (2,458,528.71328
HJD) ± 1 day

t_{E} around 26 ± 10 day

V_{0} around 15.389 ± 0.3 mag.

10^{6} sets of 4 parameters are taken randomly and, for each
set, the quadratic sum of the residuals of V(t) from the observations,
weighted with the uncertainties on the magnitudes, is computed. The set
that gives the smallest residual is selected.

The process is repeated 10 times. The averages and the standard deviations
of the selected sets of parameters are retained as the best fit to the
observations.

Actually, this is repeated a number of times to be sure that the results
are stable and that there is no degeneracy (i.e. different sets of parameters
fitting the observations).

The results are:

u_{min} = 0.1715± 0.031

t_{0} = 2,458,529.023± 0.046 HJD

t_{E} = 21.50± 0.58 days

V_{0} = 15.269± 0.018 mag

and the resulting fit is shown in the figure below:

*Green: the V(t) function.*

**With blending:** Another way to fit the observations is to take into account the
contribution of unresolved stars along the line of the sight to the overall
received light. This blending effect (Nucita et al, 2018) may be accounting
for by using the ratio of the source flux F_{s} to the total baseline flux
F_{s}+F_{blend}:

f_{s}=F_{s}/(F_{s}+F_{blend})

The magnitude with the lensing effect and the blending effect is then:

V_{b}(t)=-2.5*log[f_{s}*(A(t)-1)+1]+2.5*log(f_{s})+V_{0}

A Monte Carlo fit is again performed, with a 5th parameter f_{s,}
to be searched between 1 and 0.5. The results are, with 10 runs of 10^{7}
trials:

u_{min} = 0.1317± 0.0057

t_{0} = 2,458,529.088± 0.040 HJD

t_{E} = 26.81± 0.95 days

V_{0} = 15.592± 0.053 mag

f_{s} = 0.776± 0.034

and the resulting fit is shown in the figures below:

*Dot blue: the V*_{b}(t) function.

*Red: residuals of the observations from the V(t) function, Blue: from
the V*_{b}(t) function.
**About the microlens**

The distance d_{L} to the lensing object, as a function of its
mass M, for a given velocity v is:

with the + for the lens being closer to the lensed object, and - for it
closer to the observer.

The figure below gives d_{L} as a function of M for a velocity
v=10km/s and for v=100km/s:

*Continuous curves: d*_{L}^{+},
curves with dots: d_{L}^{-}. The 2 red curves on the left are
for v=10km/s, the 2 blue curves on the right are for
v=100km/s.

### A Monte Carlo fit of the ASAS-SN data

The ASAS-SN data are available from https://asas-sn.osu.edu/.
There are 76 measurements from HJD 2458519.15453 to 2458578.77813, obtained
with a g filter. They are then fitted with the function:

g(t)=-2.5*log A(t)+g_{0}

owing to the Monte Carlo method, as above, except for the magnitude without
the lens: g_{0} around 16.217 ± 0.6 (not 0.3 as above,
which appears to be too small here).

The results are:

u_{min} = 0.2169 ± 0.022

t_{0} = 2,458,528.845 ± 0.022 HJD

t_{E} = 18.04 ± 0.27 days

g_{0} = 15.711 ± 0.007 mag

**With blending**, the observations are fitted with the function,
the same way as with my observations:

g_{b}(t)=-2.5*log[f_{s}*(A(t)-1)+1]+2.5*log(f_{s})+g_{0}

This gives:

u_{min} = 0.151 ± 0.016

t_{0} = 2,458,528.843 ± 0.019 HJD

t_{E} = 23.9 ± 1.9 days

g_{0} = 16.15 ± 0.12 mag

f_{s} = 0.684 ± 0.070

The fit with the blending gives a value of g_{0} very close to
the one obtained from the CMC14 catalog.

The parameters obtained with blending are the same as (within the uncertainties)
those obtained from my observations, also with blending. The blending
factor is a bit stronger for ASAS-SN.

The resulting fits are shown in the figures below:

*Red: ASAS measurements, Green: the g(t) function, Dot blue: the
g*_{b}(t) function.

*Red: the residuals from the g(t) function, Blue: from the g*_{b}(t) function.

### Conclusions

Both my observations and the ASAS-SN observations are fitted with the
same gravitational microlens lightcurve. Furthermore, these observations
are in different wavelength bands, which comforts the microlens interpretation.

The lensing object may have a mass in the range of 1/100 solar mass (a
brown dwarf), anywhere along the line of sight. There is no evidence for
a binary.

### References

Bilir S. et al (2008) MNRAS __384__ 1178.

Nucita A.A. et al (2018) MNRAS __476__ 2962.

Smith J.A. et al (2002) AJ __123__ 2121.

Sokolovsky K.V. et al (2019) ATEL #12495.

### Technical notes

Telescope and camera configuration.

Computer and software configuration.

Data processing.