MBCAA Observatory

VZ Lib: a contact binary in a ternary systemObserved: 2014 (1 session, 1 ToM), 2016 (1 session, 1 ToM), 2018 (1 session, 0 ToM), 2020 (4 sessions, 3 ToM)Michel Bonnardeau

Season  HJD  uncertainty  BJD 
2014  2456733.582  0.001  2456733.582782 
2016  2457526.397  0.001  2457526.397766 
2020  2458954.580  0.001  2458954.580783 
2458990.406  0.001  2458990.406785  
2458998.468  0.001  2458998.468785 
In my 2009 paper I interpreted the times of minimum (ToM) with a light
time travel effect (LTTE) due to the 3rd body, with a period of of 34
yr. As shown in the figure below, the new data do not fit this interpretation:
The same as Fig 5 of Bonnardeau (2009) with new data. Red circles:
individual times of minima, Blue squares: average minima from ROTSE1
and ASAS3, Green dots: my new measurements, Black circles: new measurements
from Liao + (2019); Cyan line: the 2009 LTTE fit, which does not fit the
new data.
In my 2009 paper, the ToM of Tsesevich (1954) (at HJD 3.10^{4}+2,400,000 in the above figure), reported by Claria & Lapasset (1981), acts as an anchor point to determine the period of 34 yr. I recently got an access to this hard to find paper and analyzed it HERE.
I derived 5 ToMs:
Season  HJD  uncertainty 
1937  2428731.834  0.005 
1938  2429055.350  0.003 
1942  2430509.95  0.01 
1943  2430900.292  0.005 
1944  2431253.377  0.003 
With these new ToM, the resulting OC diagram is:
The same as above with new data. Red circles: individual times of minima,
Blue squares: average minima from ROTSE1 and ASAS3, Green dots: my new
measurements, Black circles: my interpretation of the Tsesevitch (1954)
data.
I do the same analysis as Liao et al (2019) (hereafter L2019). I use their 98 ToMs and I add the 5 from Tsesevich (1954) derived aboved, my 5 new observations and also 5 observations from Yue et al (2019), so a total of 113 ToMs. I compute the cycle number the same way as L2019. All these observations are listed HERE.
The OC with the new cycle counting is shown on the figure below.
The dotted blue line is from the fit ToM(e)=T+Pe+ße^{2}.
These data may be fitted with:
ToM(e)=T+Pe+ße^{2}
e the cycle number
T=2,456,093.74382 BJD
P=0.358,253,475 day
ß=1.095.10^{10} day
This is comparable to the ephemeris (2) of L2019.
The corresponding derivative of the period is P'=2ß/P=6.11.10^{10}
and the time scale t=P/2P'=P^{2}/4ß=802 kyr.
This is interpreted as a variation of the orbital period of the binary, due to mass transfer.
After BJD 2,450,000 (season 1998), one can notice what looks like an oscillation in the OC diagram. This was discovered by L2019.
I fit the data after BJD 2,450,000 (75 ToMs) with a sinusoidal function:
I start from the ephemeris (3) of L2019 and I make a Monte Carlo around
their parameters (the ranges are 10 times the L2019 uncertainties, with
10 millions trials). The result is:
ToM(e)=T+Pe+ße^{2}+asin(ωe+φ)
T= 2456093.742405 ± 0.00015 BJD
P= 0.358,254,281 ± 0.000,000,035 day
ß= 3.543.10^{11} ± 0.32.10^{11} day
a= 0.00371 ± 0.00015 day
ω= 0.002,0692 ± 0.000,0040 rad
φ= 125.67 ± 0.43^{o}
The fit and the data are shown in the figure:
Before BJD 2,450,000, the data are too sparse or the precision too poor (the ToMs are determined photographically or visually) and the oscillation is not visible.
Comparison with spectroscopy
The sinusoidal fit is interpreted as the LTTE induced by the ternary.
The figure below is a closeup of the previous figure, in time instead
of cycle number:
It can be compared with the Fig 5 (for VZ Lib B) of Lu et al (2001) of
the radial velocities at the same epoch. The radial velocities are maximum
at TJD 800 when in the middle of the sinusoid, and are minimum at TJD
0 and 1200 when the sinusoid is "changing its direction". This
is in agrement with the interpretation of the sinusoidal oscillation as
the LTTE.
Phase plot
The orbital period of the ternary is P_{3}=2πP/ω=1087.8±2.2 days=2.978
yr. The phase plot with this period:
Mass transfer
The ß parameter is different when calculated with all the data and with only the last ones. This suggests that the mass transfer is variable.
My new data fit with the ephemeris of L2019 with the LTTE.
The rate of mass transfer in the binary is probably variable.
Bonnardeau M. (2009) JAAVSO 37 137.
Claria J.J. and Lapasset E. (1981) IBVS 2035.
Eastman J., Siverd R. and Gaudi B.S. (2010) PASP 122 935.
Liao W.P., Qian S.B. and Sarotsakulchai T. (2019) AJ 157 207.
Lu W.X., Rucinski S.M. and Ogloza W. (2001) AJ 122 402.
Tsesevich B.P. (1954) Izvestiya Astronomicheskoy Observatorii 4 196. Available from http://lib.onu.ua/en/ukrayinskaodessaastronomicalpublications.
Yue Q., Zhang LY., Han XM.L. et al (2019) Res. Astron. Astrophys. 19 097.
The use of the online tool of the University of Ohio to convert HJD to BJD, at http://astroutils.astronomy.ohiostate.edu/time/hjd2bjd.html, is acknowledged.
Telescope and camera configuration.
Computer and software configuration.









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