VZ Lib: a contact binary in a ternary system
Observed: 2014 (1 session, 1 ToM), 2016 (1 session, 1 ToM), 2018 (1 session, 0 ToM), 2020 (4 sessions, 3 ToM)
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 ROTSE-1 and ASAS-3, 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 3.104+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:
With these new ToM, the resulting O-C diagram is:
The same as above with new data. Red circles: individual times of minima, Blue squares: average minima from ROTSE-1 and ASAS-3, 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 O-C with the new cycle counting is shown on the figure below.
The dotted blue line is from the fit ToM(e)=T+Pe+ße2.
These data may be fitted with:
e the cycle number
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'=P2/4ß=-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 O-C 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:
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 ± 0.43o
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 close-up 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.
The orbital period of the ternary is P3=2πP/ω=1087.8±2.2 days=2.978
yr. The phase plot with this period:
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/ukrayinska-odessa-astronomical-publications.
Yue Q., Zhang L-Y., Han X-M.L. et al (2019) Res. Astron. Astrophys. 19 097.
The use of the on-line tool of the University of Ohio to convert HJD to BJD, at http://astroutils.astronomy.ohio-state.edu/time/hjd2bjd.html, is acknowledged.
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