MBCAA Observatory

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)

Michel Bonnardeau
29 June 2020
Updated 17 Aug (5 more ToMs from Y+2019), 15 Oct 2020 (misprints)


New photometric observations are presented for this contact binary in a ternary system. A total of 113 times of minimum are analyzed and are found to be in agreement with the ephemeris of Liao et al (2019).


VZ Lib is an eclipsing contact binary system with a period of 8.6 hours (W UMa type) in a triple system. The ternary component shows up by spectroscopy, from the study of the radial velocities (Lu et, 2001). I observed it photometrically in 2007-2009 (Bonnardeau, 2009).

The photometric phase plot shows 2 minima, usually one with a round bottom the other one with a flat bottom.

New photometric observations are presented along with a new interpretation, using the ephemeris of Liao et al (2019).

New observations

I observed again VZ Lib, with the same setup (203mm S-C telescope, SBIG ST7E camera, Johnson V filter) as in 2009, in 2014, 2016, 2018 (but no minimum observed) and 2020. An example of a light curve is:

Red: VZ Lib, Blue: the check star GSC6184-00385 (shifted by -2 mag). The error bars are +/- the 1 sigma statistal uncertainty (quadratic sum from the star and from the COMP). The COMP is TYC6184-1101-1.

and a phase plot for 2020 is:

The times of minum (ToM) are listed in the table below. They are measured in HJD and converted into BJD (Eastman et al, 2010).

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

Interpretation of 2009

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.

Analysis of Tsesevich (1954)

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:

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 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.

Period variation

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+e2.

These data may be fitted with:
e the cycle number
T=2,456,093.74382 BJD
P=0.358,253,475 day
=-1.095.10-10 day
This is comparable to the ephemeris (2) of L2019.

The corresponding derivative of the period is P'=2/P=-6.11.10-10
and the time scale t=P/2P'=P2/4=-802 kyr.

This is interpreted as a variation of the orbital period of the binary, due to mass transfer.

Light time travel effect

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
= -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.

Phase plot

The orbital period of the ternary is P3=2πP/ω=1087.82.2 days=2.978 yr. The phase plot with this period:

Mass transfer

The 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.

Technical notes

Telescope and camera configuration.

Computer and software configuration.

Data processing.

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