A photometric study of the high-mass-ratio contact binary AV Puppis

TL;DR

This study presents multi-color photometric analysis of AV Puppis, revealing it as a high-mass-ratio contact binary with increasing orbital period due to mass transfer, using Wilson-Devinney modeling.

Contribution

It provides the first detailed photometric solution and orbital period analysis of AV Puppis, highlighting its peculiar high mass ratio and period increase.

Findings

AV Puppis is a high-mass-ratio contact binary with q=0.896.

The orbital period of AV Puppis is increasing at 4.83×10⁻⁷ days/year.

The period increase is caused by mass transfer from the less to the more massive component.

Abstract

The multi-color photometric light curves for a contact binary AV Puppis (AV Pup) in $VR_cI_c$ bandpasses are presented, and they are analyzed by using of the 2013 version of the Wilson-Devinney (W-D) code. The solutions suggest that AV Pup is a peculiar A-subtype W UMa contact binary with a high mass ratio ($q=m_2/m_1= 0.896$) and a fill-out factor ($f=10\%$). Combining with our newly determined times of minimum with those collected from literatures, the orbital period changes of this system are investigated. The $O-C$ analysis shows that the orbital period of AV Pup is increasing at a rate of $\mathrm{d}P/\mathrm{d}t=4.83 \times 10^{-7} \ \mathrm{days \ yr^{-1}}$, which can be explained by mass transfer from the less massive component to the more massive one.

Tables

Table 1. Table 1 : Coordinates of AV Pup, the comparison star and the check star.

Targets	Name	${\alpha }_{J2000}$	${\delta }_{J2000}$	$V_{\mathrm{mag}}$
Variable	AV Pup	08 24 32.30	-16 24 11.24	10.68
The comparison	TYC 5998-1820-1	08 24 15.30	-16 23 13.43	11.56
The check	TYC 5998-2135-1	08 24 22.63	-16 25 15.75	11.53

Table 2. Table 2 : New times of minimum for AV Pup

HJD	error	p/s	fiter
2456715.2366	0.0001	p	$V{R}_c{I}_c$
2456716.1067	0.0001	p	$V{R}_c{I}_c$
2456717.1950	0.0001	s	$V{R}_c{I}_c$
2457094.1343	0.0002	p	$V{R}_c{I}_c$
2457096.0923	0.0002	s	$V{R}_c{I}_c$
2457098.0494	0.0001	p	$V{R}_c{I}_c$

Table 3. Table 3 : All CCD times of minimum for AV Pup.

HJD	Error	Epoch	O-C	Min	Filter	References
(2400000+)
52002.5424	-	-10833.5	-0.0134	II	CCD	AAVSO
52237.2300	-	-10294.0	-0.0137	I	$R_c$	Nagai (2001)
52655.0563	-	-9333.5	-0.0145	II	$R_c$	Nagai (2004)
53020.0299	-	-8494.5	-0.0143	II	$R_c$	Nagai (2005)
53021.7705	-	-8490.5	-0.0137	II	CCD	AAVSO
53035.6907	-	-8458.5	-0.0138	II	CCD	AAVSO
53043.0860	-	-8441.5	-0.0137	II	$R_c$	Nagai (2005)
53074.6232	-	-8369.0	-0.0147	I	CCD	AAVSO
53109.6840	-	-8288.5	0.0278	II	CCD	AAVSO
53403.0552	-	-7614.0	-0.0153	I	$R_c$	Nagai (2006)
53405.0126	-	-7609.5	-0.0154	II	$R_c$	Nagai (2006)
53426.9828	-	-7559.0	-0.0132	I	$V$	Nagai (2006)
53743.2333	-	-6832.0	-0.0150	I	$V$	Nagai (2007)
53761.0689	-	-6791.0	-0.0148	I	$V$	Nagai (2007)
54119.0815	-	-5968.0	-0.0154	I	$V$	Nagai (2008)
54126.0425	-	-5952.0	-0.0146	I	$V$	Nagai (2008)
54127.7825	0.0003	-5948.0	-0.0146	I	CCD	Samolyk (2008)
54526.6873	0.0001	-5031.0	-0.0140	I	CCD	Samolyk (2008)
54526.6874	0.0002	-5031.0	-0.0139	I	CCD	Samolyk (2008)
54545.6101	0.0002	-4987.5	-0.0141	II	CCD	Samolyk (2008)
54548.0023	-	-4982.0	-0.0145	I	$V$	Nagai (2009)
54877.7380	0.0004	-4224.0	-0.0164	I	CCD	Samolyk (2009)
54901.6674	0.0002	-4169.0	-0.0125	I	CCD	Samolyk (2010b)
55175.9443	0.0005	-3538.5	-0.0094	II	CCD	Samolyk (2010a)
55232.7119	0.0003	-3408.0	-0.0106	I	CCD	Samolyk (2010a)
55271.6457	0.0001	-3318.5	-0.0102	II	CCD	Samolyk (2011a)
55612.6958	0.0002	-2534.5	-0.0080	II	$V$	Samolyk (2011b)
55622.7003	0.0002	-2511.5	-0.0087	II	$V$	Samolyk (2011b)
55630.7481	0.0002	-2493.0	-0.0086	I	$V$	Diethelm (2011)
56290.8767	0.0015	-975.5	-0.0076	II	$V$	Diethelm (2013)
56737.6404	0.0001	51.5	0.0008	II	$V$	Samolyk (2014)
56715.2366	0.0001	0.0	0.0000	I	$V{R}_c{I}_c$	This paper
56716.1067	0.0001	2.0	0.0001	I	$V{R}_c{I}_c$	This paper
56717.1950	0.0001	4.5	0.0009	II	$V{R}_c{I}_c$	This paper
57034.5430	0.0040	734.0	0.0091	I	CCD	Paschke (2015)
57094.1343	0.0002	871.0	0.0040	I	$V{R}_c{I}_c$	This paper
57096.0923	0.0002	875.5	0.0044	II	$V{R}_c{I}_c$	This paper
57098.0494	0.0001	880.0	0.0040	I	$V{R}_c{I}_c$	This paper
58133.1690	-	3259.5	0.0044	II	$BV{I}_c$	Nagai (2019)
58135.7783	0.0001	3265.5	0.0040	II	$V$	AAVSO
58203.6405	0.0001	3421.5	0.0040	II	$V$	AAVSO

Table 4. Table 4 : Photometric solutions of AV Pup.

Parameters	2014	2015
$g_1=g_2$	0.32(fixed)	0.32(fixed)
$A_1=A_2$	0.5(fixed)	0.5(fixed)
$T_1\left(K\right)$	6255(fixed)	6255(fixed)
$T_2\left(K\right)$	6145 $\pm$ 7	6150 $\pm$ 9
$q\left(M_2/M_1\right)$	0.896 $\pm$ 0.005	0.896 $\pm$ 0.003
${\Omega }_1={\Omega }_2$	3.525 $\pm$ 0.008	3.529 $\pm$ 0.005
$i\left(deg\right)$	81.222 $\pm$ 0.101	80.845 $\pm$ 0.109
$L_1/{\left(L_1+L_2+L_3\right)}_V$	0.516 $\pm$ 0.003	0.530 $\pm$ 0.008
$L_1/{\left(L_1+L_2+L_3\right)}_{R_c}$	0.509 $\pm$ 0.003	0.524 $\pm$ 0.007
$L_1/{\left(L_1+L_2+L_3\right)}_{I_c}$	0.500 $\pm$ 0.003	0.512 $\pm$ 0.006
$L_3/{\left(L_1+L_2+L_3\right)}_V$	0.052 $\pm$ 0.003	0.025 $\pm$ 0.010
$L_3/{\left(L_1+L_2+L_3\right)}_{R_c}$	0.060 $\pm$ 0.003	0.031 $\pm$ 0.009
$L_3/{\left(L_1+L_2+L_3\right)}_{I_c}$	0.071 $\pm$ 0.003	0.048 $\pm$ 0.008
$r_1\left(pole\right)$	0.3726 $\pm$ 0.0005	0.3720 $\pm$ 0.0004
$r_1\left(side\right)$	0.3932 $\pm$ 0.0005	0.3924 $\pm$ 0.0005
$r_1\left(back\right)$	0.4273 $\pm$ 0.0005	0.4263 $\pm$ 0.0006
$r_2\left(pole\right)$	0.3536 $\pm$ 0.0018	0.3538 $\pm$ 0.0011
$r_2\left(side\right)$	0.3721 $\pm$ 0.0023	0.3723 $\pm$ 0.0014
$r_2\left(back\right)$	0.4070 $\pm$ 0.0036	0.4072 $\pm$ 0.0022
$f(\%)$	10.9 $\pm$ 1.6	10.2 $\pm$ 1.1
Spot parameters:
Latitude(deg)	24.4	29.6
Longitude(deg)	144.0	97.4
Radius(deg)	31.0	16.9
T/T1	0.92	0.89

Table 5. Table 5 : A-subtype contact binaries with a high mass ratio

Name	$T_1\left(K\right)$	$T_2\left(K\right)$	$q$	$f(\%)$	References
OO Aql	5700	5472	0.844	21.4	İçli et al. (2013)
V2150 Cyg	8000	7920	0.802	19.0	Kreiner et al. (2003)
V1101 Her	5920	5690	0.800	14.2	Pi et al. (2017)
DZ Lyn	6860	5068	0.886	18.0	Martignoni et al. (2009)
AU Ser	5495	5153	0.710	19.8	Gürol (2005)

Equations

$$Min.I=\mathrm{HJD}2456715.2366+0.435010\times E.$$

$$Min.I=\mathrm{HJD}2456715.2369(3)+0.4350142(1)\times E+2.88(16)\times 10^{-10}\times E^2.$$

$$\frac{\mathrm{d}{M}_2}{\mathrm{d}t}={\dot{M}}_2=\frac{\dot{P}{M}_1{M}_2}{3P(M_2-M_1)}.$$

Full text

1 Introduction

W Ursae Majoris contact binaries are the most common eclipsing systems around the solar system (Shapley 1948). They are short-period binary systems with both components filling their inner Roche lobes and sharing a common envelope. The formation and evolutionary ending of contact binaries are still open questions in astrophysics. The most plausible scenario is that they are formed from detached binaries via angular momentum loss (AML) (Vilhu 1982) or evolutionary expansion of the components (Webbink 1976). Model calculations suggest that this type of systems will ultimately evolve into contact binaries of extreme mass ratios or even into the fast-rotating single stars under the influence of AML (Li et al. 2004b).

AV Pup (GSC 05998-02010, $\alpha_{2000}$=$08^{h}24^{m}32.\!^{s}30$, $\delta_{2000}$=$-16^{\circ}24^{\prime}11.\!^{\prime\prime}24$) was firstly reported by Hoffmeister (1930) as a variable star. Brancewicz & Dworak (1980) classified it as a semi-detached binary star with light curves of W UMa type. Wadhwa (2005) analyzed this system by using the V band photometric data of All Sky Automated Survey (ASAS) . He found this system is a contact binary with a high mass ratio of 0.80 and a low fill-out factor of 10%. After that, this system has been barely studied.

In this work, we presented two years of photometric observations in $VR_{c}I_{c}$ bandpasses for AV Pup. We also obtained new photometric solutions and a period analysis for this system. The article is organized as follows: in section 2, the new observations for AV Pup are shown; in section 3, a period analysis is conducted for AV Pup; in section 4, the photometric solutions for the system are presented; at last, the summary and some discussions are given in section 5.

2 Observations

New $VR_{c}I_{c}$ photometric observations of AV Pup were obtained in 2014 and 2015 by using the 1m Cassegrain reflector telescope at Yunnan Observatory. The telescope mounts an Andor DW436 $2048\times 2048$ CCD camera with an effective field of view of 7.3 $\times$ 7.3 $\rm{arcmin}^{2}$. The aperture photometry package in IRAF was used for the data reduction. In our observations, the nearby stars TYC 5998-1820-1 and TYC 5998-2135-1 were employed as the comparison star and the check star, respectively. Their coordinates are listed in Table 1. The new light curves observed in two recent observation seasons are shown in Figure 1. It is found in Figure 1 that the two sets of light curves are quite similar, only have a slight difference between the phases 0.25 and 0.75.

Six new times of minimum were determined by using the K-W method (Kwee & van Woerden 1956) based on our observations. Then we took the average value of three bandpasses as one minimum. They are listed in Table 2.

3 Orbital period analysis

Besides the new times of minimum derived by us from our observations, we also collected other times of minimum from the $O-C$ Gateway database111http://var.astro.cz/ocgate/, AAVSO222https://www.aavso.org/ and literatures. We only used the CCD data (listed in Table 3) with a relatively high accuracy to investigate the changes in the orbital period of AV Pup, since the visual observations are too dispersive (in $O-C$ diagram) to have a significant help for the analysis of period changes of this object. Wadhwa (2005) assigned the orbital period of AV Pup as 0.435010 d, which is different from 0.556339 d obtained by Brancewicz & Dworak (1980). We find the former one seems to be more reliable based on our new observations. Based on the orbital period 0.435010 d and a primary minimum HJD 2456715.2366, we can give the following linear ephemeris:

[TABLE]

The $O-C$ values are calculated based on Equation 1 and listed in the fourth column of Table 3. As seen in Table 3, the minimum 2453109.6840 evidently deviates from the other minima, so we neglected this value. The $O-C$ values are shown in Figure 2. A clear parabola track can be seen from this Figure. We use a least-square solution to fit all available times of minima and get the following quadratic ephemeris:

[TABLE]

The period of AV Pup shows a secular increase. The increasing rate is derived as $\mathrm{d}P/\mathrm{d}t=4.83\times 10^{-7}\ \mathrm{days\ yr^{-1}}$ based on Equation 2. Since the CCD times of minimum only last less than 20 years, there is no clear cyclic variation showing in the $O-C$ diagram.

4 Light curve solution

We analyzed our new light curves based on the 2013 version of Wilson-Divinney (W-D) code (Wilson & Devinney 1971; Wilson 1979, 1990). Wadhwa (2005) assigned the surface temperature of AV Pup as 6255 K, which is corresponding to a spectral type of F8 in the General Catalog of Variable Stars. We took this value as the effective temperature of star 1 (eclipsed at phase 0.0) in our calculation. This effective temperature means that AV Pup should have a common convective envelope, so the bolometric albedos and gravity-darkening coefficients were set as $A_{1}=A_{2}=0.5$ (Ruciński 1969) and $g_{1}=g_{2}=0.32$ (Lucy 1967), respectively. We used the logarithmic law format of limb-darkening coefficients (van Hamme 1993), which were computed internally by the DC program of W-D code.

Due to the lack of spectroscopic mass ratio, a q-search procedure was performed to determine the initial mass ratio of AV Pup. A series of fixed mass ratios ranged from 0.1 to 5.0 in a step of 0.05 were adopted. In the q-search procedure, the adjustable parameters in our calculation were: the orbital inclination ($i$), the effective temperature of star 2 ($T_{2}$ ), the surface potential ($\Omega_{1}$ and $\Omega_{2}$) and the bandpass luminosity of star 1 ($L_{1}$). Due to the diffusion of semi-detached configuration and contact configuration, we ran DC subroutine of W-D code beginning with Mode 2 (a detached configuration) for each fixed $q$. However, the program quickly converged to Mode 3 (a contact configuration) at last, which means AV Pup should be a contact binary, as derived by Wadhwa (2005). For a clear view, Figure 3 only shows the relation between $\Sigma$ (the mean residuals for input data) and $q$ in the range of $q=0.3$ to 3.5. As seen from Figure 3, the results of two q-search procedures based on the light curves observed in 2014 and 2015 are quite similar. They have a flat pattern from $q=0.5$ to $q=2.0$ and with a minimum at $q=0.85$. We took $q=0.85$ as an initial mass ratio and assigned $q$ to be an adjustable parameter for the later calculation.

As seen from Figure 1, a slight O’Connell effect is shown in the light curves of AV Pup, so we attempted to model the light curves with spots. During the calculation, a third light was also taken into account. After some attempts, we finally got the best convergent solutions with a cool spot located on star 1 for the data of two years. The results are given in Table 4 and the comparison between observed and computed light curves is shown in Figure 4.

Our solutions suggest that AV Pup is an A-subtype contact binary. It has a high mass ratio of 0.896 and an inclination around 81∘. The system is a shallow contact system with a fill-out factor around 10% , which coincides with the result of Wadhwa (2005). The slight difference between two years light curves can be explained by the spot activity. Because there is no radial velocity curves observed for this system, we can not obtain the precise absolute parameters for the components of AV Pup. Therefore, we used the mass-temperature relation (Harmanec 1988) to derive the mass of the primary star, the primary’s mass can be estimated as $M_{1}=1.27~{}M_{\odot}$, then the mass of secondary star was determined to be $M_{2}=1.14\pm 0.01~{}M_{\odot}$ based on our photometric solution. The radii and luminosity for two components can also be obtained as: $R_{1}=1.29\pm 0.01~{}R_{\odot}$, $L_{1}=2.29\pm 0.02~{}L_{\odot}$, $R_{2}=1.23\pm 0.02~{}R_{\odot}$ and $L_{2}=1.94\pm 0.10~{}L_{\odot}$.

5 Summary and discussion

In this paper, we presented two years of CCD photometric observations for AV Pup. We derived the photometric solutions for this system. Two solutions show that AV Pup is an A-subtype contact binary with a high mass ratio of $q=m_{2}/m_{1}=0.896$. The system is a shallow contact binary with a low fill-out factor around 10%. Two years of observations show a slight difference, which can be explained by the spot variation. Contact binaries tend to have a low mass ratio (Rucinski 2001), so only a few of contact binaries with high mass ratio were discovered, such as WZ And ($q=1.0$, Zhang & Zhang 2006), HT Vir ($q=0.9$, Bensch et al. 2014) and so on. Meanwhile, the A-subtype contact binaries have a relatively low mass ratio and a relatively high contact degree in general (Hilditch et al. 1988; Jiang et al. 2009). However, a few A-subtype contact binaries were found to have a high mass ratio and a shallow common envelope (listed in Table 5). AV Pup seems to have the same characteristics as these peculiar contact binaries.

We also conducted the first period change analysis for AV Pup. A least-square fitting shows that the orbital period of AV Pup is suffering a secular increase at a rate of $\mathrm{d}P/\mathrm{d}t=4.83\times 10^{-7}\ \mathrm{days\ yr}^{-1}$, which may be caused by the mass transfer from the less massive component to the more massive one. Assuming the mass transfer is conservative, we can get the mass transfer rate from the formula derived from the Kepler law:

[TABLE]

The estimated mass transfer rate is $\mathrm{d}M_{2}/\mathrm{d}t=-4.12\times 10^{-6}\ M_{\odot}\ \rm{yr}^{-1}$. This mass transfer rate seems quite high for contact binaries, but it coincides with the mass transfer properties of contact binaries in the Kepler eclipsing binary catalogue (Kouzuma 2018). The time scale of mass transfer for the donor star can be estimated as $\tau_{{}_{\rm MT}}=2.77\times 10^{5}$ yr, which is much shorter than the thermal time scale $\tau_{\rm th}\sim(GM^{2})/(RL)\sim 1.70\times 10^{7}$ yr (Paczyński 1971). This suggests that the donor star can not maintain its thermal equilibrium. This system might be in the phase evolving from a contact configuration to a semi-detached one of the thermal relaxation oscillation (Lucy 1976; Flannery 1976; Li et al. 2004a, 2005, 2008). In the same way, the period increase may be part of a long-period cyclic variation caused by a third body, which is reflected by the third light showing in the photometric solutions. By the way, we should notice that these results were achieved according to the absolute parameters only derived from the photometric observations, so spectroscopic observations are urgently needed.

Acknowledgements.

This work was partly supported by the Chinese Natural Science Foundations (Nos. 11773065, 11573061, 11573062, 11390374 and 11661161016), and the Yunnan Natural Science Foundation (Grant No. 2015FB190). New CCD photometric observations were obtained with the 1.0 m telescope at Yunnan observatory.