PHOTOMETRIC PROPERTIES FOR SELECTED ALGOL-TYPE BINARIES. VI. THE NEWLY DISCOVERED oEA STAR FR ORIONIS

Eclipsing binaries with δ Scuti type components are of particular interest for astroseismology because one may directly determine the absolute parameters, which provide us with the means to test stellar models and strong constraints on the possible mode identification. The classic Algol-type binary shows variable pulsational characteristics due to mass accretion to the primary component from the secondary component filling its Roche lobe. Mkrticanian et al. (2004) then introduced the oscillating EA (oEA) stars as the (B)A–F spectral type mass-accreting main-sequence pulsators in these systems. Rodríguez & Breger (2001) only compiled nine oEA stars. Then Soydugan et al. (2011) also published a catalog containing 43 oEA-type systems, but recently the number has reached 74 systems (Liakos et al. 2012). Moreover, Soydugan et al. (2006) and Liakos et al. (2012) subsequently found a connection between orbital and pulsation periods, as well as a correction between evolutionary status and dominant pulsation frequency for systems with δ Scuti stars.

FR Ori (=AN 282.1934; $\alpha _{J2000.0}=05^{{\rm h}}51^{{\rm m}}05\buildrel{\mathrm{s}}\over{.}72$ and δ_J2000.0 = +09°26'3746) was discovered as a short period variable by Hoffmeister (1934). Its visual magnitude ranges from 110 to 119 (Malkov et al. 2006). Brancewicz & Dworak (1980) estimated its spectral type to be A7. From the catalog of GCVS (Kholopov et al. 1985), the orbital period of this binary is 088316217, which was subsequently updated to be 088316188 (Zakirov 1994), 088316227 (Kreiner et al. 2001), 08831665 (Kreiner 2004), and 088316286 (Gális et al. 2007). This binary was observed photographically by Gaposchkin (1954) and visually by Szafraniec (1974). Zakirov (1994) photoelectrically observed this star from 1989 to 1992. The UBVR light curves were analyzed by Zakirov (1996), who obtained a mass ratio of 0.41. The deformed light curves were interpreted by an unstable process due to possible mass transfer from the secondary component nearly filling up its Roche lobe to the primary component. Shaw (1994) then included this binary in the extended list of near-contact binaries (NCBs). Another photoelectric photometric measurement of FR Ori was performed by Gális et al. (2007), who derived a detached configuration with a mass ratio of q = 0.411. The normalized U-band light curve apparently displays short-term variations. However, this kind of intrinsic activity was not confirmed from their statistical analysis, which may result from the discontinuous data during 23 nights from 2001 to 2005. Although the upward parabolic ephemeris was given, Gális et al. (2007) proposed that the orbital period of FR Ori does not show any change. They derived the photometric elements from BV light curves.

This research aims to present the detailed photometric investigations of FR Ori with a δ Scuti primary component, as a continuation of a series of the selected Algol-type eclipsing binaries (Yang 2010). In the previous papers, we have studied eight objects, i.e., RV Tri (Yang & Wei 2009), AO Ser and V338 Her (Yang et al. 2010), AL Gem and BM Mon (Yang et al. 2012a), AV Hya and DZ Cas (Yang et al. 2012b), and V1241 Tau (Yang et al. 2012c). Observations and reductions are shown in Section 2, while the orbital period changes are studied in Section 3. Photometric model and pulsation analyses are considered in Sections 4 and 5, respectively. Some results and discussions are given in the final section.

New photometry of FR Ori was performed in 2012 November and December, using the 60 cm telescope at the Xinglong Station (XLs) of the National Astronomical Observatories of China (NAOC). A Princeton Instrument 1024 × 1024 CCD camera was mounted at this telescope, whose effective field of view is 17' × 17', with a scale of 0996 pixel⁻¹. The standard Johnson/Cousins set of BVIR filters was applied. In the observing process, TYC 719-690-1 and TYC 719-397-1 were chosen as the comparison star and the check one, respectively. Typical exposure times are 40 s in the V band and 30 s in the R band, respectively. All effective CCD images were reduced by using the IRAF package in a standard fashion.

Eight high quality photometric nights were observed from November 7 to December 9 (see Table 1), yielding a total of 2984 useful observations (i.e., 1490 in the V band and 1494 in the R band). Table 2 tabulates differential magnitudes together with heliocentric Julian dates (i.e., HJD versus Δm) for all individual data. The complete light curves are displayed in the left panel of Figure 1, in which orbital phases were computed with a period of 088316227 (Kreiner et al. 2001). The general features of the light curves imply that FR Ori is a typical oEA-type binary. The depths of the primary and secondary eclipses in the V band are 0985 and 0120, which are approximately consistent with the measured values of 099 and 013 from Zakirov (1996). Meanwhile, the depths for both eclipses are 0935 and 0149 in the R band, respectively. Evidently, the short-period oscillation with an amplitude of $0\buildrel{\mathrm{m}}\over{.}02$ occurs between phase 0.1 and phase 0.9 in the light curves. The pulsating behavior around the secondary eclipses is shown in the right panel of Figure 1, whose lower part displays the magnitude differences between the comparison star and the check one. Therefore, the oscillations could probably result from the primary component. The mean errors are less than 0009, which depends on the weather of the observing night. Moreover, a primary eclipse was observed using the 85 cm telescope (Zhou et al. 2009) at the XLs on 2012 December 5. From those new observations, several minimum light times were determined using the K–W method (Kwee & Woerden 1956). Table 3 lists the eclipsing times together with their errors.

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Gális et al. (2007) proposed that the orbital period of FR Ori is constant. Up to now, its changes had not been neglected. We collected all available minimum light times, including 11 photographic, 40 visual, 4 photoelectric, and 28 CCD ones. These data, spanning over 86 yr from 1926 to 2012, are tabulated in Table 4. With the linear ephemeris given by Kreiner et al. (2001),

$$\begin{equation} \hbox{Min. I}=\hbox{HJD}\ 2427862.158+0.88316227\times E, \end{equation} \tag{ 1 }$$

we can calculate the residuals of (O − C)₁, which are listed in Table 4 and displayed in Figure 2(a). Although there exists much large scatter, the general trend of (O − C)₁ appears to be increasing. Therefore, an upward parabolic curve was assumed to fit the residual curve. Considering the different measurement precision, we assigned weight 1 to photographic and visual data (i.e., "pg" and "vi"), and weight 10 to photoelectric and CCD measurements (i.e., "pe" and "CCD"), respectively. A linear least-squares method with weights yields the following quadratic equation

$$\begin{equation} (O-C)_1=0.0069(34)-2.67(3)\times 10^{-6}E +1.07(8)\times 10^{-10}E^2, \end{equation} \tag{ 2 }$$

where the parenthesized numbers represent the standard error in units of the last decimal place. The computed values versus the observed epoch numbers for all eclipsing times are listed in Table 4, and its computed curve is plotted in Figure 2(a) as a solid line. The final residuals of (O − C)₂ are also tabulated in Table 4, and are displayed in Figure 2(b). From this figure, the regularity does not evidently exist. Using the coefficient of the quadratic term of Equation (2), we can easily calculate a continuous period increase rate of dP/dt = +8.85(±0.66) × 10⁻⁸ day yr⁻¹.

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Two-color light curves of FR Ori were simultaneously modeled with the updated version of the Wilson–Devinney program (Wilson & Devinney 1971), including a detailed reflection treatment (Wilson 1990) and Kurucz's (1993) stellar atmosphere model. Based on the estimated spectral type of A7 (Brancewicz & Dworak 1980), the mean effective temperature for the primary was adopted to be T_p = 7830 K (Cox 2000). The gravity-darkening exponents and bolometric albedo coefficients were fixed to be g_p = 1.0 (von Zeipel 1924) and g_s = 0.32 (Lucy 1967), and A_p = 1.0 and A_s = 0.5 (Rucinski 1973), which are appropriate for stars with radiative and convective envelopes, respectively. The logarithmic limb-darkening coefficients (i.e., X and Y; x and y) were interpolated into the tables of van Hamme (1993). The adjustable parameters are orbital inclination, i, the effective temperature of the secondary star, T_s, the potential of the primary star, Ω_p, and the monochromatic luminosity of the more massive component, L_p.

For lack of the spectroscopic mass ratio, the "q-search" process was performed for some fixed mass ratios, which ranged from 0.25 to 0.65 in steps of 0.05. The calculation started at Mode 2 (i.e., detached configuration), but the tested solutions always converged at Mode 5 (i.e., the semi-detached one). This implies that FR Ori is an Algol-type binary, whose less massive component fills its Roche lobe. The q-$\Sigma (O-C)^{2}_{i}$ curve is displayed in Figure 3, in which a minimum value of $\Sigma (O-C)^{2}_{i}$ occurs around q = 0.35. The free parameters were then extended to include the mass ratio q. When the third light was applied as a free parameter in the iterations, a meaningful value was not found so we did not consider the third light in the light curve analysis. We obtained a final photometric solution, which is listed in Table 5. The theoretical light curves are plotted as solid lines in the left panel of Figure 1. The final mass ratio is q = 0.325(± 0.002), which is much smaller than the value of 0.411 from Gális et al. (2007). The fill-out factor for the primary of f_p = 73.5(± 0.2)% approximately agrees with the value of f_p = 76.9%, which was computed by the statistical relation of f_p(%) = 114.7–42.8 × P for Algol-type NCBs (Yang et al. 2012c).

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Table 5. Photometric Elements for the Eclipsing Binary FR Ori

Parameter	Primary	Secondary
i	8319(± 008)
q = Mp/Ms	0.325(± 0.002)
Ω	3.2490(± 0.0052)	2.5208
T	7830 K	4583(± 10)K
X, Y	0.650, 0.271	0.629, 0.154
xV, yV	0.665, 0.319	0.794, 0.033
xR, yR	0.564, 0.303	0.727, 0.130
Lp, s/(Lp + Ls)V	0.9531(± 0.0015)	0.0469
Lp, s/(Lp + Ls)R	0.9212(± 0.0018)	0.0788
r(pole)	0.3400(± 0.0006)	0.2670(± 0.0004)
r(point)	0.3608(± 0.0008)	0.3868(± 0.0039)
r(side)	0.3495(± 0.0007)	0.2780(± 0.0004)
r(back)	0.3559(± 0.0008)	0.3108(± 0.0004)
f	73.5%(± 0.2%)	100%
$\Sigma (o-c)_i^2$	0.5380

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4.1. Preliminary Pulsation Analysis

In order to explore the pulsation frequency, the eclipses and proximity effects must be excluded by subtracting theoretical values from the observed data. As seen from Figure 1, short-period variations in light curves exist outside the primary eclipse. This kind of pulsation may be related to the primary component, which is probably located in the instability strip of the Hertzsprung–Russell diagram. Due to the absence of oscillations around the primary eclipse, the computed residuals from phase 0.9 to phase 0.1 were eliminated. Then we obtained a total of 1004 data in the V band and 1153 in the R band, which are shown in Figure 4. The V and R residuals were combined and analyzed using the software Period04 (Lenz & Breger 2005). After the first frequency computation, the residuals were subsequently pre-whitened for the next one. According to the criterion by Breger et al. (1993), the signal-to-noise ratio (S/N) for the reliable peak due to pulsation may not be less than 4.0 (i.e., S/N ⩾ 4.0). The periodogram of Figure 5 shows all four peaks above this significance limit (dotted line), which is similar to other oscillating eclipsing binaries, such as BG Peg (Liakos & Niarchos 2011). Each spectral panel in the figure corresponds to the residuals with all the previous frequencies pre-whitened. Based on residual data in the V and R bands, the results of frequency analysis are respectively given in Table 6, including frequency f_i, amplitude a_i, phase ϕ_i, S/N, and pulsation constant Q. Considering the contribution of the observations in the V and R bands, we accepted the final fitting results of the three-frequency solution (i.e., f₁, f₂, and f₃). The theoretical curves are plotted in Figure 4 as solid lines using the equation of m(t) = a₀ + ∑2a_isin [2π(f_it + ϕ_i)] (i = 1, 2, 3). Here, m(t) and a₀ are the calculated magnitude and zero point, while a_i, ϕ_i, and f_i are the amplitude, phase, and frequency of the ith frequency. The dominant frequency of f₁ = 38.638c day⁻¹ (i.e., P_puls ≃ 37.3 minutes) with S/N > 10 may be a reliable pulsating frequency, whose pulsating amplitudes were computed to be 5.84 mmag for the V band and 4.95 mmag for the R band. The other two frequencies (i.e., f₂ and f₃) needed to be further identified in the future.

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Table 6. Fourier Analysis Results for the Observations

Frequency	V Filter			R Filter			Q
	ai	ϕi	S/N	ai	ϕi	S/N
(c day−1)	(mmag)	(rad)		(mmag)	(rad)		(× 102 days)
f1 = 38.638	5.84	0.258	10.04	4.95	0.495	11.23	1.41
f2 = 45.828	3.56	0.428	5.23	2.61	0.261	4.28	1.19
f3 = 38.384	3.91	0.538	7.33	3.65	0.366	8.15	1.42
f4 = 4.667	1.98	0.427	2.88	3.21	0.321	5.20	11.71

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From the previous analysis, FR Ori is a semi-detached oEA-type binary with a mass ratio of q = 0.325(± 0.002) and a fill-out factor of f_p = 73.5(± 0.2)% for the primary component. Based on its spectral type of A7, the mass of the primary component is M₁ = 1.84 M_☉ (Cox 2000). Using Kelper's third law and photometric elements, other absolute parameters are as follows: a = 5.21 R_☉, M₂ = 0.60 M_☉, R₁ = 1.83 R_☉, and R₂ = 1.62 R_☉, respectively. The mass–radius diagram (i.e., M − R) is displayed in Figure 6, where the open circles refer to the primary components of the semi-detached oEA binaries, which are taken from Liakos et al. (2012). The solid and dotted lines denote the zero-age main sequence (ZAMS) and the terminal-age main sequence (TAMS) lines with z = 0.02, which were constructed by the rapid binary-evolution algorithm (Hurley et al. 2002). The δ Scuti type primary component of FR Ori, shown as a filled circle, lies inside the ZAMS–TAMS line limits and is closer to ZAMS line, implying that the instability for the slightly evolved primary component starts at an early stage of its evolution with fast pulsation.

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Based on the pulsation analysis, the reliable dominant pulsating frequency of FR Ori is f₁ = 38.6c day⁻¹ (i.e., $P_{{\rm puls}}=37.3 \mathrm{\,min{\rm utes}}$). This kind of pulsation occurs in other semi-detached oEAs with P_orb < 1.0 days, such as CZ Aqr, HL Dra, and HZ Dra (Liakos et al. 2012), EW Boo (Soydugan et al. 2008), IV Cas (Kim et al. 2006), TZ Dra and RR Lep (Liakos & Niarchos 2013), IU Per (Zhang et al. 2009), AO Ser (Kim et al. 2004b), VV UMa (Kim et al. 2005), and BF Vel (Manimanis et al. 2009). Using the estimated parameters of FR Ori, the mean density of the primary star could be computed to be ρ₁/ρ = ((M₁/M_☉)/(R₁/R_☉)³) = 0.2987(± 0.0018). Following the known equation of Q = P_puls(ρ/ρ_☉)^1/2, we can calculate the pulsation constants for four detected frequencies, which are listed in Table 6. Therefore, the mass-accreting primary component of FR Ori must not show radial pulsation for the domain frequency f₁ (Rodríguez et al. 1998).

From Equation (2), the orbital period of FR Ori may undergo a secular increase at a rate of dP/dt = +8.85(±0.66) × 10⁻⁸ day yr⁻¹. This case appears in other Algol-type NCBs, such as EG Cep (Zhu et al. 2009), AX Dra (Kim et al. 2004a), ZZ Aur (Oh et al. 2006), V836 Cyg (Yakut et al. 2005), KW Per (Gális et al. 2001), and TT Aur (Özdemir et al. 2001), which may arise from mass transfer from the less massive component to the more massive one. Assuming conserved mass transfer, the mass transfer rate can be computed using the following equation (Singh & Chaubey 1986):

$$\begin{equation} \frac{\dot{P}}{P}=+3(1-q)\frac{\dot{M}_p}{M_p}. \end{equation} \tag{ 3 }$$

Inserting the values of $\dot{P}$, P, M₁, and q into Equation (3), the mass increase rate of the primary was calculated to be $\dot{M}_p=+2.96(\pm 0.11)\times 10^{-8}{\,M_\odot \,{\rm yr}^{-1}}$. With mass transfer, the primary component will expand owing to additional energy from the secondary star. This will cause the fill-out factor of the primary to increase and the primary will fill its Roche lobe. Moreover, the rapid mass accretion may result in the pulsation of the primary. Finally, these kinds of Algol-type binaries, such as FR Ori, will evolve into contact configurations as the precursors to the A-type W UMa binaries (Shaw et al. 1996). In the future, high-precision photometry and spectroscopy will be necessary to determine absolute physical parameters and to check period changes, pulsating characteristics, and evolutionary status.

The authors acknowledge the anonymous referee for his/her useful comments and suggestions. This research was supported by the National Natural Science Foundation of China (Nos. U1231102, U1331202, and 11133007), the Anhui Provincial Natural Science Foundation (No. 1208085MA04), and the Anhui Provincial Foundation for Academic and Technological Leader Reserve Candidates. Many thanks are expressed to Professor J. M. Kreiner for his compiled eclipsing times, and Professor A.-Y. Zhou for his help with the pulsating analysis. New observations were obtained using the 60 cm and 85 cm telescopes at the Xinglong station of the NAOC. This work has made use of the SIMBAD Database, operated at CDS, Strasbourg, France.