New Astronomy 15 (2010) 380–384

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Orbital period analysis of eclipsing post-novae T Aurigae: Evidence of magnetic braking and an unseen companion

Zhibin Dai a,b,c,*, Shengbang Qian a,b a National Astronomical Observatories/Yunnan Observatory, Chinese Academy of Sciences, P.O. Box 110, 650011 Kunming, PR China b Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, PR China c Graduate School of the CAS, Beijing, PR China article info abstract

Article history: Four new CCD times of light minimum of T Aurigae are presented. The orbital period variation is analyzed Received 20 March 2009 by means of the standard O–C technique. The new times of light minimum indicate that a 24 yr sine- Received in revised form 8 October 2009 like period variation superimposed on a secular orbital period decrease is obviously seen in the O–C dia- Accepted 7 November 2009 gram. However, the orbital period should increase because of mass transfer between components. In Available online 14 November 2009 order to solve this apparent paradox, three possibilities including magnetic braking mechanism, which Communicated by E.P.J. van den Heuvel plays an important role in angular moment loss of binary, are proposed. The mass loss rate M_ ¼ 1010:4M yr1 is derived by assuming that the Alfvén radius of secondary is the same as that of Keywords: the sun (i.e. R 15R ). Using the observational relationship of M_ P h (McDermott and Taam, : cataclysmic variables A ’ mb orbð Þ Stars: binaries: eclipsing 1989; Rappaport et al., 1983), the Alfvén radius of secondary is estimated as RA ’ 1:9R, which only Stars: individual (T Aurigae) requires a weak magnetic field in secondary. Since the brightness variations of T Aurigae caused by App- Stars: magnetic braking legate’s mechanism need large energy beyond the total radiant energy in the time interval of 24 yr, the third body light travel-time effect is the most likely explanation for the 24-yr variation. The third body may be a brown-dwarf in case of the high orbital inclination. Ó 2009 Elsevier B.V. All rights reserved.

7 1 1. Introduction 10 M yr calculated from the orbital period changes (Beuer- mann and Pakull, 1984) is two orders of magnitude higher than 9 1 T Aurigae ( T Aurigae 1891) is a slow nova and has a pro- the 3:9 10 M yr derived by using accretion disk models. late gas shell like DQ Her (Gallagher et al., 1980). Walker (1962) In the history of O–C analysis of T Aurigae, there is the interest- discovered that T Aurigae is a short-period eclipsing binary and ing phenomenon that the significance level of orbital period de- no secondary eclipse is observed. Its is crease becomes lower and lower when more and more minima 14m:92 (Walker, 1957), however, the gas shell which is smaller are observed. The parameter k, which measures the significance le- than that of DQ Her may prevent direct spectral observations of vel at which the null hypothesis that the coefficient of the qua- the secondary, which results in the uncertain mass ratio. Although dratic term is zero can be excluded, obtained by Pringle (1975) is Bianchini (1980) derived the masses of primary and secondary as 20.73, then by Mumford (1976) is 14.72, and by Beuermann and

0:68M and 0:63M, respectively, by using the mass-radius rela- Pakull (1984) is 11.6. Additionally, Mumford (1976) and Beuer- tionship of secondary (Warner, 1976) and the spectroscopic data, mann and Pakull (1984) also found a weak evidence of a quasi- he never gave the errors of the masses of both components. periodic change (23 yr). But they did not make any further Accordingly, the system parameters of T Aurigae are still unclear. analysis. T Aurigae has evolved almost a century from outburst to now In this paper, 33 available times of light minimum are presented and the mean decline rate of its photometric magnitude is derived in Section 2, including four new times from our own observations. as 0m:0028 yr1, thus it should be in the phase II of evolutional Section 3 deals with the O–C analysis of T Aurigae. Finally, the dis- state of post-nova, which means that it has a high accretion cussions of the possible mechanisms for orbital period change are 8 1 rate 10 M yr (Duerbeck, 1992). The accretion rate 1:4 made in Section 4.

2. Observation of times of light minimum * Corresponding author. Address: National Astronomical Observatories/Yunnan Observatory, Chinese Academy of Sciences, P.O. Box 110, 650011 Kunming, PR China. Tel.: +86 08713920788; fax: +86 08713920154. Three new times of light minimum were obtained from our CCD E-mail addresses: [email protected] (Z. Dai), [email protected] (S. Qian). photometric observations with the PI1024 TKB CCD photometric

1384-1076/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.newast.2009.11.003 Z. Dai, S. Qian / New Astronomy 15 (2010) 380–384 381 system attached to the 1.0-m reflecting telescope at the Yunnan many different observatories. In this case, the average value should Observatory in China. The first two CCD photometric observations be reliable. All 33 available times of light minimum covering over were carried out on December 7, 2007 through an I filter, and the half a century listed in Table 1 have been checked carefully. third observation on April 3, 2008 was in R filter. The newest mid- eclipse time was observed on March 3, 2009 through an R filter 3. Analysis of orbital period change with the PI VersArray 1300B CCD camera attached to the 2.4-m RC telescope at Gao Meigu (GMG) observational base of Yunnan The orbital period and epochs of T Aurigae have been presented Observatory in China. The I and R filters used in 1.0-m and 2.4-m in previous papers (e.g., Walker, 1962; Pringle, 1975; Mumford, reflecting telescopes are close to the Johnson’s standard photomet- 1976; Beuermann and Pakull, 1984). Since there are several new ric system. Two nearby stars which have similar brightness in the eclipse times obtained (Paschke, 2001; Diethelm, 2004), the new same viewing field of telescope, were chosen as the comparison epochs and average orbital period of T Aurigae were derived as star and the check star. All images were reduced by using PHOT d (measure magnitudes for a list of stars) of the aperture photometry Tmin ¼ HJD 2437614:0122ð2Þþ0 :204378235ð3ÞE: ð1Þ package of IRAF. Four CCD times of light minimum were derived by with variance r ¼ 2d:12 103. The O–C values versus num- using a parabolic fitting method. Although the new eclipse times 1 bers are plotted in Fig. 1, which shows obviously secular orbital per- obtained from CCD observations have 4 significant figures, the iod change. In addition, a trend of sinusoidal variation with a period mid-eclipsing times obtained from 1982 to 2003 present large 24 yr is more significant than the O–C curves presented in previ- scatter with only 3 significant figures. This indicated that the pre- ous papers (e.g., Pringle, 1975; Mumford, 1976; Beuermann and Pa- vious times of light minimum obtained by using photoelectric kull, 1984). Thus a simultaneous quadratic-plus-sinusoidal method may have lower accuracy. Therefore, the early 24 data ephemeris is attempted to fit this variation. And the least-square listed in Table 1 are arbitrarily adopted with default errors solution leads to 0d:001 in the following O–C analysis. To obtain the correct orbital period change trend, the collected O C ¼9d:1ð3d:2Þ104 þ 1d:1ð0d:3Þ times of light minimum should be accurate. Some identical times 107E 1:d0ð0d:4Þ1012E2 þ 2:d3ð0d:3Þ of light minimum have small difference as they were observed in 103sin½0:0084E þ 188:0ð8:8Þ: ð2Þ

d 3 with variance r2 ¼ 1 :33 10 . The coefficient of the quadratic Table 1 term in Eq. (2), is similar to that derived by Beuermann and Pakull The 33 available times of light minimum for the eclipsing nova T Aurigae. (1984), and one order of magnitude lower than that derived by JD. Hel. 2400000+ Type Error Method E (O–C) Ref. Mumford (1976) and Pringle (1975). The parameter k of this fit is 34797.676 pri Pe 13780 0.00414 (1) 43.75 far larger than the previous papers, which means the signifi- 36549.790* pri Pe (3) cance level of quadratic and sinusoidal terms is larger than 99.99%. + 36548.790 pri Pe 5212 0.00287 (1) Thus the O–C diagram shown in the top plane of Fig. 1 suggests that 37614.011 pri Pe 0 0.00118 (1) 37619.943 pri Pe 29 +0.00382 (1) a secular change of the period of T Aurigae does exist. The orbital _ 37620.959 pri Pe 34 0.00208 (1) period change rate P calculated from Eq. (2) is 1:0ð0:4Þ 11 37638.944 pri Pe 122 0.00237 (1) 10 ss1. 37644.871 pri Pe 151 0.00227 (1) In order to clearly present the cyclical periodic changes of T * 37666.735 pri Pe (2) Aurigae, the quadratic element in O–C diagram is removed and 37666.738 pri Pe 258 0.00377 (2) 37666.945* pri Pe (2) we then used a sinusoidal formula to fit the quadratic residuals. 37666.944 pri Pe 259 0.00217 (2) The figure is shown in the middle panel of Fig. 1. Therefore, the 39528.630 pri Pe 9368 +0.00254 (3) 39529.652 pri Pe 9373 +0.00264 (3) 39532.716 pri Pe 9388 +0.00094 (3) 39768.980 pri Pe 10544 +0.00370 (4) 39912.657 pri Pe 11247 +0.00284 (4) 40594.668 pri Pe 14584 +0.00362 (5) 40597.734 pri Pe 14599 +0.00392 (5) 41978.918 pri Pe 21357 0.00014 (6) 41980.758 pri Pe 21366 +0.00046 (6) 41980.962 pri Pe 21367 +0.00008 (6) 41981.984 pri Pe 21372 +0.00019 (6) 42806.651 pri Pe 25407 +0.00101 (7) 42807.672 pri Pe 25412 +0.00011 (7) 43835.4896 pri Pe 30441 0.00040 (8) 43837.5331 pri Pe 30451 0.00070 (8) 45257.5540 pri 0.0040 Pe 37399 +0.00018 (9) 45258.5749 pri 0.0028 Pe 37404 0.00082 (9) 51565.2780 pri 0.003 CCD 68262 0.00122 (10) 51565.4850 pri 0.005 CCD 68263 +0.00138 (10) 52283.2610 pri 0.002 CCD 71775 +0.00098 (11) 54442.10752 pri 0.0006 CCD 82338 +0.00046 (12) 54469.29475 pri 0.00063 CCD 82339 0.00064 (12) 54560.03580 pri 0.0031 CCD 82915 0.00121 (12) 54894.19177 pri 0.0002 CCD 84550 0.00012 (12)

References: (1) Walker (1962); (2) Walker (1963); (3) Mumford (1967); (4) Fig. 1. The O–C values of T Aurigae are fitted with the ephemeris Eq. (2). The best- Mumford (1969); (5) Mumford (1970); (6) Mumford (1974); (7) Mumford (1976); fit quadratic and sinusoidal curves are plotted by the dashed line and solid line in (8) Bianchini (1979); (9) Beuermann and Pakull (1984); (10) Paschke (2001); (11) the top figure, respectively. The new four CCD data are plotted in solid diamonds, Diethelm (2004); (12) this paper. and the other O–C points are plotted in open circles. The middle figure presents the + Corrected data. fit of the O–C values after removing the quadratic element. The linear fit for the * Abandoned data. fitting residuals presented in solid line are shown in the bottom panel. 382 Z. Dai, S. Qian / New Astronomy 15 (2010) 380–384 best-fit for the O–C curve of T Aurigae should be a 24 yr periodic sion. Although the past average expansion velocity of T Aurigae’s modulation shown in the upper and middle panels of Fig. 1 super- shell is not known, the expansion velocity of the gas shell will be imposed on secular orbital period decrease. increasing due to new later ejecta. In that case, the speed of the new ejecta should be > 678:8kms1, so that they can catch up 4. Discussion and accelerate the old ejecta. Although the envelope above its burning layer has been bloating more than a century, there is no 4.1. Secular orbital period decrease evidence to show that the bloated envelope fully fills the Roche- lobe of the . Thus a steady mass transfer from the In standard theoretical model of CV, mass transfer rate is a cru- white dwarf to the red dwarf via Lagrange point of binary system cial parameter which determines the evolution of CV. The bright is impossible. This means the ejected masses from the envelope shoulder of T Aurigae observed near phase 0.85 in the can only be a fast wind from the white dwarf, which can be partly and He II-intensity variations indicate that the orbital inclination accreted to the red dwarf, which may cause a slight period de- is 60° (Bianchini, 1980). Thus its eclipse is not the occultation crease. However, this small decrease will be offset by the much lar- of the white dwarf, but of a hot spot near the rim of the accretion ger period increase due to the fact that most of the wind matter is disk, which suggests that the existence of a hot spot is a strong evi- lost from the system at a high velocity. Hence, the net result of this dence of mass transfer between both components. Supposing that wind from a not Roche-lobe filling star will be a period increase, the mass and the angular moment are conserved, we can attempt contrary to what is observed. to estimate its mass transfer rate by using the simple formula 4.1.3. Magnetic braking _ _ M2 M1 P The orbital period of T Aurigae is P 4:9 h, which is far larger ¼ ; ð3Þ M2 M2 M1 3P than the period-gap of cataclysmic variables, such that the effect of angular momentum loss by gravitation radiation can be ne- where M and M are the masses of primary and secondary, respec- 1 2 glected. Thus according to the standard evolutional theory of cata- tively, and P is the orbital period. The models of nova eruption as a clysmic variables (Warner, 1995), magnetic braking will play an thermonuclear runaway (Starrfield, 1989; Martin, 1989) imply that important pole in the evolution of T Aurigae. Both effects that a the eruptions on the surface of white dwarf need a threshold mass wind from the white dwarf and a mass transfer from the red dwarf of 0:6M . Therefore, a mass of the white dwarf, < 0:45M , de- to the white dwarf produced by magnetic braking, imply that the rived by Beuermann and Pakull (1984) is too low, but M 0:68 de- 1 true mass transfer between both components for T Aurigae is very rived by Bianchini (1980) can be accepted. Therefore, using the complicated. However, the existence of the hot spot suggests that a masses of both components derived by Bianchini (1980), net mass transfer is from the red dwarf to the white dwarf. This M ¼ 0:68M and M ¼ 0:63M , the mass transfer rate M_ can be 1 2 2 indicates that with the masses proposed by Bianchini an orbital calculated to be 5:1 108M yr1, which implies that an orbital period increase is expected, which is inconsistent with the obser- period increase for T Aurigae should be expected due to the mass vations. Thus, to explain the period decrease, magnetic braking is ratio q ¼ M =M less than unity (i.e. M < M ). However, all the pre- 2 1 2 1 needed. vious O–C analysis did not find the orbital period increase. Thus, The observed period decrease rate P_ ¼1:0 1011 ss1 can be there are several possibilities proposed for solving this apparent described as paradox, such as: (i) M2 > M1, or (ii) reverse mass transfer from the bloated white dwarf or accretion disk to the red dwarf, or (iii) _ _ _ _ P ¼ Pmt þ Pml þ Pmb; ð4Þ magnetic braking. _ _ _ where Pmt; Pml and Pmb are the period change rates caused by mass 4.1.1. M > M transfer, mass loss and magnetic braking, respectively. For the con- 2 1 _ The masses of both components of T Aurigae are not clear so far. servative case (i.e. Pml ¼ 0), the magnetic braking of the secondary Therefore, if we assumed that the masses of the red dwarf and the can result in the orbital period decrease of T Aurigae. According to white dwarf are reversed from the values proposed by Bianchini, Tout and Hall (1991), the term of magnetic braking in Eq. (4) can be described as that is: 0:68M and 0:63M, respectively, which corresponds to  the first possibility, then the secular period decrease shown in _ 2 Pmb RA M1 þ M2 _ Fig. 1 can be explained by mass transfer with a rate of ¼ 2 Mmb; ð5Þ 8 1 P a M1M2 5:1 10 M yr , which means T Aurigae is possibly in the phase _ II of hibernation cycle (Prialnik and Shara, 1986), which is a nearly where RA; a and Mmb are the Alfvén radius of secondary, the separa- constant accretion phase after approximate one century since out- tion of the binary and the stellar wind mass loss rate via magnetic burst. This result would be in accord with the assumption of Duer- braking, respectively. The effect of the mass transfer produced by beck (1992). magnetic braking should be combined with that produced by over- flow from Roche-lobe of the red dwarf (The magnetic braking drives 4.1.2. Reverse mass transfer the mass transfer by Roche-lobe overflow). If we adopted the mean _ 9 1 Gallagher et al. (1980) have obtained a monochromatic image of mass transfer rate, Mmt ¼ 3:9 10 M yr , derived from the opti- the faint of T Aurigae, the angular size of which is roughly cal flux of the binary system (Beuermann and Pakull, 1984), then 00 _ 20 . Obviously, there are tightly material connections between the the orbital period increase rate, Pmt, can be calculated to be outer part of gas shell and the inner thicker central object. Such 7:6 1013 ss1, which in absolute value is much smaller than the connections may indicate that the ejection has lasted over a hun- observed orbital decrease rate of 1:0 1011 ss1. This indicates dred years via a certain efficient mechanism and will continue in that the latter is basically equal to the orbital decrease rate by mag- _ 11 1 the future. Using the distance of T Aurigae, 830pc presented by netic braking, hence Pmb is 1:08 10 ss . Using the third Kep-

Beuermann and Pakull (1984), the size of the gas shell can be de- ler law, the separation of the binary is estimated to be about 1:68R. 2 _ 9 2 1 rived as 8300AU and the average expansion velocity of the gas According to Eq. (5), RAMmb is calculated to be 8:9 10 RM yr . shell is 678:8kms1. Herbig and Smak (1992) and Mukai and Assuming that the Alfvén radius of the secondary of T Aurigae is the

Still (2003) have pointed out that the gas shell of DQ Her, which same as that of the sun (i.e. 15R), a low mass loss rate _ 10:4 1 is an identical twin to T Aurigae, is in an accelerated state of expan- Mmb ¼ 10 M yr is obtained, which is nearly two orders of Z. Dai, S. Qian / New Astronomy 15 (2010) 380–384 383

8:6 1 0 magnitude lower than the predicted value 10 M yr , which is approximately zero. The projected distance, a sinðiÞ, from the bin- _ derived from the relationship of Mmb PorbðhÞ (McDermott and ary pair to the mass-center of this triple system can be calculated Taam, 1989; Rappaport et al., 1983). This predicted mass loss rate by the amplitude of sinusoidal fit. Combined with the Third Kepler indicates RA ¼ 1:9R, which is smaller than RA ¼ 5:2R of the Law, the mass function of the third component, f ðmÞ, is estimated nova-like system AC Cnc derived by Qian et al. (2007). According by the formula, to the mean empirical radius-period relationship of cataclysmic 4 2 variables (Warner, 1995) p 0 3 f ðmÞ¼ 2 ða sinðiÞÞ ; ð7Þ GP3 13=12 6 6 R2 ¼ 0:094Porb ðhÞð1:3 PorbðhÞ 9Þ; ð6Þ where P3 and i are the orbital period and the inclination of the third body, respectively. The parameters of the third body orbit and their where R2 is in solar units, the secondary radius R2 ’ 0:53R is esti- errors are listed in Table 2. Considering a combined mass of mated, which suggests that the derived Alfén radius 1:9R is only 3 times the secondary radius. Therefore, if the observed period de- 0:68M þ 0:63M for the eclipsing pair of T Aurigae, the mass of crease of T Aurigae is due to magnetic braking, the secondary the third body can be evaluated, which depends on inclination. should have a relatively weak magnetic field. In this way, magnetic Inspection of Fig. 2 suggests that the third body of the system braking can well explain the observed period decrease. should be a M-type dwarf star when i < 56 . But if the inclination is high (i.e. > 56), then the third body may be a brown-dwarf star and the distance from the parent binary is larger than 8:8 AU which 4.2. A third body light travel-time effect should be a safe distance during the common envelope evolution of the parent binary. A notable trend in the O–C diagram of T Aurigae is a 24 yr periodic variation. Since Beuermann and Pakull (1984) did not ana- 5. Conclusion lyze the cyclical periodic changes, we attempted to study two pos- sible mechanisms the Applegate mechanism and the light travel- The 33 observed times of light minimum covering 55 years are time effect to explain this variation. A detailed calculation suggests collected, and a new O–C diagram presents a significant trend of that Applegate’s mechanism cannot explain the observed sinusoi- cyclical periodic changes with a 24 yr period superimposed on dal variation of orbital period. A more plausible mechanism is the secular orbital period decrease. The decrease rate of orbital per- the light travel-time effect. This effect is caused by a remote com- iod P_ ¼1:0ð0:4Þ1011 ss1 is calculated from Eq. (2).Ifwe panion, who orbits round a binary pair and results in the distur- adopt the masses of both components derived by Bianchini bance of the light travel-time. The good sinusoidal fit shown in (1980), an orbital period increase is expected, from the effects Fig. 1 suggests the eccentricity of the orbit of the third body is purely due to mass transfer from the secondary to the white dwarf. However, this conflicts with our observed orbital period decrease. Table 2 Therefore, three possible explanations are discussed for solving this The parameters for the third body orbit of T Aurigae. apparent paradox. It appears that magnetic braking can explain the

Parameter Value observed period decrease of T Aurigae, which would indicates that the Alfvén radius of the secondary is small RA ¼ 1:9R implying a P 24:0yr 3 weak magnetic field of the secondary. In order to explain the a0sinðiÞ 0:40ð5ÞAU 4 periodic variation shown in Fig. 1, Applegate’s mechanism and light f ðM3Þ 1:1ð4Þ10 M e 0 travel-time effect are discussed. But the former requires a too large Residual 1:76 106 energy to be afforded by the thermonuclear reactions in a K-type or G-type main sequence star. Therefore, we regarded that the light travel-time effect is a more plausible interpretation. A brown-dwarf star as a third component of system is possible as long as the inclination of the third body larger than 56. To further examine the period decrease and the periodic variation of the O–C diagram of T Aurigae, more high precise observations and the accurate phys- ical parameters of T Aurigae are needed.

Acknowledgements

This work was partly Supported by Special Foundation of Pres- ident of The Chinese Academy of Sciences and West Light Founda- tion of The Chinese Academy of Sciences, Yunnan Natural Science Foundation (2008CD157), and Yunnan Natural Science Foundation (No. 2005A0059M) and Chinese Natural Science (Nos. 10573032, 10573013 and 10433030). CCD photometric observations of T Aurigae were obtained with the 1.0-m and 2.4-m telescopes at Yunnan Observatory. We thank the referee very much for the help- ful comments and suggestions that helped to improve this paper greatly.

References

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