Cyclical Period Changes in Z Chamaeleontis

arXiv:astro-ph/0207438v1 20 Jul 2002 o.Nt .Ato.Soc. Astron. R. Not. Mon. h sasotpro ( short-period a is Cha Z INTRODUCTION 1 .Baptista R. Chamaeleontis Z in changes period Cyclical vlesol oad hre ria eid o iescal time (on should 10 periods binary of orbital the the shorter consequence, towards sustain a slowly evolve to As order process. in transfer momentum mass con- must angular they that loose existence implies tinuously the binaries overﬂow), mass-transfer cessa lobe as the Roche CVs of via therefore transfer an (and mass to separation of lead tion orbital would the situations in such con- increase Since in star. transfer accreting the the mass CVs than servative most mass lower In has primary). star star (the donor dwarf matte late-type white transfers companion a and a lobe binaries, to Roche its these overﬁlls secondary) In (the (CV). variable clysmic ⋆ .Vrielmann S. cetd20 uy1.Rcie 02Jn 9 noiia for original in 19; June 2002 Received 19. July 2002 Accepted 5 4 3 2 1

wutatmsaatuta.a(A) [email protected] (MSC) (PAW); [email protected] [email protected] (EO); [email protected] c srpyisGop colo hmsr n hsc,Keele Physics, and Chemistry Rondebos of Town, School Cape Group, of SãoAstrophysics Paul University de Astronomy, Universidade of IAG, Department - Astronomia de Departamento Pesquisas de Nacional 88040-900 Astrof´ısica, Trindade, Divisão Instituto de Campus F´ısica, UFSC, de Departamento mi:bpatous.r(B;ciodsip.r(J;s (FJ); [email protected] (RB); [email protected] email: 02RAS 2002 8 − 10 9 r.Psil ehnsssgetdfrdriving for suggested mechanisms Possible yr). 1 .Jablonski F. , 4 .A Woudt A. P. , 000 P orb – 20)Pitd4Nvme 08(NL (MN 2018 November 4 Printed (2002) 1–4 , 1 = iue h ttsia infiac fti eidb nFts slarg is F-test an ∆ by change, period period this fractional of derived significance The statistical The minute. h eodr tr niceetlvraini h oh oeo t of ac lobe magnetic Roche solar-type the in a variation by ∆ incremental of caused An perio star. possibly strictly secondary not is the is change probably, most amplitudes, period or, and cyclical sinusoidal s periods not and cycle is first different variation the quite the to with fits ephemerides Separate o to CVs. order lead long-period one the is of but those (CVs), than variables cataclysmic short-period other te yalna lssnsia ucinwt eid28 period liter with function the sinusoidal cyclica plus from present linear data collected a observed-minus-calculated The by mid-eclipse (1972-2002). an fitted observations construct of of to period times years timings 30 orbital used eclipse the We new in Cha. our changes Z cyclical nova of dwarf identification the report We ABSTRACT iais cisn tr:idvda:ZCha. Z individual: stars: – eclipsing r binaries: previously words: brightness Key quiescent the of Mattei. & modulation Ozkan the and change . 8h)elpigcata- eclipsing hr) 78 R L 2 /R 2 .Oliveira E. , 4 L 2 n .S Catalán S. M. and ≃ crto,aceindss–sas wr oa tr:evolutio stars: – novae dwarf stars: – discs accretion accretion, 1 . 7 saii,S .dsCmo,Brazil Campos, dos J. S. Espaciais, .ac.uk (SV); × im- 02Jn 14 June 2002 m es 10 r - nvriy el,SaosieS55BG ST5 Stafforshire Keele, University, Florianópolis, Brazil , − h70,SuhAfrica South 7700, ch ,Sa al,Brazil São Paulo, o, 4 3 srqie nodrt xli ohteosre period observed the both explain to order in required is , itdms rnfrrt fe hspro iiu slow is minimum period resulting this after trend, pr ( rate secular the transfer However, the mass period. orbital reverses dicted increasing and an in star thereafter this of sion an&Pkl 94.Ised oto h elobserved well the Beuer- of (e.g., most Instead, decrease pos- 1984). period a Pakull orbital show & an stars mann studied of the have detection CVs of itive to in none decrease (and attempts disappointing: period period However, been orbital orbital precision. long-term the the high measure determine with and to derivative) time used in its of be mark period fiducial usually a orbital can provide the Eclipses in CVs. changes eclipsing the measuring by detected 1995). (Warner stage evolutionary such in observed eysotpros hntescnaysa eoe fully becomes star secondary the ( when degenerate periods, short very n i h eodr trswn (for wind star’s secondary brak- the magnetic are via loss ing momentum angular continuous the rvttoa aito (for radiation gravitational M ˙ 2 h eua vlto ftebnr a npicpebe principle in can binary the of evolution secular The ≃ 10 − P/P 5 12 A M T M E 2 tl l v1.4) file style X ∼ < ⊙ 4 = 0 yr . 08 . − 4 1 × M n e V r xetdt be to expected are CVs few and ) ⊙ 10 ± ,ms oslast nexpan- an to leads loss mass ), ⋆ P − radapiue1 amplitude and yr 2 orb 7 scmaal ota of that to comparable is , < aitosta a be can that variations l cn afo h data the of half econd r Kn 98.At 1988). (King hr) 3 antd smaller magnitude f escnaystar secondary he i.Teobserved The dic. iga covering diagram P orb pre yAk, by eported fteeclipsing the of rta 99.9%. than er niaigthat indicating iiyccein cycle tivity > tr and ature r and hr) 3 . 0 ± – n 0 . e- 2 2 R. Baptista et al.

Table 1. Log of the observations. Table 2. New eclipse timings. Date Filter Telescope Cycles Cycle HJD BJDD (O−C) a 1995 Oct 23 V 1.6m/LNA 130 874, 130 875 (2,450,000+) (2,450,000+) (cycles) 2000 Apr 14 W 0.6m/LNA 152 817–152 820 130 874 0014.70294 0014.70358 (4) +0.0115 2002 Feb 12 R 1.9m/SAAO 161 795, 161 797, 161 799 152 818 1649.51443 1649.51515 (4) −0.0043 2002 Feb 13 R 1.9m/SAAO 161 810, 161 812 161 803 2318.89047 2318.89119 (4) −0.0072 a Observed minus calculated times with respect to the linear eclipsing CVs † show cyclical period changes (e.g., Bond & ephemeris of Table 3. Freeth 1988; Warner 1988; Robinson, Shetrone & Africano 1991; Baptista, Jablonski & Steiner 1992; Echevarria & Al- phase resolution. The combined light curve is smoothed with vares 1993; Wolf et al. 1993; Baptista et al. 1995; Baptista, a median filter and its numerical derivative is calculated. A Catalán & Costa 2000). The most promising explanation of median-filtered version of the derivative curve is then an- this effect seems to be the existence of a solar-type (quasi- alyzed by an algorithm which identifies the points of ex- and/or multi-periodic) magnetic activity cycle in the sec- trema (the mid-ingress / egress phases of the white dwarf). ondary star modulating the radius of its Roche lobe and, The mid-eclipse phase, φ0, is the mean of the two measured via gravitational coupling, the orbital period on time scales phases. Finally, we adopt a cycle number representative of of the order of a decade (Applegate 1992; Richman, Apple- the ensemble of light curves and compute the corresponding gate & Patterson 1994). The relatively large amplitude of observed mid-eclipse time (HJD) for this cycle including the these cyclical period changes probably contributes to mask measured value of φ0. This yields a single, but robust mid- the low amplitude, secular period decrease. eclipse timing estimate from a sample of eclipse light curves. Z Cha seemed to be a remarkable exception in this sce- These measurements have a typical accuracy of about 4 s. nario. The eclipse timings analysis of Robinson et al. (1995) For Z Cha the difference between universal time (UT) shows a conspicuous orbital period increase on a time scale 7 and terrestrial dynamical time (TDT) scales amounts to of P/|P˙ | = 2 × 10 yr, not only at a much faster rate than 9 19 s over the data set. The difference between the baricen- predicted (≃ 10 yr) but also with the opposite sign to the tric and the heliocentric corrections is smaller than 1 s as expected period decrease. Z Cha is close to the ecliptic pole. The mid-eclipse timing In this Letter we report new eclipse timings of Z Cha have been calculated on the solar system baricentre dynam- which indicate a clear reversal of the period increase ob- ical time (BJDD), according to the code by Stumpff (1980). served by Robinson et al. (1995). The revised (O−C) dia- The terrestrial dynamical (TDT) and ephemeris (ET) time gram shows a cyclical period change similar to that observed scales were assumed to form a contiguous scale for our pur- in many other well studied eclipsing CVs. The observations poses. The new eclipse timings are listed in Table 2. The and data analysis are presented in section 2 and the results corresponding uncertainties in the last digit are indicated in are discussed and summarized in section 3. parenthesis. The data points were weighted by the inverse of the squares of the uncertainties in the mid-eclipse times. We 2 OBSERVATIONS AND DATA ANALYSIS arbitrarily adopted equal errors of 5 × 10−5 d for the optical timings in the literature (Cook & Warner 1984; Cook Time-series of high-speed differential CCD photometry of 1985; Wood et al. 1986; van Amerongen, Kuulkers & van Z Cha were obtained on October 1995 and April 2000 at the Paradijs 1990), and a smaller error of 2 × 10−5 d for the Laboratório Nacional de Astrof´ısica, Brazil, and on February timing of Robinson et al. (1995), half the error in our mea- 2002 at the South African Astronomical Observatory. The surements, and combined the 74 timings to compute revised observations were performed under good sky conditions and ephemerides for Z Cha. Table 3 presents the parameters covered a total of 11 eclipses while the target was in qui- of the best-fit linear, quadratic and linear plus sinusoidal escence. The time resolution ranged from 10 s to 30 s. The ephemerides with their 1-σ formal errors quoted. We also April 2000 run was made in white light (W). A summary list the root-mean-squares of the residuals and the χ2 value of these observations is given in Table 1. Data reduction ν2 for each case, where ν2 is the number of degrees of freedom. included bias subtraction, flat-field correction, cosmic rays removal, aperture photometry extraction and absolute flux Fig. 1 presents the (O−C) diagram with respect to the calibration. A more complete analysis of these data will be linear ephemeris in Table 3. van Teeseling (1997) reports presented in a separate paper. Here we will concentrate on that a positive offset of 90 s (plus an additional offset of the measurement of the mid-eclipse times. 0.0025 cycles) was needed in order to centre the x-ray eclipse Mid-eclipse times were measured from the mid-ingress of Z Cha around phase zero with respect to the ephemeris of and mid-egress times of the white dwarf eclipse using the Robinson et al. (1995). We used this information to assign a derivative technique described by Wood, Irwin & Pringle representative eclipse cycle to his measurement and to com- (1985). For a given observational season, all light curves pute the (O−C) value with respect to the linear ephemeris were phase-folded according to a test ephemeris and sorted in Table 3. His x-ray timing is plotted as a cross in Fig. 1 in phase to produce a combined light curve with increased and is fully consistent with our results. The significance of adding additional terms to the lin- † i.e., those with well-sampled observed-minus-calculated (O−C) ear ephemeris was estimated by using the F-test, follow- eclipse timings diagram covering more than a decade of ing the prescription of Pringle (1975). Not surprisingly, observations. the quadratic ephemeris is no longer statistically signifi-

c 2002 RAS, MNRAS 000, 1–4 Cyclical period changes in Z Cha 3

Table 3. Ephemerides of Z Cha cant. From the σ1 and σS values in Table 3 we obtain F (3, 69) = 130.7, which corresponds to a 99.99% confidence Linear ephemeris: level for the linear plus sinusoidal ephemeris with respect to BJDD = T0 + P0 · E the linear fit. The best-fit linear plus sinusoidal ephemeris is T0 = 2440264.68070 (±4)d P0 = 0.0744993048 (±5) d shown as a solid line in the lower panel of Fig. 1. 2 −3 2 1 × χν2 = 49.2, ν = 72 σ = 3.27 10 cycles However, the eclipse timings show systematic and sig- Quadratic ephemeris: nificant deviations from the best-fit linear plus sinusoidal 2 2 BJDD = T0 + P0 · E + c · E ephemeris. The fact that χν2 > 1 emphasizes that the linear plus sinusoidal ephemeris is not a complete description of T0 = 2440264.68088 (±8)d P0 = 0.074499300 (±2) d −14 −3 c = (+2.8 ± 1.1) × 10 d σ2 = 3.13 × 10 cycles the data, perhaps signalling that the period variation is not 2 sinusoidal or not strictly periodic. We explored these possi- χν2 = 48.0, ν2 = 71 bilities by making separate fits to the first half of the data Sinusoidal ephemeris: set (E < 80 × 103 cycle) and to the second half of the data BJDD = T0 + P0 · E + A· cos [2π(E − B)/C] set (E > 80 × 103 cycle). The results are shown in the lower 3 T0 = 2440264.6817 (±1) d B = (120 ± 4) × 10 cycles panel of Fig. 1, respectively, as dotted and dashed curves. 3 P0 = 0.074499297 (±2) d C = (136 ± 7) × 10 cycles The older timings point towards a longer cycle period with −4 −3 A = (7.2 ± 1.0) × 10 d σS = 1.09 × 10 cycles 2 a lower amplitude (A= 1.13 min, Pcyc = 29 yr), whereas the χ = 3.99, ν2 = 69 ν2 more recent timings are best described by a shorter cycle period of larger amplitude (A= 1.23 min, Pcyc = 23 yr). These results indicate that the period changes are not sinusoidal or not periodic.

3 DISCUSSION

Our results reveal that the orbital period of Z Cha is no longer increasing as previously found by Robinson et al. (1995). Instead, the (O−C) diagram shows conspicuous cyclical, quasi-periodic changes of amplitude 1 min on a time-scale of about 28 yr. Cyclical orbital period changes are seen in many eclipsing CVs (Warner 1995 and references therein). The cycle periods range from 4 yr in EX Dra (Baptista et al. 2000) to about 30 yr in UX UMa (Rubenstein, Patterson & Africano 1991), whereas the amplitudes are in the range 0.1-2.5 min. Therefore, Z Cha fits nicely in the overall picture drawn from the observations of orbital period changes in CVs. If one is to seek for a common explanation for the cyclical period changes in CVs, then models involving apsidal motion or a third body in the system shall be discarded as these require that the orbital period change be strictly periodic, whereas the observations show that this is not the case (Richman et al. 1994 and references therein). We may also discard explanations involving angular momentum exchange in the binary, as cyclical exchange of rotational and orbital angular momentum (Smak 1972; Biermann & Hall 1973) re- quires discs with masses far greater than those deduced by direct observations, and the time-scales required to allow the spin-orbit coupling of a secondary of variable radius are Figure 1. The (O−C) diagram of Z Cha with respect to the much shorter than the tidal synchronization scales for these linear ephemeris of Table 3. The optical timings from the litera- systems (∼ 104 yr, see Applegate & Patterson 1987). ture are shown as open circles, the x-ray timing from van Teesel- The best current explanation for the observed cyclical ing (1997) is shown as a cross, and the new timings are indi- period modulation is that it is the result of a solar-type mag- cated as solid circles. The dashed line in the upper panel depicts netic activity cycle in the secondary star (Applegate & Pat- the quadratic ephemeris of Robinson et al (1995) while the solid line in the lower panel shows the best-fit linear plus sinusoidal terson 1987; Warner 1988; Bianchini 1990). Richman et al. ephemeris of Table 3. Best-fit linear plus sinusoidal ephemerides (1994) proposed a model in which the Roche lobe radius of 3 for the data on the first half of the time interval (E < 80 × 10 the secondary star RL2 varies in response to changes in the cycle, dotted curve) and for the last half of the time interval distribution of angular momentum inside this star (caused (E > 80 × 103 cycle, dashed curve) are also shown in the lower by the magnetic activity cycle), leading to a change in the panel. orbital separation and, therefore, in the orbital period. As a consequence of the change in the Roche lobe radius, the mass transfer rate M˙ 2 also changes. In this model, the orbital

c 2002 RAS, MNRAS 000, 1–4 4 R. Baptista et al. period is the shortest when the secondary star is the most quiescent brightness modulation is very close to half of the oblate (i.e., its outer layers rotate faster), and is the longest period of the observed Pmod and may correspond to the first when the outer layers of the secondary star are rotating the harmonic of a non-sinusoidal or non-strictly periodic period slowest. change. The fractional period change ∆P/P is related to the The analysis of Ak et al. (2001) covers only 18 years amplitude ∆(O − C) and to the period Pmod of the modu- of observations. It would be interesting to see whether the lation by (Applegate 1992), 28 yr orbital period change also appear as a modulation in the quiescent magnitude in a dataset covering a larger time- ∆P ∆(O − C) A = 2π = 2π . (1) interval. A simple and interesting test of the Richman et al. P Pmod C (1994) model is to check its prediction that the maximum Using the values of A and C in Table 3, we find ∆P/P = of the brightness modulation coincides with the minimum 4.4 × 10−7. This fractional period change is comparable to of the orbital period modulation, which occurred at E ≃ 4 those of other short-period CVs, but is one order of mag- 5.2 × 10 cycle (or about JD 2 444 150) for Z Cha. nitude smaller than those of the CVs above the period gap Finally, we remark that, if the magnetic activity cy- (∆P/P ≃ 2 × 10−6) [Warner 1995]. cle explanation is right, our confirmation that Z Cha also The predicted changes in Roche lobe radius and mass shows cyclical period changes underscores the conclusion of transfer rate are related to the fractional period change by Ak et al. (2001) that even fully convective secondary stars (Richman et al. 1994), possess magnetic activity cycles (and, therefore, magnetic fields). 2/3 −1 ∆RL2 1+ q ∆Ω ∆P = 39 −3 , (2) RL2 q 10 Ω P and by, ACKNOWLEDGMENTS

2/3 −1 We are grateful to the LNA staff for valuable assistance dur- ∆M˙ 2 5 1+ q ∆Ω ∆P = 1.22 × 10 , (3) ing the observations. This work was partially supported by ˙ q 10−3Ω P M2 the PRONEX/Brazil program through the research grant where ∆Ω/Ω is the fractional change in the rotation rate of FAURGS/FINEP 7697.1003.00. RB acknowledges financial the outer shell of the secondary star involved in the cyclical support from CNPq through grant no. 300 354/96-7. EO ac- exchange of angular momentum, q (= M2/M1) is the binary knowledges financial support from FAPESP through grant mass ratio, and the minus signs were dropped. no. 99/05603-6. SV thanks the South African Claude Harris In the framework of the disc instability model (Smak Leon Foundation for funding a postdoctoral fellowship. 1984, Warner 1995 and references therein), the mass trans- ferred from the secondary star will accumulate in the outer disc regions during the quiescent phase. Hence, changes in REFERENCES M˙ 2 will mainly affect the luminosity Lbs of the bright spot where the infalling material hits the outer edge of the disc. Ak T., Ozkan M. T., Mattei J. A., 2001. A&A, 369, 882 Applegate J. H., 1992. ApJ, 385, 621 The luminosity of the bright spot is L ∝ M˙ 2. The bright bs Applegate J. H., Patterson J., 1987. ApJ, 322, L99 spot in Z Cha contributes about 30 per cent of the total Baptista R., Catalán M. S., Costa L., 2000. MNRAS, 316, 529 optical light (on an average over the orbital cycle) [Wood Baptista R., Horne K., Hilditch R., Mason K. O., Drew J. E., et al. 1986]. Therefore, one expects that the changes in mass 1995. ApJ, 448, 395 transfer rate lead to a modulation in the quiescent bright- Baptista R., Jablonski F. J., Steiner J. E., 1992. AJ, 104, 1557 ness of the system of ∆m = (∆Lbs/L) ≃ 0.3 (∆M˙ 2/M˙ 2) ≃ Beuermann K., Pakull M. W., 1984. A&A, 136, 250 (0.06−0.12) mag for ∆Ω/Ω =(1−2)×10−3 (Richman et al. Bianchini A., 1990. AJ, 99, 1941 1994) and q = 0.15 (Wood et al. 1986). Biermann P. L., Hall D., 1973. A&A, 27, 249 Ak, Ozkan & Mattei (2001) reported the detection of Bond I. A., Freeth R. V., 1988. MNRAS, 232, 753 cyclical modulations of the quiescent magnitudes and out- Cook M. C., Warner B., 1984. MNRAS, 207, 705 Cook M. C., 1985. MNRAS, 216, 219 burst intervals of a set of dwarf novae, which they inter- Echevarria J., Alvarez M., 1993. A&A, 275, 187 preted as the manifestation of a magnetic activity cycle Gilliland R. L., 1981. ApJ, 248, 1144 in their secondary stars. They found that the quiescent King A. R., 1988. QJRAS, 29, 1 brightness of Z Cha is modulated with an amplitude of Pringle J., 1975. MNRAS, 170, 633 ∆m = 0.16 mag on a time scale of 14.6 yr. Unfortunately, Richman H. R., Applegate J. H., Patterson J., 1994. PASP, 106, they do not list the epoch of maximum brightness. 1075 The observed amplitude of the brightness modulation Robinson E. L., Shetrone M. D., Africano J. L., 1991. AJ, 102 is larger than that predicted from the orbital period change Robinson E. L., et al., 1995. ApJ, 443, 295 with the assumption of ∆Ω/Ω =(1 − 2) × 10−3. The model Rubenstein E. P., Patterson J., Africano J. L., 1991. PASP, 103, of Richman et al. (1994) can account for both the measured 1258 Smak J. I., 1972. Acta Astr., 22, 1 period changes and the observed brightness modulation if −3 −4 Smak J., 1984. PASP, 96, 5 ∆Ω/Ω ≃ 2.7 × 10 . This yields ∆RL2/RL2 ≃ 1.7 × 10 . Stumpff P., 1980. A&AS, 41, 1 The predicted change in the Roche lobe radius of the van Amerongen S., Kuulkers E., van Paradijs J., 1990. MNRAS, secondary star in Z Cha is comparable to the observed 242, 522 change in the radius of the Sun as a consequence of its van Teeseling A., 1997. A&A, 319, L25 magnetic activity cycle (Gilliland 1981). The period of the Warner B., 1988. Nature, 336, 129

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c 2002 RAS, MNRAS 000, 1–4