Orbital variations and outbursts of the unusual variable star V1129 Centauri
aa r X i v : . [ a s t r o - ph . S R ] J un Orbital variations and outbursts of theunusual variable star V1129 Centauri Albert Bruch
Laborat´orio Nacional de Astrof´ısica, Rua Estados Unidos, 154,CEP 37504-364, Itajub´a - MG, Brazil(Published in: New Astronomy, Vol. 57, p. 51 – 58 (2017))
Abstract
The variable star V1129 Cen is classified in the GCVS as being of β Lyr type.Unusual for such stars, it exhibits outbursts roughly once a year, lasting for ∼
40 days.For this reason, a relationship to the dwarf novae has been suspected. Here, for thefirst time a detailed analysis of the light curve of the system is presented. Based onobservations with high time resolution obtained at the Observat´orio do Pico dos Diasand on the long term ASAS light curve the orbital variations of the system are studied.They are dominated by ellipsoidal variations and partial eclipses of a probably slightlyevolved F2 star in a binary with an orbital period of 21 h m . Comparison with thecharacteristics of dwarf novae show that the observational properties of V1129 Cen canbe explained if it is just another dwarf novae, albeit with an unusually bright and earlytype mass donor which outshines the accretion disk and the mass gainer to a degreethat many normal photometric and spectroscopic hallmarks of cataclysmic variablesremain undetected.Keywords: Stars: binaries: eclipsing – Stars: variables: general – Stars: novae, cata-clysmic variables – Stars: dwarf novae – Stars: individual: V1129 Cen Cataclysmic variables (CVs) are binary stars where a Roche-lobe filling late-type component(the secondary) transfers matter via an accretion disk to a white dwarf primary. A particularsubclass of CVs are the dwarf novae which occasionally exhibit outbursts with amplitudesof a few magnitudes, lasting from days to weeks. These are caused by a temporary increaseof the brightness of the accretion disks in these systems.It may be surprising that even after decades of intense studies of CVs there are still anappreciable number of known or suspected systems, bright enough to be easily observed withcomparatively small telescopes, which have not been studied sufficiently for basic parametersto be known with certainty. In some cases even their very class membership still requiresconfirmation.Therefore, I started a small observing project aimed at a better understanding of thesestars. First results have been published by Bruch (2016, 2017a) and Bruch & Diaz (2017).Here, I present time resolved photometry and a limited amount of spectroscopy of the Based partially on observations taken at the Observat´orio do Pico dos Dias / LNA ∼ m . 7 not many details are knownabout the star. It is classified as a β Lyr type eclipsing binary in the 17 th name list of variablestars (Kazarovetz et al. 2008). β Lyr systems are binaries made up of stars in tight or evensemi-detached orbits. Their evolutionary state may range from two main sequence stars toa pair with a highly evolved secondary component and a less evolved primary with masstransfer between them (Hoffman et al. 2008). Due to the proximity of the stellar componentsthe light curves are dominated by ellipsoidal variations often in combination with mutualeclipses.In the particular case of V1129 Cen, however, apart from variations typical for such stars,recurring at a period of 0.893025 days, S. Otero found faint outbursts with a duration of ∼
40 days recurring on the time scale of one year. The ASAS (Pojmanski 2002) long termlight curve contains several such events which reach an amplitude of up to 0 m . 6 (upper frameof Fig. 1). The spectral type of F2 V of V1129 Cen (Houk 1978) is later than that of the largemajority of β Lyr stars but much earlier than that of the donor star in any CV. Unusual fora star of this type, Walter et al. (2006) observed emission of He II λ A on 2006, Jan 16.2UT which, however, was absent on 2006, Jan 19.3 UT. Both of these observations ocurredduring an outburst as is shown by the insert in the figure, where the corresponding epochsare marked by vertical lines. The authors leave the question open whether the emission wastransient or if the source was eclipsed during the second observation. It is not clear whatcauses this unusual (for a β Lyr star) behaviour. Ritter & Kolb (2003) have included thestar as a possible U Gem type dwarf nova in the on-line version of their catalogue.If the system indeed contains a dwarf nova or behaves like one, persistent mass transferthrough an accretion disk should take place and thus flickering should be expected to bepresent. Whether this would be observable or not depends on the degree of modulation of theflickering light source and its relative contribution to the total light of this peculiar system.In order to verify the presence of flickering and to investigate the question whether or notthe properties of V1129 Cen are compatible with a dwarf nova classification, I observed thestar on several occasions in 2014, 2015 and 2016. Because of their superior quality I willconcentrate here on the 2016 light curves. These data are complemented by observationsretrieved from the ASAS data archive. Additionally, I obtained a few spectra in 2015 inorder to verify the eventual presence of emission lines as observed by Walter et al. (2006).This study is organized as follows: In Sect. 2 the observations and data reduction tech-niques are briefly presented. Sect. 3 then deals with the results of the observations andof model calculations. A discussion follows in Sect. 4. Finally, the conclusions are brieflysummarized in Sect. 5.
All photometric observations were obtained at the 0.6-m Zeiss and the 0.6-m Boller &Chivens telescopes of the Observat´orio do Pico dos Dias (OPD), operated by the Laborat´orioNacional de Astrof´ısica, Brazil. Time series imaging of the field around the target star wasperformed using cameras of type Andor iKon-L936-B and iKon-L936-EX2 equipped withback illuminated, visually optimized CCDs. A summary of the observations is given in The internet links to the corresponding communications cited in the online version of theRitter & Kolb catalogue (http://varsao.com.ar/NSV 19488.htm) or in Walter et al. (2006)(http://ar.geocities.com/varsao/NSV 19448.htm) appear not be active any more.
Top:
ASAS-3 long term light curve of V1129 Cen. The insert contains an expandedview of the outburst selected by the broken-lined box. The vertical lines mark the epochsof detection (blue) and non-detection (magenta) of He II λ A emission by Walter etal. (2006). Centre:
The same data (without outbursts) folded on the orbital period. Theoutlying green data points were disregarded in the model fits discussed in Sect. 3.3. The redgraph represents the best model fit.
Bottom:
Difference between the observed light curveand the best model fit. The zero level is indicated by the red broken line in order to bettervisualize systematic deviations. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)3able 1: Journal of observationsDate Start End B (UT) (UT)2016 Mar 09 1:19 5:10 ∗ ∗∗∗ unreliable ∗∗ spectroscopic observationsTable 1. Some light curves contain gaps caused by intermittent clouds or technical reasons.In order to resolve any rapid flickering variations the integration times were kept short.Together with the small readout times of the detectors this resulted in a time resolution ofthe order of 5 s . In contrast to observations of other targets within the observing projectmentioned in Sect. 1, in spite of the short integration times the high brightness of V1129 Cennot only permitted but demanded (in order to avoid saturation) the use of a filter. A B filter was chosen. Even so, I did not perform a rigorous photometric calibration but expressthe brightness as the magnitude difference between the target and the nearby comparisonstar UCAC4 223-607051 ( B = 13 . . The average nightly B magnitudeof the target is included in Table 1.In addition to the photometric observations, eight spectra of 600 sec exposure time wereobtained on 2015, February 14, at the 1.6-m Perkin Elmer telescope of OPD. An AndoriKon-L936-BR-DD camera was employed. Exposures of a He-Ar lamp for wavelength cali-bration were taken after every second stellar exposure. From the FWHM of the lines in thecomparison spectra a spectral resolution of ≈ It seems that the comparison star shows small variations on the time scale of months and years which,however, have no bearing on the results of this study.
The light curves are dominated by variations on hourly time scales, reflecting the β Lyr typevariations, but contain no obvious flickering. As examples, Fig. 2 shows two light curves of2016, April 7 and 8. The black dots represent the data points at the original time resolution,while the same data, binned in intervals of 2 minutes, are shown in red.Before dealing in more detail with the issue of flickering, I first turn to the β Lyr typevariations of V1129 Cen. To this end, the individual light curves were folded on the abovequoted period, using as zero point of phase the epoch of primary minimum (as cited onthe AAVSO International Variable Star Index webpage ). In two nights a small magnitudeadjustment was applied, calculated from the difference of the differential magnitudes in therespective phase intervals during the night in question and the other nights. This is probablydue to slight variability of the quite red ( B − V = 1 m . 53; Zacharias et al. 2013) primarycomparison star as revealed by a comparison with two check stars.The resulting β Lyr type light curve, shown in Fig. 3, binned in phase intervals of width0.005, does not cover all phases. Moreover, a small shift of the primary minimum with respectto phase 0 (already corrected for in the figure) was observed. Its magnitude was determined β Lyr type variations,binned in phase intervals of 0.005 (dots). The red line represents the best model fit (seeSect. 3.3). (For interpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.)to be 0 . ± .
001 by fitting polynomials of various degrees to the minimum. This meansthat the period communicated by Otero requires a slight correction. The observed phaseshift, the minimum epoch (referring to 2002) and the minimum epoch observed in 2016 thenpermit to calculate updated ephemeries for V1129 Cen:BJD min = 2457483 . . × E where E is the cycle number. This does, or course, not take into account a possible periodvariations such as that observed in the prototype star β Lyr (Harmanec & Scholz 1993) at amuch higher rate (19 sec/yr) that any possible variation implied by the difference of Otero’speriod and the present value.For comparison, the ASAS-3 data were also folded on the orbital period (rejecting theobservations taken during outbursts; Fig. 1, bottom). While noisy, the β Lyr type variationsare obvious. The lower amplitude compared to Fig. 3 may be due to the different passbandof the ASAS-3 data ( V vs. B ). Having in mind the report of Walter et al. (2006) of transient He II λ A emission inthe spectrum of V1129 Cen, I obtained the spectroscopic observations mentioned in Sect. 2.The mean of eight individual exposures is shown in Fig. 4 (black curve). Since no fluxcalibration of the spectra was performed it is shown here normalized to the continuum. Forcomparison, standard star spectra of spectral type F0 V and F3 V (i.e., close to the spectraltype of V1129 Cen), taken from the compilation of Jacoby et al. (1984) and normalized inthe same way are also shown in the figure (shifted upward and downward for clarity). Theirresolution was degraded to match that of V1129 Cen. No trace of λ A emission is seen. I turn my attention now to the implications of the absence of detectable flickering in thelight curves of V1129 Cen. 6igure 4: Average continuum normalized spectrum of V1129 Cen on 2015, Feb. 14 (black),together with the spectra of two standard stars of similar spectral type F0 V (red) and F3 V(green). (For interpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.)I first determine the scatter of the data points of the binned versions of the light curvesshown in Fig. 2 (adding also the night of 2016, April 6) after subtraction of the orbitalvariations. To this end a Gaussian was fit to the distribution of the difference betweendata points of the binned light curves and a Fourier filtered version of the same data whichremoves variations on time scales > m . In all nights it has a FWHM of about δm = 0 m . 01.What must be the magnitude difference between a flickering light source and a brighterconstant star in order to render the flickering unobservable? Assuming the presence of alight source in the system which flickers such that a light curve treated in the same way asabove leads to a distribution of data points with a FWHM of δm it is possible to calculate asa function of δm the magnitude difference ∆ m of that light source and of the entire systemnecessary for the observed FWHM not to exceed δm . This leads to the relationship shownin Fig. 5. Considering that the total amplitude of the flickering variations is significantlylarger than the FWHM of the distribution of data points [e.g., in V504 Cen Bruch (2017b)observed a total amplitude of 0 m . 62, while the FWHM does not exceed 0 m . 16] the range of δm in the figure extends to extremely strong flickering.According to Gaia DR1 (Brown et al. 2016), V1129 Cen has a parallax of 3 . ± .
40 mas.This translates into a distance of 312 ±
39 pc. The ASAS-3 long term light curve shows thatthe V magnitude varies between 9 m . 47 and 9 m . 96 (disregarding outburst), with an averageof 9 m . 65. While the transformation of ASAS magnitudes to a standard photometric systemmay not be particularly accurate, errors are expected not to exceed a typical value of 0 m . 05 .Moreover, the average magnitude of 9 m . 65 is identical to the V magnitude cited in theTycho-2 catalogue (Høg et al. 2000).The interstellar absorption towards V1129 Cen appears to be small. The observed colours B − V = 0 . U − B = 0; Kilkenny & Laing 1990) match quite well with those of anunreddened star of the same spectral type F2 V; B − V = 0 . U − B = 0 .
00; FitzGerald1970. Neglecting thus absorption, the distance and the apparent average magnitude translateinto an absolute magnitude of M V = 2 . ± .
29, slightly ( ∼ m . 75) brighter than an F2 type However, the authors marked these values as uncertain. m between a light source with a flickering amplitude δm and the same plus an additional (constant) light source such that the observed flickeringamplitude drops to δm = 0 . M V = 7 m . 2 . Whilein long period systems it includes a non-negligible contribution of the mass donor, for thesake of a conservative upper limit I consider this value to be the magnitude of a possibleaccretion disk in V1129 Cen. The magnitude difference between the entire system and theaccretion disk is thus at least ∆ m = − m . 0. Comparing this value with the graph in Fig. 5it is obvious that the not flickering light sources in V1129 Cen can easily hide any flickeringeven if the disk light would be 100% modulated. The complete phase coverage of the ASAS data warrents an attempt to model the light curveof V1129 Cen in the expectation that some system parameters can be delimited. To this end,I employ the Wilson-Devinney code (Wilson & Devinney 1971, Wilson 1979) as implementedin MIRA. Before proceeding, a word on nomenclature is in order to avoid confusion withnomenclature usually used in CV research: I will refer to the optically dominating F2 staras the primary component, independent whether it is the mass gainer or mass loser (if thereis mass transfer in the system) or whether it is the more massive or the less massive star. Itwill be designated by the index 1 subsequently. Consequently its companion is the secondarystar (index 2). The mass ratio is defined as q = M /M .Considering the large number of model parameters required by the Wilson-Devinney codeto calculate a light curve it is appropriate to fix as many of them as possible before tryingto adjust the model light curve to the observed data.It turns out that the atmospheric parameters albedo A , limb darkening coefficient u andgravity darkening coefficient y have only a minor influence on the results. Therefore, u and A simple linear law of the kind I ( µ ) /I (1) = 1 − u (1 − µ ) is used. Here, I (1) is the specific intensity at are interpolated in the tables of Claret & Bloemen (2011) [using their results based onATLAS model, least squares calculations, adopting solar chemical composition, the surfacegravity of a normal F2 main sequence star and no microturbulence; for details, see Claret &Bloemen (2011)] at the temperature of 7 040 K as determined by Kordopatis et al. (2013)for the primary star. Similarly, u and y for the secondary component refer to a temperatureof 4 500 K (determined from preliminary model fits) and a surface gravity calculated fromthe mass and radius of a main sequence star of that temperature. According to Rafert &Twigg (1980) hotter stars with radiative envelopes should have an albedo of A = 1 . A = 0 .
5. I adopt the latter value for the secondarystar of V1129 Cen. The temperature of the primary falls in the transition region between thetwo regimes. For simplicity, I adopt A = 0 .
75. Furthermore, the primary temperature isfixed to the above mentioned value of T = 7 040 K. A phase shift to make up for a possibleslight error of the epoch of primary eclipse was fixed to the value determined in preliminarycalculations. Any contribution of an accretion disk and/or hot spots possibly present in thesystem was ignored.The model parameters left free to be adjusted to the data where then the mass ratio q of the components, the orbital inclination i , the temperature T and the dimensionlesssurface potential Ω of the secondary star. β Lyr stars are binaries in a tight orbit, butit is not always evident if they are detached or semi-detached. Therefore, calculations forboth cases were performed, choosing the corresponding mode of the Wilson-Devinney code.In the latter case the surface potential of the primary star is determined by the mass ratiowhich defines the potential at the Roche surface. In the alternative case no limitations onthe size of the components relative to their Roche lobes is assumed and the surface potentialof the primary was also left free to be adjusted. Finally, the normalization constant wasalso considered a free parameter. It turned out that the best fit parameters of the detachedmodel were not significantly different from those of the semi-detached model. Therefore, tobe definite, I will subsequently only regard the results derived from the latter.The SIMPLEX algorithm (Caceci & Cacheris 1994) was adopted to find the optimal modelparameters which lead to the minimal χ between observations and calculations. Someoutlying data points in the observed light curve (green dots in Fig. 1) were disregarded. Thebest fit model is shown in the central frame of Fig. 1 as a red curve. The lower frame containsthe differences between the observed and calculated data. The broken red line indicates thezero level in order to better visualize systematic deviations of the O − C curve from zero.The fit parameters are summarized in Table 2. Here, the Roche lobe filling factor of thesecondary is calculated from its surface potential and is thus not an independent quantity.The model fit is not completely satisfactory. There are systematic residuals between dataand fit. In particular, the fit appears to slightly underestimate the brightness after theprimary minimum (phase range 0 . < φ < . . < φ < . χ , min = 2 .
9. Some ingredients are therefore probably missing in themodel. If the outbursts of V1129 Cen are indeed related to dwarf nova outbursts this is notsurprising because an accretion disk (and possibly associated bright spots) are then expectedto be present in the system. These cannot be modeled by the Wilson-Devinney code.Even so, considering that the orbital modulation is evidently dominated the the ellipsoidalvariations of the primary component together with a substantial primary and a smallersecondary eclipse (all determined by the component temperatures, their relative sizes andthe mass ratio), the missing model ingredients may demand small corrections, but the best the centre of the stellar disk, and µ = cos γ , where γ is the angle between the line of sight and the emergentradiation. χ hyperspace, defined by the residuals betweenthe observed light curve of V1129 Cen and model calculations, at the location of the best fitparameters. The colour coding (see colour bar at the top of the figure) is such that purplecorresponds to χ = χ , min and dark red represents χ ≥ χ , min . (For interpretation of thereferences to colour in this figure legend, the reader is referred to the web version of thisarticle.) 10able 2: Parameters of the model fit to the V1129 Cen light curveParameter Best fit Best fit acceptable range( V band) ( B band) (from V band data)Albedo (prim.) A fixed 0.75 0.75Albedo (sec.) A fixed 0.50 0.50limb dark. coef. (pr.) u fixed 0.55 0.65limb dark. coef. (sec.) u fixed 0.79 0.89grav. dark. coef. (pr.) y fixed 0.24 0.29grav. dark. coef. (sec.) y fixed 0.64 0.83Temperature (prim.) (K) T fixed 7040 7040Temperature (sec.) (K) T adjusted 4490 5210 ( < o ) i adjusted 74.6 74.3 ( 67 . . . 90 )Mass ratio q adjusted 0.61 0.61 ( 0.45 . . . 0.77)Surface potential (sec.) Ω adjusted 7.55 7.32 ( 5.8 . . . >
11 )Roche lobe filling factor (sec.) adjusted 0.27 0.28 ( 0.17 . . . 0.37)fit parameters should at least approximately reflect reality.Parameter correlations make it difficult to assign meaningful statistical errors to the pa-rameter values. In order to investigate this issue Fig. 6 shows two-dimensional cuts throughthe χ hyperspace at the location of the best fit parameters. In order to facilitate compar-ison, the colours coding of all frames is such that purple corresponds the χ , min and darkred to twice that value or higher (see colour bar at the top of the figure). It is then seenthat, for instance, the orbital inclination and the mass ratio are strongly correlated (centralframe in the upper row of Fig. 6) which makes it impossible to determine either of themwith any degree of precision. Assuming as criterion that solutions leading to χ > χ , min are unacceptable the diagram shows that the mass ratio can be anything from 0.39 up to avalue beyond the limits of the explored parameter range. However, other cuts through the χ hyperspace permit to better restrict q (i.e., the q − T plane; lower left frame of Fig. 6).Exploring the individual cuts in this way leads to permitted parameter ranges as quoted inthe last columns of Table 2 As a check, the Wilson Devinney model was also fit to the B light curve (red line inFig. 3). Again, the fit is not perfect, exhibiting the same excess of observed light in thephase range after primary minium already seen in the V-band data. With the exceptionof the secondary star temperature which is higher by ≈
700 K when the B band data areused, the best fit parameters listed in Table 2 are practically identical to those derived fromthe V band. Even so, T remains comfortably within the acceptable range. The agreementof the results obtained from data in different bands and using radically different observingprocedures gives confidence that they are not corrupted by errors or systematics of theobservations.The results of the model calculations nicely fit in with independent knowledge aboutV1129 Cen. Assuming the mass M of the primary not to be significantly different fromthat of a normal F2 V star ( ∼ M ⊙ ; Allen 1973) the mass ratio and the orbital periodtogether with Kepler’s third law yield the component separation A . Using the approximationfor the volume radius of the Roche lobe provided by Eggleton (1983), the assumption of asemi-detached configuration determines the radius R of the primary in units of A as a The lower limit for the range of T is ill defined because the Wilson-Devinney code issued warningswhen T < q . For the best fit value of q this results in a primary star radius of R = 2 . R ⊙ .This is 1.7 times the radius of a F0 V star according to Allen 1973), confirming the conclusiondrawn in Sect. 3.2 that the star has evolved off the main sequence. Since the brightnessscales with the square of the radius, the V1129 Cen primary should be 1 m . 2 brighter that itsmain sequence equivalent. This is somewhat more than the values found in Sect. 3.2 (0 m . 75)but not significantly so considering the uncertainty of M V and q . The main issue concerning V1129 Cen is the question about the nature of the semi-periodicoutbursts. Are these genuine dwarf nova type eruptions? If so, how can they come about ina system that otherwise appears to have a configuration different from normal cataclysmicvariables?Outbursts of dwarf nova are caused by an increase of matter transferred through anaccretion disk and the corresponding release of energy. This may be due to a limit cycle inthe disk which during quiescence is in a cool and low viscosity state. Matter transferred froma donor star increases the disk mass and its temperature until the temperature for hydrogenionization is reached, resulting in an increased viscosity which causes the disk matter to bedumped on the central star (the thermal-viscous instability model; Lasota 2001). While thisis the commonly adopted mechanism for dwarf nova outbursts, at least in some systems itseems not to work and there is evidence that instead an increased mass transfer from thecompanion star is responsible for the brightening of the accretions disk and thus the dwarfnova outburst [see the discussion in Baptista (2012)].
What are the characteristics of the brightenings of V1129 Cen and how do they relate tothose of normal dwarf nova outbursts? They last for about 40 days which is significantlylonger than observed in most dwarf novae. However, as Szkody & Mattei (1984) and Gicger(1987) showed, there is a clear correlation between orbital period and outburst duration.Extrapolating the relation of Gicger (1987) to the period of V1129 Cen leads to 40.7 daysin remarkable agreement with the average outburst duration measured in the ASAS-3 lightcurve.While most dwarf nova outbursts rise rapidly and decline more slowly, the V1129 Cenoutbursts are more symmetrical. This may also be a consequence of the long orbital periodsince outburst of other long period CVs show similar shapes [BV Cen, P orb = 0 .
611 days,Bateson (1974); GK Per , P orb = 1 .
997 days, Pezzuto et al. (1996), Evans et al. (2009);V630 Cas, P orb = 2 .
564 days, Shears & Poyner (2009)].Similarly, using a mean outburst interval of 347 days (from Fig. 1, assuming one unob-served outburst close to JD 2452400) V1129 Cen fits in very nicely in a linear relationshipbetween the orbital period and the logarithm of the outburst intervals of BV Cen interval:150 days; Menzies et al. 1986, GK Per ( ∼ GK Per is well known to be a classical nova, but it also exhibits dwarf nova outbursts. .2 Scenarios If the bright states in V1129 Cen are in fact dwarf nova type outbursts there must be anaccretion disk somewhere in the system. In principle, at least three possible scenarios can beenvisaged: (1) The source of the outbursts is accidentally in the line of sight to V1129 Cenbut not physically related to it; (2) V1129 Cen is not a simple binary star but a quadrupleformed by two pairs, i.e., the dominating β Lyr type component which has a normal dwarfnova as a companion at a distance where the evolution of either system does not interferewith the other one; (3) the mass gainer in V1129 Cen is surrounded by an accretion disk asmodeled, e.g., in the case of the prototype β Lyr by Mennickent & Djuraˇsevi´c (2013). Thefirst possibility can, or course, not be excluded, but it is quite unlikely considering the lowspace density of dwarf novae. Therefore, I will not consider it further.
Exploring the second scenario, I first remark that the considerations of Sect. 4.1 aboutcorrelations between the outburst duration, shape and intervals, and the orbital period areirrelevant in this case because the observed period of V1129 Cen is then not that of thedwarf nova. The question may be asked whether this scenario is compatible with basicevolutionary considerations. Are the evolutionary time scales of the β Lyr star and thedwarf nova compatible with their co-existence in a single multiple star system? This comesdown to the question if the progenitor of the white dwarf in the dwarf nova system was moremassive than the F2 star because in that case the former had enough time to go througha common envelope phase and become a cataclysmic variable while the F star still remainson or close to the main sequence.Several initial – final mass relations for white dwarfs have been published in the literature.Let M prog be the mass of the progenitor of a white dwarf of mass M WD . Using any of therelations given by Zhao et al. (2012), Salaris et al. (2009) or Catalan et al. (2008), therequirement that M prog > . M ⊙ [i.e., the mass of a F2 V star according to Allen (1973)]leads to M WD > . M ⊙ . This holds for single stars. As Ritter (2010) points out, inbinaries the mass transfer sets a premature end to the nuclear evolution of the donor star.Therefore, the resulting white dwarf mass is smaller than in the case of single star evolution.The mean mass of white dwarfs in CVs is 0.83 M ⊙ (Zorotovic et al. 2011). Thus, there isample space for the progenitor to have a mass high enough to evolve into a red giant and toinitiate the common envelope phase which results in the formation of a CV before the maincomponent, i.e., the F star, leaves the main sequence.On the other hand, the observed outburst amplitude, while not rendering this scenarioimpossible, casts some doubt upon it. Fig. 1 shows that the amplitude of different outburstsrange between 0 m . 6 and 0 m . 4. To be definite, the mean of the extremes, 0 m . 5, will be adoptedhere. Remembering that the absolute magnitude of the dominating F2 star in V1129 Cenis M V = 2 m . 18 (see Sect. 3.2) and assuming that the secondary of the β Lyr type systemand the quiescent dwarf nova contribute negligibly to the total light, the magnitude of theoutbursting light source should then be ∼ m . 6 fainter than the F star. Thus, its absolutemagnitude is ∼ m . 8. Together with the conservative limit for the magnitude differencebetween the entire system and the accretion disk derived in Sec. 3.2 this means that thedwarf nova should have an outburst amplitude of at least − m . 4. This is an uncomfortablyhigh value. Amplitudes as large as this are more typical for superoutbursts of SU UMastars than for normal dwarf nova outbursts. But the ASAS long term light curves does notshow evidence of the dichotomy between normal and superoutbursts characterizing thosesystems. Moreover, the absolute magnitude of the outbursting light source must also be13uite high in this scenario. In normal dwarf novae the absolute V band outburst magnitude M max increases with the orbital period P orb , reflecting the larger size of the accretion diskin systems with longer periods. The relationship given in Eq. 13 of Warner(1987) results ina range of 4 . ≥ M max ≥ .
15 for P orb between 1.5 h and 10 h. This holds for an averageinclination of 57 o .7 of the accretion disk. Assuming i = 74 . m . 08 less luminous and thus much fainter than the lower brightness limit estimated above.Therefore, the dwarf nova companion to the β Lyr type binary in the V1129 Cen must haverather extreme properties compared to an average dwarf nova for this scenario to be viable. β Lyr type binary
Turning to the third scenario, I assume that V1129 Cen consists of only two stellar com-ponents, one of which is surrounded by an accretion disk. In fact, similar models havesuccessfully been adjusted to the light curves of several β Lyr type systems: AU Mon(Djuraˇsevi´c et al. 2010), V393 Cen (Mennickent et al. 2012), V455 Cyg (Djuraˇsevi´c etal. 2012), OGLE 05155332-6925581 (Garrido et al. 2013) and the prototype β Lyr itself(Mennickent & Djuraˇsevi´c 2013). In all of these the disk revolves around the optically dom-inating primary star which is thus the mass gainer, receiving matter from a Roche lobefilling secondary star of lower mass. However, in the quoted examples the binary is alwaysmuch hotter and more massive than in the case of V1129 Cen, harbouring primary starsof spectral type O and B and masses ranging from 7 M ⊙ to 13 M ⊙ . Moreover the accretiondisks are all extremely massive, geometrically and optically thick, and hot. The usual diskinstability type mechanism for dwarf nova outbursts cannot work in such disks.But what about the alternative case where the optically dominating star is the mass donorand the accretion disk revolves around the companion? This configuration would be similarto that of a normal cataclysmic variable with the difference that the donor would have amuch earlier spectral type than any other CV.In order to evaluate the consequences of this picture I regard the results of the modelcalculations of Sect. 3.3. Although they provide formal values for Ω and T , these cannotbe used to draw conclusions on the nature of the secondary star (here: the mass gainer).The Wilson-Devinney code assumes the secondary to be a spherical object (distorted bythe Roche potential). If the companion to the F2 star is in reality a star surrounded by anaccretion disk, the fit parameters referring to the secondary will therefore represent an illdefined mixture of stellar and accretion disk parameters.However, this does not affect the brightness of the components. Adopting the best fitparameters the model calculations show that the primary component (here: the mass looser)is ∼
160 times brighter than the secondary at phase 0.25. This corresponds to a magnitudedifference of − m . 5, compatible with the minimum magnitude difference derived from theabsence of obserable flickering (see Sect. 3.2). The stark brightness contrast between thecomponents also demands a high S/N ratio in order to detect the contribution of the expectedemission lines from the accretion disk in the spectrum (provided that the disk is in a lowvicosity state; emission lines in the bright, high viscosity state tend to be weak or evenreplaced by absorptions). Measuring the ratio of the flux at the top of the H β emissionline to the flux of the surrounding continuum in the spectra of CVs reproduced by Zwitter& Munari (1995, 1996) yields a maximum of ∼
5. Taking this as an upper limit for thecorresponding ratio in the supposed accretion disk in V1129 Cen, a S/N ratio of at least 32is then required for a spectrum to exhibit a trace of a H β emission. Thus, the absence ofan emission core in the H β absorption line in Fig. 4 is not incompatible with the idea of adwarf nova-like accretion disk around the secondary component.14hile the large outburst amplitude derived in Sect. 4.2.1 may still represent a certainproblem, this is different for the absolute magnitude of ∼ m . 8 of the outbursting light source.Provided that an extrapolation of Eq. 13 of Warner (1987) [Warner (1995) restricts itsvalidity to orbital periods ≤ h ] to the period of V1129 Cen (21 h .4) does not lead to anexcessive error, the accretion disk in outburst may be even as bright as 1 m . 3.The fact that in this scenario the mass donor is of significantly earlier spectral type thanin any other known CV does not invalidate it. In recent population synthesis calculationsfor CVs, Goliasch & Nelson (2015) explicitly took into account the nuclear evolution of highmass donor stars. They show that CVs with donor star masses corresponding to early Fstars can form, in particular if the donor has already evolved off the main sequence. At firstglance, the fact that all values of q within the acceptable range quoted in Tab. 2 lead to adonor star mass significantly in excess of that of the mass gainer appears problematic sincethis is in contrast to normal CVs where the mass donor is always less massive than the massgainer. But also in this case the calculations of Goliasch & Nelson (2015) indicate that thedonor can be much more massive than the gainer, in particular if it is evolved. However,the stability and the rate of mass transfer may then become an issue. Can it be kept lowenough for the disk to remain in a quiescent low state prone to dwarf nova outbursts? Usingthe same stellar evolution code as Goliasch & Nelson (2015), Kalomeni et al. (2016) havecalculated a dense grid of evolutionary tracks for binaries with white dwarf primaries. Intheir Fig. 16 they plot as a function of the donor star mass and the orbital period the ratio˙ M / ˙ M crit of the mass transfer rate ˙ M and the critical transfer rate ˙ M crit above which theaccretion disk is stable against the thermal-viscous instability. The latter is based on thestability criterion of Lasota (2001). The figure shows that at the orbital period of V1129 Cenand a donor star mass close the that of an unevolved (or only slightly evolved) early F typestar configurations with ˙ M / ˙ M crit < M crit for outbursts to occur due a thermal-viscous diskinstability and, in consequence, a high outburst luminosity. Smak (1983) provides an ex-pression for ˙ M crit . I neglect the small correction factor involving the the ratio between thewhite dwarf radius and the disk radius R d and follow Osaki (1996) adopting the expressionlog T eff , crit = 3 . − . R d / cm) for the critical disk temperature and R d = 0 . A ,where A is the component separation. A is calculated from Kepler’s third law, using the typ-ical mass of an F0 V star and the mass ratio as quoted in Table 2. The critical mass transferrate for a disk instability to occur is then ∼ . × − M ⊙ / y. This leads to an approximatelower limit of the outbursting disk luminosity of L d , o = G ˙ MM WD /R WD = 637 L ⊙ where G is the gravitational constant and the white dwarf radius R WD has been calculated from itsmass and the mass-radius relation of Nauenberg (1972). On the other hand, interpolationin the tables of Allen (1973) and allowing for the larger radius due to evolution leads toa luminosity of 12 . L ⊙ for the F-star in V1229 Cen. Since the bolometric and the visualmagnitude difference between the two system components will not be grossly different, theoutbursting accretion disk should outshine the F-star by more than 4 magnitudes in visuallight, in contrast to what is observed.This appears to be a serious problem if the outbursts are expected to be due to a thermal-viscous instability. Assuming the alternative, a temporarily enhanced mass transfer from thedonor star, it obviously vanishes. Moreover, within the scenario of a hierarchical quadrupolesystem it is, of course, also not existent. 15 Conclusions
Based on its optical light curve V1129 Cen has been classified as a β Lyr type system. Itdistinguishes itself from other members of this class by quasi-periodic eruptions, suggestinga relationship of the star with dwarf novae. Here, I investigated its light curve in some detailin order to either substantiate or reject this relationship.Based on model calculations and comparisons with cataclysmic variables it is concludedthat the properties of V1129 Cen are not in contradiction with the hypothesis that thesystem either contains, or that it constitutes a dwarf nova, albeit with rather extremecharacteristics. In the first case V1129 Cen would be a hierarchical quadruple system,formed of two pairs, the optically dominating of which being a normal β Lyr type variable.The second pair would be an ordinary dwarf nova. However, while this scenario cannot a priori be discarded, such a configuration appears to be rather artificial. Alternatively,V1129 Cen may consist of a Roche-lobe filling, slightly evolved F2 star which loses massvia an accretion disk to a companion star; i.e., a cataclysmic variable with an unusuallyearly type mass donor. The high brightness of the F star is able to completely outshine theaccretion disk and the mass gainer (except during the occasional outbursts) such that thenormal photometric or spectroscopic hallmarks of CVs are not detected. A possible problemwith this scenario arises if the outbursts are due to a thermal-viscous instability (as opposedto a temporarily increased mass transfer from the donor star) because then the accretiondisk should become much brighter than observed.As a caveat I stress that this does not mean that the nature of V1129 Cen is elucidatedbeyond doubt. I have shown that its properties are compatible with the hypothesis that thesystem is a dwarf nova with a very early type mass donor, but it would be premature toreject just for this reason another configuration for the star and alternative explanations forthe outbursts.
Acknowledgements
I gratefully acknowledge the use of the ASAS-3 data base which provided valuable supportiveinformation for this study.