The Clusters AgeS Experiment (CASE): The blue straggler Star M55-V60 caught amidst rapid mass exchange
M. Rozyczka, J. Kaluzny, I.B. Thompson, S.M. Rucinski, W. Pych, W. Krzeminski
aa r X i v : . [ a s t r o - ph . S R ] M a r The Clusters AgeS Experiment (CASE):The blue straggler Star M55-V60 caught amidstrapid mass exchange ∗ M. R o z y c z k a , J. K a l u z n y , I. B. T h o m p s o n ,S. M. R u c i n s k i , W. P y c h and W. K r z e m i n s k i Nicolaus Copernicus Astronomical Center, ul. Bartycka 18, 00-716 Warsaw,Polande-mail: (jka, mnr, wk, wp)@camk.edu.pl The Observatories of the Carnegie Institution of Washington, 813 SantaBarbara Street, Pasadena, CA 91101, USAe-mail: [email protected] Department of Astronomy and Astrophysics, University of Toronto, 50 St.George Street, Toronto, ON M5S 3H4, Canadae-mail: [email protected]
ABSTRACTWe analyze light and velocity curves of the eclipsing blue straggler V60 in the field of theglobular cluster M55. We derive M p =1 . ± . M ⊙ , R p =1 . ± . R ⊙ , M bolp =3 . ± . M s = 0 . ± . M ⊙ , R s = 1 . ± . R ⊙ , M bols = 4 . ± . m − M ) V = 14 . ± . globular clusters: individual: M55 – blue stragglers – stars: individual: V60-M55 The eclipsing variable M55-V60 (henceforth V60) was discovered in 1997 withinthe CASE project (Kaluzny et al. 2010). Located 27 arcsec from the centerof M55, it is a proper motion member of the cluster (Zloczewski et al. 2011).At V max = 16 . B − V ) max = 0 .
41 mag the system belongs to thepopulation of blue stragglers. Kaluzny et al. (2010) compiled photometricdata from several seasons and found that the light curve was characteristic ofshort-period low-mass Algols: deep primary eclipses with DV ≈ . DV ≈ .
20 mag. The orbital period,equal to 1.183 d, was found to systematically increase. Such properties indicatea semidetached binary in the mass-transfer phase, with the donor being the lessmassive (secondary) component filling its Roche lobe.In this paper we analyze the velocity curve of V60 and refine the preliminaryphotometric solution obtained by Kaluzny et al. (2010). Spectroscopic andphotometric data are described in Sect. 2 and Sect. 3. The analysis of the datais detailed in Sect. 4 and our results are discussed in Sect. 5. ∗ This paper uses data obtained with the Magellan 6.5 m telescopes located at Las Cam-panas Observatory, Chile.
The photometric data collected between 1997 and 2009 were discussed in Kaluznyet al. (2010), but for completeness we repeat here the most important points oftheir discussion.According to their findings, season-to-season variations of the light curve inquadratures and in the secondary eclipse do not exceed 0.010-0.015 mag in V -band. A significantly stronger variability is observed in the primary minimum,whose depth ranged from V = 18 .
62 mag in 1999 to V = 18 .
57 mag in 2007and 2009. The primary minimum is symmetric in V , allowing for a precisedetermination of times of minimum (however, as we show and discuss in Sect.4, the symmetry is broken in B ). The O − C diagram of the times of minimum(see Fig 3. in Kaluzny et al. 2010) indicates that the orbital period of V60, whichin 2008 was equal to 1.1830214 ± dP/dt =3 . × − ; i.e. it would be doubled in just ∼ years.A preliminary photometric solution favors a semi-detached configurationwith the secondary filling its Roche lobe, consistent with the observed be-havior of the period. The luminosity ratios of the components in V and B bands (obtained from the same solution at quadratures) yield apparent colors( B − V ) p ≈ . B − V ) s ≈ . V p = 17 .
11 mag the primary of V60 is located among theSX Phoenicis pulsating variables on the color-magnitude diagram (CMD) ofM55. A sinusoidal variation with an amplitude of ∼ ± V -light curves.For the present analysis we use observations from five seasons in which botheclipses were covered (i.e. 1999, 2006, 2007, 2008 and 2009). The data werephased according to the times of minima given in Table 4 of Kaluzny et al.(2010) and merged into the composite B and V light curves (with 663 and 2666points, respectively) shown in Fig. 1. Our radial velocity data are based on eight observations obtained with the MIKEEchelle spectrograph (Bernstein et al. 2003) on the Magellan II (Clay) telescopeat the Las Campanas Observatory. Seven of them were made in 2004 betweenJune 27th and October 3rd, and the eight one in 2005 on September 11th. Eachobservation consisted of two 1200–1800 s exposures interlaced with an exposureof a Th/Ar lamp. For all observations a 0 . × . × ∼ λ ) scale, convolved them with a Gaussian with FWHM=15 km/s, andrebinned them to 3 km/s steps (i.e. 5 pixels per a resolution interval or 2.5times over-sampling). This procedure improved the quality of the spectra andadjusted the resolution to better reflect the actual rotational broadening of thelines. The final spectra have 22,300 data points in the wavelength interval of400 - 500 nm, where the S/N ratio was the highest. The data reprocessed in thisway were analyzed with the help of a code based on the broadening function(BF) formalism of Rucinski (2002). The BFs were determined over 261 stepsof 3 km/s in a process which is effectively a least squares solution of 22,300linear equations with a 22,300/261 = 85 times over-determinacy. Templateswith [Fe / H] = − .
0, almost exactly matching the value of -1.94 given by Harris(1996; 2010 edition), were selected from the Synthetic Stellar Library of Coelho et al . (2005). Measurement errors, estimated based on the residuals from the fitdescribed in the next paragraph, amount to 3.6 km s − (primary) and 1.9 km s − (secondary). Rotational profile fits which are performed automatically withinthe BF formalism yielded v rot sin i equal to 46 . ± . − for the primaryand 63 . ± . − for the secondary (corrections for the assumed Gaussiansmoothing with FWHM = 15 km/s were taken into account).The velocity curve was fitted with the help of the spectroscopic data solverwritten and kindly provided by Guillermo Torres. On the input to the solverthe observed velocities had to be transformed into mass-center velocities of thecomponents in order to account for their asphericity. This was done iterativelyby applying the solver to the uncorrected velocities, feeding the solution intoPHOEBE31a implementation (Prˇsa & Zwitter 2005) of the Wilson-Devinneymodel (Wilson & Devinney 1971; Wilson 1979), finding the corrections, andapplying the solver again to the corrected velocities. The advantage of thisprocedure is that Torres’s code automatically calculates the errors of the fittedorbital parameters, which otherwise would have to be estimated with PHOEBEby Monte-Carlo techniques. The measured orbital velocities are listed in Ta-ble 1 together with mass-center corrections and residuals from the fit. Thefitted velocity curve generated by PHOEBE is shown in Fig. 2, and the orbitalparameters obtained from the fit are listed in Table 2 together with formal 1- σ errors returned by the fitting routine. A closer look at the primary eclipse in B reveals a significant asymmetry iden-tifiable in each observing season: the ascending branch is by up to 0.2 magbluer than the descending one (see Fig. 3). As such an excess is not possibleto model within the standard approach, we were forced to discard the affectedobservational points between phases 0.0 and 0.07. In principle, the pulsationalmodulation with an amplitude of ∼ V mentioned in Sect. 2, whichis at least partly responsible for the vertical scatter of points in Fig. 1 shouldalso be removed. However, an amplitude this low is suggestive of nonradial pul-sations which are commonly observed in SX Phe stars (e.g. Pych et al. 2001;Olech et al. 2005), and the results of such a procedure applied to the primaryeclipse would be unreliable.The photometric solution was also found with the help of PHOEBE utilitywhich employs the Roche geometry to approximate the shapes of the stars,uses Kurucz model atmospheres, treats reflection effects in detail, and, mostimportantly, allows for the simultaneous analysis of B and V data. For theradiative envelope of the primary we adopted a gravity brightening coefficient g p =1 . A p =1 .
0. The same coefficients for the convectiveenvelope of the secondary were set to g s = 0 .
32 and A s = 0 .
5. The effects ofreflection were included. Limb darkening coefficients were interpolated from thetables of Claret (2000) with the help of the JKTLD code. † Full synchronizationof both components was assumed.An approximate temperature of the primary T p was calculated from thedereddened B − V index obtained by Kaluzny et al. (2010), using a color-temperature calibration based on the data from the Dartmouth Stellar Evo-lution Database (Dotter et al. 2008). We decided to employ the syntheticcalibration because the starting value ( B − V ) p = 0 .
23 mag was too close tothe applicability limit of the empirical calibration compiled by Casagrande etal. (2010) which is formally valid for 0.18 mag < ( B − V ) < E ( B − V ) = 0 .
08 mag with an assumed error of 0.01 mag was used (Harris1996, 2010 edition). The next approximation was found based on PHOEBE-provided contributions of each component to the total light at quadratures in B and V bands which allow to calculate the updated observed ( B − V ) p . Theupdated ( B − V ) p was dereddened and translated into temperature the sameway as before. The procedure was repeated until the convergence was reachedat T p = 8160 ±
140 K (the error is due to uncertainties in calibration, reddeningand zero points of B and V photometry). The temperature of the secondary, T s , was automatically adjusted by PHOEBE.The fitted photometric parameters of V60 are listed in Table 3 together withthe errors estimated based on additional fits to each of the seasonal B and V lightcurves (the ascending branch of the primary eclipse was removed from each B -curve while fitting). Table 4 contains the final absolute parameters of the system,hereafter referred to as the standard solution. The residuals from the final fitare shown in Fig. 4. The blue excess on the ascending branch of the main eclipseis clearly visible; it is also evident that the largest V -residuals occur within themain eclipse. Apparently, the stream(s) of gas between the components generatean additional light in the system which PHOEBE is not able to account for. Thelikely variability of such a light source might be responsible for the enhancedscatter observed in V -band at the bottom of the main eclipse.For T p =8160 K and the primary’s gravitational acceleration g p =4 . M bol =3 . ± .
09 mag (Table 4), the absolute V magnitude of the primary is M V p =3 . ± .
09 mag. From the light curve solution we obtained V p = 17 . ± . m − M ) V =14 . ± .
09 mag. Thisis consistent with the value of 13.89 listed by Harris (1996; 2010 edition). With E ( B − V )=0 . ± .
01 mag, the foreground absorption in V -band is A V =0 . ± .
03 mag, corresponding to an absolute distance modulus ( m − M ) =13 . ± . A F W = 0 .
15 mag, the absolute distance modulus becomes( m − M ) = 13 .
73 mag.We would like to note, however, that the primary’s bolometric luminositywe derive strongly depends on the effective temperature deduced from the colorindex. If instead of T p =8160 K we used T p =7450 K resulting from the empiricalcalibration of Casagrande et al. (2010), we would obtain an unacceptably low † value of the absolute distance modulus ( m − M ) = 13 .
39 mag. This casts comedoubts on the validity of that calibration for blue low-metallicity stars, andindeed, a closer inspection of Fig. 14 in Casagrande et al. (2010) stronglysuggests that for [Fe / H] = − . B − V < .
35 mag their T eff − ( B − V )relation is but an extrapolation. The important conclusion following from our analysis is that the mass transferin V60 must be to a good approximation conservative. This is because the totalmass of the system, M = 1 .
59 M ⊙ , is almost exactly two times larger than theM55 turnoff mass of ∼ ⊙ (e.g. Zaggia et al. 1997). This, together withthe rate of period lengthening and system parameters found in Sect. 4, impliesan orbital expansion rate dA/dt = 3 . × − R ⊙ y − and a mass transfer rate dM/dt = 1 . × − M ⊙ y − . Thus, V60 is in a phase of a rapid mass exchange,which, given the low mass of the H-shell burning secondary, cannot last longerthan a few hundred thousand years. With this in mind, it is interesting to seethat the present primary must be quite far from thermal equilibrium, as itstemperature is over a thousand K lower than the temperature of a 1 . ⊙ staron the 1 .
26 M ⊙ evolutionary track, which according to Dotter et al. (2008)should be equal to 9350 K. We also note that the original mass ratio must havebeen close to unity – otherwise the original primary would have left the mainsequence much earlier, and the system would be in a more advanced evolutionarystate (e.g. detached, or semidetached with the present primary filling its Rochelobe).The blue excess of the system between phases 0.0 and 0.07 (hereafter BEx)is a puzzling feature which to our knowledge has no counterpart in other Algols.Suspecting it might be spurious, we checked if there was a systematic shiftbetween phases calculated for B and V data points. None was detected. Wethen tried various means to remove BEx or at least to make it weaker. First, wefitted the complete B curve allowing PHOEBE to find a global phase shift ∆ ϕ that would center the main B -minimum at phase 0. Subsequently, with ∆ ϕ keptfixed, both B and V curves were fitted. This procedure indeed made the blueexcess smaller, but the V -fit became significantly worse both in the primary andthe secondary minimum. In a second series of experiments we fitted the curveswith the descending branch removed from either B or B and V primary minima,allowing for a global phase shift or keeping it fixed at 0. Since the residuals didnot look any better in any of those fits, we had to accept the standard solutionas the best one we were able to obtain. The encouraging finding was that theparameters of all the trial fits did not differ from the standard ones by morethan a factor of ∼ J orb , possibly by magnetic braking (see e.g. Eggleton andKiseleva-Eggleton 2002). At the present value of J orb the minimum orbitalseparation (which is achieved when M s = M p ) would be 0.94 R ⊙ – far too smallto accommodate two 0.8 M ⊙ stars. Of course, the loss of J orb must have occurredafter the equalization of masses, i.e. when the original mass ratio was reversedand the orbital separation began to increase.Numerous spectroscopic and photometric effects observed in Algol-like sys-tems are attributed to three dynamical agents: a stream of matter flowing out ofthe secondary, a regular or transient accretion disk formed by the stream aroundthe primary, and shock waves excited where the stream hits the disk or directlyimpacts the primary. V60 is a compact system in which there is no space fora regular accretion disc (e.g. Richards 1992), so that the stream directly hitsthe primary and induces shock waves(s) in its atmosphere. BEx, if real, mustalso originate in a shock. The problem is that the shock cannot be localized inthe standard place where the trailing hemisphere of the secondary is hit by thestream (S1 in Fig. 5): if that were the case, then BEx would show up on the descending branch of the main minimum. We calculate that if a particle leavingthe L point is to miss the trailing hemisphere and land onto the leading one(path a ending at S2 in Fig. 5) an initial velocity of ∼ v orb is needed, where v orb is the orbital velocity of the secondary around the mass center. Since inreality the initial velocity is on the order of the thermal velocity, i.e. about atenth of v orb , the stream must follow path b in Fig. 5 and hit the star at S1.Another shock at S2 can only be formed by the matter reflected off the primaryand flowing along the continuous line in Fig. 5. Such an interpretation is not anew one – in fact, it closely resembles the schematic Algol model derived fromspectroscopic observations by Gillet et al. (1989) and shown in their Fig. 3.Unfortunately, V60 is too faint for a detailed spectroscopic study, and the onlyobservational proof for the existence of S2 would be a UV emission coincidingin phase with BEx.We note that speculations about the possibility of stream reflection are notentirely unrealistic: a partial reflection was observed in models of flows in acataclysmic binary obtained by Rozyczka (1987). Admittedly, in those simula-tions the stream reflected off the accretion disk, but the physics involved wassufficiently simple that the results may be safely applied to a stellar atmosphere.It should also be mentioned that a reflection from the primary component in anAlgol-type system was observed in simulations performed by Richards (1998),however it was to a large extent predetermined by boundary conditions.Assuming the above explanation of the origin of BEx is feasible we still haveto explain why the emission from S2 is only visible in a narrow range of phases,and why the emission from S1 is not visible at all. The only possibility we seeis that both shocks are hidden behind gas stream(s): S1 entirely, and S2 partly.This speculation can be verified by detailed hydrodynamical simulations whichare beyond the scope of this paper. Acknowledgements.
We thank Joe Smak for helpful discussions and forthe permission to use his code for integration of particle trajectories. JK and MRwere supported by the grant 2012/05/B/ST9/03931 from the Polish NationalScience Centre.
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