Photometric and Spectroscopic analysis of four contact binaries
TT HE A STRONOMICAL J OURNAL
Typeset using L A TEX twocolumn style in AASTeX62
PHOTOMETRIC AND SPECTROSCOPIC ANALYSIS OF FOUR CONTACT BINARIES P ANCHAL , A.
1, 2
AND J OSHI , Y. C. Aryabhatta Research Institute of observational sciencES (ARIES). Nainital, Uttrakhand, India. Department of Physics, DDU Gorakhpur University, Gorakhpur, India. (Received October 07, 2020; Accepted February 25, 2021)
ABSTRACTWe present the photometric and spectroscopic analysis of four W UMa binaries J015829.5+260333 (hereinafteras J0158), J030505.1+293443 (hereinafter as J0305), J102211.7+310022 (hereinafter as J1022) and KW Psc. The
V R c I c band photometric observations are carried out with the 1.3-m Devasthal Fast Optical Telescope (DFOT). Forlow resolution spectroscopy, we used 2-m Himalayan Chandra Telescope (HCT) as well as the archival data from4-m LAMOST survey. The systems J0158 and J0305 show a period increase rate of 5 . ± . × − days yr − and 1 . ± . × − days yr − , respectively. The period of J1022 is found to be decreasing with a rate of4 . ± . × − days yr − . The period analysis of KW Psc displays no change in its period. PHOEBE packageis used for the light curve modeling and basic parameters are evaluated with the help of GAIA parallax. The asymmetryof light curves is explained with the assumption of cool spots at specific positions on one of the components of the sys-tem. On the basis of temperatures, mass ratios, fill-out factors and periods, the system J1022 is identified as W-subtypesystems while the others show some mixed properties. To probe the chromospheric activities in these W UMa binaries,their spectra are compared with the known inactive stars spectra. The comparison shows emission in H α , H β and Ca II .To understand the evolutionary status of these systems, the components are plotted in mass-radius and mass-luminosityplanes with other well characterized binary systems. The secondary components of all the systems are away from ZAMSwhich indicates that secondary is more evolved than the primary component. Keywords: methods: observational – techniques: photometric – spectroscopic – binaries: eclipsing – stars:fundamental parameters INTRODUCTIONEclipsing binaries (EBs) are the key sources to determinestellar parameters with high precision. One interesting classof EBs is contact binary stars (CBs). These are low tempera-ture systems with components sharing a convective envelope.Due to the contact geometry, their temperatures are almostsame and mostly they show equal size primary and secondaryminima (Kuiper 1941; Kraft 1967; Lucy 1967, 1968). The WUMa-type CBs (EWs) are particularly interesting as these aremore abundant than other type of EBs (Shapley 1948). Sec-ondly, the closeness of components of these systems allowsus to directly perceive interaction between them and their at-mosphere. Their orbital period is less than a day and both thecomponents in EWs are located on or just above the main se-quence with spectral type later than F (Kraft 1967; Okamoto& Sato 1970; Moss 1972; Bilir et al. 2005). In most of theEWs deeper primary minima occurs when larger and more [email protected] massive component passes in front of the smaller, less mas-sive component. However, reverse can also occur in somecases. EWs are further divided into A and W-subtypes (Bin-nendijk 1970). The A-subtype systems are earlier spectraltype with higher mass and luminosity as compared to W-subtypes. In A-subtype systems, mass-ratio ( M / M ) is gen-erally less than 0.5 and moderate or insignificant activity isobserved. In W-subtype systems, less massive component ishotter and there is continuous change in the period with time(Binnendijk 1970; Ruci´nski 1973).Many previous studies explain the origin of CBs fromsmall period detached EBs (DEBs) (e.g., van’t Veer &Maceroni 1989; Li et al. 2004). The loss of angular mo-mentum (AML) due to magnetic braking is assumed to beleading formation mechanism for CBs (Li et al. 2007). Theejection of mass due to magnetic activities can result in de-crease in orbital or spin angular momentum, which can bringboth components close to each other (Huang 1966; Okamoto& Sato 1970; Vilhu 1982). If AML continues even aftercontact phase, it can result in mass transfer between the a r X i v : . [ a s t r o - ph . S R ] F e b P ANCHAL & J
OSHI components. Evolution of EWs depends upon AML, massloss and mass transfer between the two components (St˛epie´n& Gazeas 2012; Yildiz & Do˘gan 2013). Analysing the LAM-OST data for 7938 EWs, Qian et al. (2017) determined theparameters of CBs e.g., gravitational acceleration (log g),metallicity, temperature, radial velocity and found that about80% EWs have metallicity less than zero, which implies thatEWs are old population systems. Many EWs are found tobe magnetically active due to dynamo mechanism. The pres-ence of magnetic field effects their evolution (Kraft 1967;Eker et al. 2008). Most of the EWs show asymmetrical lightcurves (LCs) i.e. difference in brightness at phases 0.25 and0.75. This is generally explained by the presence of cool orhot spots on their surface. This effect is known as O’Connelleffect (O’Connell 1951). However, the amount of this asym-metry can change with course of time due to evolution andmovement of spots on the stellar surface.In this work, we present the multi-band photometric andlow-resolution spectroscopic analysis of four EWs. Thesetargets are chosen from Catalina Real Time Transient Sur-vey (CRTS) which provides a catalog of ∼ ,
000 pe-riodic variables (Drake et al. 2014). Out of these vari-ables ∼ ,
000 are classified as contact or ellipsoidal bina-ries. The J0158 ( α = 01 h m s . δ = + ◦ (cid:48) (cid:48)(cid:48) ),J0305 ( α = 03 h m s . δ = + ◦ (cid:48) (cid:48)(cid:48) ), J1022( α = 10 h m s . δ = + ◦ (cid:48) (cid:48)(cid:48) ) and KW Psc( α = 22 h m s . δ = + ◦ (cid:48) (cid:48)(cid:48) ) are EWs, withapproximate period of 0.227665, 0.246984, 0.2584680 and0.234276 day, reported as in the CRTS Catalog. The list oftargets and related information is given in Table 1. Table 1.
Basic information about the sources taken from differentsurveys
Source RA DEC Period V B-V J-K Parallax(J2000) (J2000) (days) (mag) (mag) (mag) (mas)J0158 01:58:29.5 +26:03:33 0.227665 12.71 0.629 0.305 1.445J0305 03:05:05.1 +29:34:43 0.246984 12.18 0.952 0.668 6.344J1022 10:22:11.7 +31:00:22 0.258468 12.53 0.792 0.494 3.702KW Psc 22:58:31.7 +05:52:23 0.234276 12.16 0.980 0.593 7.055 a a The (B-V) is taken from APASS survey (Henden et al. 2015), (J-K) istaken from 2MASS survey (Skrutskie et al. 2006) and the parallax is fromGAIA (Gaia Collaboration et al. 2020).
The paper is structured as follows: The information aboutphotometric and spectroscopic observations is given in Sec-tion 2. The period estimation and period change is discussedin Section 3 which is followed by photometric analysis inSection 4. The procedure used to determine physical param-eters is described in Section 5. The spectroscopic analysisof these EWs is provided in Section 6. The final results arediscussed in Section 7. OBSERVATIONS
Table 2.
The observation log for the targets observed using 1.3-mDFOT.
Object Date of Start Jd End Jd Total Exposure Obs.obs. frames time time(2450000+) (2450000+) (V,R,I) (sec) (hrs)2018-11-20 8443.1216 8443.3557 51, 50, 50 120,50-60,50 5.62J0158 2018-12-27 8480.1687 8480.2068 06, 06, 06 180,120,80 0.912019-10-14 8771.1721 8771.4613 84, 84, 84 40, 25, 20 6.942018-11-26 8449.1484 8449.3725 57, 56, 55 75, 35, 30 5.382018-12-01 8454.3645 8454.3779 04, 04, 04 75, 35, 30 0.322018-12-21 8474.2458 8474.3154 18, 18, 18 75, 35, 30 1.67J0305 2018-12-22 8475.0528 8475.1139 15, 15, 15 75, 35, 30 1.472018-12-27 8480.2023 8480.2422 10, 10, 10 75, 35, 30 0.962019-01-17 8501.0352 8501.1620 32, 32, 32 75, 35, 30 3.042019-11-10 8798.1963 8798.4309 66, 66, 66 75, 35, 30 5.632019-03-19 8562.1683 8562.2574 21, 20, 20 60, 35, 30 2.142019-03-20 8563.1543 8563.1805 08, 07, 07 60, 35, 30 0.63J1022 2019-03-21 8564.1612 8564.2565 26, 27, 27 60, 35, 30 2.292019-04-01 8575.1951 8575.2849 24, 24, 24 60, 40, 30 2.162019-04-02 8576.2056 8576.2341 08, 08, 08 60, 40, 30 0.682018-10-11 8403.0627 8403.1523 25, 25, 25 30, 25, 20 2.152018-10-12 8404.1082 8404.1592 15, 15, 15 30, 25, 20 1.222018-10-20 8412.0703 8412.2057 42, 41, 41 30, 25, 20 3.25KW 2018-11-26 8449.0536 8449.1280 20, 20, 20 70, 25, 20 1.79Psc 2018-12-01 8454.0309 8454.0706 10, 10, 10 70, 25, 20 0.952018-12-27 8480.0801 8480.1280 15, 15, 15 30, 25, 20 1.502019-10-14 8771.1260 8771.1495 07, 07, 07 30, 30, 30 0.55
Photometry
The photometric observations of these targets have beenacquired from the 1.3-m DFOT, Nainital employing a 2 k × k CCD detector having a field of view of ∼ (cid:48) × (cid:48) . As ob-servations were carried out on different nights having vary-ing moon illuminations, the exposure time varied across theframes. The total number of frames collected for J0158,J0305, J1022 and KW Psc were around 140, 200, 85 and130, respectively in each band ( V R c I c ). Observing log forphotometric observations is given in Table 2. Table 3.
Parameters of targets from the LAMOST data
Targets Date T ef f Sub logg Fe/H SNR(K) class (dex)J0158 08-12-2014 6151 F7 4.033 0.178 428.4414-11-2014 4917 G9 4.451 -0.423 239.10J0305 19-11-2014 4839 G9 4.358 -0.406 189.3103-01-2015 4721 K5 4.410 -0.490 276.6002-02-2012 5382 G8 4.317 -0.259 245.76J1022 26-12-2013 5211 G8 4.142 -0.380 58.9706-04-2015 5305 G7 4.306 -0.375 232.12KW Psc 01-11-2012 4822 G9 4.485 -0.414 63.41
All the pre-processing steps like bias subtraction, flat field-ing, cosmic ray removal were completed using IRAF rou-tines. The instrumental magnitudes of target stars and com-parison stars were computed by aperture photometry us-ing DAOPHOT (Stetson 1992). Initially, five nearby fieldstars were selected having brightness similar to our tar-HOTOMETRY AND SPECTROSCOPY OF CONTACT BINARIES 3 m a g J0158 IR+0.2V+0.4
Phase m a g J1022 IR+0.08V+0.16
Phase -0.40.00.40.8 KW Psc IRV
Figure 1.
The VRI band observed LCs of the sources. The different symbols show different date of observation. gets for preparing differential LC. On the basis of differen-tial LCs (Target star-Comparison star and Comparison star-Check star), most appropriate comparison stars and checkstars were selected. For J0158, J0305, J1022 and KW Psc,we used TYC 1760-1359-1, TYC 1795-913-1, TYC 2510-242-1 and TYC 575-86-1 as comparison stars, respectively.The observed LCs in VRI bands are shown in Figure 1.2.2.
Spectroscopy
The Large sky Area Multi-Object Fibre SpectroscopicTelescope (LAMOST) is a 4-m aperture telescope with afield of view (FoV) of 5 ◦ × ◦ . Such large FoV and a com-bination of 4000 fibers makes it a highly efficient tool forspectroscopy. It covers a spectral range of 370 nm to ∼ ∼ . The parametersmentioned in LAMOST database for these sources are givenin Table 3. The spectral type was again estimated using thePyHammer, which uses empirical stellar spectra library withspectral types ranging from O5 to L3 and metallicity rangingfrom -2.0 dex to +1.0 dex. It covers a spectral range of 365to 1020 nm (Kesseli et al. 2017, 2020).In addition to LAMOST spectroscopic data, HimalayaFaint Object Spectrograph Camera (HFOSC) on 2-m HCTwas also used for observations. The observing log for these http://dr5.lamost.org/ Table 4.
The log of spectroscopic observations for the targets ob-served using 2-m HCT.
Object Date Mid-UT Mid-UT Exposure SNR(for GR7) (for GR8) (Sec)J0158 2019-11-17 14:02 14:33 1500 106J0305 2019-11-17 15:07 15:33 1500 92J1022 2019-11-17 22:31 22:56 1500 111KW Psc 2019-11-17 12:57 13:23 1500 100 observations is given in Table 4. The combination of Gr7 andGr8 grisms were used for observations. The Gr7 has a spec-tral range of 380-684 nm and a resolution of 1330. The Gr8provides a wavelength range of 580-835 nm with resolutionof 2190. For Gr7 spectra FeAr arc lamp and for Gr8 FeNearc lamp were used for wavelength calibrations. For spec-troscopic data reduction, IRAF package was used. Reducedcalibrated spectra were normalized for further analysis. ORBITAL PERIODThe temporal variation in the orbital period of CBs pro-vides useful information about mass transfer rate, presenceof third body and other characteristics. Although Drake et al.(2014) mentioned the approximate period of these systems,their periods were further determined with the present datausing the Period04 software (Lenz & Breger 2004). Figure 2shows the power spectra corresponding to all the four sources using present data (green color) and archival data (blackcolor)
The phase folded LC were plotted and visually anal-ysed corresponding to these peaks. While for the systemsJ0305 and KW Psc, the best phase folded LCs were achievedcorresponding to their highest peaks of power spectra, it wasthe nearby peaks close to the maximum peak in case of J0158and J1022 which gave the best phase folded LCs. As the LCof CBs can be represented by twofold sine waves, the actual P
ANCHAL & J
OSHI P o w e r J0158 Present datasuperWasp data 0.040.080.120.16 J0305 Present datasuperWasp data0 10 20 30 40
Frequency(days ) P o w e r J1022 Present datasuperWasp data 0 10 20 30 40
Frequency(days ) Figure 2.
Power spectra of four binary systems obtained using Period04. The power spectra obtained using SuperWASP data (for J0158, J0305and J1022) and CRTS (for KW Psc) is over-plotted. period of the system would be twice the period obtained fromperiodogram. The periods for J0158, J0305, J1022 and KWPsc are therefore found to be 0.447273 0.246982, 0.258484and 0.234298 days, respectively.
Since the spectra shownin Fig. 2 for each star are affected by strong side-lobesdue to our short observing runs, we also obtained peri-odograms using SuperWASP data for J0158, J0305 andJ1022 and CRTS data for KW Psc, which are over-plottedin Fig. 2. These periodograms show that periods ob-tained with the present data are very close to the periodsdetermined with those of the archival data. We furtherascertained our estimated periods through Period04 us-ing the python periodogram based on the Lomb-Scarglemethod (Lomb 1976; Scargle 1982) and similar valueswere found . While for later three systems, the newly es-timated periods are close to earlier periods given by Drakeet al. (2014) but for J0158 newly estimated period is almosttwice of that reported by Drake et al. (2014). The estimatedperiod of J0158 is however a good match to those reportedby Chen et al. (2018) and Heinze et al. (2019). The CRTStime series data used by Drake et al. (2014) was reanalyzedand found that the power spectra of J0158 as represented bytwo sine waves indeed gave a period of 0.45 day.The TOMs for primary or secondary eclipse were esti-mated with the help of Minima27 software using the Kwee& van Woerden (1956) method. To examine the periodchange, we searched for the multi-epoch photometric dataor any available TOM information for these sources in theliterature. Surveys like Catalina Sky Survey (CSS; Drakeet al. 2014), Wide Angle Search for Planets (SuperWASP; Butters et al. 2010), North Sky Variability Survey (NSVS;Wo´zniak et al. 2004), All Sky Automated Survey for Super-Novae (ASAS-SN; Jayasinghe et al. 2018) and others pro-vide a good database of photometric data. The three sources(J0158, J0305 and J1022) were observed in these surveys butwith the poor cadence. For systems J0305 and J1022, wewere able to find half or complete phase of LCs on differ-ent days in SuperWASP data as their period is around 0.25days. But for J0158, we could get only half LCs on differ-ent days as its period is ∼
10 hrs. We also constructed theLCs for these three sources from CSS multi-epoch data asCSS time resolution was less than the SuperWASP. The sys-tem KW Psc was not observed in any of the above surveysalthough we found 19 TOMs available for this system on O-C gateway . In the following sub-sections, we individuallyanalyze the four sources using their accumulated data.3.1. J0158
For J0158, a total of 27 TOMs (21 TOMs from Super-WASP data, 4 from ASAS data and 2 from our data) weredetermined, as given in sample Table 5. The updated linearephemeris is estimated as:
HJD o = 2453229 . ± . + . ± . × E (1)Here, HJD o represents TOM corresponding to primary min-ima and E is the number of epoch. The quadratic fit to the( O − C ) is shown in Figure 3 (a). The ( O − C ) shows an up-ward parabolic variation as shown in Figure 3 (a) which can http://var2.astro.cz/ocgate/ HOTOMETRY AND SPECTROSCOPY OF CONTACT BINARIES 5 -0.012-0.0060.0000.0060.012 ( O C ) (a) Parabola fitJ0158 TOMs0 4000 8000 12000 Epoch -0.010.000.01 ( O C ) ( O C ) (b) Parabola fitJ0305 TOMs0 5000 10000 15000 Epoch -0.0020.0000.002 ( O C ) Figure 3.
O-C diagrams for (a) J0158 and (b) J0305 with quadratic regression. The lower panels show the residuals of the fit. be represented by the following equation:( O − C ) = 0 . ± . − . ± . × − × E + . ± . × − × E (2)This trend shown by J0158 suggests a continuous increase inits period. The modified quadratic ephemeris can thereforebe expressed as: HJD o = 2453229 . ± . + . ± . × E + . ± . × − × E (3)On the basis of above equation, the rate of period increasewas estimated as 5 . ± . × − days yr − for the sys-tem J0158. The change in orbital period for contact binariesis normally due to the mass-transfer or mass-loss from onecomponent to the other which can be calculated from the re-lation given by Kwee (1958).1 M dM dt = q − q ) 1 P d pdt (4)Here, q is the mass ratio defined by M / M . The above equa-tion suggests that for a system with increasing period, the dM will be negative if q > q <
1. If the pe-riod of system is decreasing then q > dM and vice-versa. The negative dM corresponds to masstransfer from primary component to the secondary compo-nent. The positive period change rate for J0158 along with q < . × − M (cid:12) yr − . The M used in aboveequation in determined in Section 5. Table 5.
TOMs estimated for J0158, J0305, J1022 and KW Pscusing data from different surveys ID HJD o Error Min Cycle ( O − C ) ( O − C ) Ref(2450000+) (days) (days)J0158 3229.67908 0.00042 p 0 -0.00571 -0.00679 1J0158 3232.64338 0.00038 s 6.5 -0.00108 -0.00215 1... ... ... ... ... ... ... ..J0305 3228.68060 0.00041 p -3469 0.02795 0.00041 1J0305 3229.66817 0.00048 p -3465 0.02759 0.00005 1... ... ... ... ... ... ... ..J1022 4075.64602 0.00022 p -17365 -0.01739 0.00816 1J1022 4100.71649 0.00015 p -17268 -0.01984 0.00333 1... ... ... ... ... ... ... ..KW Psc 4354.42230 0.00010 p -2819 0.00596 0.00095 2KW Psc 5014.84300 0.00000 p 0 -0.00225 -0.00030 3... ... ... ... ... ... ... ..Here [1], [2] and [3] show TOMs estimated by SuperWASP, Gokay et al. (2010) andDiethelm (2010). This is only sample table.
J0305
For J0305, we were able to estimate 41 TOMs which com-prises 32 from SuperWASP, 1 from CSS, 4 from ASAS and4 from our data. The corresponding (O-C) diagram with aquadratic fit is shown in Figure 3 (b). Like J0158, this sys-tem also shows an upward parabolic trend. The updated lin-ear ephemeris for J0305 is given by:
HJD o = 2454085 . ± . + . ± . × E (5)The modified quadratic ephemeris for J0305 was determinedas: HJD o = 2454085 . ± . + . ± . × E + . ± . × − × E (6) P ANCHAL & J
OSHI -0.040.000.040.08 ( O C ) (a) Parabola fitJ1022 TOMs-15000 -10000 -5000 0 Epoch -0.0100.0000.010 ( O C ) -0.04-0.020.00 ( O C ) (b) Linear fitKW Psc TOMs0 5000 10000 15000 Epoch -0.0030.0000.003 ( O C ) Figure 4.
O-C diagrams for (a) J1022 and (b) KW Psc with quadratic and linear regression, respectively. The lower panels show the residuals.
Similarly, the second order polynomial fitted to ( O − C ) asshown in Figure 3 (b) is as follows:( O − C ) = 0 . ± . − . ± . × − × E + . ± . × − × E (7)Using the quadratic ephemeris equation, we found thatthe rate of period change for J0305 is 1 . ± . × − days yr − . We used Equation 4 to determine themass transfer rate in J0305 which is found to be 1 . × − M (cid:12) yr − . The increasing period and q < J1022
For J1022, we estimated 22 TOMs that includes 16 fromSuperWASP, 4 from ASAS and 2 from our data. The (O-C)diagram for J0122 is shown in Figure 4 (a). The quadraticfit shows downward parabolic variation. This means that pe-riod of J1022 is decreasing with time. The updated linearephemeris for J1022 is found to be
HJD o = 2458564 . ± . + . ± . × E (8)From the (O-C) diagram, the updated quadratic ephemerisfor J1022 was found as follows: HJD o = 2458564 . ± . + . ± . × E − . ± . × − × E (9)The rate of decrease in period, according to the above equa-tion, is found to be 4 . ± . × − days/year. Thedecrease in period can be attributed to AML via mag-netic braking, gravitational wave radiation (GWR) or mass loss/transfer. We also estimated period decay rate due toGWR and magnetic braking which are estimated using equa-tions given by Kraft et al. (1962) and Guinan & Bradstreet(1988), respectively. The period decrease rate due to GWRcorresponds to 2 . × − days/year which is very smallin comparison to the observed rate. The period decrease dueto magnetic braking is found to be 7 . × − days/yearwhich is ∼
2% of the observed period decay rate. There-fore most plausible mechanism behind the observed periodchange could be the mass transfer between the two compo-nents. We obtained a mass transfer rate of 2 . × − M (cid:12) per year from secondary to the primary which can explainthe period change in the system J0122.3.4. KW Psc
As mentioned earlier, KW Psc was not observed in anyof the surveys except ASAS. From previous studies (Gokayet al. 2010; Diethelm 2010, 2011, 2012, 2013), 23 TOMswere collected for KW Psc. From these values, the updatedlinear ephemeris is estimated as:
HJD o = 2455014 . ± . + . ± . × E (10)The (O-C) diagram for KW Psc is shown in Figure 4 (b) andthe residual plot is shown in the lower panel of Figure 4 (b).The ( O − C ) for KW Psc can be written as:( O − C ) = − . ± . − . ± . × E (11)The O-C diagram is a straight line with negative slope whichmeans that its period is almost constant over a period ofatleast 12 years during 2007 to 2019. PHOTOMETRIC ANALYSISHOTOMETRY AND SPECTROSCOPY OF CONTACT BINARIES 7For photometric analysis of LCs in different bands, weused PHOEBE-1.0 (PHysics Of Eclipsing BinariEs) pack-age (Prša & Zwitter 2005). It is an open source modelingprogram based on Wilson-Devinney code (Wilson & Devin-ney 1971) for computing theoretical photometric and radialvelocity curves in the binary systems. It can work with twodifferent minimization algorithms namely differential correc-tions and Nelder & Mead’s Simplex. In present analysis, dif-ferential corrections minimization algorithm was used. Aspresent systems are reported to be EWs, hence, the over-contact binary not in thermal contact mode was used duringtheir photometric analysis.4.1.
Effective Temperature
Although these sources were selected from Drake et al.(2014) but these were also observed in other surveys like Su-perWASP, ASAS, KELT, 2MASS, NSVS etc. as discussedin Section 2. Their magnitudes in B , V , J , H and K bandswere collected from available archival catalogs. We calcu-lated the effective temperature ( T e f f ) using the (J-H)- T e f f re-lation from Collier Cameron et al. (2007) as given below. T e f f = − . J − H ) + . J − H ) color index is taken from 2MASS and T e f f rep-resents effective temperature of the star. For J0158, J0305,J1022 and KW Psc, the T e f f is determined as 6140 ( ± ± ± ± T e f f is also calculated with( B − V ) o − T e f f relations given by Wang (1994) and Torres(2010). The T e f f obtained from different equations as well asthose provided in the LAMOST survey are listed in Table 6.It can be seen from the table that the T e f f obtained usingdifferent methods are almost similar for all sources exceptJ0305. Finally, we calculated the average temperature andused it as T e f f for the primary component during LC modelfitting. Table 6. T ef f (in ◦ C ) determined from different empirical relationsand LAMOST data. J0158 J0305 J1022 KW Psc Ref6140 ±
105 4829 ±
105 5440 ±
118 5047 ±
138 16274 ±
11 5445 ±
51 5380 ± ± ±
11 4826 ±
38 5299 ±
69 4822 ±
69 46156 ±
35 5125 ±
41 5369 ±
46 4921 ±
51 5Here [1], [2], [3], [4] and [5] represents the T ef f determined using relation by CollierCameron et al. (2007), Wang (1994), Torres (2010), LAMOST DR5 and the meantemperature used in present analysis. q-search and Modeling The accurate determination of mass-ratio requires multi-epoch radial velocity (RV) information for each component. Due to absence of RV data, q-search technique was used forthe estimation of q parameter from the photometric data (e.g.,Joshi et al. 2016; Joshi & Jagirdar 2017). In this process, wefixed the gravity darkening coefficients as g = g = 0 .
32 andbolometric albedo as A = A = 0 . T e f f of primary as determined in Section 4.1.Then, we varied the q parameter from 0.1 to higher values insteps of 0.02-0.05 and ran the PHOEBE program correspond-ing to each value of q. In this process, other parameters likesecondary T e f f , primary component surface potential ( Ω ),primary component luminosity ( L ) and inclination ( i ) are setas free parameters. The sum of squared residuals ( Σ res ) ob-tained corresponding to best fit is plotted verses correspond-ing q . The Figure 5 shows that the solution is converged atsome specific value of q corresponding to minimum Σ res for each system. The q is estimated as 0.55( ± ± ±
1) and 0.44( ±
1) for J0158, J0305, J1022 and KW Psc,respectively.The best q and corresponding parameters obtained in q-search are initial estimates. The Figure 5 shows that q-searchhas given a wide range of equiprobable q for J0305, J1022and KW Psc. The final parameters, associated errors anduniqueness of the these solutions were explored with the helpof PHOEBE scripter. The scripter was run for 15000 itera-tions with differential correction minimizations. All the pa-rameters e.g. i, q, secondary T e f f , Ω , Ω and L were setfree with initial values obtained during q-search process. Af-ter every 50 iterations a kick of ±
5% was introduced to allparameters. The fit converged to minimum after these kicksafter 5-10 iterations. The output was saved after each itera-tion. The final values were determined by guassian fitting tothe histograms of these iteration results. The Figure 6 showssome of the gaussian fitted histograms. For all four systems,the estimated parameters were almost similar to the best fitparameters obtained during q-search process. The final q forJ0158, J0305, J1022 and J2258 are found to be 0.67, 0.31,3.23, 0.42, respectively, after the gaussian fitting. The heuris-tic scanning was used for checking the stability of adoptedsolution in the nearby parameter space. Almost 50-60 valuesof q and i within ±
5% of the above obtained values were usedto generate a grid of ∼ q versus i in these models. It isa 2-D histogram representing the variation of chi squares inthe q-i parameter hyperspace obtained by heuristic scanning.The blue end of the color scale represents the minimum chisquare. The "+" signs indicates the position of final adoptedmodel in q-i space. It can be seen that determined models arein the bluer regions which corresponds to a better fit model.For J0158, the estimated input q is from 0.67( ± ANCHAL & J
OSHI ( r e s ) J0158 0.3 0.6 0.9 1.20.160.200.240.28 J03051 2 3 4 q ( r e s ) J1022 1.0 2.0 3.0 q Figure 5.
The estimation of q-parameter for the EWs marked at the top right corner of each panel. q N (a) Gaussian Fit
63 64 65 66 i( o ) N (b) Gaussian Fit Secondary T eff (K) N (c) Gaussian Fit N (d) Gaussian Fit Figure 6.
Hitograms obtained for four parameters using heuristic scanning and parameter kicking. mary T e f f is 6156 ( ±
35) K. The final photometric solutionsshow that the secondary T e f f is less than the primary T e f f by ∼
160 K. We determined fill-out factors for primary and sec-ondary components as 0.282 ( f , f ) respectively. The J0158LCs show small asymmetry at phases 0.25 and 0.75. This isa well known effect of CBs and known as O’Connel effect(O’Connell 1951). To understand this asymmetricity in theLCs of J0158, we considered a spot on primary while mod-eling it. It is not possible to identify the presence of spoton any component without Doppler imaging technique. Twodifferent set of sport parameters can generate similar LC. The non-uniqueness of spot parameters obtained using photomet-ric data alone is discussed previously by many authors. Ac-cording to Eker (1999), the reasonable accuracy in spot pa-rameters can be achieved only if photometric data accuracyis better than 0.0001 mag. We arbitrarily selected a cool spotfor all the systems. The position and other spot parameterswere decided on the basis of minimum cost function. Thebest fit model found that the spot was at co-latitude of 90 o and longitude of 145 o . The position of spot was fixed whiledetermining its radius and temperature ratio. The radius and T spot / T star were estimated as 17 o and 0.93.HOTOMETRY AND SPECTROSCOPY OF CONTACT BINARIES 9 q i ( ) (a) q i ( ) (b) q i ( ) (c) q i ( ) (d) Figure 7.
The q-i parameter space mapping for Figure 7 (a). J0158, Figure 7 (b). J0305, Figure 7 (c). J1022 and Figure 7 (d). KW Psc. The +sign represents the final model q-i. The low chi-square regions are represented by blue color and red color represents high chi-square regions. m a g J0158 IR+0.2V+0.4
ObservationModel without spotModel with spot
ObservationModel without spotModel with spot -0.06 0.00 0.06 r e s -0.06 0.00 0.060.60.91.21.5 m a g J1022 IR+0.08V+0.16
ObservationModel without spotModel with spot -0.40.00.40.8 KW Psc IRV
ObservationModel without spotModel with spot -0.4 -0.2 0.0 0.2 0.4
Phase -0.06 0.00 0.06 r e s -0.4 -0.2 0.0 0.2 0.4 Phase -0.06 0.00 0.06
Figure 8.
The Observed and model fitted LCs in
V RI bands as shown by red, green and blue open circles. The lower panels of each plot showthe residuals of the fitted model.
The observed LCs of J0305 have almost similar primaryand secondary minima. The primary and secondary T e f f aredetermined as 5125 ( ±
41) and 5112 ( ±
3) K, respectively.The temperature difference between components is ∼
10 Kwhich shows that they are in good thermal contact. J0305also shows asymmetry in the observed LCs. The (
Max - Max ) for J0305 is about 0.04 mag. The fill-out factor forJ0305 is 0.105. A cool spot on secondary was used whilemodeling the system J0305. Initially, spot was fixed at co-latitude of 90 o and longitude of 90 o but it was further moved towards the pole to get better fit. Finally, the best fit foundthe spot at co-latitude of 69 o and longitude of 75 o . The ra-dius and T spot / T star are estimated as 23 o and 0.88. The restof parameters are summarized in Table 7. For J1022, it canbe seen in Figure 1 that the primary and secondary minimaare at different levels. The photometric solutions show thatthe secondary T e f f is less than primary by ∼
300 K. The fill-out factor was found to be 0.177 and 0.194 for both primaryand secondary. Although LCs show very small asymmetric-ity, we still applied a cool spot on primary to improve our fit0 P
ANCHAL & J
OSHI -0.40.00.4 w -0.40.00.4 w -0.40.00.4 w -0.8 0.0 0.8 v -0.40.00.4 w -0.8 0.0 0.8 v -0.8 0.0 0.8 v -0.8 0.0 0.8 v Figure 9.
Spot distribution on surface of eclipsing binaries. The first, second, third and fourth row from upper shows geometry of J0158, J0305,J1022 and KW Psc with spots at phases 0, 0.25, 0.50 and 0.75, respectively. and determined the best fit parameters. The sum of squaredresiduals ( Σ res ) reduced to 0.02 from 0.024 after includingthe spot. The radius and T spot / T star are estimated as 19 o and0.95. The spot position was found at co-latitude of 94 o andlongitude of 235 o as shown in Figure 9.For KW Psc, we obtained secondary T e f f as 4830 ( ± T e f f , so, both the compo-nents are in good thermal contact. The fill-out factors werecalculated as 0.192 ( f ) and 0.231 ( f ). The (Max -Max )for KW Psc is about -0.02. For this asymmetry, we used acool spot on secondary at co-latitude of 76 o and longitude of120 o with radius and T spot / T star of 31 o and 0.96, respectively.The other parameters obtained from LCs fitting are given inTable 7. Figure 9 illustrates the geometrical representation ofthe systems having spots on specific positions. PHYSICAL PARAMETERSThe parameters like q , i , f , L / ( L + L ), r , r are esti-mated by modeling of observed LCs. All the four sourcesare observed in GAIA. The GAIA parallaxes ( π ) given in Ta-ble 1 are used to determine the absolute magnitude using : M V = m V − log (1000 /π ) + − A V (13)where M V , m V , π and A V represent absolute magnitude inV-band, apparent magnitude in V-band, parallax and extinc-tion in V-band. The π is in milli-arcsec. The A V is used Table 7.
Results from LC fitting for all the four systems. The valuesin parentheses are errors in last digits.
Parameters J0158 J0305 J1022 KW Pscq ( M / M ) 0.67(12) 0.31(1) 3.23(14) 0.42(1)i ( ◦ ) 64.58(44) 71.65(18) 75.41(72) 78.74(17) T (K) 6156(35) 5125(41) 5369(46) 4921(51) T (K) 5991(25) 5112(3) 5083(6) 4830(3) Ω Ω Ω Ω Ω in Ω out L / ( L + L )(V) 0.616 0.746 0.320 0.706 L / ( L + L )(R) 0.612 0.745 0.308 0.701 L / ( L + L )(I) 0.608 0.745 0.301 0.698 r (pole) 0.407 0.457 0.271 0.438 r (side) 0.433 0.492 0.283 0.469 r (back) 0.471 0.518 0.322 0.499 r (average) 0.436 0.488 0.291 0.468 r (pole) 0.341 0.268 0.461 0.298 r (side) 0.459 0.279 0.497 0.312 r (back) 0.403 0.315 0.525 0.353 r (average) 0.398 0.287 0.494 0.320 f , f from Schlafly & Finkbeiner (2011) and average m V fromDrake et al. (2014). The absolute V-band magnitudes arefound to be 3.284, 5.581, 5.309 and 6.232 mag for J0158,J0305, J1022 and KW Psc, respectively. For estimating ab-solute bolometric magnitude ( M bol ) from absolute magni-HOTOMETRY AND SPECTROSCOPY OF CONTACT BINARIES 11tude, the bolometric corrections were used from Worthey &Lee (2011) corresponding to the T e f f , metallicity and sur-face gravity of each system (-0.04, -0.24, -0.16 and -0.31 forJ0158, J0305, J1022 and KW Psc, respectively). The M bol for J0158, J0305, J1022 and KW Psc are found to be 3.244,5.341, 5.149 and 5.922 mag, respectively.The total luminosity ( L + L ) was determined using : L T ( L (cid:12) ) = L + L = 10 − . M bol − M bol (cid:12) ) (14)Here M bol (cid:12) is taken as 4.73 mag (Torres 2010). Using theabove equation, the total luminosity was calculated as 4.311,0.625, 0.745 and 0.366 in L (cid:12) units, for J0158, J0305, J1022and KW Psc, respectively. The luminosity for individualcomponent is determined by using the L / ( L + L ) obtainedfrom LCs fitting in PHOEBE. For J0158, J0305, J1022 andKW Psc, L is calculated as 2.655, 0.466, 0.238 and 0.258 L (cid:12) , respectively.Total luminosity in terms of T e f f , relative radii of primary( r ), relative radii of secondary ( r ) and separation of com-ponents (A) is given as: L T = T ( Ar ) + T ( Ar ) (15)Here, T and T are in solar temperature units ( T (cid:12) = 5770 K).The separation, A, is in solar radius unit. The relative radiifor primary or secondary is determined as: r i = ( r pole × r side × r back ) − / (16)Here r pole , r side , r back are obtained from the photometric LCsmodeling. The i is 1 for primary and 2 for secondary.The T and L T are already determined for all the systems.The T , r and r are determined by solution of LCs fittings.Finally, the Equation 15 was used for calculating the separa-tion between components. The separation between two com-ponents in the sources J0158, J0305, J1022 and KW Psc arefound to be 3.165, 1.772, 1.881 and 1.483 R (cid:12) , respectively. Table 8.
Absolute parameters determined using GAIA parallax andLC solutions for all the four systems. The values in parentheses areerrors in last digits.
Parameters J0158 J0305 J1022 KW Psca( R (cid:12) ) 3.165(121) 1.772(54) 1.881(49) 1.483(47) M ( M (cid:12) ) 1.262(171) 0.927(85) 0.313(27) 0.557(53) M ( M (cid:12) ) 0.846(189) 0.287(28) 1.011(97) 0.234(23) R ( R (cid:12) ) 1.381(53) 0.865(26) 0.547(14) 0.694(22) R ( R (cid:12) ) 1.259(48) 0.509(16) 0.929(24) 0.474(15) L ( L (cid:12) ) 2.655(182) 0.466(17) 0.238(9) 0.258(2) L ( L (cid:12) ) 1.655(113) 0.159(6) 0.507(19) 0.107(1) To determine the total mass ( M + M ) of the system, weused the Kepler’s law. The constant factor in the Kepler’slaw is described in terms of R (cid:12) , day, M (cid:12) . A P = 74 . M + M ) (17) Here A, P, M and M are in units of R (cid:12) , days, M (cid:12) and M (cid:12) ,respectively.Using the earlier estimated values, we determined the M + M as 2.108, 1.214, 1.325 and 0.790 M (cid:12) for J0158,J0305, J1022 and KW Psc, respectively. The mass of indi-vidual components ( M and M ) are determined using the q value obtained through the LCs fitting. The radii of primary( R ) and secondary ( R ) are determined from mean radii ( r i )and separation A by using following relation: R i = Ar i (18)The radii R i and A are in R (cid:12) units. Using the r i estimatedthrough the Equation (17), we calculated R i for each system.In Table 8, we give all the physical parameters determinedfor the four binary systems. The errors in these parametersare given in the parenthesis of each value which come as aresult of error propagated through various equations used todetermine the physical parameters considering the errors inindividual parameters.The position of these systems on M - L and M - R diagramare shown in Figure 10 along with the other previously stud-ied EWs (e.g., Yildiz & Do˘gan 2013). It can be seen thatsystems J0305, J1022 and KW Psc are near the group of Wsub-type EWs. The primary component of all the systems ismore closer to ZAMS as compared to the secondary. Usingthe mass and radius of previously studied cool contact bina-ries, Hilditch et al. (1988) and Maceroni & van’t Veer (1996)also noted similar trend in EWs. The secondary componentsare above ZAMS, which indicates that they have higher ra-dius than a main sequence star with similary mass. As sug-gested by Ste¸pie´n (2004), this is not possible only due to en-ergy transfer from primary to the secondary component, so,the secondary components must be more evolved with He-depletion cores. CHROMOSPHERIC ACTIVITIESThe phenomenon of magnetic activities is often seen in thelate type rotating stars having convective envelopes whichresult in the formation of star spots, flares or plagues. Thesurface chromospheric activity depends on stellar rotationrate. The spectral emission lines H α , H β , Mg I b triplet, Na
I D D , Ca II H & K , Ca II IRT etc are optical and near-infrared indicators of chromospheric activity (Barden 1984;Montes et al. 1995) and equivalent width of these lines pro-vide a good measure of activity level in the late type rotatingstars.In case of binary stars, the total flux in spectra at a spe-cific time contains contribution from chromospheric and pho-tospheric flux of both the stars. The reconstruction of ab-sorption profile and spectral subtraction techniques are com-monly used for studying chromospheric activity of stars,however, former is widely used in the case of binary sys-2 P
ANCHAL & J
OSHI -0.8 -0.4 0.0 0.4 log ( M / M ) -1.2-0.60.00.61.2 l o g ( L / L ) A-type primaryA-type secondaryW-type primaryW-type secondaryThis work primaryThis work secondary -0.8 -0.4 0.0 0.4 log ( M / M ) -0.4-0.20.00.20.4 l o g ( R / R ) A-type primaryA-type secondaryW-type primaryW-type secondaryOur data primaryOur data secondary
Figure 10.
The diagram shows the position of our systems with previously studies systems (Yildiz & Do˘gan 2013) on Mass-Luminosity andMass- Radius planes. The continuous lines are ZAMS taken from Mowlavi et al. (2012) corresponding to z=0.014. ( Å ) N o r m a li z e d i n t e n s i t y (a) H H
Ca IRTCa HK 2014-12-08J0158 spectraSynthetic spectraSubtracted spectra 4800 6000 7200 8400 ( Å ) N o r m a li z e d i n t e n s i t y (b) H H
Ca IRTCa HK 2014-11-142014-11-192015-01-03J0305 spectraSynthetic spectraSubtracted spectra
Figure 11.
The LAMOST spectra for (a) J0158 and (b) J0305 over plotted with synthetic spectra. The black continuous line shows thesubtracted spectra with excess emission lines. tems. The spectral subtraction technique is based on the as-sumption that the level of photospheric flux is almost same inthe stars having similar spectral type. This suggests that aninactive star of similar spectral type can be used to estimatethe photospheric flux contribution for an active star (Barden1984; Montes et al. 1995) which may be seen in the form ofexcess emission.The LAMOST spectra (for J0158, J0305 and KW Psc) andHCT spectra (for J0158, J0305, J1022 and KW Psc) are anal-ysed for chromospheric activity signatures. The noise in thespectra can also produce some emission like features in thesubtracted spectra, so, only the high SNR specra of objectsand inactive stars are selected. The inactive stars having small rotational velocity are appropriate candidates for thetemplate spectra due to less rotational broadening. Here, thesynthetic spectra is constructed using the STARMOD pro-gram (Huenemoerder & Ramsey 1984; Barden 1984) whichuses the inactive template spectra for both components ofEWs and generate a composite spectra after introducing ro-tational broadening and radial velocity shifts. The stars HD233641 (Wright et al. 2004), HD 238130, HD 77712, HD219829 (Strassmeier et al. 2000) and BD+43 2328 (Valdeset al. 2004) are used for preparation of composite syntheticspectra. The spectra obtained after subtracting syntheticspectra from observed spectra are shown in Figures 11 to 12.These spectra show emission in H α , H β and Ca II H & K HOTOMETRY AND SPECTROSCOPY OF CONTACT BINARIES 13 ( Å ) N o r m a li z e d i n t e n s i t y (a) H Ca IRTCa HK 2012-02-022013-12-262015-04-06J1022 spectraSynthetic spectraSubtracted spectra 4800 6000 7200 8400 ( Å ) N o r m a li z e d i n t e n s i t y (b) H H
Ca IRTCa HK 2012-11-01KW Psc spectraSynthetic spectraSubtracted spectra
Figure 12.
Same as in Figure 11 but for (a) J1022 and (b) KW Psc. N o r m a li z e d i n t e n s i t y J0158 spectra (HCT)Synthetic spectra J0305 spectra (HCT)Synthetic spectra4800 6000 7200 8400 ( Å ) N o r m a li z e d i n t e n s i t y J1022 spectra (HCT)Synthetic spectra 4800 6000 7200 8400 ( Å ) KW Psc spectra (HCT)Synthetic spectra
Figure 13.
The spectra of target sources obtained from the HCT (red color) and the synthesized spectra (blue color). and
Ca II IRT lines. Here, the spectra from HCT are shownin Figure 13 in red color while the synthetic spectra gener-ated from LAMOST data are shown with blue color in thesame figure. It is to be noted here that the spectral subtrac-tion technique has not been applied on HCT spectra due tounavailability of comparison stars in those observations.As we have earlier noticed asymmetry in the LCs of thesesystems which might have resulted due to some magnetic ac-tivities. The excess emission found in the differential spectraseems to confirm this notion. As SNR at both ends of spectrawas poor we therefore could calculate the equivalent widthof H α line only. We used the spectral range from 653.5 nm to659.5 nm and fitted Gaussian profile to determine the equiv-alent width. For J0158 and J0305 the equivalent widths were found to be 0 . ± .
017 and 1 . ± . . ± . . ± . DISCUSSION AND CONCLUSIONThe detailed study of EWs are useful in understanding theirformation mechanism and different evolution stages. A long-term photometric and spectroscopic study can thus throwlight on their period change and associated processes likemass transfer, third body and spot evolution. In this study,we present the multi-band photometric and low resolutionspectroscopic analysis of four EWs. Due to absence of ra-dial velocity curves of these systems, mass ratios of the bi-nary components are determined from photometric LCs with4 P
ANCHAL & J
OSHI the q -search method. For all the systems q is found to beless than 0.7 except J1022 for which a higher value of 3.23is found. As the components are close to each other in EWs,the interaction between the components is quite common inthese systems. This can result in a period change throughmass transfer/loss among components. The presence of ad-ditional companion or long term cyclic magnetic activity isalso prevalent for contact binaries which can cause cyclicvariation in the (O-C) diagram. For the four EBs studiedhere, we could able to collect the TOM information duringlast 13-15 years only and with this limited time span it wasvery difficult to retrieve any specific information about thelong term cyclic variations. However, a preliminary (O-C)analysis of these systems shows a change in period for threesystems (J0158, J0305 and J1022) but no such variation wasnoticed in the case of KW Psc. The mass loss can be thereason for change in their periods hence we also calculatedmass-transfer rates for these systems.Asymmetry in LCs of all the systems is observed and levelof asymmetry show change from V to I band with beingmaximum in V band.The LCs from SuperWASP data showthat these systems exhibit variation from positive O’Connellto negative O’Connell effect with passage of time. Eventhe depths of eclipsing minima are seen to be changingin these two systems. The analysis of present observa-tions and the SuperWASP observations shows that for J0305 Max − Max (2) varies from 0.06 to -0.06. Similarly, this dif-ference for J1022 varies from 0.04 to -0.2. This behaviour in-dicates that spots are not fixed but form and move with time.Different empirical relations are available in literature fordetermining parameters like mass, radius, luminosity etc.However, these relations can be biased due to the specificEWs sample used during their formulation. Therefore, inthe present analysis, we followed the procedure adopted byLiu et al. (2020) for calculating the physical parameters. Re-cently Sun et al. (2020) derived parameters of 2335 late-typecontact binaries from the CSS survey including the systemJ0305. They found a mass-ratio of 0.19 for J0305 which issmaller than the estimated value of 0.31 in the present study.However, it should be noted that Sun et al. (2020) used only V band data in their analysis and a primary component coolerby 150 K than the present value hence some disagreementbetween the two estimates could be possible . The totalmass ( M t ) determined for all the systems is above minimumtotal mass limit for EWs except for KW Psc. This indicatesthat significant amount of mass loss had taken place in KW Psc system in the past. As we have not found any periodchange in KW Psc during last 12 years, we believe that theobserved low mass of this system can be due to any previ-ous magnetic activities in the form of some burst. Never-theless, a more detailed study is required to find the exactcause of total low mass in this system. As W UMa type sys-tems with q > < H α , H β and Ca triplet region. Small emission is also visiblein Ca HK region but considerable amount of noise in blueregion makes it difficult to analyse. Although there is 3 to4 year difference between LAMOST spectroscopic observa-tions and our photometric observations, the presence of spotsin LCs modeling can still be assumed an indirect proof oftheir activities. The equivalent widths of different lines insubtracted spectra can give measure of magnetic activity inthese systems, however, further spectroscopic observationswith better resolution at different phases will be more usefulin the study of chromospheric activities in EBs. ACKNOWLEDGEMENTSThe work presented here has been carried out under theDST project "INT/AUSTRIA/BMWF/P-14". We thank thestaff of IAO, Hanle and CREST, Hosakote, that made theseobservations possible. The facilities at IAO and CREST areoperated by the Indian Institute of Astrophysics, Bangalore.Guoshoujing Telescope (the Large Sky Area Multi-Object Fi-bre Spectroscopic Telescope LAMOST) is a National MajorScientific Project built by the Chinese Academy of Sciences.Funding for the project has been provided by the NationalDevelopment and Reform Commission. LAMOST is oper-ated and managed by the National Astronomical Observato-ries, Chinese Academy of Sciences. In this work we havealso used the data from the European Space Agency (ESA)mission GAIA, processed by the GAIA Data Processing andAnalysis Consortium (DPAC). This work also make use ofthe Two Micron All Sky Survey and SIMBAD database.REFERENCES
Barden, S. C. 1984, in Bulletin of the American AstronomicalSociety, Vol. 16, 893 Bilir, S., Karatas, Y., Demircan, O., & Eker, Z. 2005, MNRAS,357, 497