Long-Term Variation of the Spin Period of a Magnetic Cataclysmic Variable, MU Camelopardalis
Long-Term Variation of the Spin Period of a Magnetic Cataclysmic Variable, MU Camelopardalis
Journal of Astronomy and Space Sciences. 2011. Mar, 28(1): 9-12
Copyright ©2011, The Korean Space Science Society
This is an Open Access article distributed under the terms of theCreative Commons Attribution Non-Commercial License( permits unrestrictednon-commercial use, distribution, and reproduction in any medium,provided the original work is properly cited.
  • Received : December 20, 2010
  • Accepted : February 11, 2011
  • Published : March 15, 2011
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About the Authors
Ami Yun
Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea
Yonggi Kim
Institute for Basic Science Research, Chungbuk National University, Cheongju 361-763, Korea
Chul-Sung Choi
Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea

Results of an analysis of 11 nights of R-filter CCD photometry data of an intermediate polar MU Camelopardalis (MU Cam) obtained at the Korean 1.0 m telescope at Mt. Lemmon are reported. After checking the spin period with our data, P spin =0. d 01373801(59), we compiled the reported data of maxima timing and an O-C diagram analysis has been carried out to understand the spin period variation. A significant spin period variation was detected, and fitting the O-C points to a cubic parabola led to an ephemeris of BJD max = 2453682.4178(94) + 0.0137380(13) E − 2.07(55)× 10 -11 E 2 + 2.28(52) × 10 -15 E 3 . The torque experienced by the magnetic compact star accreting in a disk is estimated as τ ≈1.815×10 35 gcm2 / s 2 in a simple approximation in order to show how important monitoring the period variation is. Thus we conclude that monitoring the long-term spin period variation will help to understand the physical condition of magnetic compact stars.
MU Camelopardalis (MU Cam) was first observed by the ROSAT All-Sky Survey (RASS) as an X-ray source, 1RXS J062518.2+733433, and later it has identified as an optical counterpart of this X-ray source by Kazarovets et al.(2006). Wei et al. (1999) classified this object as a cataclysmic variable with the spin period of 0.d01374127(5) and the orbital period of 0. d 19661(27). Even though no definite characteristics about the eclipse have been reported yet, the optical pulse profile represents a sinusoidal single peak. Staude et al. (2003) reported a relativly strong HeII emission line which shows the existence of photons able to ionize the atoms. This characteristic has been discussed by other authors (Araujo-Betancor et al. 2003,Staude et al. 2003, 2008, Kim et al. 2005a, Kozhevnikov et al. 2006). These observational characteristics led to the classification of this object as an intermediate polar or DQ Her type magnetic cataclysmic variable.
The spin period of intermediate polars generally vary in the course of time (Warner 1986, 1995, Patterson 1994,Hellier 2001). Many corrections of the MU Cam spin period have been reported by several authors (Araujo-Betancor et al. 2003, Staude et al. 2003, Kim et al. 2005a). In order to study the rotational evolution of magnetic white dwarfs in intermediate polars, a long time-base monitoring of the spin period variation is definitely needed.This object has been included in the list of key targets of the inter-longitude astronomy (ILA) project (Andronov et al. 2003). As results of this project, deceleration and acceleration of the spin in the intermediate polars have already been detected: deceleration in BG CMi by Kim et al. (2005b) and alternatively, acceleration in FO Aqr (Andronov et al. 2005).
In this paper, we present results based on 11 nights of R charge-coupled device (CCD)-photometry obtained in 2005-2006 with a 1 m telescope of the Korean Astronomy Observatory at Mt. Lemmon in the USA.
MU Cam was observed with a 2 K by 2 K CCD camera mounted on the 1 m telescope at Mt. Lemmon Optical Astronomy Observatory during the 2005 and 2006 season. Given the CCD plate scale of 0.64 arcsec/pixel at f/7.5 Cassegrain focus, the image field of view was 22.2 arcmin by 22.2 arcmin. We obtained R-filter CCD photometry data from 11 nights from November 2005 to April 2006. The observational log is presented in Table 1 with exposure time and total observation points. A total of 907 points of observation were used for this study.
To determine the instrumental magnitudes of stars in the field of MU Cam, the IRAF/DAOPHOT package (Massey & Davis 1992) has been used. For the final determination of magnitudes, the computer program multi-column view by Andronov & Baklanov (2004) has been used, which uses the method of multiple comparison stars (Kim et al. 2004).
In the method of multiple comparison stars, an independent R brightness estimate of 7 bright stars in the vicinity of the MU Cam was made based on the method described in Kim et al. (2005a). The standardized R light curve has been obtained by using an artificial star which made it possible to increase accuracy estimates. The R magnitude of MU Cam varied from 15.5 mag to 14.7 mag in the 2005-2006 season as shown in Fig. 1 . A bright state and a faint state are not shown in this season, which is clearly seen by Kim et al. (2005a).
The spin period of MU Cam has been found from the
Lager Image
Spin folded light curve of MU Cam in 2005-2006 season. The used spin period is 0.d01373801(59) and the line is the connection of mean magnitude at each spin phase. The Y-axis represents the standardized magnitude and the X-axis the spin phase of MU Cam. The pulse phase has been repeated over two cycles.
power spectrum analysis (Lenz et al. 2005) using the usual Fourier transformation as following:
Lager Image
Here Z is a zero point of f(t), A i , Ω i Φ i are the amplitude at the frequency i , the peak frequency and the phase in the power spectrum, respectively. With the found spin period of 0. d 01373801(59), we constructed a spin folded light curve for MU Cam in the 2005-2006 season as shown in Fig. 1 .
Observational log of MU Cam.MU Cam: MU Camelopardalis.
Lager Image
Observational log of MU Cam. MU Cam: MU Camelopardalis.
Times of maxima using Gaussian fitting.Peak point, time and Gaussian sigma are A(0), A(1) and A(2) in Eq. (2).Constant is the constant value of fitted Gaussian curve. Sigma and perror are values in the best fitted Gaussian curve.
Lager Image
Times of maxima using Gaussian fitting. Peak point, time and Gaussian sigma are A(0), A(1) and A(2) in Eq. (2).Constant is the constant value of fitted Gaussian curve. Sigma and perror are values in the best fitted Gaussian curve.
MU Cam is a faint object (R magnitude~15.5-14.7 in the 2005-2006 season) and has a relatively short spin period, which leads to very small points of observation near the extremes. The exact estimation of times of extreme needs a very complicated numerical analysis. Such analysis will be presented separately elsewhere. In this paper, we want to check the general behaviour of the spin period in the time series. For this purpose a simple Gausian fitting has been adapted. The fitting equation is
Lager Image
where A(0), A(1) and A(2) are the peak value, the position at peak center and the Gausian width respectively. A total of 56 times of extremes have been found in our data, and 23 maximum timing data are used for the O-C analysis. These times of maxima obtained by Gaussian fitting are listed in Table 2 .
The found spin period of MU Cam, 0.d01373801(59), seems to be the same value as Staude et al. (2003) and Kim et al. (2005a) in the error interval. But it is necessary to check for the possible period variations, P , which are usually seen in intermediate polars.
Staude et al. (2003) presented a precise ephemeris,
Lager Image
using a compilation of their own maxima timings and maxima timings obtained from the photometric data of Arajo-Betancor et al. (2003). With this basic ephemeris, Kim et al. (2005a) tried to fit a cubic parabola to the O-C diagram with their timing in the season of 2004-2005 as well as the data of Staude et al. (2003), because the parabolic fit did not deviate significantly from the line. They found statistically significant variation in an ephemeris:
Lager Image
Adding our maxima timings of 2005-2006 to this O-C diagram and fitting to a cubic parabola leads to an ephemeris
Lager Image
which exhibits a possible trend to spin up. The fitting result is shown in Fig. 2 . Even if we see a clear variation of the spin period of MU Cam, it is unclear whether the spin period will become slower or faster in the future. Staude et al. (2008) suggested that MU Cam has different accretion states which causes to the significant change in brightness and also the change of the spin period. In order to study this problem in more detail, we need further monitoring of this interesting intermediate polar.
Recently, a deceleration of the spin period ( Pspin > 0 in BG CMi, Kim et al. 2005b) and an acceleration of the spin period ( Pspin < 0 in FO Aqr, Andronov et al. 2005) have been detected. This situation assumes that magnetic compact stars accreting in a disk should experience a torque more complex than the simple and easily calculated matter torque that Ghosh & Lamb (1979) explained theoretically. However, Patterson (1994) shows that the magnetic moment controls the spin rate of intermediate polars. The variation of accretion rate can cause the change of the magnetic moment of the compact star and the spin rate. On the observational point of view, monitoring the variation of the spin period of intermediate polars is very important for studies of the rotational evolution of magnetic white dwarfs in intermediate polars. Therefore, a long time-base monitoring is highly needed for these objects.
Even if a more complicated treatment is needed for understanding the angular momentum from the disk in the magnetic compact star, we can estimate the torque of MU Cam by using a simple consideration in order to
Lager Image
O-C values for times of spin maxima calculated with the linear ephemeris Eq. (3). The data published by Staude et al. (2003) are marked as x the data published by Kim et al. (2005a) are marked as + and our data are marked as ?. The curved line and dashed lines show the cubic ephemeris Eq. (5) and the corresponding 1σ error corridor.
show how important monitoring the period variation is.
The torque ( τ ) is a variation of the angular momentum (L) per unit of time. By using L = Iω and ω=2π/P, we obtain
Lager Image
where I is the moment of inertia (and ω is the angular velocity given by the spin period (P) of the star (ω=2π/P). With results of this paper ( P ≈ −4.07 ×10 -8 s / s and P = 0. d 013738008) as well as using the moment of inertia ( I ~10 50 g cm 2 , Frank et al. 2002), we obtain a torque of ≈ 1.815×10 35 gcm 2 / s 2 . It is also important to mention that the distance of MU Cam is unknown, so that a further estimate of the physical situation of this system in comparison with other intermediate polars is not possible. However, we conclude that monitoring the long-term spin period variation will help to understand the physical condition in magnetic compact stars. A detailed consideration of the accretion torque in magnetic compact stars will be published elsewhere.
This work was supported by the research grant of the Chungbuk National University in 2009.
Araujo-Betancor S , Gänsicke BT , Hagen H-J , Rodriguez-Gil P , Engels D 2003 1RXS J062518.2+733433: a new intermediate polar A&A 406 213 - 219    DOI : 10.1051/0004-6361:20030787
Andronov IL , Antoniuk KA , Augusto P , Baklanov AV , Chinarova LL 2003 Inter-longitude astronomy project: some results and perspectives A&AT 22 793 - 798    DOI : 10.1080/1055679031000124501
Andronov IL , Baklanov AV 2004 Monitoring of cataclysmic variables at Kolonica Observatory Astron Sch Rep 5 264 - 272
Ghosh P , Lamb FK 1979 Accretion by rotating magnetic neutron stars. III - Accretion torques and period changes in pulsating X-ray sources ApJ 234    DOI : 10.1086/157498
Hellier C 2001 Cataclysmic variable stars: how and why they vary Springer Verlag Berlin
Kazarovets EV , Samus NN , Durlevich OV , Kireeva NN , Pastukhova EN 2006 The 78th name-list of variable stars IBVS 5721 1 -
Kim YG , Andronov IL , Jeon YB 2004 CCD photometry using multiple comparison stars JASS 21 191 - 200    DOI : 10.5140/JASS.2004.21.3.191
Kim YG , Andronov IL , Park SS , Chinarova LL , Baklanov AV 2005a Two-color VR CCD photometry of the intermediate polar 1RXS J062518.2+733433 JASS 22 197 - 210    DOI : 10.5140/JASS.2005.22.3.197
Kim Y , Androniv IL , Park SS , Jeon Y-B 2005b Orbital and spin variability of the intermediate polar BG CMi A&A 441 663 - 674    DOI : 10.1051/0004-6361:20052995
King AR , Frank J , Raine DJ 2002 Accretion power in astrophysics 3rd ed Cambridge University Press Cambridge
Kozhevnikov VP , Zakharova PE , Nikiforova TP 2006 Photometry of the intermediate polar 1RXS J062518.2+733433: characteristics of its periodic brightness variations ARep 50 902 - 914    DOI : 10.1134/S1063772906110047
Lenz P , Breger M 2005 Period04 user guide CoAst 146 53 - 136    DOI : 10.1553/cia146s53
Massey P , Davis LE 1992 A user’s guide to Stellar CCD photometry with IRAF
Patterson J 1994 The DQ Herculis stars PASP 106 209 - 238    DOI : 10.1086/133375
Staude A , Schwope AD , Krumpe M , Hambaryan V , Schwarz R 2003 1RXS J062518.2+733433: a bright soft intermediate polar A&A 406 253 - 257    DOI : 10.1051/0004-6361:20030705
Staude A , Schwope AD , Schwarz R , Vogel J , Krumpe M 2008 The changing accretion states of the intermediate polar MU Camelopardalis A&A 486 899 - 909    DOI : 10.1051/0004-6361:20067013
Warner B 1995 Cataclysmic variable stars Cambridge University Press Cambridge
Warner B 1986 Multiple optical orbital sidebands in intermediate polars MNRAS 219 347 - 356
Wei JYDW , Xu XY , Dong JY , Hu 1999 An AGN sample with high X-ray-to-optical flux ratio from RASS. I. The optical identification A&AS 139 575 - 599    DOI : 10.1051/aas:1999514