Idling Magnetic White Dwarf in the Synchronizing Polar by Cam. the Noah-2 Project

Cent. Eur. J. Phys. • 6(3) • 2008 • 385-401 DOI: 10.2478/s11534-008-0076-3

Central European Journal of Physics

Idling magnetic white dwarf in the synchronizing polar BY Cam. The Noah-2 project

Research Article

Ivan L. Andronov12∗† , Kirill A. Antoniuk3, Vitalii V. Breus2, Lidia L. Chinarova2, Wonyong Han4, Young Beom Jeon4, Yonggi Kim56, Sergey V. Kolesnikov2, Joon Young Oh5, Elena P. Pavlenko3, Nikolay M. Shakhovskoy3

1 Odessa National Maritime University, Mechnikov str., 34, Odessa 65029, Ukraine 2 Astronomical Observatory and Department of Astronomy, Odessa National University, T.G. Shevchenko Park, Odessa 65014, Ukraine 3 Crimean Astrophysical Observatory, Nauchny 98409, Ukraine 4 Korea Astronomy and Space Science Institut, Daejeon 305-348, Korea 5 University Observatory, Chungbuk National University, Cheongju 361-763, Korea 6 Institute for Basic Science Research, Chungbuk National University, Cheongju 361-63, Korea

Received 21 December 2007; accepted 29 February 2008

Abstract: A multi-color study of the variability of the magnetic cataclysmic variable BY Cam is presented. The observations were obtained at the Korean 1.8 m and Ukrainian 2.6 m, 1.2 m and 38 cm telescopes in 2003-2005, 56 observational runs cover 189 hours. The variations of the mean brightness in different colors are correlated with a slope dR/dV = 1:29(4), where the number in brackets denotes the error estimates in the last digits. For individual runs, this slope is much smaller ranging from 0.98(3) to 1.24(3), with a mean value of 1.11(1). Near the maximum, the slope becomes smaller for some nights, indicating more ”blue” spectral energy distribution, whereas the night-to-night variability has an ”infrared” character. For the simultaneous UBVRI photometry, the slopes increase with wavelength from dU/dR = 0:23(1) to dI/dR = 1:18(1). Such wavelength dependence is the opposite of that observed in non-magnetic cataclysmic variables, in agreement with the model of cyclotron emission. The principal component analysis shows two components of variablitity with different spectral energy distributions (with a third at the limit of detection), which possibly correspond to different regions of emission. The highest peak in the scalegram analysis corresponds to the 200 min spin variability, its quarter and to the 30 min and 8 min QPOs. The amplitudes of these components are dependent on wavelength and luminosity state. The light curves were fitted by a statistically optimal trigonometrical polynomial (up to 4th order) to take into account a 4-hump structure. The dependences of these parameters on the phase of the beat period and on mean brightness are discussed. The amplitude of spin variations increases with an increasing wavelength and with decreasing brightness. The linear ephemeris based on 46 mean minima for 2003–2005 is HJD 2453213:010(3) + 0:137123(3)E: The extensive tables of the original observations and of results of analysis are published in an electronic form. The nearby star GSC 4081-1562 was found to be an eclipsing red variable. PACS (2008): 97.80.Gm, 98.62.Mw, 97.30.Qt Keywords: cataclysmic variables • close binaries • X-Ray binaries • individual stars (BY Cam) © Versita Warsaw and Springer-Verlag Berlin Heidelberg.

∗ E-mail: [email protected] † E-mail: [email protected] 385 Idling magnetic white dwarf in the synchronizing polar BY Cam. The Noah-2 project

1. Introduction

Cataclysmic variables are close binaries consisting of a red dwarf which is filling its Roche lobe, and a white dwarf. Accretion structure is strongly dependent on the characteristics of the flow as well as on the magnetic field of the compact star (see e.g. monographs by Warner [1] and Hellier [2]). The object BY Cam (H0538+608) was discovered as an X-ray source by Forman et al. [3]. Remillard et al. [4] classified it as an AM Herculis-type system. Mason et al. [5, 6] provided near simultaneous polarimetry and phase- resolved spectroscopy and noticed extreme variations in the accretion geometry. Andronov and Fuhrmann [7] suggested that these variations are due to a small asynchronism between the spin and orbital rotation of the magnetic Figure 1. Finding chart for BY Cam. The size of the field is white dwarfs. This implies that there are slow periodic 5.6’, North is at the top and East isto the left. For a cross-identification, the stars from Henden and Honeycutt changes to the magnetic axis of the white dwarf (and cor- [21] (marked with “H”) and Sumner (B. Sumner (2000), responding changes to the accretion structure) in respect ftp://ftp.aavso.org/public/calib/sumner/bycam.seq) d (marked with “S”) are shown. of the red dwarf with a period of 14: 52 [8]. These changes are sometimes called “idlings” (or alternately scrollings or slewings). In classical polars, the white dwarf is synchronized with the orbital motion, but the orientation of the magnetic axis may undergo cyclic changes in respect to the central line of the rotating cataclysmic binary system. Such changes were called “swingings” [9], contrary to the idlings in the asynchronous polars caused by different orbital- and spin periods of the white dwarf. As the magnetic axis changes with respect to the secondary (donor star), the location of the accretion column above the white dwarf’s photosphere also change, as do other characteristics of the column. From the cyclotron humps in the infrared spectra, Crop- per et al. [10] estimated the magnetic field strength of Figure 2. Dependence of nightly mean brightness (in V and R filters) the white dwarf to be 41 MGs, which is larger than the on time. R observations are taken for all 4 telescopes, field strength in AM Her itself. This puts the object be- whereas V are shown only for the 1.8 m BOAO telescope. The error estimates of the correponding color index V − R tween relatively numerous groups of DQ Her-type stars is much smaller than that for the original colors because of (or intermediate polars) with rapidly rotating white dwarfs a much smaller amplitude in its variability. The transitions between the bright and faint states usually take weeks, but and the AM Her-type stars (or classical polars) which can sometimes occur in just one day. are synchronised [11]. Another asynchronous system was Nova Cyg 1975 = V1500 Cyg [12], thus the desynchro- nization may be caused by a Nova outburst. Two more recent asynchronous polars are known (V1432 Aql and CI relatively rare objects. Ind). Sometimes these stars are called BY Cam-type stars To study BY Cam, Silber et al. [8] have organized the [13, 14]. Noah Project with a large flow of data obtained during According to the last “live” electronic version of the cat- more than 40 nights. Mason et al. [16] have succeeded in alogue (dated 01.09.2006) by Ritter and Kolb [15], the explaining contradictions between different periods using number of classical, asynchronous and intermediate po- a model which alternates the active poles of the white lars is 77, 4 and 38 respectively, (from a total number of dwarf. In this paper, we report results from the “Noah- cataclysmic variables of 641). Asynchronous polars are 2” project initiated to study different types of variability

386 Ivan L. Andronov et al.

Figure 3. Dependence of the nightly mean color V −R on the brightness in R for the BOAO observations and the best ﬁt (Eq. 2).

Figure 4. The V − R diagram for the 4-harmonic fits to the BOAO data. The phase distance between two subsequent points Figure 5. The individual light (V;R) and color index (V − R) curves (points) for the BOAO data. The original data are plotted is 0.01P=2 min. The line R −R¯ = V −V¯ with an unity slope is shown for reference of individual slopes within 7 nights. once and are not repeated, but the fit is repeated for clarity. The four-harmonic fits for individual runs are shown by solid lines. Strong night-to-night variability of the shape is present, with an easy visual separation of the two curves observed in the faint state and five in the bright state.

2. Observations and comparison of this interesting object. We have obtained 56 nights of observational data for this project (more than the 40 stars nights initially planned for the Noah-1 project), and more attention is paid to the color information. Extensive tables 2.1. Observations of individual observations, and the model parameters are presented electroically. The observations were made using four observatories:

387 Idling magnetic white dwarf in the synchronizing polar BY Cam. The Noah-2 project

• Bohyunsan Optical Astronomy Observatory where the initial epoch corresponds to the minumum of (BOAO) of the Korea Astronomy Observatory and mean brightness. The light curves are modulated with this Space Science Institute (KASI). The observations period, thus the corresponding phase is important when were obtained with a thinned SITe 2k CCD camera comparing light curves from different beat cycles (see be- attached to the 1.8 m telescope. The instrumental low). Altogether observations were made on 56 nights: 7 V and R systems were used in a mode with with changing filters (VR, BOAO, 1.8 m, 33h); one night alternating filters. To determine instrumental in V (1.8 m); 4 nights with 3-sec photometry (R, ZTSh, magnitudes of stars, the IRAF/DAOPHOT package 2.6 m); and one in a mode of simultaneous 5-color 10-sec h [17] were used. photometry (UBVRI, AZT-11, 1.25 m, 4: 7). The remaining 47 runs consist of monochromatic CCD (R, K-380, 0.38 m) • The 2.6 m reflector ZTSh at the Crimean Astro- photometry. physical Observatory (CrAO) with the wide-R filter (partially overlapping with V). This was equipped with a new version of the photometer-polarimeter, 2.2. Comparison stars which allows determination of both linear and cir- cular polarization. The computer program used for The photometric BV standards in the field have been pub- the data reduction was introduced by Breus et al. lished by Henden and Honeycutt [21], of which some were [18]. chosen as comparison star candidates by Sumner1. They are marked in Fig. 11 by “H” and “S” with a number, • the 1.25 m reflector with AZT-11 UBVRI photo- respectively. Henden2 has published another (more ex- meter-polarimeter [19]. tended) sequence also in BV only, with magnitudes, which • The 38 cm K-380 relector at the CrAO. Some results are slightly different from that of Henden and Honeycutt of this monitoring have been published separately [21]. For the R photometry, no published standards have [20]. However, in the present study, we have re- been found. analyzed these data together with our new data to The brightness of the comparison star C0 (GSC 4094:2109) make a more complete study. was determined using the UBVRI photometer-polarimeter ◦ by linking to the standard star BD+27 2120 [22]: m m m m m U=10: 20, B=10: 11, V =9: 95, R=9: 74, I=9: 67 [23]. The magnitudes of the comparison star C7 (GSC 4081:280) m m from our measurements are U=15: 405, B=13: 468, m m m V =11: 762, R=10: 390, I=9: 359. These BV magnitudes are in fairly good agreement with another estimate B= m m 13: 473, V =11: 761 [21]. This star was used for photo- electric photometry at the 1.25 m telescope in CrAO. For the CCD photometry obtained at the 1.8 m BOAO telescope we used stars C1-C5 as the “artificial” comparison star3 [24, 25]. At the CrAO 38 cm telescope, star C11 was used as the comparison star, with C8 as the check star. To determine relative brightness of comparison stars Figure 6. The individual light curves (points) in R for the data obtained at 2.6 m Shain telescope. As in Fig. ??, The origi- used at different telescopes, we measured stars C7-C20 nal data are plotted once and are not repeated, but the fit on 10 pairs of CCD images obtained in the BOAO. As is repeated for clarity. The four-harmonic fits for individual V R runs are shown by solid lines. both BOAO and instrumental systems are close to the standard ones4 [26], no color correction was applied. The adopted brightness of comparison star C5 (GSC The V and R brightnesses of the comparison stars based m m 4081:509) is V =13: 373 and R=12: 595. Other published on the BOAO observations are shown in Table 2.2 (and m m m m values of V =13: 408±0: 008 [21] and V =13: 392±0: 0325 see a more detailed discussion below). The log of observations is presented in Table 2 (available only electronically). In an addition to usually presented 1 ftp:/ftp.aavso.org/public/calib/sumner/bycam.seq values, we have also added the phase for the mid-run 2 ftp://ftp.aavso.org/public/calib/bycam.dat 3 according to the beat period ephemeris [20] http://ksss.or.kr/dtp/J200409/kimyonggi.ps 4 http://ksss.or.kr/dtp/J200509/ykkim.ps Tphot:beatmin:(HJD) = 2453089:2473 + 14:568E (1) 5 ftp://ftp.aavso.org/public/calib/bycam.dat

388 Ivan L. Andronov et al.

m m accuracy is 0: 01-0: 03 [20]. For 3-sec integrations at the m m Table 1. Brightness of BY Cam and the comparison stars from the 2.6 m telescope, the accuracy is 0: 02-0: 03. BOAO observations (VR). The values of σ correspond to the r.m.s. scatter of a single observation in respect to the artificial comparison star. 2.3. New variable star GSC 4081:562 Star V σV R σR α h m s; δ The star C4 (GSC 4081:562, 2000 = 5 42 41 2000 = BY 14.867 0.320 13.992 0.442 ◦ 0 60 52 19”) was suspected to be an eclipsing variable in the C1 16.517 0.004 15.456 0.006 m m m m range 13: 27-13: 45 in V and 11: 43-11: 56 in R (based C2 12.982 0.001 11.815 0.001 on nightly mean values from the BOAO data). The am- C3 16.781 0.015 15.891 0.027 m m plitude variation is small (∆V = 0: 18; ∆R= 0: 13), the C4 13.375 0.003 11.490 0.004 m m color index varies from a maximum of V −R=1: 84 to 1: 89 C5 13.373 0.004 12.595 0.004 at the minimum, with an eclipse duration of a few days. C6 14.793 0.003 13.690 0.002 m The formal error estimates are smaller than 0: 003, but C7 11.762 0.001 10.390 0.001 m in the final publication, we round them to 0: 01. The C8 12.106 0.002 11.027 0.001 minimum occurred at JD 2453054. A very large color in- C9 13.610 0.007 12.824 0.007 m dex B − V =1: 856 argues for a late–type red component, C10 15.863 0.010 14.907 0.017 possibly a giant. Using the magnitudes at the maximum C11 14.523 0.003 13.678 0.002 and minimum, we have determined the magnitudes of the C12 16.383 0.017 15.451 0.041 m m eclipsed body: V =15: 32 and R=13: 82. The resulting C13 16.645 0.010 15.795 0.011 m color index V-R=1: 50 corresponds to a hotter star. Dur- C14 17.834 0.030 16.932 0.056 ing the night, some photometric waves were observed with C15 15.400 0.007 14.298 0.005 m a typical peak-to-peak amplitude ∼ 0: 02; which may be C16 13.997 0.005 13.216 0.003 caused by differences in extinction for stars with such dif- C17 15.347 0.010 14.370 0.004 ferent color indices. A detailed study of this object will C18 17.449 0.034 16.611 0.058 be published separately. C19 16.387 0.007 15.396 0.009 C20 17.424 0.016 16.564 0.030 C21 15.295 0.007 14.235 0.005 3. Active vs inactive states are in reasonable agreement with our data. This star was The prototype polar AM Her is characterized by tran- set as the “main” one, as it has a color index closest to sitions between high and low luminosity states, which active inactive that of the variable star. The magnitudes of C11 (GSC Hudec and Meinunger [27] called and re- m 4094:467) determined by Pavlenko [20] are V =14: 55, spectively. During the period 1928-1976 the star was m R=13: 96. These values have been used for the K-380 mostly in the high state with 7 “excursions” to the low d: and ZTSh data. This V magnitude coincides with the state, with durations of 130-700 Recently Ka a and USNO value, and is intermediate between our BOAO- Honeycutt [28] detected 10 inactive states in AM Her dur- m m based estimate V =14: 514 and the value 14: 572 [21] and ing 1990-2004, which seem to be more abundant than in coincides with the USNO value. However, the magni- previous decades. Based on their studies of magnetic and tude in R differs from the BOAO value more significantly: non-magnetic variables, they interpret relatively rare low m R=13: 68. Because of the difference between the photo- states as resulting from different mechanisms for the sys- metric systems used, there still may be some systematic tems above and below the period gap. Long-period sys- shifts, which are much smaller than the ∼ 1m amplitude. tems are the result of starspots at the secondary at the Thus we analyse the runs from different telescopes sepa- inner Lagrangian point [29], whereas for short-period sys- rately. tems the cause is irradiation feedback on the secondary All original observations (HJD, magnitude) are presented star [30, 31]. electronically in Tables 2.2, 3 (V , R data obtained in the Another mechanism which is effective in a case of chan- BOAO), 5 (ZTSh R data), 6 (UBVRI brightness, color and nelling the accretion flow close to the inner Lagrangian principal components, see section 6) and 7 (K-380 R data). point is a magnetic valve [32] combined with a “swinging The r.m.s. accuracy estimates for a single BOAO measure- dipole” [9], i.e. changing the orientation of the magnetic m ment from the brightness-scatter dependence are 0: 004- axis of the white dwarf on a time-scale of 3-11 yr. This is m m m 0: 007 (V ) and 0: 003-0: 013 (R) for the maximum and definitely not the case for BY Cam, where the spin-orbital minimum brightness, respectively. For the K380 data, the synchronization has not yet been reached. However, in

389 Idling magnetic white dwarf in the synchronizing polar BY Cam. The Noah-2 project

Table 2. Journal of observations of BY Cam: JD- integer part of the starting Julian date (used for a legend of the run, e.g. 52634V); HJDstart - begin of observations (HJD-2400000); telescope (Z=2.6 m, K=1.8 m, A=1.25 m, P=0.38 m); ﬁlter; exp - exposure in seconds; N - number of observations; duration of the run in days. In the electronic version of the table, there are additional columns: HJDfinish end of observations (HJD-2400000); magnitude range for individual data points mmax , mmin; nightly mean hmi and its accuracy estimate σ(hmi); r.m.s. deviation of the single observation from the mean σ(m); 'b - phase of the run center according to the “beat period” ephemeris T = 2453089:2473 + 14:568E [20]. The table is available on-line as Supplementary Data 1.

JD HJDstart Tel. Filter exp N Duration JD HJDstart Tel. Filter exp N Duration 53091 53091.23030 P R 121 66 0.13730 52634 52634.93815 K V 28 523 0.31725 53096 53096.29030 P R 181 8 0.02170 52966 52966.46461 Z R 3 1536 0.15014 53097 53097.24900 P R 181 30 0.07460 52967 52967.47386 Z R 3 2089 0.16433 53098 53098.23720 P R 164 57 0.14690 53022 53022.26800 P R 121 119 0.26880 53099 53099.26270 P R 216 49 0.14550 53022 53022.37087 A U 10 1216 0.19424 53100 53100.25430 P R 181 43 0.12200 53022 53022.37087 A B 10 1216 0.19424 53103 53103.25840 P R 181 64 0.15660 53022 53022.37087 A V 10 1216 0.19424 53105 53105.25480 P R 181 50 0.12630 53022 53022.37087 A R 10 1216 0.19424 53108 53108.30560 P R 181 12 0.02850 53022 53022.37087 A I 10 1216 0.19424 53112 53112.23240 P R 181 55 0.12970 53033 53033.92933 K V 105 175 0.29699 53113 53113.25170 P R 181 37 0.10970 53033 53033.93985 K R 105 176 0.28708 53114 53114.24320 P R 181 48 0.12120 53033 53033.94088 K V − R 48 325 0.28544 53317 53317.38640 P R 130 87 0.13250 53034 53034.92420 K V 53 126 0.34822 53318 53318.36800 P R 130 91 0.14640 53034 53034.92481 K R 106 125 0.34820 53319 53319.37450 P R 130 88 0.13340 53034 53034.92481 K V − R 48 236 0.34761 53320 53320.39170 P R 130 98 0.14990 53035 53035.92456 K V 105 107 0.16614 53321 53321.46440 P R 130 89 0.14640 53035 53035.92516 K R 105 107 0.16615 53331 53331.40630 P R 130 90 0.14020 53035 53035.92516 K V − R 48 200 0.16554 53332 53332.39910 P R 138 86 0.14040 53037 53037.36310 P R 121 80 0.12700 53341 53341.34490 P R 130 93 0.14130 53048 53048.95327 K V 106 100 0.15222 53344 53344.55190 P R 181 57 0.13600 53048 53048.95400 K R 106 100 0.15205 53355 53355.19460 P R 181 58 0.13640 53048 53048.95887 K V − R 48 192 0.14662 53357 53357.19320 P R 181 81 0.27090 53051 53051.93498 K V 105 69 0.11917 53358 53358.20390 P R 181 63 0.13770 53051 53051.93560 K R 106 68 0.11782 53366 53366.21630 P R 181 33 0.07490 53051 53051.93560 K V − R 48 126 0.11782 53367 53367.15090 P R 181 49 0.10710 53053 53053.93887 K V 48 142 0.17939 53370 53370.39879 Z R 3 2612 0.16804 53053 53053.93947 K R 102 140 0.17935 53371 53371.41926 Z R 3 960 0.05926 53053 53053.93947 K V − R 46 280 0.17879 53380 53380.27430 P R 181 66 0.14690 53058 53058.25650 P R 121 100 0.17380 53383 53383.96821 K V 167 61 0.12332 53064 53064.27290 P R 181 22 0.05280 53383 53383.96911 K R 168 113 0.29899 53065 53065.20350 P R 121 38 0.08510 53383 53383.96911 K V − R 79 117 0.11962 53066 53066.23430 P R 121 41 0.08330 53406 53406.20850 P R 181 32 0.17780 53067 53067.27850 P R 156 3 0.00480 53408 53408.30860 P R 181 58 0.12420 53068 53068.22690 P R 158 2 0.01340 53409 53409.19840 P R 181 82 0.17660 53070 53070.20850 P R 43 22 0.02590 53410 53410.18280 P R 181 68 0.14810 53073 53073.20320 P R 130 63 0.11660 53411 53411.19420 P R 181 72 0.15320 53089 53089.24730 P R 156 40 0.12000 53412 53412.18360 P R 181 82 0.17680

this case one can suggest variations of the latitude of the variations on a scale of a few years are seen in long-term magnetic axis (and, correspondingly, of the axis of the ac- brightness variations [34] and seasonal variations of the cretion column). Similar precession-like variations may outburst cycle length of dwarf novae [35] and are usually be expected in a case of non-coincidence of the spin and interpreted as a solar-type magnetic cycles [36]. Such orbital rotational axes of the white dwarf [33]. Accretion changes may also be partialy caused by minor variations

390 Ivan L. Andronov et al.

Table 3. Table of V observations (HJD-2400000, magnitude) obtained at the 1.8 m BOAO telescope, Korea. The table is available on-line as Supplementary Data 2.

Table 4. Table of R observations (HJD-2400000, magnitude) obtained at the 1.8 m BOAO telescope, Korea. The table is available on-line as Supplementary Data 3.

Table 5. Table of R observations (HJD-2400000, magnitude) obtained at the 2.6 m ZTSh telescope at the CrAO, Ukraine. The table is available on-line as Supplementary Data 4.

Table 6. Table of brightness, color and principal components (HJD-2453022, U, B, V , R, I, U − B, B − V , V − R, R − I, B − R, U1, U2, U3, U4, U5) obtained at the 1.25 m AZT-11 telescope at the CrAO, Ukraine. The table is available on-line as Supplementary Data 5.

Table 7. Table of R observations (HJD-2400000, magnitude) obtained at the 0.38 m K-380 telescope at the CrAO, Ukraine. The table is available on-line as Supplementary Data 6.

Table 8. Color gradients dR/dV and dV/dR, number of pairs of interpolated VR measurements n, mean magnitude in V and R, correlation coeﬃcient and the ratio to its statistical error (for individual nights, bright- and faint states, and data with a substructed corresponding nightly mean). The table is available on-line as Supplementary Data 7.

Table 9. The characteristics of the statistically optimal (up to 4-harmonic) fits to the individual runs and their error estimates: 'beat ; tmean; mmean; number of the statistically significant degree of the trigonometric polynomial , unbiased estimate of the “unit weight error” r.m.s. s s0; accuracy of the fit sC 'max ; mmax ; mmax − mmean; tmax ;'min; mmin; mmin − mmin; tmin;'max − 'min; mmin − mmax ; the light curve m(') for ' = 0.0, 0.1,... 0.9. The table is available on-line as Supplementary Data 8.

m of the orbital separation due to a third body which can state ∼ 17: 5: Thus we may conclude that all our mea- cause a ’trigger-like’ amplified response in the accretion surements correspond to a “high” state (according to usual rate [37]. All these mechanisms to produce quasi-perodic terminology), and thus we will use terms bright and faint variations of the luminosity on a few-year (or decade) to distinguish between the runs with a mean magnitude timescale may act simultaneously. difference of ∼ 1m: Turning now to BY Cam, the analysis of the published AFOEV (2005) data shows a wave with relatively sharp minima at JD 2451800 and 2453500, with a difference of 4. Brightness-color dependence m ∼ 1700d and a full amplitude 0: 8. Similar conclusions may be drawn from the AAVSO data, which are slightly shifted in time. 4.1. Nightly mean values d Honeycutt and Ka a [13] suggested a 145 periodicity from the CCD data obtained using the 41 cm Robotic The Korean CCD data were mainly obtained in two colors V R Telescope (RoboScope) from 1991 to 2004. Unfortunately, (alternate switching and filters) for an analysis of these data sources cannot be corrected to 198 min vari- the color variations. To determine quasi-simultaneous VR V − R 6 ability with a large (∼ 1m) amplitude, even in the simplest data for the calculation of (similarly to BG CMi form of a mean-phase curve. Thus the scatter of the light [26] and MU Cam=1RXS J062518.2+733433 [39]), we have curve is highly affected by this kind of variability of the used a local cubic fit for interpolation of the brightness in V R vice versa star. when observations were made in (and ), see Andronov and Baklanov7 [24] for details. Thus the number The complete light curve from our observations in the V of quasi-simultaneous data is slightly less than twice the and R filters is shown in Fig. 2. One may note that the minimum number of points (from two filters), as is well abrupt ∼ 1m variability of the nightly mean brightness illustrated by Table 2 (Journal of observations). One may sometimes occurs on a timescale of ∼ 1d (from our data), whereas slow transitions from bright to itfaint luminosity states and vice versa last ∼ 16d and ∼ 35d; respectively. 6 http://ksss.or.kr/dtp/J200509/ykkim.ps Szkody et al. [38] detected a system in the low-luminosity 7 http://uavso.pochta.ru/mcv

391 Idling magnetic white dwarf in the synchronizing polar BY Cam. The Noah-2 project

note that generally the mean value of hV −Ri= 6 hV i−hRi; (differently seen at different mean values of brightness) if different sets of points are used (i.e. for hRi we used has much lower color temperature than the one responsi- original values of the brightness, whereas for hV −Ri only ble for the 3h brightness variability. At the maximum, the the interpolated ones may be used). color temperature becomes even larger. Of our 7 nights, two nights correspond to a faint luminosity This may be illustrated also using the 4-harmonic fits to state, and five to a bright luminosity state. Fig. 3 shows our light curves (Fig. 4). The V,R’ diagram shows a rela- a dependence of the nightly mean (V − R) color on the tively narrow zone. However, sometimes there are loops, R brightness. Note that the error estimate for the color as the variations in V and R are not precisely simultane- index hV − Ri is much smaller than that of hRi; because ous. the variations in two filters V and R are highly correlated, The infrared dependence of the spin-variation amplitudes thus a color index has a much smaller amplitude (different on wavelength is the opposite of a blue one observed for different nights) than brightness in an individual filter. in non-magnetic cataclysmic variables, e.g. TT Ari [41], h The high correlation (ρ = 0:97 ± 0:11) is present, with a where a ∼ 3 variability is interpreted by rotation of the best fit dependence: accretion disk. The present result for BY Cam is in quali- tative agreement with the model of cyclotron emission with m hV − Ri = 0: 939(30) − 0:219(24)(hRi − 13:98) (2) a maximum in the infrared. Increasing the mass transfer leads to an increase in the cyclotron emission, so the sys- Here we have used the form y(x) = y¯ + b · (x − x¯) of tem becomes more red. The spin variability is due to pe- a linear depencence, which minimizes the error estimate riodic changes in the orientation of the accretion column of the zero point [40]. The amplitude of variations in the with respect to the line of sight. The flux is dependent on nightly mean values (which mainly characterize the lumi- additional parameter - the angle between the column and nosity changes) for R is larger than for V, with gradient the line of sight. There may also be eclises of the bottom dV /dR = ∆R/∆V = 0:88(2) (or dR/dV = 1:29(4)). part of the column. Additional polarimeteric and spectral For small-amplitude variability seen e.g. in the inter- observations are required for quantitative modeling of the mediate polars and nova-like variables, the slope dV/dR observed dependencies, as the number of model parame- may be converted to the color excess ∆(V − R) = ters (mass of the white dwarf, accretion rate, orientation −2:5 lg(dV/dR) in respect of the mean color index [41]. and thickness of accretion columns, density distribution, However, in BY Cam, the amplitude is large, thus we prefer strength and configuration of the magnetic field, orbital to use slopes instead of color excesses for V −R and other inclination) exceeds the number of dependencies. This colors. may be the subject of another paper.

4.2. Nightly run values 5. Spin variability The slope value 1.29(4) characterizes only the mean brightness level. For faster variability, we have deter- 5.1. Periods and their origin mined the slopes for the individual nights. These are listed in Table 7, which is available only electronically. They As the emission lines undergo significant changes with the vary from 0.98(3) to 1.24(3), with a value 1.200(8) for all 7 phases of both spin- and beat periods, they are not good nights. The latest value is dominated by the variations in indicators of the orbital motion. A linear regression to the the mean brightness. To eliminate the strong dependence timings of inferior conjunction of the red dwarf gives described above, we have removed corresponding nightly mean values, thus obtaining a significantly smaller slope TSP (HJD) = 2451137:3952(36) + 0:13975284(14)E (3) of 1.105(11), which is consistent with mean slopes both for combined “all bright” and “all faint” runs. [42], known as the “201 minute” (or “orbital”) period. This One may also suggest a minor effect of changing slope differs from previously published estimates. The spectro- during the night, in a sense that ∆R/∆V is smaller for scopic period is distinctly different from the photometric the bright parts of the 3h light curve, and is larger near one with an ephemeris for 1991-2004: the minimum. An examination of the V −V;R¯ −R¯ diagram m shows that this change of slope occurs at V − V¯ ≈ 0: 10: T HJD : : E For corresponding branches of the diagram and all data, phot:min:( ) = 2448486 98(3) + 0 137120(2) (4) we have obtained values of 0.85(4) ind 1.23(2) for the slope. The latter value is much closer to that for the mean bright- [4]. This difference was explained by Mason et al. [16] ness, 1.29(4), indicating that the main source of emission as a 2ω − Ω frequency, where ω is a spin frequency of

392 Ivan L. Andronov et al.

the white dwarf, and Ω is an orbital frequency, following 6. UBVRI Photometry the model by Wynn and King [43] for intermediate polars. This photometric period coincides with that from the more 6.1. Color gradients recent ephemeris The light curve obtained on January 17, 2004 at the AZT- Tphot:min:(HJD) = 2453022:268 + 0:137120E (5) 11 telescope of CrAO is shown in the upper part of Fig. 7. It shows two unequal minima, onto which are superim- posed possible quasi-periodic oscillations and ﬂickering. [20]. Using all available timings for the main maximum, In the deeper minimum, the photon counting statistics are Pavlenko et al. [44] have published an ephemeris much worse, which causes an increase in observational errors. T HJD : : E: spin( ) = 2453089 307 + 0 1384274 (6) The color indices (middle part of Fig. 7) show that during minima the emission becomes bluer, in the sense of We also will use the “beat” ephemeris correponding to a a decrease in the color indices. The amplitude of or- −1 −1 −1 synodic (spin-orbital beat) period Pbeat = (Pspin − Porb) bital variation increases with wavelength. The slopes are (Eq. 1). These two ephemerides have been used for further dU/dR = 0:23(1), dB/dR = 0:43(1), dV /dR = 0:78(1), study. dI/dR = 1:18(1). This behaviour is opposite to that of eclipsing cataclysmic variables with an accretion disk [1]. 5.2. 4-harmonic model Qualitatively this situation may be explained by a redder spectral energy distribution for the accretion column than For periodic light curves, it is usual to apply a multi- for the white dwarf. harmonic ﬁt with a determination of the statistically optimal value of the degree of the trigonometric polynomial, 6.2. Principal component (PC) analysis (A) s: Andronov et al. [46] applied the PCA to the determination

s of a statistically significant number of variability sources X m t C C πjt/P C πjt/P : and their characteristics. They did this for 3 cataclysmic ( ) = 1 + ( 2j sin(2 ) + 2j+1 cos(2 )) (7) j=1 variables with different degrees of influence of the magnetic field on accretion. This method is an effective tool to determine components of variability, which have different Here, m(t) is a signal at time t; P is an adopted period (we d spectral energy distributions, i.e. the wavelength depen- have used P = 0: 137120 published by Pavlenko [20]), and dencies of the amplitudes of variability. For two-color Ck ; (where k = 1; ··· ; (2s + 1)) is a parameter determined observations of the same accuracy and subtracted mean using the least squares method. A description of work- value, this method is known as “orthogonal regression”;√ ing formulae for the computer program was presented by U U x x / ; 8 s the principal components√ kα are k1 = ( k1 + k2) 2 Andronov [45]. We have applied the fixed value of = 4 U x − x / ; x k2 = ( k1 k2) 2 where kα are observations at after noting a 4-hump model of the light curve [20] which point k in channel (filter) α: The first principal component is often seen in our data. shows common features in different channels (although The individual light curves for different telescopes are with channel-dependent amplitude), and other PCs de- shown in Figures 5–6 together with the corresponding fits. scribe differences. The color-brightness diagrams, which The characteristics of the maxima and minima will be dis- are often used in astronomy (the Herzsprung-Russel dia- cussed in section 7, and are presented in the electronic gram, diagrams for variable stars), are also a modification Table 8. of the PCA with an aim to get more information on the ob- Fig. 5 shows the fits for the V , R and V − R curves jects. Polarimetry is also related to PCA, being applied obtained in BOAO. There is significant variability of the to “ordinary” and “extraordinary” waves in the emission. shape, which prevents us from putting all the data on an For multi-color photometry, PCA is a supplementary sta- ordinary joint phase curve. However, the curves for the tistically optimal tool used to extract components of vari- bright state show a smaller scatter as compared to two ability which may be overlooked if analyzing the colors curves for the faint state. These two curves are upper lim- only. Formerly, a method was proposed [41], which al- its in the V − R diagram because of the mean brightness- lowed extraction of only the first component. color dependence mentioned above. Applying the PCA formalism [46] to the present data, we have found that the difference in the amplitude of the first 8 http://il-a.pochta.ru/oap7_049.pdf principal component (U1) is much larger than for others. It

393 Idling magnetic white dwarf in the synchronizing polar BY Cam. The Noah-2 project

explains 84% of the overall variance in all colors. The sec- analysis, which is most effective for quasi-periodic oscil- ond component U2 is responsible for 10% of the variance, lations, where one expects to determine a characteristic so the total contribution of the remaining components (U3, cycle length, rather than a constant period. Contrary U4 and U5) is only 5.8%. Despite a scatter in the third to periodogram-, wavelet- and auto-correlation methods, component, it has obvious variations in the orbital time which are higly affected by slow (periodic or aperiodic) scale. The amplitude signal-to-noise ratio obtained using trends, the Λ−scalegram is insensitive to polynomial the “running parabola” scalegram analysis [47] is 26, 14, trends up to degree 3. Thus, in the presence of strong as- 8, 4 and 4 for U1–U5, thus we conclude that first 3 prin- inusoidal spin variability (as in BY Cam and many other cipal components are statistically significant. Relatively cataclysmic variables), we prefer to use this method to es- large values for U4 and U5 are due to larger errors in the timate effective (mean) amplitudes and periods (or cycles) second, deeper minimum. of different components of variability. The dependence of the matrix Vij on the number of chan- The height of the peak is proportional to the square of nels (filtera) i and on the number of the PCs j is shown in the effective amplitude. The most pronounced peaks are Fig. 7 and is listed in the table below. The first (largest seen for the scalegram for the first PC (U1) correspond- d d d in the amplitude) PC shows both 3-hour and faster vari- ing to effective periods of 0: 122, 0: 37, 0: 21 (in order ability, as one may see in Fig. 7. Its contribution mono- of decreasing height at the scalegram). The positions of tonically decreases with the number of channel (and cor- the peaks are shown by vertical lines for comparison with responding wavelength), as one may see from Fig. 7. The other scalegrams. The highest peak corresponds to the V /V ratios i1 41 (which are equal to ratios of the amplitudes most prominent 3-hour variability. It is slightly less than a U of variability with a shape k1) are equal to 0.29, 0.47, photometric period, which is expected for a non-sinusoidal 0.83, 1 and 1.20. These values are different from the ra- curve [48]. The second period is close to Pphot/4; con- tios dU/dR...dI/dR because 3 components are statisti- firming a 4-peak structure of the light curve, which was cally significant (for an exact linear dependence of the pointed out by Pavlenko [20]. brightness variations in different colors, i.e. the presence The third peak corresponds to ∼30 min QPOs. Previously, of only one statistically significant component, the values QPOs in BY Cam were reported to occur at phases with in a pair for a given color must coincide). different estimates of their amplitude and time scale: 5 U I The first PC, k1, mostly resembles variations in and min [4], 10 and 15 min [8], 5-10 and 30 min [49, 50]. R d , with a weaker match to the variations in U. Such be- The fourth peak occurs at 0: 0056=8 min and agrees with haviour may be interpreted for this system, assuming that smaller periods mentioned above. However, its ampli- BY Cam contains sources of emission with different spec- tude is smaller than for other peaks. Although the peaks tral energy distributions: the dominant source of variabil- seem too small when compared to the main peak, the ity (first PCA) is due to cyclotron emission of the accretion corresponding effective semi-amplitudes are large enough m m m m column, so it has an amplitude, which strongly increases (0: 58, 0: 33, 0: 24 and 0: 11 for four peaks for U1, re- with wavelength. This resembles AM Her, a classical po- spectively). lar with an accretion column (infrared-dominated variabil- For U2, the peaks are of much smaller amplitude, but ity), but is quite opposite to the nova-like variable TT Ari nearly at the same places, as for U1. The highest peak (ultraviolet-dominated variability), which has an accretion of Λ(∆t) corresponds to a 30 min component, similar to disk. the scalegram for the U filter. This is also in agreement V i For the second PC in BY Cam, the dependence of i2 on with the conclusion from the infrared (U1) and blue (U2). V V has opposite slope to i1, i.e. i2 monotonically decreases The third U3 has a small amplitude with variations mainly with wavelength. This means that the second (in ampli- concentrated in the 3-hour peak. tude) component has a blue spectral energy distribution, In Fig. 10, the scalegram for 3-sec photometry (all 4 contrary to the infrared first PC. An examination of the nights) obtained at 2.6m telescope ZTSh is also shown. Uk curve (Fig. 7) shows that the second PC 2 is dominated Besides the dominating peak, it also has smaller peaks ∼ Uk by 30 min variability, whereas 1 is spin-dominated. close to the same positions. The Λ−scalegrams for other runs show night-to-night variability of the shape, and 6.3. Scalegram analysis its corresponding amplitudes and periods. This causes an overlap of the peaks and a decrease in the peak-to- The Λ−scalegrams [48] are shown in Fig. 10 for the continuum ratio. Thus an absence of well pronounced sec- original UBVRI data, for the corresponding color indexes ondary peaks agrees with the former conclusion of signif- and for the PCs. All the curves have the same scale, icant variability of the characteristics of these brightness but shifted for clarity. This method is a kind of wavelet oscillations, either during the run, or from run to run.

394 Ivan L. Andronov et al.

The height of the primary peak, which corresponds to the asynchronous polar V1432 Aql (see Ref. [52] for results of 3h variability, characterizes the amplitude of variations. the recent observational campaign on that object). Using the 4-harmonic fits, this value was determined for Periodic phase variations for the spin variability with the all runs which sufficiently cover the photometric phase, orbital phase were reported by Kim et al. [26] for another and will be discussed in the last section in more detail. magnetic cataclysmic variable 1RXS J062518.2+733433 = bright faint We split the BOAO and K-380 data into and MU Cam. This system is an intermediate polar, and such parts. a dependence may argue for a diskless model of the sys- For the BOAO data, the height of the peak and corre- tem [53]. Although the spin period in BY Cam is close to R sponding effective amplitude is larger for the filter than the orbital period in contrast to the intermediate polars, V all bright faint for the filter for , and data sets, in agree- the asynchronous polars may be also called “nearly syn- < : ment with the direct determination of the slope dV/dR 1 chronous” intermediate polars. Asynchronous polars (or The effective amplitude is larger by a factor of ∼ 1:3 dur- BY Cam-stars [13, 14]) fall between the classical and inter- ing the faint state than in the bright one for both BOAO mediate polars. The ratio of the spin period to the orbital and K-380 data. The position of the peak in the faint state one for the magnetic white dwarfs in cataclysmic binaries switches to half of the period, indicating the redistribution leads to a phenomenological classification [11], but it has of harmonic-component amplitudes in the light curve. a strong physical explanation [1, 2, 53]: for small magnetic moments (for a given accretion rate and orbital separation), the thread radius is small, and there is a strong 7. Characteristics of individual light accretion disk but with little evidence of accretion columns curves (non-magnetic systems, e.g. TT Ari). With an increasing magnetic moment, the inner radius of the accretion disk increases, and accretion columns become stronger (disk-fed As one of the main results of the first Noah project, Silber intermediate polars). Accretion disks may be disrupted in et al. [8] pointed out that the phase of the sine-wave fits disk-less intermediate polars, but the stable spin period is for the 3h variability show an abrupt jump with a period of d shorter than the orbital one. Asynchronous polars evolve 7: 26, which was interpreted as half of the complete beat to a phase-locked synchronous rotation, which is typical period [16]. This suggested that there are two switch- for classical polars of AM Her-type. However, because ings of the accreting column from one pole to the other. d of the influence of other system parameters, sometimes If the 7: 26 period dominates, this means that two accret- ◦ systems with a larger magnetic field for the white dwarf ing poles at the white dwarf are separated by ∼ 180 in may stay on the less-magnetic branch of the classification longitude (with a similar latitude) and there will be two described above. waves during one beat period. Diversity of the location or structure will lead to an inequality of these waves. The main characteristics of these fits to BY Cam have been plotted as a function of the beat phase (Eq. 1) in Fig. 11. Pavlenko [20], based on 31 runs in the inactive state, has The statistically significant degree s of the polynomial fit suggested a more complicated structure with 3 possible was determined for each run separately, and ranges from jumps at the phases 'beat = 0:25; 0.55 and 0.78 with a s = 1 (sinusoidal variation) to s = 4: These fits, together possible interval of erratic phase variations between the with the light curve at the 10 equidistant phases, are pre- beat phases 0.0 and 0.25. The mean slopes of the O-C sented electronically in Table 8. Each point represents diagrams between the main switches at 'beat = 0:25; 0.78 d one night of the observations. As the majority of data correspond to the “true” spin period Pspin = 0: 138428: were obtained in the R photometric system, we have used However, an additional jump at 'beat = 0:55 was inter- this sample for better statistics. Incomplete curves, where preted as a switch between 3 (or even 4) accretion zones. d the data cover less than 0: 1 have been excluded from the In the beat-phase intervals 0.25-0.55 and 0.55-0.78 for BY analysis, to avoid large errors of the fit in gaps. 46 nights Cam, Pavlenko [20] had suggested a larger phase/beat of data are included. phase slope, d'/d'beat) (and thus an apparent photomet- P P P /P '/ ' ; P ric period, as = 0(1+( 0 beat)d d beat) where is To reduce the effect of the inhomogeneous distribution of P a trial value of photometric period; 0, its adopted initial phases of observation, we have used the orbit-averaged m C value; and Pbeat is the beat period). mean mean (i.e. the coefficient 1 in the fit) instead of It should be noted that in some nearly-synchronous polars the sample mean. the accreting region moves rather smoothly in longitude As one may see from the dependence of this mean value, even while accreting onto a single pole, as the treading the bright and faint states are well separated from each region drifts due the asynchronism. At first, such a model other. There are only 3 nights (from 45) in between these was discussed by Geckeler and Staubert [51] for another two groups. The transitions are much less frequent (i.e.

395 Idling magnetic white dwarf in the synchronizing polar BY Cam. The Noah-2 project

6%) than the bright (n=11, 24%) and faint (n=32; 70%) If one will define m˜ mean = (mmax + mmin)/2; then the val- states. The range of mean values in the bright state (∼ ues (mmax − m˜ mean) = −(mmin − m˜ mean); and there will be m m 0: 3) is smaller than for the faint state (∼ 1: 1): This is an exact negative correlation. The absence of correlation also valid separately for the maxima (“max” in Fig. 11 and argues for a high variability of the shape of the light curve. minima (“min”), arguing for a better stability of the light The dependence of the photometric phases 'ph on the beat curve in the bright state. phases 'beat is shown at the bottom part of Fig. 11. In Not unexpectedly, the maxima and minima in the bright the previous studies, only one phase of the maximum was state are brighter than these characteristics for the runs in taken into account (one-harmonic fit by Silber et al. [8] or the faint state. In the faint state, the mean, maximum and an “asymptotic parabola” fit by Pavlenko [20]). Assuming minimum values show minima at the beat phases 'beat = a complicated structure of the light curve and applying a 0 and 0.5. The initial epoch was chosen by Pavlenko 4-harmonic fit, we have used the phases of both maximum [20] to correspond to the minimum of the sample mean 'min and minimum 'max and the phase difference between brightness, so our result for the orbital mean just shows them. The last value is called the “asymmetry” and is an that the difference between the sample and orbital mean important parameter listed in the General Catalogue of values is much smaller than the amplitude of the curve. Variable Stars [54, 55]. m m The maximum and mean values min and max are cor- The corresponding dependencies have following differ- ρ : :m related ( = 0 91(6)) with mean values of 13 97(3) and ences. The parameter 'max has jumps at 'beat = 0.78 :m 15 04(3). If (as for truly monoperiodic stars) there were no and 0.23, as found by Pavlenko [20]. However, all the pa- phase shifts, these values could be named as the maximum rameters show outlying points in corresponding diagrams, and minimum value of the mean phase curve. The slope which are characterized by relatively small formal error m m d max /d min=0.74(5) is significantly smaller than unity, estimates, and thus may be classified as statistically sig- m − m indicating an increase of the amplitude ( min max ) nificant. The original brightness variations, which cause m on min. A more usual form is seen for the amplitude such pecularities, may be produced by cloud-type inho- m − m m ( min max ) vs. mean. The correlation coefficient mogeneties of the accretion stream. Such flare-like events ρ : = 0 40(14) is much smaller, but the correlation is still with an amplitude of hundreds millimagnitudes are dis- σ significant at the 3 level. The corresponding mean values tinctly seen at our curves. A filter could be applied to the :m :m :m :m :m :m are 14 53(7) (13 59-15 46) and 1 07(3) (0 74-1 46) for bad curves, those which produce outlying points, giving m m − m ; mean and ( min max ) respectively. The slope is pos- smoother curves (Fig. 11). The criteria for such filtering m − m m : : itive d( min max )/d mean = +0 17(6) may be elaborated in the future. In this work we present To remove obvious correlations between the brightness at the results of modeling of all curves in extensive electronic some phases due to variations in the mean brightness, and tables as observational facts, without removing any out- to check the stability of the light curve, we have introduced lying data. In other words, present results show that the two related parameters ”mmax −mmean” and ”mmin−mmean”: situation is much more complicated, not because of bad For this further analysis, we have classified intermediate observations, but because of the complexity of the system. points as bright, thus determining a dividing value of the At present, we may conclude that outlying points really m mean brightness of R=14: 21. exist, but, by removing them, one may suggest good se- m m The parameter mmax − mmean (from -0: 6 to -0: 3) for the quences for the remaining points. One can naively ex- bright state is much closer to zero than that for the faint pect that the light curve is dependent purely on the beat m m state (from -1: 0 to -0: 4). This indicates a more extended phase (thus on the periodically varying orientation of the hump for the bright state and more stable shape of the magnetic field and the structure of the accretion flow). m light curve. For the (mmin −mmean) values, the range (0: 4- The scatter in the diagrams (Fig. 11) argues for addi- m 0: 7) for the bright state is also smaller than for the faint tional valuable processes, particularly, mean magnitude m m state (0: 29-0: 88), but there is no significant systematic changes, and large-amplitude flares. shift. For our data, we suggest that the minimum phases show Both characteristics (mmax − mmean) and (mmin − mmean) the main jump at slightly larger phase 'beat = 0:92 for have a large scatter. In the beat phase interval 0.03- the faint data, and possibly a more smooth variation for 0.15, there are 5 outlying points (nights) with an ampli- the bright data. There are obvious outlying points, which tude, which is nearly twice as large as for the nearby correspond to the global minimum, whereas for the phase beat phases. The mean values for 46 runs are h(mmax − light curve two local minima may occur inside a “main” m m m mmean)i = −0: 57 (from -0: 83 to -0: 31) and h(mmin − minimum. This does not challenge a general conclusion of m m m mmean)i = +0: 52 (from 0: 29 to 0: 88). Unexpectedly, switching accretion from one pole to another while idling there is no correlation between these two characteristics. of the white dwarf in respect to the secondary.

396 Ivan L. Andronov et al.

Figure 7. The individual light curves (points) in R for the data Figure 8. The individual light curve (UBVRI), color index obtained at the K-380 telescope. As in Fig. ??, The curves (U − B, B − V , V − R, R − I, B − R) and original data are plotted once and are not repeated, principal component (U1,...,U5) curves (points) for but the ﬁt is repeated for clarity. The four-harmonic data obtained at the AZT-11 telescope. The direc- ﬁts for individual runs are shown by solid lines. tion and scale are the same for all graphs. The interval between minor tics is 0:m2.

397 Idling magnetic white dwarf in the synchronizing polar BY Cam. The Noah-2 project

amplitude; c) the bright light curve is more stable; d) the bright light curve has a smaller value of |mmax − mmean| indicating larger duration of the maximum (which is usually split into two humps).

• The slopes dV/dR are closer to unity for the variability during a night, than for the mean brightness, indicating that the variability due to changing orientation is more blue than the emission from the mean accretion component, and is more red than the total emission. This may be tentatively interpreted as a sequence with decreasing temper- j\i 1 2 3 4 5 ature “white dwarf+red dwarf”, “accretion structure 1 0.1541 0.7440 -0.3797 -0.5132 0.1233 varying with orientation”, and “accretion structure 2 0.2550 0.4891 -0.0900 0.7985 -0.2238 which does not vary with orientation”. However, at 3 0.4455 0.1977 0.8123 -0.2333 -0.2196 present, this conclusion is far from the theoretical 4 0.5393 -0.1452 0.0022 0.1459 0.8166 modeling. 5 0.6495 -0.3835 -0.4335 -0.1528 -0.4687 • Contrary to the intermediate polars BG CMi and

Figure 9. Dependence of the matrix of eigenvectors Vij on the num- MU Cam, the variations in different colors show an ber of channels i and on the number of principal compo- increase of amplitude with wavelength. nents j (see Andronov et al. [46] for a detailed description). • The second principal component of variability is characterized by a decrease in amplitude with The mean value of 'min is 0.058(24), so the deviation wavelength. The amplitudes for the 30 min, P/4 from zero is formally not statistically significant. How- and P variations are comparable, indicating that 30 ever, the initial epoch in Eq. 5 may be corrected to min QPOs are more blue than the spin variability. Tphot:min(HJD) = 2453022:276(3) (assuming the period of Pavlenko [20]). Our 46 minima timings are best fitted to • The characteristics of 46 pairs of spin maxima and the ephemeris minima for the season in 2003-2005 have been determined. Tphot:min:(HJD) = 2453213:010(3) + 0:137123(3)E: (8) • The optimal mathematical model for the four- hump light variations corresponds to a fourth-order The period value differs from that of Pavlenko [20] by 1σ; trigonometrical polynomial. The dependences of i.e. not significantly. The maximum phase shift due to these parameters on the phase of the beat period the difference between the periods for our 46 minima is and on mean brightness are discussed. In an ad- only 0.01(1). This is comparable with the mean accuracy dition, the 30 min and 8 min quasi-periodic oscil- of the phase determination for a single curve. Thus a lations are present with a variable amplitude and recomputation of all phases is not necessary. effective cycle length. The asymmetry 'max − 'min has a drastic range of variations from 0.18 to 0.80, which is much larger than a mean • The ephemeris for the orbital minima has been cor- accuracy estimate of 0.012. There is a slight evidence rected. (at the 3σ limit) for a double-hump structure with minima close to the phases of jumps. The determined parameters may be used for comparison with theoretic models of accretion in magnetic cataclysmic variables. Further multi-color monitoring is needed for 8. Conclusions studies of variability of accretion structure and rotation of the white dwarf. • The main differences between the spin light curves in the bright and faint brightness states are: a) the mean color index V − R is larger for the bright Acknowledgements state (this argues that the emission region asso- ciated with accretion has an infrared energy dis- This work was supported by the Korea Research Founda- tribution); b) the bright light curve has a smaller tion Grant funded by the Korean Government (MOEHRD,

398 Ivan L. Andronov et al.

Figure 10. Λ-scalegrams [48] for the individual light curves Figure 11. Dependence of the main parameters of the 4- (UBVRI), color index curves (U − B, B − V , V − R, harmonic ﬁts for individual runs on the phase of R − I, B − R) and principal component (U1,...,U5) the beat (synodic) period. Each point represent curves for the data obtained at the AZT-11 tele- one night of observations. For the phase range 0- scope and (bottom) for all 4 nights obtained at 1, the data are marked by asterisks and crosses ZTSh. The vertical lines mark the positions of the for the bright and faint states, respectively. The three most prominent peaks in the scalegram for error bars are shown, but are often smaller than the ﬁrst principal component U1. the symbols on the left-hand side of the plots; on the right-hand side (phases from 1 to 2) only error bars are shown. The slope of the inclined lines correspond to the spin period of the white dwarf, the jumps are interpreted as switch of accretion from one pole to another.

Basic Research Promotion Fund) (KRF-2007-C00121). The data acquision with 1.8 m telescope was supported 399 Idling magnetic white dwarf in the synchronizing polar BY Cam. The Noah-2 project

by Korea Astronomy Observatory Research Fund 2003. Observatory, S. Petersburg, Russia 1992) 158 We thank anonymous referees for their fruitful comments. [24] I.L. Andronov, A.V. Baklanov, Astron. School Rep. 5, E.P.P. thanks J. Babina for her assistance in observations. 264 (2004) [25] Y.G. Kim, I.L. Andronov, Y.B. Jeon, J. Astrophys. Space Sci. 21, 3, 191 (2004) References [26] Y.G. Kim, I.L. Andronov, S.S. Park, L.L. Chinarova, A.V. Baklanov, Y.B. Jeon, J. Astrophys. Space Sci. 22, 197 (2005) [1] B. Warner, Cataclysmic Variable Stars (Cambridge [27] R. Hudec, L. Meinunger, Inf. Bull. Var. Stars 1184, 1 Univ. Press, Cambridge, 1995) (1976) [2] C. Hellier, Cataclysmic Variable Stars. How and why [28] S. Ka a, R.K. Honeycutt, Astron. J. 130, 742 (2005) they vary (Springer-Verlag, Berlin, 2001) 210 [29] M. Livio, J.E. Pringle, Astrophys. J. 427, 956 (1994) [3] W. Forman et al., Astrophys. J. Suppl. 38, 357 (1978) [30] M.M. Basko, R.A. Sunyaev, Astrophys. Space Sci. 23, [4] R.A. Remillard et al., Astrophys. J. 302, 11 (1986) 117 (1973) [5] P.A. Mason, J.W. Liebert, G.D.Schmidt, Inf. Bull. Var. [31] A.R. King, J.P. Lasota, Astron. Astrophys. 140, L16, Stars 3104, 1 (1987) (1984) [6] P.A. Mason, J. Liebert, G.D. Schmidt, Astrophys. J. [32] I.L. Andronov, Astrophysics 20, 165 (1984) 346, 941 (1989) [33] I.L. Andronov, Astron. Soc. Pacif. C. Ser. 334, 447 [7] I.L. Andronov, B. Fuhrmann, Inf. Bull. Var. Stars 2976, (2005) 1 (1987) [34] A. Bianchini, Astron. J., 99, 1941 (1990) [8] A.D. Silber et al., Mon. Not. R. Astron. Soc. 290, 25 [35] I.L. Andronov, L.I. Shakun, Astrophys. Space Sci. 169, (1997) (Paper I) 237 (1990) [9] I.L. Andronov, Astrophys. Space Sci. 131, 557 (1987) [36] H.R. Richman, J.H. Applegate, J. Patterson, Publ. As- [10] M. Cropper et al., Mon. Not. R. Astron. Soc. 236, 29 tron. Soc. Pacif. 106, 1075 (1994) (1988) [37] I.L. Andronov, L.L. Chinarova, Astron. Soc. Pacif. Conf. [11] J. Patterson, Publ. Astron. Soc. Pacif. 106, 209 (1994) Ser. 261, 47 (2002) [12] H.S. Stockman, G.D. Schmidt, D.Q. Lamb, Astrophys. [38] P. Szkody, R.A. Downes, M. Mateo, Publ. Astron. Soc. J. 332, 282 (1988) Pacif. 102, 1310 (1990) [13] R.K. Honeycutt, S. Ka a, Mon. Not. R. Astron. Soc. [39] Y.G. Kim, I.L. Andronov, S.S. Park, Y.B. Jeon, Astron. 364, 917 (2005) Astrophys. 441, 663 (2005) [14] P.A. Mason, Rev. Mex. AC 20, 180 (2004) [40] E.T. Whittaker, G. Robinson, The Calculus of Obser- [15] H. Ritter, U. Kolb, Astron. Astrophys. 404, 301 (2003), vations (Blackie and Son., London, 1924) http:/physics.open.ac.uk/RKcat/cbcat [41] J. Tremko, I.L. Andronov, L.L. Chinarova, et al., Astron. [16] P.A. Mason, G. Ramsay, I. Andronov, S. Kolesnikov, Astrophys. 312, 121 (1996) N. Shakhovskoy, E. Pavlenko, Mon. Not. R. Astron. [42] R. Schwarz, A.D. Schwope, A. Staude, R.A. Remillard, Soc. 295, 511 (1998), (Paper II) Astron. Astrophys. 444, 213 (2005) [17] P. Massey, L.E. Davis, A User’s Guide [43] G.A. Wynn, A.R. King, Mon. Not. R. Astron. Soc. 255, to Stellar CCD Photometry with IRAF, 83 (1992) http://iraf.noao.edu/iraf/ftp/iraf/docs/daophot2.ps.Z [44] E.P. Pavlenko, M. Andreev, Ju. Babina, S. Tkachenko, [18] V.V. Breus, I.L. Andronov, S.V. Kolesnikov, N.M. Astron. Soc. Pacif. Conf. Ser. 362, 183 (2007) Shakhovskoy, Astron. Astrophys. Transact. 26, 241 [45] I.L. Andronov, Odessa Astron. Publ. 7, 49 (1994) (2007) [46] I.L. Andronov, N.M. Shakhovskoj, S.V. Kolesnikov, [19] V. Piirola, O. Vilhu, J. Kyrolainen, N. Shakhovskoi, Y. In: R.Silvotti, D. deMartino (eds.), ”White Dwarfs”, Eﬁmov, ESA SP-236, 245 (1985) Naples, Italy, 2002, (Naples, Italy 2003) 325 [20] E.P. Pavlenko, Astrophysics 49, 105 (2006) [47] I.L. Andronov, Astron. Astrophys. Suppl. 125, 207 [21] A.A. Henden, R.K. Honeycutt, Publ. Astron. Soc. Pacif. (1997) 107, 324 (1995) [48] I.L. Andronov, Astron. Soc. Pacif. Conf. Ser. 292, 391 [22] T. Neckel, R. Chini, Astron. Astrophys. Suppl. 39, 411 (2003) (1980) [49] E.P. Pavlenko, S.Yu. Shugarov, S.V. Antipin, D.A. [23] I.L. Andronov, S.V. Kolesnikov, E.P. Pavlenko, N.M. Sokolov, G. Borisov, I. Budzinovskaya, In: A. Evans, Shakhovskoj, In: Yu.V. Glagolevskij, I.I. Romanyuk J.H. Wood (eds.), Proceed. of the Keele Conference on (Eds.), Proceed. of Intern. Meeting ”Stellar Mag- Cataclysmic Variables and Related Objects (Keele, netism”, S. Petersburg, Russia (Special Astrophysical

400 Ivan L. Andronov et al.

England, 1996) 217 J., 614, 349 (2004) [50] T.A. Somova, N.N. Somov, J.M. Bonnet-Bidaud, M. [54] P.N. Kholopov (ed.), General Catalogue of Variable Mouchet, Bull. Spec. Astron. Obs. 45, 120 (1998) Stars (Moscow, Nauka, 1985) [51] R.D. Geckeler, R. Staubert, Astron. Astrophys. 325, [55] N.N. Samus et al., General Catalogue of Vari- 1070 (1997) able Stars (live electronic edition), (2006), [52] I.L. Andronov, A.V. Baklanov, V. Burwitz, Astron. As- http://www.sai.msu.su/groups/cluster/gcvs/gcvs/ trophys. 452, 941 (2006) [53] A.J. Norton, G.A. Wynn, R.V. Somerscales, Astrophys.

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