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Photometry of three chromospherically active stars: V340 Gem, SAO 62042 and FI Cnc
New Astronomy 14 (2009) 109–120
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Photometry of three chromospherically active stars: V340 Gem, SAO 62042 and FI Cnc A. Erdem *, E. Budding, E. Soydugan, F. Soydugan, S.S. Dog˘ru, D. Dog˘ru, M. Tüysüz, A. Dönmez, H. Bakisß, Y. Kaçar, C. Çiçek, Z. Eker, O. Demircan Çanakkale Onsekiz Mart University Observatory, Terziog˘lu Kampüsü, 17020 Çanakkale, Turkey
a r t i c l e
i n f o
Article history: Received 13 December 2007 Received in revised form 6 June 2008 Accepted 6 June 2008 Available online 12 June 2008 Communicated by W. Soon PACS: 97.10.Jb 97.10.Kc 97.30.Nr
a b s t r a c t We present a photometric study of three chromospherically active stars with long periods (V340 Gem, SAO 62042 and FI Cnc). The observations were made at the ÇOMU Observatory in 2006 and 2007. We have made initial photometric analyses of V340 Gem and SAO 62042, which are newly discovered RS CVn–type SB1 binaries, and established the photometric variations of FI Cnc, which is a single G8III active star. Photometric rotation periods of these stars were obtained by analyzing their light variations. The light variations, observed over three or more consecutive orbital cycles, were investigated by using spot models with the program SPOT. We also discussed the surface differential rotation coefficient for the primary component of the SB1 binary star SAO 62042 in this study, using our own photometric period together with an orbital period taken from the literature. Ó 2008 Elsevier B.V. All rights reserved.
Keywords: Stars: activity Stars: rotation Stars: spots Stars: individual (V340 Gem, SAO 62042, FI Cnc)
1. Introduction According to models, magnetic activity of solar and late-type stars originates from envelope convection and differential rotation. Current theoretical studies show how differential rotation depends on global stellar parameters, such as spectral type and rotation period (e.g. Kitchatinov and Rudiger, 1999). It is also clear, physically, that the interaction of axial rotation with envelope convection should create differential rotation. It is important to observe evidence of stellar magnetic activity to test model predictions. Stellar surface differential rotation depends on latitude, and this can sometimes be assessed from observations. Photometric data may give an opportunity to predict surface differential rotation from rotation period variations. In this view, the most likely explanation of changes of (short-term) photometric period of an active star is the variation of rotation period of predominating starspot features (Messina and Guinan, 2006). However, we should note here that observed variations of the pho-
* Corresponding author. Tel.: +90 286 2180019; fax: +90 286 2180533. E-mail address: [email protected] (A. Erdem). 1384-1076/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.newast.2008.06.001
tometric period can also be related to the growth and decay of starspots. In the present work, we have selected three chromospherically active stars V340 Gem, SAO 62042 and FI Cnc to study their photometric variations. The basic parameters of these stars were taken from SIMBAD and the Tycho Catalogue, and these are listed in Table 1. 2. Observations and reductions The above-named three active stars were observed at the Çanakkale Onsekiz Mart University Observatory (Demircan et al., 2003) in the years 2006 and 2007. A summary of observations is presented in Table 2. For SAO 62042 and FI Cnc, the 30-cm Schmidt– Cassegrain reflector, equipped with an SBIG ST–10XME CCD camera in the first season of observations (between February and June of 2006), and an SBIG STL–1001E CCD camera in the second season (between November 2006 and April 2007) was used. For V340 Gem, the SBIG STL–1001E CCD camera was used for all observations between November 2006 and May 2007. The SBIG STL–1001E and SBIG ST–10XME CCD cameras give image scales of 1.63 arcseconds per pixel and 0.45 arcseconds per pixel, respectively. The observed
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Table 1 Basic parameters for program stars from SIMBAD and Tycho Catalogue 0 00
Star
HD No
GSC no.
a (2000) h m s
d (2000)°
V340 Gem Comparison Check
57267 57106 57206
1913 0930 1917 0475 1917 0494
07 21 33 07 20 55 07 21 16
+26 09 33 +26 37 27 +26 29 40
3001 3001 3001 3001
10 10 10 10
+37 +37 +37 +37
SAO 62042 Comparison Check-1 (first season) Check-2 (second season) FI Cnc Comparison Check
72146 72052
1282 1385 1329 1138
1947 0489 1947 0367 1947 0089
26 26 26 26
23 25 35 03
08 32 17 08 32 18 08 31 52
V (mag)
B—V(mag)
Spectral type
7.60 8.06 8.29
0.786(15) 1.478(33) 0.108(22)
G2V K2 A0
13 05 43 07
9.61 10.53 10.90 9.35
1.007(52) 1.056(133) 0.674(124) 0.430(33)
K2
F5
+29 19 10 +29 28 01 +29 42 41
7.37 8.77 8.21
0.951(12) 0.516(22) 0.406(18)
G5 F8 F3V
45 44 45 53
Table 2 Photometric results of program stars Variable
Time range 2,400,000 +
Filter
N obs
Dm0 (mag)
As (mag)
P s (days)
T s (HJD) 2,400,000 +
V340 Gem
54047–54230 54047–54211 54047–54211 54047–54211 53770–53882 53770–53897 53770–53897 53798–53897
B V Rc Ic B V Rc Ic
23 24 24 25 32 34 38 24
0.915(6) 0.458(5) 0.236(6) 0.025(6) 0.936(4) 0.812(4) 0.775(3) 0.749(2)
0.085(9) 0.085(8) 0.083(9) 0.080(9) 0.075(5) 0.063(5) 0.059(4) 0.055(3)
35.93(32) 36.10(23) 36.23(28) 36.37(31) 19.02(13) 19.74(14) 19.77(11) 19.43(15)
54119.50(50) 54119.64(40) 54118.77(46) 54118.81(51) 53827.41(23) 53827.07(25) 53826.93(20) 53826.89(21)
SAO 62042(second season)
54075–54199 54075–54199 54075–54199 54075–54199
B V Rc Ic
19 19 19 19
0.941(4) 0.811(4) 0.772(4) 0.740(3)
0.105(6) 0.094(6) 0.090(6) 0.073(5)
19.02(7) 19.05(8) 19.04(7) 18.99(8)
54075.05(20) 54075.04(24) 54075.21(22) 54075.19(23)
FI Cnc(first season)
53770–53882 53770–53879 53770–53879 53790–53879
B V Rc Ic
26 25 25 17
1.054(4) 1.415(3) 1.623(3) 1.852(2)
0.051(4) 0.045(4) 0.036(3) 0.026(3)
28.36(36) 28.53(37) 28.88(46) 29.76(63)
53850.36(47) 53851.68(52) 53850.47(55) 53851.91(64)
FI Cnc(second season)
54013–54207 54013–54207 54024–54207 54013–54207
B V Rc Ic
17 18 18 20
1.109(3) 1.482(4) 1.690(3) 1.912(3)
0.071(5) 0.059(7) 0.054(5) 0.050(6)
28.46(12) 28.30(16) 28.40(14) 28.71(20)
54109.28(27) 54108.96(37) 54109.53(31) 54109.22(43)
SAO 62042(first season)
Standard deviations in the last digits are given in parenthesis.
field of view (FOV) values for both cameras are 29 arcmin across and 12 arcmin 18 arcmin, respectively. All CCD observations were made with standard BVRc Ic filters, sequentially. We obtained about eight images in each filter for every target star each observational night. Exposure times varied between a couple of seconds and 10 s, depending on the brightness of the object and sky conditions. Several bias frames and twilight sky flats, to correct for pixel-to-pixel variations on the chip, were taken intermittently during observations. The data related to comparison and check stars, used in these observations, are given in Table 1. Comparison and check stars were close enough to their respective target star to be observed within the same FOV. All images were bias and dark subtracted and flat-fielded using C-Munipack software (http://integral.sci.muni.cz/cmunipack). In order to obtain light variations of these active stars, we have performed differential photometry with respect to the comparison stars on the CCD frame. The instrumental magnitudes resulting from C-Munipack were used to construct the differential light curves. To check the magnitudes of selected comparison stars for constancy, differential magnitudes in sense of comparison and check stars in all filters have been plotted versus observational time in the right panels of Figs. 1–5. BVRc Ic light curves of these observed active stars are also shown in the left panels of Figs. 1–5. In forming these light curves, we used averaged values for each data set obtained in one observing night. To calculate the standard error of the averaged observational points, shown as error bars in the left panels of Figs. 1–5, we also used the standard deviation of the
differential light variations of the comparison relative to the check star collected during the same night. However, the observational data were not transformed into the standard BVRc Ic system. 3. Analysis 3.1. Photometric variability We used a differential corrections (DC) method to estimate rotation periods from the photometric variations of these three active stars. The DC technique is well-known in processing observational data. Such a DC method is used to fit observational light and radial velocity curves of eclipsing binary stars, for example in the ‘Wilson Devinney code’ (cf. Wilson and Devinney, 1971). The DC technique was applied to determine the periodicity of O C diagrams of eclipsing binaries by Erdem and Güdür (1998). In the differential corrections (DC) method, we applied the following equation:
DmðtÞ ¼ Dm0 þ As sin
2p ðT obs T s Þ ; Ps
ð1Þ
where DmðtÞ is the predicted differential magnitude, Dm0 is the differential magnitude of the zero-point, As the semi-amplitude, Ps the period and T s the time of minimum of the sinusoidal variation of the light curves, and T obs is the time of observations. A similar procedure was followed by Kim et al. (1997) to find periodic behavior in the observational light and colour variations of the eclipsing
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Fig. 1. Differential instrumental BVRc Ic light variations and their sinusoidal representation (solid line) of V340 Gem (left panel). Differential instrumental BVRc Ic magnitudes in the sense of comparable star minus check star versus time (right panel).
binary YY Eri. By using DC method, the Eq. (1) applied to each of our data sets in Table 2. Solutions of this method for Dm0 , As , T s and Ps are presented in Table 2. The sinusoidal best-fit curves and the observational points are plotted against HJD time in Figs. 1–5. We used the Fourier transform technique to support and check our results obtained from the DC method (shown in Table 2), by using the Period04 program of Lenz and Breger (2005). However, Period04 gave acceptable periods for only SAO 62042 and FI Cnc. These findings agree with the periods obtained from the DC method and previous literature values. Periodograms from the Fourier transforms are plotted in Fig. 6 using only the V filter data as examples. These diagrams show the frequencies with the highest amplitude, along with the corresponding phase shifts from time T 0 ¼ 0. We considered the criterion of Breger et al. (1993) for the reality of any peak, which is supported by Kuschnig et al. (1997)’s simulation study. Our signal-to-noise ratios S/N in the amplitude spectrums for both active stars, SAO 62042 and FI Cnc, are 12, which can be accepted as a safe condition by the criterion. The amplitude of the highest peak for SAO 62042 was found to be 0.0792 mag, however, which is only about 3.3 times larger than the mean noise amplitude. Even though this falls below the accepted criterion value, we note that, according to Kuschnig et al. (1997), it should still be regarded with high (95%) confidence, on the basis of normal statistics. 3.2. Starspot modelling The approach to starspot modelling we have used follows the methods presented by Budding and Demircan (2007). Various lines
of evidence support the notion of relatively large, distinct areas of concentrated maculation (‘starspots’) on active cool stars. Studies of the colour variations yield temperature differences between such starspots and the surrounding photosphere to be of order 1000 K, i.e. comparable to the situation for sunspot umbrae and implying photospheric magnetic field concentrations of order several thousand gauss over relatively large areas. Suggestions of oversimplification of the real physical situation and uniqueness questions about the modelling of surface maculation should be kept in mind in the analysis of photospheric maculation. These limitations relate to the real information content of available data. Adequate characterization of this information, without over-interpretation, is noteworthy, particularly when part of wider or more long-term studies. The role of the v2 statistical variate, corresponding to the model’s fit, is relevant here. Both model inadequacy and over-interpretation can be judged by studying the v2 value and its derivatives with respect to the model’s adjustable parameters in the vicinity of the optimal fit. v2 is given by
v2 ðaj Þ ¼
N X ½loi lc ðaj ; ti Þ2 =r2i ;
ð2Þ
i¼1
where there are N observations loi at times t i and corresponding calculated points lc ðaj ; t i Þ and r2i denotes the expected variance of the observational errors, for the parameters aj . The notation is fairly general here: details are spelled out in Budding and Demircan (2007). A minimal set of parameters required for the specification of a single spot involves (1) longitude of spot centre k, (2) latitude of spot centre b, (3) inclination of the rotation axis to the line of sight
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Fig. 2. As per Fig. 1 but for SAO 62042 in the first season data of 2006.
i, (4) angular extent of the spot c. The apparent mean semimajor axis of the spot k follows as k ¼ sin c. The reference light level (5) for the unspotted (‘immaculate’) state is U, which is normally set at unity, at least initially. The luminosity (6) of the spotted star as a fraction of the reference level U is then L1 . These two light levels will, of course, coincide when there is only one detectable source of light. The starspot’s flux (7) relative to the normal photosphere jk will be normally small for the visual region or shorter wavelengths. Typically, jk K 0:1 for the stars and spectral ranges met in practice. The linear limb-darkening coefficient (8) for the spotted star’s photosphere, u, is the final quantity of this minimal set, thus amounting to eight parameters in all. The parameters of Dl and m in Tables 3–5 representing our spot models are the accuracy of the observed data, in the means of the external uncertainties of observational points, and the number of free unknowns, respectively. Using the foregoing equation for v2 , a suitable form for the calculated light level at phase / can be written as,
lc ð/Þ ¼ U L1 ð1 jk Þrc ðu; c; z0 ðk; b; i; /ÞÞ;
ð3Þ
where the parameters aj are written out as k, b, i, etc. The light loss function rc , which depends on the projected distance of the spot centre from the centre of the disk z0 , allows for the varying light intensity over the photospheric disk. This rc can then be set as a linear combination of the r-integrals (spelled out in Budding and Demircan, 2007) with suitable limb-darkening coefficients. It is common practice to adopt a linear cosine formula for available accuracies, so that
rc ¼
3 ½ð1 uÞr00 þ ur01 : 3u
ð4Þ
The program SPOT (cf. http://www.winsite.com/search, within the program suite CURVEFIT) implements the foregoing formulae to fit photometric data from cool stars such as those given in the present paper. Applications of SPOT, CURVEFIT are discussed in chapter 10 of Budding and Demircan (2007), where the similar procedures of, for example, Collier et al. (1986), Strassmeier and Oláh (1992) and Lanza et al. (2002) are compared. Observed times ti are converted to phases /i using the ephemerides given in the preceding section. 4. Results and discussion 4.1. V340 Gem V340 Gem (BD + 26 1531 = HD 57267 = GSC 1913 0930 = HIP 35664, V = 7.60) is classified as a semi-regular pulsating star in the SIMBAD. This star has been recently observed by Frasca et al. (2006), together with five late-type binaries both photometrically and spectroscopically. They obtained both the light variation in the V filter and the radial velocity curve of the primary (more massive) component. They analysed the orbital elements of the system and found the mass of the primary to be 2:5 0:5 M and gave a spectral classification as G8III. They also examined Ha and X-ray emission of the system and studied its space velocity. They noted that V340 Gem displays all the characteristics of an RS CVn SB1 binary and is consistent with a young disk population. The differential instrumental light variations of V340 Gem, in averaged (smoothed) data points, relative to the comparison star and also those of the comparison star relative to the check star in BVRc Ic filters, observed between November 2006 and May 2007
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Fig. 3. As per Fig. 1 but for SAO 62042 in the second season data of 2006/2007.
are presented in the left and right panels of Fig. 1, respectively. We calculated external uncertainties for all comparison minus check magnitudes and found them to be 11, 15, 15 and 11 mmag in B, V, Rc and Ic filters, respectively. A similar procedure was followed by Strassmeier et al. (1999) to examine the quality of long-term multicolour photometric data of observed 47 active stars. Our observed light variations of V340 Gem allow an estimation of the rotation period – attributed only to the primary component. Unfortunately, due to insufficient data, the Fourier transform technique does not give any definitive conclusion about periodicity in this case. Therefore, we used only the DC method to estimate the photometric rotation period. This method requires initial estimates for the fitting parameters. Starting values were thus taken from Frasca et al. (2006). The results are given in Table 2 and plotted in the left panel of Fig. 1. We found the mean photometric period to be P photo ¼ 36:16 0:29 day, which is very close to the orbital period of the system P orb ¼ 36:24 day from Frasca et al. (2006). We were thus able to plot phased light curves in the left panel of Fig. 7 using the epoch T 0 = 2452196.58 HJD and P orb ¼ 36:24 day from the radial velocity solution of Frasca et al. The photometric results in Table 2 shows the differential amplitude of the light variation in the V filter to be similar to that of Frasca et al.’s V data. Cool starspots give rise to light variations whose amplitude increases towards shorter wavelengths. B-band light curve is expected to have an amplitude larger than a V-band light curve, which in turn is larger than an I-band light curve. In the case of V340 Gem, our results in Table 2 give almost similar wave amplitudes of the maculation effect in the separate filter data sets in BVRc Ic within the standard errors. On the other hand, if we consider the colour curves, the presence of only cool spots gives rise to col-
our variations which are correlated to V-band variations. This is a general behavior shown by spotted stars: the fainter the star the redder its colour. Messina (2008) argued that the absence of the V magnitude–colour correlation must be ascribed either to a variable contribution from the secondary component, or a facular colour contribution, which can be significant only at shorter wavelengths (U and B filters). In the case of V340 Gem, it seems that the infrared colours (V—R and V—I), where the facular contribution is negligible, show evidence of correlation with redder colours when the stars is fainter, except for scattered points around phase 0.1 (see Fig. 7). However, B—V variations are not correlated to V-band variations. But we need more data with higher accuracy to enable a clear decision on this point.1 In using the SPOT program, we adopted i (inclination of system) = 60° (V340 Gem is SB1 system and does not show eclipses, as can be seen from Figs. 1 and 7). We set L1 =Ltotal (fractional luminosity of the primary star) to be effectively unity (given the absence of a visible secondary spectrum). The limb-darkening coefficients of the primary star were taken from van Hamme (1993) according to T eff ¼ 4850 (Frasca et al., 2006). With these parameters fixed, we obtained the spot parameters given in Table 3 and present this spot model in the right panel of Fig. 7. We first adopted values of jk , the ratio of the mean flux of the spot to the normal photospheric flux (over the spectral window centred at k), on the basis of an assumed temperature decrement in the starspot of 1000 K. Later, jk parameter was allowed to become a free parameter during the iterations. We followed same process
1
We are grateful to a referee for drawing attention to the significance of this point.
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Fig. 4. As per Fig. 1 but for FI Cnc in the first season data of 2006.
for jk in the spot modelling of other two stars in this study. In Fig. 7 the effective phase of the maculation effect appears to be centred at phase 0.8. In the 2001 V light variation of Frasca et al. (2006), the decrease of the V light also appears centred around phase 0.8. However, since there are no data between 2001 (Frasca et al.) and 2006/2007 (present work), we cannot be sure that the phase of minimum has remained constant. The phase could have been varying and by chance is found in 2006 at same position as in 2001. The data are not enough really to confirm if there is an active longitude, nor, if so, to determine its lifetime. However, our results support Frasca et al. (2006)’s study, in which V340 Gem is classified as an SB1 RS CVn binary star, rather than the semi-regular pulsating star given in SIMBAD. 4.2. SAO 62042 SAO 62042 (BD +38 2140) is a fairly nearby star with a TYCHO parallax of 27.9(18.7) mas, and newly discovered as a chromospherically active binary. We found only one previous published study, namely that of Frasca et al. (2006), who observed the star both photometrically and spectroscopically. The radial velocity curve of only the primary component was obtained, for which elements were provided. A spectral classification K1IV was given, although it was noted that the star’s position in the HR diagram appeared more consistent with a Main-Sequence condition. Frasca et al. reported SAO 62042 to display all the main characteristics of a young BY Dra system, especially regarding X-ray luminosity. As mentioned above, we have two different data sets from differential observations of SAO 62042 in the years 2006 and 2007. Our differential instrumental observations of this active star
together with comparison and check stars are presented in Figs. 2 and 3. In the right panels of these figures, the differential magnitudes of comparison minus check stars show more scatter, especially in B filter. We found the uncertainties to be 27, 14, 19 and 21 mmag in B, V, Rc and Ic filters, respectively, for the first season, and 21, 14, 19 and 18 mmag in B, V, Rc and Ic filters, respectively, for the second season. From our differential observations of SAO 62042, the determined periodicity results, using the DC method, are given in Table 2 and shown in Figs. 2 and 3. The Fourier transform technique supports only the results of the second of these data sets (see Fig. 6). We found mean photometric periods of P photo ¼ 19:49 0:14 day and 19:03 0:08 day for the first and second season, respectively. We have plotted the phased light curves in Figs. 8 and 9, using the epoch T s = 2453827.08 HJD and the mean photometric period Ps = 19.26 day. Since Porb ¼ 15:465 day from Frasca et al. (2006), it is clear that Pphoto is significantly greater than Porb . The photometric results in Table 2 also show the differential amplitude of the light variations of the second season to be larger than those of the first. From the phased colour curves in Figs. 8 and 9, especially the infrared colour variations (V—R and V—I) (aside from the scattered points shown by open ellipses) in the first season, and the (V—I) variation in the second season, we find similar periods to the V-band results. This is in keeping with the cool starspot scenario. In using the SPOT program for analysis of SAO 62042 we adopted i (inclination of system) = 60° (SAO 62042 is SB1 system and does not show eclipses, as can be seen from Figs. 2, 3, 8, 9.). We set L1 =Ltotal (fractional luminosity of the primary (more massive and hotter) star) to be effectively unity (given the absence of a
A. Erdem et al. / New Astronomy 14 (2009) 109–120
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Fig. 5. As per Fig. 1 but for FI Cnc in the second season data of 2006/2007.
visible secondary spectrum). The limb-darkening coefficients of the primary star are taken from van Hamme (1993) according to T eff ¼ 4750 (Frasca et al., 2006). With these parameters fixed, we obtained the spot parameters given in Table 4 and present our spot models in the right panels of Figs. 8 and 9. According to these spot models of SAO 62042 in Table 4, the latitude parameters of the spot in both seasons are relatively high. For longitude parameters, the main spot formation migrated in longitude from 270° to 215° in almost one year, if the same maculation region is being followed in both seasons. The mean angular radius of the spot became larger in one year.
Amplitude (mag)
0.12 0.10 0.08 0.06 0.04 0.02 0.00 0.0
0.2
0.4
0.6
0.8
1.0
c/d
4.3. FI Cnc
0.05
Amplitude (mag)
0.04 0.03 0.02 0.01 0.00 0.0
0.2
0.4
c/d
0.6
0.8
1.0
Fig. 6. Periodograms obtained from Fourier transforms technique for the V 2006/ 2007 data of SAO 62042 (upper panel) and the V 2006 data of FI Cnc (lower panel).
FI Cnc (BD +29 1772 = HD 72146 = GSC 1947 0489 = HIP 41875, V = 7.37) is classified as a variable (single) star in the SIMBAD database. Strassmeier et al. (1994) noted that the spectrum of this star shows strong CaII H and K emission lines. Fekel and Balachandran (1994) classified it as a single G8III, measuring its rotational velocity as vsini ¼ 15 km s1 and finding a significant lithium abundance. Henry et al. (1995) observed FI Cnc together with 64 other active late-type stars both photometrically and spectroscopically in their automated search for variability in chromospherically active stars. They found a photometric period of 28:5 0:1 day, the maximum photometric amplitude in V band being 0.16 mag, with cycle-to-cycle variations in amplitude evident. They argued that the star has a moderately rapidly rotation, measuring the projected equatorial rotation velocity to be 14 1 km s1. They found the star to show strong and variable Ha emission. Fekel (1997)
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Fig. 7. The left panel shows the phased light and colour curves of V340 Gem in 2006/2007. In the right panel the curve represent the best-fit spot model for these observed data.
Table 3 Starspot parameter sets for V340 Gem
k (deg) b (deg) c (deg)
jk U uk Dl
v2 =m
B
V
Rc
Ic
290(3) 69(5) 25(3) 0.03(2) 1.065(3) 0.893 0.011 2.71
292(3) 64(7) 25(3) 0.07(4) 1.073(3) 0.745 0.015 1.36
283(3) 64(9) 26(4) 0.13(3) 1.076(3) 0.641 0.015 2.29
284(4) 63(18) 26(7) 0.18(3) 1.069(3) 0.537 0.011 1.54
Standard deviations in the last digits are given in parenthesis.
found a projected rotational velocity of 17.4 km s1 and inferred a minimum radius of 9.8 R . Strassmeier et al. (2000) made a spectroscopic Ca II H and K survey of 1058 late-type stars selected from
the Hipparcos catalogue. For FI Cnc they found a spectral type G5, rotational velocity of 18.8 km s1, photometric amplitude in yband of 0.11 mag and photometric period of 29.14 day, using red-wavelength spectroscopic and Strömgren–Crawford system photometric observations. Koen and Eyer (2002) examined the periodicity of many variable stars using Hipparcos data, and found a photometric period of 35.84 day, which is quite larger than previous estimates. Their mean amplitude was only 0.031 mag. The star is also known as a source in the radio and X-ray wavelengths (J083217.3 + 291909 and J083217.4 + 291920). We have again two different data sets from observations of FI Cnc in 2006 and 2007. The differential observations of this active star, together with comparison and check star data, are presented in Figs. 4 and 5. In the right panels of these figures, the differential magnitudes of comparison minus check stars show a rather greater scatter. We found error measures to be 21, 13, 13 and 19 mmag in
Table 4 Starspot parameter sets for SAO 62042 First season data (2006)
k (deg) b (deg) c (deg)
jk U uk Dl
v2 =m
Second season data (2006/2007)
B
V
Rc
Ic
B
V
Rc
Ic
277(6) 72(9) 25(6) 0.03(2) 1.076(5) 0.911 0.027 0.67
271(4) 69(7) 22(3) 0.06(3) 1.065(2) 0.763 0.014 2.57
269(5) 68(9) 22(4) 0.10(4) 1.054(3) 0.656 0.019 0.92
268(8) 67(13) 22(6) 0.16(5) 1.054(4) 0.548 0.021 0.36
214(5) 72(5) 29(4) 0.03(2) 1.098(5) 0.911 0.021 1.05
215(4) 72(5) 29(4) 0.06(3) 1.103(3) 0.763 0.014 2.04
219(5) 71(9) 29(6) 0.11(4) 1.091(5) 0.656 0.019 0.93
216(6) 68(10) 25(5) 0.16(5) 1.070(4) 0.548 0.018 0.78
Standard deviations in the last digits are given in parenthesis.
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A. Erdem et al. / New Astronomy 14 (2009) 109–120 Table 5 Starspot parameter sets for FI Cnc First season data (2006)
k1 (deg) b1 (deg) c1 (deg) k2 (deg) b2 (deg) c2 (deg)
jk U uk Dl
v2 = m
Second season data (2006/2007)
B
V
Rc
Ic
B
V
Rc
Ic
183(14) 41(20) 13(4) 303(6) 41(10) 16(3) 0.05(4) 1.035(4) 0.867 0.021 0.20
188(17) 45 12(2) 304(4) 45 15(1) 0.10(5) 1.027(3) 0.719 0.013 0.66
185(8) 45 13(3) 301(4) 45 15(3) 0.13(5) 1.025(3) 0.619 0.013 0.50
187(20) 45 10(4) 307(11) 45 13(5) 0.19(8) 1.022(4) 0.521 0.019 0.12
270(6) 70(10) 27(7) – – – 0.05(4) 1.057(4) 0.867 0.018 0.60
264(8) 69(12) 23(6) – – – 0.09(4) 1.044(4) 0.719 0.018 0.74
273(9) 68(18) 22(9) – – – 0.13(5) 1.037(5) 0.619 0.021 0.39
272(8) 66(22) 22(9) – – – 0.20(5) 1.050(4) 0.521 0.020 0.24
Standard deviations in the last digits are given in parenthesis.
Fig. 8. As per Fig. 7 but for SAO 62042 in the first season data of 2006.
B, V, Rc and Ic filters, respectively, for the first season, and 18, 18, 21 and 20 mmag in B, V, Rc and Ic filters, respectively, for the second season. The periodicity results using the DC method on FI Cnc are given in Table 2. The Fourier technique supports only the results of the first of these data sets (see Fig. 6). We found mean photometric periods of Pphoto ¼ 28:88 0:46 day and 28:47 0:16 day for the first and second season, respectively. Our photometric period values support those of Henry et al. (1995) and Strassmeier et al. (2000) (28.5 day and 29.14 day, respectively) but are at variance with Koen and Eyer (2002)’s value (35.84 day). We used the same light elements (T s = 2453851.11 HJD and P s = 28.68 day) in the separate data seasons to plot the phased light curves in the left panels of Figs. 10 and 11, and also to deduce spot migration. The photometric results in Table 2 also show the differential amplitude of
the light variations of the second season to be quite larger than those of the first season. From the phased colour curves in the left panels of Figs. 10 and 11, apart from the scattered points marked by open ellipses, the results are in keeping with the expected behavior of cool spots. In using the SPOT program for analysis of FI Cnc we adopted that i (inclination of system)=70° and L1 =Ltotal = 1 (FI Cnc was taken to be a single star). The limb-darkening coefficients are from van Hamme (1993) with T eff ffi 5000 (according to Strassmeier et al. (2000)). With these parameters fixed, we obtained the spot parameters given in Table 5 and present these spot models in the right panels of Figs. 10 and 11. The phased light curves of FI Cnc in the first season shows a large maculation wave with an asymmetric structure (see Fig. 10), having two separate minima: one is shallow, the other is quite
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Fig. 9. As per Fig. 7 but for SAO 62042 in the second season data of 2006/2007.
Fig. 10. As per Fig. 7 but for FI Cnc in the first season data of 2006.
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A. Erdem et al. / New Astronomy 14 (2009) 109–120
Fig. 11. As per Fig. 7 but for FI Cnc in the second season data of 2006/2007.
deeper. We therefore considered a two spot model for the first season. The mean angular radius of the spot became larger (almost by a factor of two) in one year. According to the longitude parameters, the main spot formation, if continuing through both data sets, migrated in longitude from about 300° to 270° in almost one year. In fact, it could be that two spots of the first season merged into one spot in the second season. 5. Conclusions This paper has collected together BVRc Ic photometric data on the three active cool stars V340 Gem, SAO 62042 and FI Cnc from the ÇOMU Observatory in 2006 and 2007. V340 Gem and SAO 62042 are among the program stars listed as RS CVn SB1 binaries by Frasca et al. (2006), while FI Cnc is a single active giant star (Fekel and Balachandran, 1994). We have confirmed systematic variations, of relatively low amplitudes, consistent with the photometric effects of very large regions of surface maculation, whose aspect varies with the mean rotation rate of the latitude at which the ‘starspots’ are located. The presented study gives the first photometric analyses of V340 Gem and SAO 62042. We have characterized these effects in terms of heuristic starspot model parameter sets. Seasonal changes of maculation region size and surface position were thence indicated. These latter effects are frequently found in cool active stars and are consistent with differential rotation operating at relatively greater scales in higher latitudes. The particular stars studied here appear to show relatively large differential rotation rates, particularly SAO 62042, and this may indicate a near polar location for this star’s main macula.
The periods and surface differential rotation (SDR) could be checked by using the following well-known equation: 2
Pb ¼ P eq =ð1 k sin bÞ;
ð5Þ
where Pb is the period at latitude b, P eq is the equatorial period and k is the surface differential rotation coefficient. For SAO 62042, if we take the photometric rotation period as P b , the orbital period as P eq (under the assumption of synchronous rotation) and the starspot latitude as b, we found k to be about 0.22. For the Sun, k has been derived from sunspot latitudes and periods to be 0.19 by Kitchatinov (2005), based on the Newton and Nunn (1951)’s study. According to this value, our k value for SAO 62042 is slightly larger than that of the Sun. Since Brown et al. (2004) show that k should increase with age, this difference could be due to the age of SAO 62042. On the other hand, Messina and Guinan (2006) suggested that the growth and decay of the starspots may produce variations of the apparent photometric period, i.e. the apparent period may well be affected by changes of surface structure in the maculation region itself. In the case of V340 Gem, the orbital period (Porb = 36.24 day) and photometric period (Pphoto ¼ 36:16 0:29 day) are almost equal within the estimated uncertainty; therefore, it does not make much sense to search for SDR in this star. For FI Cnc, the two photometric periods (Pphoto ¼ 28:88 0:46 day and 28:47 0:16) found in this study are effectively the same, to within the estimated error; thus they also do not give support to SDR. While noting such preliminary indications, this paper does not emphasize details of interpretation, as it is hoped data such as that presented will be continued and prove to be of more general significance when forming part of more comprehensive long-term studies.
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Acknowledgements We thank the anonymous referee for their helpful comments in improving this manuscript. This study was supported by the Turkish TUBITAK under the Grant No. 105T083. References Breger, M., Stich, J., Garrido, R., et al., 1993. A&A 271, 482. Brown, B.P., Browning, M.K., Brun, A.S., Toomre, J., 2004. In: Danesy, D. (Ed.), Proceedings of the SOHO 14/GONG 2004 Workshop (ESA SP-559), Helio- and Asteroseismology: Towards a Golden Future, 12–16 July, 2004, New Haven, Connecticut, USA, p. 341. Budding, E., Demircan, O., 2007. Introduction to Astronomical Photometry, second ed. Cambridge University Press. Collier, C.A., Bedford, D.K., Evans, T.L., Rucinski, S.M., Vilhu, O., White, N.E., 1986. In: Zeilik, M., Gibson, D.M. (Eds.), Lecture Notes Physics, 254, p. 313. Demircan, O., Erdem, A., Özdemir, S., Çiçek, C., Bulut, I., Soydugan, F., Soydugan, E., Bakis, V., Kabas, A., Bulut, A., Tüysüz, M., Zejda, M., et al., 2003. IBVS, 5364. Erdem, A., Güdür, N., 1998. A&AS 127, 257. Fekel, F.C., 1997. PASP 109, 514.
Fekel, F.C., Balachandran, S., 1994. In: Caillault, J.-P. (Ed.), Cool Stars, Stellar Systems, and the Sun, Eighth Cambridge Workshop. ASP, San Francisco, p. 279. Frasca, A., Guillout, P., Marilli, E., Freire Ferrero, R., Biazzo, K., Klutsch, A., 2006. A&A 454, 301. Henry, G.W., Fekel, F.C., Hall, D.S., 1995. AJ 110, 2926. Kim, C.-H., Jeong, J.H., Demircan, O., Müyesseroglu, Z., Budding, E., 1997. AJ 114, 2753. Kitchatinov, L.L., 2005. Physics – Uspekhi 48 (5), 449. Kitchatinov, L.L., Rudiger, G., 1999. A&A 344, 911. Koen, C., Eyer, L., 2002. MNRAS 331, 45. Kuschnig, R., Weiss, W.W., Gruber, R., Bely, P.Y., Jenkner, H., 1997. A&A 328, 544. Lanza, A.F., Catalano, S., Rodono, M., et al., 2002. A&A 386, 583. Lenz, P., Breger, M., 2005. CoAst 146, 53. Messina, S., 2008. A&A 480, 495. Messina, S., Guinan, E.F., 2006. Ap&SS 304, 191. Newton, H.W., Nunn, M.L., 1951. MNRAS 111, 413. Strassmeier, K.G., Oláh, K., 1992. A&A 259, 595. Strassmeier, K.G., Handler, G., Paunzen, E., Rauth, M., 1994. A&A 281, 855. Strassmeier, K.G., Serkowitsch, E., Granzer, Th., 1999. A&AS 140, 29. Strassmeier, K.G., Washuettl, A., Granzer, Th., Scheck, M., Weber, M., 2000. A&AS 142, 275. van Hamme, W., 1993. AJ 106, 2096. Wilson, R.E., Devinney, E.J., 1971. AJ 166, 605.
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New Astronomy journal homepage: www.elsevier.com/locate/newast
Photometry of three chromospherically active stars: V340 Gem, SAO 62042 and FI Cnc A. Erdem *, E. Budding, E. Soydugan, F. Soydugan, S.S. Dog˘ru, D. Dog˘ru, M. Tüysüz, A. Dönmez, H. Bakisß, Y. Kaçar, C. Çiçek, Z. Eker, O. Demircan Çanakkale Onsekiz Mart University Observatory, Terziog˘lu Kampüsü, 17020 Çanakkale, Turkey
a r t i c l e
i n f o
Article history: Received 13 December 2007 Received in revised form 6 June 2008 Accepted 6 June 2008 Available online 12 June 2008 Communicated by W. Soon PACS: 97.10.Jb 97.10.Kc 97.30.Nr
a b s t r a c t We present a photometric study of three chromospherically active stars with long periods (V340 Gem, SAO 62042 and FI Cnc). The observations were made at the ÇOMU Observatory in 2006 and 2007. We have made initial photometric analyses of V340 Gem and SAO 62042, which are newly discovered RS CVn–type SB1 binaries, and established the photometric variations of FI Cnc, which is a single G8III active star. Photometric rotation periods of these stars were obtained by analyzing their light variations. The light variations, observed over three or more consecutive orbital cycles, were investigated by using spot models with the program SPOT. We also discussed the surface differential rotation coefficient for the primary component of the SB1 binary star SAO 62042 in this study, using our own photometric period together with an orbital period taken from the literature. Ó 2008 Elsevier B.V. All rights reserved.
Keywords: Stars: activity Stars: rotation Stars: spots Stars: individual (V340 Gem, SAO 62042, FI Cnc)
1. Introduction According to models, magnetic activity of solar and late-type stars originates from envelope convection and differential rotation. Current theoretical studies show how differential rotation depends on global stellar parameters, such as spectral type and rotation period (e.g. Kitchatinov and Rudiger, 1999). It is also clear, physically, that the interaction of axial rotation with envelope convection should create differential rotation. It is important to observe evidence of stellar magnetic activity to test model predictions. Stellar surface differential rotation depends on latitude, and this can sometimes be assessed from observations. Photometric data may give an opportunity to predict surface differential rotation from rotation period variations. In this view, the most likely explanation of changes of (short-term) photometric period of an active star is the variation of rotation period of predominating starspot features (Messina and Guinan, 2006). However, we should note here that observed variations of the pho-
* Corresponding author. Tel.: +90 286 2180019; fax: +90 286 2180533. E-mail address: [email protected] (A. Erdem). 1384-1076/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.newast.2008.06.001
tometric period can also be related to the growth and decay of starspots. In the present work, we have selected three chromospherically active stars V340 Gem, SAO 62042 and FI Cnc to study their photometric variations. The basic parameters of these stars were taken from SIMBAD and the Tycho Catalogue, and these are listed in Table 1. 2. Observations and reductions The above-named three active stars were observed at the Çanakkale Onsekiz Mart University Observatory (Demircan et al., 2003) in the years 2006 and 2007. A summary of observations is presented in Table 2. For SAO 62042 and FI Cnc, the 30-cm Schmidt– Cassegrain reflector, equipped with an SBIG ST–10XME CCD camera in the first season of observations (between February and June of 2006), and an SBIG STL–1001E CCD camera in the second season (between November 2006 and April 2007) was used. For V340 Gem, the SBIG STL–1001E CCD camera was used for all observations between November 2006 and May 2007. The SBIG STL–1001E and SBIG ST–10XME CCD cameras give image scales of 1.63 arcseconds per pixel and 0.45 arcseconds per pixel, respectively. The observed
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Table 1 Basic parameters for program stars from SIMBAD and Tycho Catalogue 0 00
Star
HD No
GSC no.
a (2000) h m s
d (2000)°
V340 Gem Comparison Check
57267 57106 57206
1913 0930 1917 0475 1917 0494
07 21 33 07 20 55 07 21 16
+26 09 33 +26 37 27 +26 29 40
3001 3001 3001 3001
10 10 10 10
+37 +37 +37 +37
SAO 62042 Comparison Check-1 (first season) Check-2 (second season) FI Cnc Comparison Check
72146 72052
1282 1385 1329 1138
1947 0489 1947 0367 1947 0089
26 26 26 26
23 25 35 03
08 32 17 08 32 18 08 31 52
V (mag)
B—V(mag)
Spectral type
7.60 8.06 8.29
0.786(15) 1.478(33) 0.108(22)
G2V K2 A0
13 05 43 07
9.61 10.53 10.90 9.35
1.007(52) 1.056(133) 0.674(124) 0.430(33)
K2
F5
+29 19 10 +29 28 01 +29 42 41
7.37 8.77 8.21
0.951(12) 0.516(22) 0.406(18)
G5 F8 F3V
45 44 45 53
Table 2 Photometric results of program stars Variable
Time range 2,400,000 +
Filter
N obs
Dm0 (mag)
As (mag)
P s (days)
T s (HJD) 2,400,000 +
V340 Gem
54047–54230 54047–54211 54047–54211 54047–54211 53770–53882 53770–53897 53770–53897 53798–53897
B V Rc Ic B V Rc Ic
23 24 24 25 32 34 38 24
0.915(6) 0.458(5) 0.236(6) 0.025(6) 0.936(4) 0.812(4) 0.775(3) 0.749(2)
0.085(9) 0.085(8) 0.083(9) 0.080(9) 0.075(5) 0.063(5) 0.059(4) 0.055(3)
35.93(32) 36.10(23) 36.23(28) 36.37(31) 19.02(13) 19.74(14) 19.77(11) 19.43(15)
54119.50(50) 54119.64(40) 54118.77(46) 54118.81(51) 53827.41(23) 53827.07(25) 53826.93(20) 53826.89(21)
SAO 62042(second season)
54075–54199 54075–54199 54075–54199 54075–54199
B V Rc Ic
19 19 19 19
0.941(4) 0.811(4) 0.772(4) 0.740(3)
0.105(6) 0.094(6) 0.090(6) 0.073(5)
19.02(7) 19.05(8) 19.04(7) 18.99(8)
54075.05(20) 54075.04(24) 54075.21(22) 54075.19(23)
FI Cnc(first season)
53770–53882 53770–53879 53770–53879 53790–53879
B V Rc Ic
26 25 25 17
1.054(4) 1.415(3) 1.623(3) 1.852(2)
0.051(4) 0.045(4) 0.036(3) 0.026(3)
28.36(36) 28.53(37) 28.88(46) 29.76(63)
53850.36(47) 53851.68(52) 53850.47(55) 53851.91(64)
FI Cnc(second season)
54013–54207 54013–54207 54024–54207 54013–54207
B V Rc Ic
17 18 18 20
1.109(3) 1.482(4) 1.690(3) 1.912(3)
0.071(5) 0.059(7) 0.054(5) 0.050(6)
28.46(12) 28.30(16) 28.40(14) 28.71(20)
54109.28(27) 54108.96(37) 54109.53(31) 54109.22(43)
SAO 62042(first season)
Standard deviations in the last digits are given in parenthesis.
field of view (FOV) values for both cameras are 29 arcmin across and 12 arcmin 18 arcmin, respectively. All CCD observations were made with standard BVRc Ic filters, sequentially. We obtained about eight images in each filter for every target star each observational night. Exposure times varied between a couple of seconds and 10 s, depending on the brightness of the object and sky conditions. Several bias frames and twilight sky flats, to correct for pixel-to-pixel variations on the chip, were taken intermittently during observations. The data related to comparison and check stars, used in these observations, are given in Table 1. Comparison and check stars were close enough to their respective target star to be observed within the same FOV. All images were bias and dark subtracted and flat-fielded using C-Munipack software (http://integral.sci.muni.cz/cmunipack). In order to obtain light variations of these active stars, we have performed differential photometry with respect to the comparison stars on the CCD frame. The instrumental magnitudes resulting from C-Munipack were used to construct the differential light curves. To check the magnitudes of selected comparison stars for constancy, differential magnitudes in sense of comparison and check stars in all filters have been plotted versus observational time in the right panels of Figs. 1–5. BVRc Ic light curves of these observed active stars are also shown in the left panels of Figs. 1–5. In forming these light curves, we used averaged values for each data set obtained in one observing night. To calculate the standard error of the averaged observational points, shown as error bars in the left panels of Figs. 1–5, we also used the standard deviation of the
differential light variations of the comparison relative to the check star collected during the same night. However, the observational data were not transformed into the standard BVRc Ic system. 3. Analysis 3.1. Photometric variability We used a differential corrections (DC) method to estimate rotation periods from the photometric variations of these three active stars. The DC technique is well-known in processing observational data. Such a DC method is used to fit observational light and radial velocity curves of eclipsing binary stars, for example in the ‘Wilson Devinney code’ (cf. Wilson and Devinney, 1971). The DC technique was applied to determine the periodicity of O C diagrams of eclipsing binaries by Erdem and Güdür (1998). In the differential corrections (DC) method, we applied the following equation:
DmðtÞ ¼ Dm0 þ As sin
2p ðT obs T s Þ ; Ps
ð1Þ
where DmðtÞ is the predicted differential magnitude, Dm0 is the differential magnitude of the zero-point, As the semi-amplitude, Ps the period and T s the time of minimum of the sinusoidal variation of the light curves, and T obs is the time of observations. A similar procedure was followed by Kim et al. (1997) to find periodic behavior in the observational light and colour variations of the eclipsing
A. Erdem et al. / New Astronomy 14 (2009) 109–120
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Fig. 1. Differential instrumental BVRc Ic light variations and their sinusoidal representation (solid line) of V340 Gem (left panel). Differential instrumental BVRc Ic magnitudes in the sense of comparable star minus check star versus time (right panel).
binary YY Eri. By using DC method, the Eq. (1) applied to each of our data sets in Table 2. Solutions of this method for Dm0 , As , T s and Ps are presented in Table 2. The sinusoidal best-fit curves and the observational points are plotted against HJD time in Figs. 1–5. We used the Fourier transform technique to support and check our results obtained from the DC method (shown in Table 2), by using the Period04 program of Lenz and Breger (2005). However, Period04 gave acceptable periods for only SAO 62042 and FI Cnc. These findings agree with the periods obtained from the DC method and previous literature values. Periodograms from the Fourier transforms are plotted in Fig. 6 using only the V filter data as examples. These diagrams show the frequencies with the highest amplitude, along with the corresponding phase shifts from time T 0 ¼ 0. We considered the criterion of Breger et al. (1993) for the reality of any peak, which is supported by Kuschnig et al. (1997)’s simulation study. Our signal-to-noise ratios S/N in the amplitude spectrums for both active stars, SAO 62042 and FI Cnc, are 12, which can be accepted as a safe condition by the criterion. The amplitude of the highest peak for SAO 62042 was found to be 0.0792 mag, however, which is only about 3.3 times larger than the mean noise amplitude. Even though this falls below the accepted criterion value, we note that, according to Kuschnig et al. (1997), it should still be regarded with high (95%) confidence, on the basis of normal statistics. 3.2. Starspot modelling The approach to starspot modelling we have used follows the methods presented by Budding and Demircan (2007). Various lines
of evidence support the notion of relatively large, distinct areas of concentrated maculation (‘starspots’) on active cool stars. Studies of the colour variations yield temperature differences between such starspots and the surrounding photosphere to be of order 1000 K, i.e. comparable to the situation for sunspot umbrae and implying photospheric magnetic field concentrations of order several thousand gauss over relatively large areas. Suggestions of oversimplification of the real physical situation and uniqueness questions about the modelling of surface maculation should be kept in mind in the analysis of photospheric maculation. These limitations relate to the real information content of available data. Adequate characterization of this information, without over-interpretation, is noteworthy, particularly when part of wider or more long-term studies. The role of the v2 statistical variate, corresponding to the model’s fit, is relevant here. Both model inadequacy and over-interpretation can be judged by studying the v2 value and its derivatives with respect to the model’s adjustable parameters in the vicinity of the optimal fit. v2 is given by
v2 ðaj Þ ¼
N X ½loi lc ðaj ; ti Þ2 =r2i ;
ð2Þ
i¼1
where there are N observations loi at times t i and corresponding calculated points lc ðaj ; t i Þ and r2i denotes the expected variance of the observational errors, for the parameters aj . The notation is fairly general here: details are spelled out in Budding and Demircan (2007). A minimal set of parameters required for the specification of a single spot involves (1) longitude of spot centre k, (2) latitude of spot centre b, (3) inclination of the rotation axis to the line of sight
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Fig. 2. As per Fig. 1 but for SAO 62042 in the first season data of 2006.
i, (4) angular extent of the spot c. The apparent mean semimajor axis of the spot k follows as k ¼ sin c. The reference light level (5) for the unspotted (‘immaculate’) state is U, which is normally set at unity, at least initially. The luminosity (6) of the spotted star as a fraction of the reference level U is then L1 . These two light levels will, of course, coincide when there is only one detectable source of light. The starspot’s flux (7) relative to the normal photosphere jk will be normally small for the visual region or shorter wavelengths. Typically, jk K 0:1 for the stars and spectral ranges met in practice. The linear limb-darkening coefficient (8) for the spotted star’s photosphere, u, is the final quantity of this minimal set, thus amounting to eight parameters in all. The parameters of Dl and m in Tables 3–5 representing our spot models are the accuracy of the observed data, in the means of the external uncertainties of observational points, and the number of free unknowns, respectively. Using the foregoing equation for v2 , a suitable form for the calculated light level at phase / can be written as,
lc ð/Þ ¼ U L1 ð1 jk Þrc ðu; c; z0 ðk; b; i; /ÞÞ;
ð3Þ
where the parameters aj are written out as k, b, i, etc. The light loss function rc , which depends on the projected distance of the spot centre from the centre of the disk z0 , allows for the varying light intensity over the photospheric disk. This rc can then be set as a linear combination of the r-integrals (spelled out in Budding and Demircan, 2007) with suitable limb-darkening coefficients. It is common practice to adopt a linear cosine formula for available accuracies, so that
rc ¼
3 ½ð1 uÞr00 þ ur01 : 3u
ð4Þ
The program SPOT (cf. http://www.winsite.com/search, within the program suite CURVEFIT) implements the foregoing formulae to fit photometric data from cool stars such as those given in the present paper. Applications of SPOT, CURVEFIT are discussed in chapter 10 of Budding and Demircan (2007), where the similar procedures of, for example, Collier et al. (1986), Strassmeier and Oláh (1992) and Lanza et al. (2002) are compared. Observed times ti are converted to phases /i using the ephemerides given in the preceding section. 4. Results and discussion 4.1. V340 Gem V340 Gem (BD + 26 1531 = HD 57267 = GSC 1913 0930 = HIP 35664, V = 7.60) is classified as a semi-regular pulsating star in the SIMBAD. This star has been recently observed by Frasca et al. (2006), together with five late-type binaries both photometrically and spectroscopically. They obtained both the light variation in the V filter and the radial velocity curve of the primary (more massive) component. They analysed the orbital elements of the system and found the mass of the primary to be 2:5 0:5 M and gave a spectral classification as G8III. They also examined Ha and X-ray emission of the system and studied its space velocity. They noted that V340 Gem displays all the characteristics of an RS CVn SB1 binary and is consistent with a young disk population. The differential instrumental light variations of V340 Gem, in averaged (smoothed) data points, relative to the comparison star and also those of the comparison star relative to the check star in BVRc Ic filters, observed between November 2006 and May 2007
A. Erdem et al. / New Astronomy 14 (2009) 109–120
113
Fig. 3. As per Fig. 1 but for SAO 62042 in the second season data of 2006/2007.
are presented in the left and right panels of Fig. 1, respectively. We calculated external uncertainties for all comparison minus check magnitudes and found them to be 11, 15, 15 and 11 mmag in B, V, Rc and Ic filters, respectively. A similar procedure was followed by Strassmeier et al. (1999) to examine the quality of long-term multicolour photometric data of observed 47 active stars. Our observed light variations of V340 Gem allow an estimation of the rotation period – attributed only to the primary component. Unfortunately, due to insufficient data, the Fourier transform technique does not give any definitive conclusion about periodicity in this case. Therefore, we used only the DC method to estimate the photometric rotation period. This method requires initial estimates for the fitting parameters. Starting values were thus taken from Frasca et al. (2006). The results are given in Table 2 and plotted in the left panel of Fig. 1. We found the mean photometric period to be P photo ¼ 36:16 0:29 day, which is very close to the orbital period of the system P orb ¼ 36:24 day from Frasca et al. (2006). We were thus able to plot phased light curves in the left panel of Fig. 7 using the epoch T 0 = 2452196.58 HJD and P orb ¼ 36:24 day from the radial velocity solution of Frasca et al. The photometric results in Table 2 shows the differential amplitude of the light variation in the V filter to be similar to that of Frasca et al.’s V data. Cool starspots give rise to light variations whose amplitude increases towards shorter wavelengths. B-band light curve is expected to have an amplitude larger than a V-band light curve, which in turn is larger than an I-band light curve. In the case of V340 Gem, our results in Table 2 give almost similar wave amplitudes of the maculation effect in the separate filter data sets in BVRc Ic within the standard errors. On the other hand, if we consider the colour curves, the presence of only cool spots gives rise to col-
our variations which are correlated to V-band variations. This is a general behavior shown by spotted stars: the fainter the star the redder its colour. Messina (2008) argued that the absence of the V magnitude–colour correlation must be ascribed either to a variable contribution from the secondary component, or a facular colour contribution, which can be significant only at shorter wavelengths (U and B filters). In the case of V340 Gem, it seems that the infrared colours (V—R and V—I), where the facular contribution is negligible, show evidence of correlation with redder colours when the stars is fainter, except for scattered points around phase 0.1 (see Fig. 7). However, B—V variations are not correlated to V-band variations. But we need more data with higher accuracy to enable a clear decision on this point.1 In using the SPOT program, we adopted i (inclination of system) = 60° (V340 Gem is SB1 system and does not show eclipses, as can be seen from Figs. 1 and 7). We set L1 =Ltotal (fractional luminosity of the primary star) to be effectively unity (given the absence of a visible secondary spectrum). The limb-darkening coefficients of the primary star were taken from van Hamme (1993) according to T eff ¼ 4850 (Frasca et al., 2006). With these parameters fixed, we obtained the spot parameters given in Table 3 and present this spot model in the right panel of Fig. 7. We first adopted values of jk , the ratio of the mean flux of the spot to the normal photospheric flux (over the spectral window centred at k), on the basis of an assumed temperature decrement in the starspot of 1000 K. Later, jk parameter was allowed to become a free parameter during the iterations. We followed same process
1
We are grateful to a referee for drawing attention to the significance of this point.
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Fig. 4. As per Fig. 1 but for FI Cnc in the first season data of 2006.
for jk in the spot modelling of other two stars in this study. In Fig. 7 the effective phase of the maculation effect appears to be centred at phase 0.8. In the 2001 V light variation of Frasca et al. (2006), the decrease of the V light also appears centred around phase 0.8. However, since there are no data between 2001 (Frasca et al.) and 2006/2007 (present work), we cannot be sure that the phase of minimum has remained constant. The phase could have been varying and by chance is found in 2006 at same position as in 2001. The data are not enough really to confirm if there is an active longitude, nor, if so, to determine its lifetime. However, our results support Frasca et al. (2006)’s study, in which V340 Gem is classified as an SB1 RS CVn binary star, rather than the semi-regular pulsating star given in SIMBAD. 4.2. SAO 62042 SAO 62042 (BD +38 2140) is a fairly nearby star with a TYCHO parallax of 27.9(18.7) mas, and newly discovered as a chromospherically active binary. We found only one previous published study, namely that of Frasca et al. (2006), who observed the star both photometrically and spectroscopically. The radial velocity curve of only the primary component was obtained, for which elements were provided. A spectral classification K1IV was given, although it was noted that the star’s position in the HR diagram appeared more consistent with a Main-Sequence condition. Frasca et al. reported SAO 62042 to display all the main characteristics of a young BY Dra system, especially regarding X-ray luminosity. As mentioned above, we have two different data sets from differential observations of SAO 62042 in the years 2006 and 2007. Our differential instrumental observations of this active star
together with comparison and check stars are presented in Figs. 2 and 3. In the right panels of these figures, the differential magnitudes of comparison minus check stars show more scatter, especially in B filter. We found the uncertainties to be 27, 14, 19 and 21 mmag in B, V, Rc and Ic filters, respectively, for the first season, and 21, 14, 19 and 18 mmag in B, V, Rc and Ic filters, respectively, for the second season. From our differential observations of SAO 62042, the determined periodicity results, using the DC method, are given in Table 2 and shown in Figs. 2 and 3. The Fourier transform technique supports only the results of the second of these data sets (see Fig. 6). We found mean photometric periods of P photo ¼ 19:49 0:14 day and 19:03 0:08 day for the first and second season, respectively. We have plotted the phased light curves in Figs. 8 and 9, using the epoch T s = 2453827.08 HJD and the mean photometric period Ps = 19.26 day. Since Porb ¼ 15:465 day from Frasca et al. (2006), it is clear that Pphoto is significantly greater than Porb . The photometric results in Table 2 also show the differential amplitude of the light variations of the second season to be larger than those of the first. From the phased colour curves in Figs. 8 and 9, especially the infrared colour variations (V—R and V—I) (aside from the scattered points shown by open ellipses) in the first season, and the (V—I) variation in the second season, we find similar periods to the V-band results. This is in keeping with the cool starspot scenario. In using the SPOT program for analysis of SAO 62042 we adopted i (inclination of system) = 60° (SAO 62042 is SB1 system and does not show eclipses, as can be seen from Figs. 2, 3, 8, 9.). We set L1 =Ltotal (fractional luminosity of the primary (more massive and hotter) star) to be effectively unity (given the absence of a
A. Erdem et al. / New Astronomy 14 (2009) 109–120
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Fig. 5. As per Fig. 1 but for FI Cnc in the second season data of 2006/2007.
visible secondary spectrum). The limb-darkening coefficients of the primary star are taken from van Hamme (1993) according to T eff ¼ 4750 (Frasca et al., 2006). With these parameters fixed, we obtained the spot parameters given in Table 4 and present our spot models in the right panels of Figs. 8 and 9. According to these spot models of SAO 62042 in Table 4, the latitude parameters of the spot in both seasons are relatively high. For longitude parameters, the main spot formation migrated in longitude from 270° to 215° in almost one year, if the same maculation region is being followed in both seasons. The mean angular radius of the spot became larger in one year.
Amplitude (mag)
0.12 0.10 0.08 0.06 0.04 0.02 0.00 0.0
0.2
0.4
0.6
0.8
1.0
c/d
4.3. FI Cnc
0.05
Amplitude (mag)
0.04 0.03 0.02 0.01 0.00 0.0
0.2
0.4
c/d
0.6
0.8
1.0
Fig. 6. Periodograms obtained from Fourier transforms technique for the V 2006/ 2007 data of SAO 62042 (upper panel) and the V 2006 data of FI Cnc (lower panel).
FI Cnc (BD +29 1772 = HD 72146 = GSC 1947 0489 = HIP 41875, V = 7.37) is classified as a variable (single) star in the SIMBAD database. Strassmeier et al. (1994) noted that the spectrum of this star shows strong CaII H and K emission lines. Fekel and Balachandran (1994) classified it as a single G8III, measuring its rotational velocity as vsini ¼ 15 km s1 and finding a significant lithium abundance. Henry et al. (1995) observed FI Cnc together with 64 other active late-type stars both photometrically and spectroscopically in their automated search for variability in chromospherically active stars. They found a photometric period of 28:5 0:1 day, the maximum photometric amplitude in V band being 0.16 mag, with cycle-to-cycle variations in amplitude evident. They argued that the star has a moderately rapidly rotation, measuring the projected equatorial rotation velocity to be 14 1 km s1. They found the star to show strong and variable Ha emission. Fekel (1997)
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Fig. 7. The left panel shows the phased light and colour curves of V340 Gem in 2006/2007. In the right panel the curve represent the best-fit spot model for these observed data.
Table 3 Starspot parameter sets for V340 Gem
k (deg) b (deg) c (deg)
jk U uk Dl
v2 =m
B
V
Rc
Ic
290(3) 69(5) 25(3) 0.03(2) 1.065(3) 0.893 0.011 2.71
292(3) 64(7) 25(3) 0.07(4) 1.073(3) 0.745 0.015 1.36
283(3) 64(9) 26(4) 0.13(3) 1.076(3) 0.641 0.015 2.29
284(4) 63(18) 26(7) 0.18(3) 1.069(3) 0.537 0.011 1.54
Standard deviations in the last digits are given in parenthesis.
found a projected rotational velocity of 17.4 km s1 and inferred a minimum radius of 9.8 R . Strassmeier et al. (2000) made a spectroscopic Ca II H and K survey of 1058 late-type stars selected from
the Hipparcos catalogue. For FI Cnc they found a spectral type G5, rotational velocity of 18.8 km s1, photometric amplitude in yband of 0.11 mag and photometric period of 29.14 day, using red-wavelength spectroscopic and Strömgren–Crawford system photometric observations. Koen and Eyer (2002) examined the periodicity of many variable stars using Hipparcos data, and found a photometric period of 35.84 day, which is quite larger than previous estimates. Their mean amplitude was only 0.031 mag. The star is also known as a source in the radio and X-ray wavelengths (J083217.3 + 291909 and J083217.4 + 291920). We have again two different data sets from observations of FI Cnc in 2006 and 2007. The differential observations of this active star, together with comparison and check star data, are presented in Figs. 4 and 5. In the right panels of these figures, the differential magnitudes of comparison minus check stars show a rather greater scatter. We found error measures to be 21, 13, 13 and 19 mmag in
Table 4 Starspot parameter sets for SAO 62042 First season data (2006)
k (deg) b (deg) c (deg)
jk U uk Dl
v2 =m
Second season data (2006/2007)
B
V
Rc
Ic
B
V
Rc
Ic
277(6) 72(9) 25(6) 0.03(2) 1.076(5) 0.911 0.027 0.67
271(4) 69(7) 22(3) 0.06(3) 1.065(2) 0.763 0.014 2.57
269(5) 68(9) 22(4) 0.10(4) 1.054(3) 0.656 0.019 0.92
268(8) 67(13) 22(6) 0.16(5) 1.054(4) 0.548 0.021 0.36
214(5) 72(5) 29(4) 0.03(2) 1.098(5) 0.911 0.021 1.05
215(4) 72(5) 29(4) 0.06(3) 1.103(3) 0.763 0.014 2.04
219(5) 71(9) 29(6) 0.11(4) 1.091(5) 0.656 0.019 0.93
216(6) 68(10) 25(5) 0.16(5) 1.070(4) 0.548 0.018 0.78
Standard deviations in the last digits are given in parenthesis.
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A. Erdem et al. / New Astronomy 14 (2009) 109–120 Table 5 Starspot parameter sets for FI Cnc First season data (2006)
k1 (deg) b1 (deg) c1 (deg) k2 (deg) b2 (deg) c2 (deg)
jk U uk Dl
v2 = m
Second season data (2006/2007)
B
V
Rc
Ic
B
V
Rc
Ic
183(14) 41(20) 13(4) 303(6) 41(10) 16(3) 0.05(4) 1.035(4) 0.867 0.021 0.20
188(17) 45 12(2) 304(4) 45 15(1) 0.10(5) 1.027(3) 0.719 0.013 0.66
185(8) 45 13(3) 301(4) 45 15(3) 0.13(5) 1.025(3) 0.619 0.013 0.50
187(20) 45 10(4) 307(11) 45 13(5) 0.19(8) 1.022(4) 0.521 0.019 0.12
270(6) 70(10) 27(7) – – – 0.05(4) 1.057(4) 0.867 0.018 0.60
264(8) 69(12) 23(6) – – – 0.09(4) 1.044(4) 0.719 0.018 0.74
273(9) 68(18) 22(9) – – – 0.13(5) 1.037(5) 0.619 0.021 0.39
272(8) 66(22) 22(9) – – – 0.20(5) 1.050(4) 0.521 0.020 0.24
Standard deviations in the last digits are given in parenthesis.
Fig. 8. As per Fig. 7 but for SAO 62042 in the first season data of 2006.
B, V, Rc and Ic filters, respectively, for the first season, and 18, 18, 21 and 20 mmag in B, V, Rc and Ic filters, respectively, for the second season. The periodicity results using the DC method on FI Cnc are given in Table 2. The Fourier technique supports only the results of the first of these data sets (see Fig. 6). We found mean photometric periods of Pphoto ¼ 28:88 0:46 day and 28:47 0:16 day for the first and second season, respectively. Our photometric period values support those of Henry et al. (1995) and Strassmeier et al. (2000) (28.5 day and 29.14 day, respectively) but are at variance with Koen and Eyer (2002)’s value (35.84 day). We used the same light elements (T s = 2453851.11 HJD and P s = 28.68 day) in the separate data seasons to plot the phased light curves in the left panels of Figs. 10 and 11, and also to deduce spot migration. The photometric results in Table 2 also show the differential amplitude of
the light variations of the second season to be quite larger than those of the first season. From the phased colour curves in the left panels of Figs. 10 and 11, apart from the scattered points marked by open ellipses, the results are in keeping with the expected behavior of cool spots. In using the SPOT program for analysis of FI Cnc we adopted that i (inclination of system)=70° and L1 =Ltotal = 1 (FI Cnc was taken to be a single star). The limb-darkening coefficients are from van Hamme (1993) with T eff ffi 5000 (according to Strassmeier et al. (2000)). With these parameters fixed, we obtained the spot parameters given in Table 5 and present these spot models in the right panels of Figs. 10 and 11. The phased light curves of FI Cnc in the first season shows a large maculation wave with an asymmetric structure (see Fig. 10), having two separate minima: one is shallow, the other is quite
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Fig. 9. As per Fig. 7 but for SAO 62042 in the second season data of 2006/2007.
Fig. 10. As per Fig. 7 but for FI Cnc in the first season data of 2006.
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Fig. 11. As per Fig. 7 but for FI Cnc in the second season data of 2006/2007.
deeper. We therefore considered a two spot model for the first season. The mean angular radius of the spot became larger (almost by a factor of two) in one year. According to the longitude parameters, the main spot formation, if continuing through both data sets, migrated in longitude from about 300° to 270° in almost one year. In fact, it could be that two spots of the first season merged into one spot in the second season. 5. Conclusions This paper has collected together BVRc Ic photometric data on the three active cool stars V340 Gem, SAO 62042 and FI Cnc from the ÇOMU Observatory in 2006 and 2007. V340 Gem and SAO 62042 are among the program stars listed as RS CVn SB1 binaries by Frasca et al. (2006), while FI Cnc is a single active giant star (Fekel and Balachandran, 1994). We have confirmed systematic variations, of relatively low amplitudes, consistent with the photometric effects of very large regions of surface maculation, whose aspect varies with the mean rotation rate of the latitude at which the ‘starspots’ are located. The presented study gives the first photometric analyses of V340 Gem and SAO 62042. We have characterized these effects in terms of heuristic starspot model parameter sets. Seasonal changes of maculation region size and surface position were thence indicated. These latter effects are frequently found in cool active stars and are consistent with differential rotation operating at relatively greater scales in higher latitudes. The particular stars studied here appear to show relatively large differential rotation rates, particularly SAO 62042, and this may indicate a near polar location for this star’s main macula.
The periods and surface differential rotation (SDR) could be checked by using the following well-known equation: 2
Pb ¼ P eq =ð1 k sin bÞ;
ð5Þ
where Pb is the period at latitude b, P eq is the equatorial period and k is the surface differential rotation coefficient. For SAO 62042, if we take the photometric rotation period as P b , the orbital period as P eq (under the assumption of synchronous rotation) and the starspot latitude as b, we found k to be about 0.22. For the Sun, k has been derived from sunspot latitudes and periods to be 0.19 by Kitchatinov (2005), based on the Newton and Nunn (1951)’s study. According to this value, our k value for SAO 62042 is slightly larger than that of the Sun. Since Brown et al. (2004) show that k should increase with age, this difference could be due to the age of SAO 62042. On the other hand, Messina and Guinan (2006) suggested that the growth and decay of the starspots may produce variations of the apparent photometric period, i.e. the apparent period may well be affected by changes of surface structure in the maculation region itself. In the case of V340 Gem, the orbital period (Porb = 36.24 day) and photometric period (Pphoto ¼ 36:16 0:29 day) are almost equal within the estimated uncertainty; therefore, it does not make much sense to search for SDR in this star. For FI Cnc, the two photometric periods (Pphoto ¼ 28:88 0:46 day and 28:47 0:16) found in this study are effectively the same, to within the estimated error; thus they also do not give support to SDR. While noting such preliminary indications, this paper does not emphasize details of interpretation, as it is hoped data such as that presented will be continued and prove to be of more general significance when forming part of more comprehensive long-term studies.
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