Period Changes in SX Phoenicis Stars: IV. BL Camelopardali

PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF THE PACIFIC, 125:639 643, 2013 June 2013. The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A. Period Changes in SX Phoenicis Stars: IV. BL Camelopardali GEORGE J. CONIDIS AND PAUL A. DELANEY Department of Physics and Astronomy, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada; gconidis@yorku.ca Received 2013 February 04; accepted 2013 May 07; published 2013 May 30 ABSTRACT. A total of 73 new times of maximum light for BL Cam were observed through the years 2005 2011, which are combined with 1392 times of maxima taken from literature. A more accurate period of 0.039097912(1) days was found, and an updated linear ephemeris is presented. This newly presented linear ephemeris was used to calculate revised O C values, which were fitted with a parabolic curve to measure the rate of change of the pulsation period, found to be ð1=pþðdp=dtþ ¼1:37ð2Þ 10 7 yr 1. Although the parabolic fit has a physical interpretation, it is noted that a cubic more appropriately fits the behavior of the O C diagram. 1. INTRODUCTION SX Phe stars are Population II stars (low metallicity) occupying a location within the instability strip of the Hertzsprung-Russell diagram. BL Cam (α 2000 ¼ 3 h 47 m 19 s, δ 2000 ¼þ63 22 0 07 ) is found to have a metallicity of ½Fe=HŠ ¼ 2:4, indicating its placement among the Population II stars of the Milky Way (McNamara 1997). It has a B V ¼ 0:18 and a predicted absolute visual magnitude M v ¼ 3:13 from the period-luminosity relation from Cohen & Sarajedini (2012). This places BL Cam well within the instability strip boundaries as given by Henry et al. 2001. Therefore, BL Cam satisfies the criteria to be classified as a SX Phe star. In total there are 14 field SX Phe stars identified within the Milky Way (Fauvaud et al. 2010). The fundamental period of pulsation of 0.039098 days has an accompanying change in the visual magnitude of 0:33 mag, where the mean visual magnitude is V 13:1 (Fauvaud et al. 2010). From consistent monitoring of BL Cam, there have been extensive studies on the multiperiodic nature of BL Cam (Fauvaud et al. 2010, 2006; Fu et al. 2008; Rodriguez et al. 2007). The first secondary period detected was identified as the first overtone period of 0.0306 days (Hintz et al. 1997). The ratio of the first overtone to fundamental period was found to be 0.783, but the overtone period is found to be transient in nature. Fu et al. (2008) did not detect the first overtone period of 0.0306 days, but instead found two closely spaced periods, 0.03971 days and 0.03910 days to be excited, where the later corresponds to the fundamental period. It has been found through high quality multisite photometry (Rodriguez et al. 2007) that there are 21 independent excited pulsation modes with amplitudes ranging from 1.6 to 7.4 mmag, not including the fundamental mode. Determining whether these modes correspond to a radial or nonradial mode has proved to be nontrivial (Breger et al. 2008), since the expected nonradial modes have periods very close to the excited radial modes. The behavior of the primary period is not predicted by the stellar evolutionary models. The changes to the primary period have been explained as a light travel-time effect caused by two stellar companions in orbit about BL Cam (Fauvaud et al. 2010). This article presents 73 new observed times of maximum light, calculated from observations taken at the York University Observatory (YUO) over the years 2005 2011. These new times of maxima have been combined with all available published maxima in literature to calculate a new linear ephemeris and corresponding observed minus calculated (O C) values. The new linear ephemeris allows a more accurate determination of the primary pulsation period, and a quadratic polynomial fit of the O C diagram yields the rate of change of the primary pulsation from the coefficient of the second order term. 2. INSTRUMENTAL SETUP, DATA CALIBRATION, AND MEASUREMENT OF MAXIMA The newly presented data was collected on a 60 cm Cassegrain telescope located at the York University Observatory, Toronto, Canada. The telescope was outfitted with a SBIG ST-9 CCD camera in conjunction with a f=6:6 focal reducer, yielding a field of view of 5 5. Due to the greater response of the camera in the infrared, all exposures have been acquired through a Johnson I-band filter, effectively reducing exposure times and increasing temporal accuracy of the found maxima. Exposure lengths were varied from 90 to 120 s because of variable weather and seeing conditions. Along with target exposures, every observing run has accompanying dark and flat field frames taken during the same night. Figure 1 shows a representative field of view for the telescope and camera configuration used to collect the new data in this article. For all data collected, the software package AIP4Win (Berry & Burnell 2000) was used for photometric reductions. The data taken on the ST9 CCD were corrected using flat and dark frames taken during the same observing run. A representative 639

640 CONIDIS & DELANEY using the Origin 8 software package, which is then imported into the Maple (version 13) software package to determine the time of maximum light. The 73 times of maxima are then heliocentric corrected using the IDL program helio_jd.pro, yielding our quoted values in Table 1. 3. ANALYSIS AND DISCUSSION Including the newly presented data in this article, there are a total of 1465 times of maxima being considered (available through the Centre de Données astronomiques de Starsbourg (CDS) online data archive at http://cdsweb.u strasbg.fr/). We used the linear ephemeris from Hintz et al. (1997), HJD max ¼ 2443125:8026 þ 0:03909783E (1) to calculate a cycle number (E) for each observed maximum. Fitting a linear trend to the Heliocentric Julian Date versus cycle number, we find the more accurate period, 0.039097912(1) days, which yields the new linear ephemeris FIG.1. BL Cam field of view; shown is an unreduced image from the YUO. Comparison and check stars are also indicated with an appropriate label. North is down and east is to the left. light curve and corresponding error values for a single observing run are shown in Figure 2. Time of maximum light were determined by fitting a polynomial to adjacent points to the maximum differential magnitude. Two methods were used to produce and analyze the aforementioned polynomial fit. The polynomial fit is produced HJD max ¼ 2443125:7943ð3Þþ0:039097912ð1ÞE; (2) where the zero point is arbitrarily chosen to be the time of the observed maxima, HJD o ¼ 2443125:80260 days. Using the new linear ephemeris (eq. [2]), one can determine the rate of change of the observed period over the time spanned by the observations of the times of maxima. The change in period is calculated by finding the corresponding cycle number for a given time of maximum, then evaluating the linear ephemeris at the chosen cycle number to calculate the expected time of maximum. The nonzero difference of these two values is an indication that period is changing, where the difference value is known as an observed minus calculated, or O C, value (see Fig. 3). Assuming that BL Cam is changing continuously, the parabolic fit to the data in the O C diagram is: O C ¼ 8:3ð3Þ 10 3 1:08ð3Þ 10 9 E þ 2:86ð7Þ 10 13 E 2 : (3) FIG.2. Difference magnitude (I band) light curve of BL Cam on the night of 2011 February 3 at the YUO. The comparison minus check star light curve is shown at the bottom. The coefficient of the second order term from the quadratic polynomial fit yields a period change of ð1=p ÞðdP =dtþ ¼ 1:37ð2Þ 10 7 yr 1. This rate confirms that the primary pulsation period of BL Cam is increasing with time (Fauvaud et al. 2010; Fu et al. 2008). The agreement of the parabolic fit to the O C data is quite poor with a standard deviation (σ) of 0.0045, compared to the range of the O C data, which is 0.017 a factor of only 3.77 greater. The poor fit of the quadratic (Fig. 3, top) suggests the consideration of other models to explain the period change of BL Cam. It is possible that BL Cam s primary pulsation period has undergone an instantaneous change to its pulsation period at

TABLE 1 NEW TIMES OF MAXIMA FROM YUO PERIOD CHANGES IN SX PHE STARS: IV. BL CAM 641 Maxima Cycle O C Maxima Cycle O C (HJD) (E) (HJD) (E) (1) (2) (3) (1) (2) (3) 2,453,403.617642..... 262,874 0.001177 2,454,903.573980 301,238 0.002865 2,453,426.607328..... 263,462 0.001063 2,454,905.569297 301,289 0.004189 2,453,460.584100..... 264,331 0.000377 2,454,905.607672 301,290 0.003466 2,453,460.623388..... 264,332 0.000187 2,454,906.584832 301,315 0.003178 2,453,460.663155..... 264,333 0.000483 2,454,907.562402 301,340 0.003300 2,453,433.568291..... 263,640 0.000471 2,454,911.591126 301,443 0.004939 2,453,748.541274..... 271,696 0.000675 2,4549,14.522653 301,518 0.004123 2,453,762.578495..... 272,055 0.001746 2,454,914.560941 301,519 0.003312 2,453,790.571774..... 272,771 0.000920 2,454,915.541194 301,544 0.006117 2,453,790.611311..... 272,772 0.001359 2,454,923.592633 301,750 0.003387 2,453,796.554060..... 272,924 0.001225 2,455,261.552515 310,394 0.000918 2,453,796.592847..... 272,925 0.000914 2,455,261.591212 310,395 0.000517 2,453,797.531567..... 272,949 0.001285 2,455,261.631769 310,396 0.001976 2,453,797.569304..... 272,950 0.000076 2,455,262.570020 310,420 0.001877 2,453,800.580831..... 273,027 0.000911 2,455,262.609447 310,421 0.002206 2,453,801.557398..... 273,052 0.000031 2,455,264.521976 310,470 0.001063 2,453,801.596245..... 273,053 0.000220 2,455,264.562293 310,471 0.000156 2,453,802.613900..... 273,079 0.000889 2,455,264.600890 310,472 0.000345 2,453,810.549091..... 273,282 0.000796 2,455,265.540051 310,496 0.000466 2,453,811.567268..... 273,308 0.000835 2,455,265.580698 310,497 0.002015 2,453,811.604395..... 273,309 0.001136 2,455,596.543380 318,962 0.000873 2,453,815.555055..... 273,410 0.000635 2,455,596.581667 318,963 0.000062 2,454,117.547660..... 281,134 0.000968 2,455,609.563559 319,295 0.001447 2,454,117.585988..... 281,135 0.000198 2,455,609.601306 319,296 0.000096 2,454,146.556412..... 281,876 0.000931 2,455,616.524078 319,473 0.002538 2,454,155.588131..... 282,107 0.000829 2,455,616.563036 319,474 0.002397 2,454,160.516666..... 282,233 0.001368 2,455,616.602083 319,475 0.002346 2,454,845.629277..... 299,756 0.001268 2,455,616.641780 319,476 0.002946 2,454,848.560953..... 299,831 0.000600 2,455,621.528297 319,601 0.002224 2,454,852.589639..... 299,934 0.002201 2,455,621.567114 319,602 0.001943 2,454,865.570320..... 300,266 0.002376 2,455,621.606421 319,603 0.002152 2,454,867.642381..... 300,319 0.002247 2,455,622.583689 319,628 0.001972 2,454,869.597178..... 300,369 0.002148 2,455,622.623726 319,629 0.002911 2,454,879.527654..... 300,623 0.001755 2,455,623.600113 319,654 0.001851 2,454,879.567141..... 300,624 0.002144 2,455,623.639960 319,655 0.002600 2,454,893.566197..... 300,982 0.004148 2,455,635.607339 319,961 0.006018 2,454,894.541145..... 301,007 0.001647 NOTE. (1) Heliocentric Julian Date; (2) Cycle number, E; (3) O C using the newly found linear ephemeris (eq. [2]). E 150; 000. This is supported by examining the O C residuals (Fig. 3, bottom). The O C diagram has a well established curvature for E<150; 000ðE < Þ, compared to the E>150; 000ðE > Þ region. If this instantaneous period change is assumed to be true, this would imply that both eras would be well modeled by a linear trend on the O C diagram. Since the E < portion of the O C curve is extremely undersampled, this disjointed behavior could be a result of the sampling. A linear and quadratic polynomial fitting to both eras of the O C diagram are presented in Table 2. The fit applied is indicated by the first column with either L (linear) or Q (quadratic). The coefficients of the fittings are labelled with a subscript value equal to the corresponding power of the cycle number E. p The standard deviation, σ ¼ ffiffiffiffiffi χ 2, where χ 2 is the usual statistical measure of the goodness of a fit, is given in the fifth column, and the region in cycle space is stated in the sixth column by E < (below) or E > (above), with the partition applied at E ¼ 150; 000. For the E < era, the quadratic fit is a much better representation of the graph given the fittings lower σ value. The period found for this era is, 0.039097798(4) days (Fig. 4, top). This combined with the second order coefficient of the quadratic fit for this era gives the rate of change of the pulsation period in this era to be, 1 dp P dt ¼ 3ð1Þ 10 8 yr 1. This rate of change to

642 CONIDIS & DELANEY TABLE 2 LINEAR (L) AND QUADRATIC (Q) FITTINGS OF THE TWO REGIONS OF THE O C DIAGRAM IF BL CAM IS TOHAVE HAD A DISCONTINUOUS PERIOD CHANGE AT E ¼ 150; 000 Fit c 0 c 1 c 2 σ 10 4 Region L... þ9:1ð4þ 10 3 1:13ð4Þ 10 7 n/a 8.9 E < Q... þ9:8ð1þ 10 3 1:99ð9Þ 10 7 7:8ð8Þ 10 14 4.3 E < L... 8:6ð4Þ 10 3 3:2ð1Þ 10 8 n/a 12 E > Q... 5ð1Þ 10 3 6ð1Þ 10 8 5ð2Þ 10 14 12 E > NOTE. The coefficients are c 0, constant, c 1, first order, and c 2, second order terms. The standard deviation of the fit, σ, is given in the fifth column. The region relative to E ¼ 150; 000 is given in the sixth column. FIG. 3. Top: All O C data points fitted with a quadratic (eq. [3]). Bottom: The residuals of the quadratic fitting. The vertical dashed line is at E ¼ 150; 000. The solid horizontal line is the x-axis. the primary pulsation period is significantly slower than the overall rate of change found for the entire data set for BL Cam. For the E < era, the scatter (and sampling) is much greater. There is no preferred fit as both σ values are identical (Fig. 4, bottom). The second order fitting is not sampling any new features of the O C diagram. Therefore, the linear fitting is favored in this region, which yields a pulsation period of 0.039097944(1) days. The sudden period change between these two eras is found to be ΔP ¼ 0:0126ð4Þ s, assuming the quadratic period for the E < era. Although a discontinuous change in period is supported by the data, it is highly unlikely that nature would support an abrupt change in pulsation period that has such a large amplitude. It has been shown for the δ Scuti star 4 CVn (Breger 2000) that it is possible to have transient frequencies active on stars, indicating FIG.4. Top: O C diagram of the data in the E < regime is plotted. Bottom: O C diagram of the data in the E > regime is plotted. In both plots, the quadratic fit is indicated by the dashed curve, while the linear fitting is the solid line.

PERIOD CHANGES IN SX PHE STARS: IV. BL CAM 643 frequencies in 4 CVn are <25 mmag through a Johnson V filter. This implies that the momentum associated with these pulsations is low enough that they can, on short times scales, be damped or stimulated. This is not the case for BL Cam as it has a photometric amplitude of 0:33 in the Johnson V filter, which is 10 larger than the pulsations detected on 4 CVn. This would require a large instantaneous change to the source of the pulsation, which would require a more drastic scenario such as a third body collision. Examining the quadratic fit to the entire O C data set, which had a σ ¼ 0:00045, indicates a poor fit compared to the cubic fit, which has a σ ¼ 0:00032 (Fig. 5, top). This implies that a physical interpretation other than cycle to cycle period fluctuations (Percy et al. 2007) should be considered for BL Cam. This seems to suggest that there is an additional process changing the primary pulsation period, which is not accounted for in the standard O C quadratic model outlined by Kalimeris et al. (1994). FIG. 5. Top: O C curve for all BL Cam data. The third-order polynomial fit (dashed curve) is clearly seen to be a much better representation of the O C behaviour than the second-order polynomial fitted curve (solid curve). Bottom: The 73 new O C values contributed from the York University Observatory. that abrupt changes in frequencies are an allowed possibility for pulsators. One should bare in mind that the amplitudes of the 4. CONCLUSION BL Cam is found to have a primary pulsation period of 0.039097912(1) days determined to be increasing at a rate of ð1=pþðdp=dtþ ¼1:37ð2Þ 10 7 yr 1. This assumes the O C diagram is best represented by a quadratic. This has been shown to be a poor assumption, since a cubic polynomial is a better representation of the O C diagram. This is problematic since the physical meaning of the third order term is not understood in physical terms. We wish to thank the Department of Physics and Astronomy of York University for their funding and support and the members of the York University Observatory team for their help in collecting these data: Victor Arora, Allan Bayntun, Pooi Yee Chung, Behnam Doulatyari, Sandy Hsu, Vincent Huynh, Kenneth Lam, Matthew Lightman, Sara Mazrouei, Lindsay Nolan, Tatiana Ouvarova, Brenden Petracek, Olga Pukhovich, Lianne Manzer, Jesse Aaron Rogerson, Ted Rudyk, Senthuran Senthilnathan, Brenda Shaw, Mark Schuster, Christian Surdivall, and Rachel Ward. As well, many thanks are given to the anonymous referee for their time and the excellent feedback provided. REFERENCES Berry, R., & Burnell, J. 2000, The Handbook of Astronomical Image Processing (Richmond: Willmann-Bell) Breger, M., Lenz, P., & Pamyatnykh 2000, MNRAS, 396, 291 Breger, M., Lenz, P., & Pamyatnykh, A. A. 2008, CoAst, 157, 56 Cohen, R., & Sarajedini, A. 2012, MNRAS, 419, 342 Fauvaud, S., Rodríguez, E., Zhou, A. Y., et al. 2006, A&A, 451, 999 Fauvaud, S., Sareyan, J.-P., Ribas, I., et al. 2010, A&A, 515, A39 Fu, J.-N., Zhang, C., Marak, K., Boonyarak, C., Khokhuntod, P., & Jiang, S. Y. 2008, Chinese J. Astron. Astrophys., 8, 237 Henry, G. W., Fekel, F. C., Kaye, A. B., & Kaul, A. 2001, AJ, 122, 3383 Hintz, E. G., Joner, M. D., McNamara, D. H., Nelson, K. A., Ward Moody, J., & Kim, C. 1997, PASP, 109, 15 Kalimeris, A., Livaniou, H. R., & Rovithis, P. 1994, A&A, 282, 775 McNamara, D. H. 1997, PASP, 109, 1221 Percy, J. R., Bandara, K., & Cimino, P. 2007, J. AAVSO, 35, 343 Rodríguez, E., Fauvaud, S., Farrell, J. A., et al. 2007, A&A, 471, 255