aa r X i v : . [ a s t r o - ph ] S e p Pulsation of EE Cam
M. Breger
Institut f¨ur Astronomie der Universit¨at Wien, T¨urkenschanzstr. 17, A–1180 Wien, Austria [email protected]
S. M. Rucinski
Department of Astronomy and Astrophysics, University of Toronto David DunlapObservatory, P.O. Box 360, Richmond Hill, Ontario, Canada [email protected] andP. Reegen
Institut f¨ur Astronomie der Universit¨at Wien, T¨urkenschanzstr. 17, A–1180 Wien, Austria [email protected]
ABSTRACT
EE Cam is a previously little studied Delta Scuti pulsator with amplitudesbetween those of the HADS (High-Amplitude Delta Scuti stars) group and the av-erage low-amplitude pulsators. Since the size of stellar rotation determines bothwhich pulsation modes are selected by the star as well as their amplitudes, the staroffers a great opportunity to examine the astrophysical connections. Extensivephotometric measurements covering several months were carried out. 15 signifi-cant pulsation frequencies were extracted. The dominant mode at 4.934 cd − wasidentified as a radial mode by examining the phase shifts at different wavelengths.Medium-dispersion spectra yielded a v sin i value of 40 ± − . This showsthat EE Cam belongs to the important transition region between the HADS andnormal Delta Scuti stars. Subject headings: stars: variables: delta Scuti — stars: individual (EE Cam) 2 –
1. Introduction
The Delta Scuti stars are common pulsators on and near the main-sequence situatedinside the classical instability strip. They generally pulsate with nonradial modes and smallphotometric amplitudes in the millimag range. These stars also essentially share the highrotational velocity of the average star of spectral type A. However, a number of PopulationI stars shows dominant radial modes, amplitudes in excess of 0.3 mag and rotates with aprojected rotational velocity less than 30 km s − . The members of this subgroup are calledHADS (High-Amplitude Delta Scuti stars).For the Delta Scuti stars, there exists a strong connection between rotation and pulsationproperties, such as amplitude. We are presently engaged in a program to examine the starsbetween the two extremes of amplitude (e.g., for 44 Tau, see Antoci et al. 2007; Zima et al.2007). We note that with extensive data and nonradial mode identifications the aspect anglecan be determined accurately, so that the true rotational velocity can be obtained from thespectroscopic v sin i measurements.The list of pulsators in the HIPPARCOS catalogue (ESA 1997), as reanalyzed for mul-tiperiodicity by Koen (2001), contains a number of stars belonging to this ’intermediate’group. EE Cam (HIP 27199, HD 37857) is a promising target with reported peak-to-peakamplitudes near 80 millimag. Its rotational velocity is presently unknown, but was sus-pected to be low because of the relatively large pulsational amplitude. In particular, weare interested in detecting another variable such as 44 Tau (Antoci et al. 2007) which has a v sin i value of only 2 km s − , in order to separate the effects of true low rotational velocityand geometric aspect. Olson (1980) classified EE Cam as an F3 giant (gF3). The catalogby Nordstrom et al. (2004) gives a temperature of 6530K and a [Fe/H] abundance of 0.06relative to the Sun. Koen (2001) analyzed the Hipparcos data and suggested two frequenciesof 4.93 and 5.21 c/d, respectively.
2. New photometry
In 2006 and 2007, photometric observations were performed using the Vienna UniversityAutomatic Photoelectric Telescope (APT; Strassmeier et al. 1997; Granzer, Reegen & Strassmeier2001) located at Washington Camp, Arizona, USA. The “Wolfgang” telecope acquired alto-gether 304 hours of Str¨omgren vy data from 2006 February 14 to 2006 April 2 and from 2006September 19 to 2007 April 5. The three-star technique was employed with HD 35606 (C1, V = 8 . m B − V = 0 .
48, F8) and HD 32745 (C2, V = 8 . m B − V = 0 .
96, G0) as compar-ison stars. Since for C2, long-term variability at time scales of days could not be excluded, 3 –the data reduction was applied solely relying on C1. While the three-star technique wasnot applied in the final reductions, the importance of the technique in checking for possiblesmall-amplitude variability in the chosen comparison stars was again demonstrated.A complete list of the measurements used to extract the light curves is provided inTable 1. Typical examples of light curves of EE Cam are shown in Fig. 1 together with themultifrequency solution derived in the next section.
3. Multiple frequency analysis
The pulsation frequency analyses were performed with a package of computer programswith single-frequency and multiple-frequency techniques (PERIOD04 , Lenz & Breger 2005),which utilize Fourier as well as multiple-least-squares algorithms. The latter technique fitsup to several hundred simultaneous sinusoidal variations in the magnitude domain and doesnot rely on sequential prewhitening. The amplitudes and phases of all modes/frequenciesare determined by minimizing the residuals between the measurements and the fit. Thefrequencies can also be improved at the same time.To decrease the noise in the power spectra, we have combined the measurements ob-tained in the y and v passbands. The dependence of the pulsation amplitude on wavelengthwas compensated by multiplying the v data set by an experimentally determined factor of0.64 and increasing the weight of these data points correspondingly. This scaling createssimilar amplitudes in both passbands but does not falsify the power spectra. Note that dif-ferent colors and data sets were only combined to detect new frequency peaks in the Fourierpower spectrum and to determine the significance of the detection. The effects of imperfectamplitude scaling and small phase shifts between colors can be shown to be negligible forperiod finding. For prewhitening, separate solutions were obtained for each color by multipleleast-square fits. In the analysis of the Delta Scuti Network campaign data, we usually applya specific statistical criterion for judging the reality of a newly discovered peak in the Fourierspectra, viz., a ratio of amplitude signal/noise = 4.0 (see Breger et al. 1993).Our analysis consists of a number of different steps to be repeated. Each step involvesthe computation of a Fourier analysis (power spectrum) from the original data or a pre-viously prewhitened fit. The dominant peaks in the power spectrum were then examinedfor statistical significance and possible effects of daily and annual aliasing. For computing SigSpec analysis (Reegen 2007), which employs a statis-tical treatment of Discrete Fourier Transform (DFT) amplitudes that would be produced bywhite noise, provided exact consistency with the results obtained from the above procedure.Fig. 2 shows the details of the search for the multiple frequencies, which are listed in Table 2.The average residuals of the 15-frequency fit in the y passband were ± − found by Koen (2001) are inexact agreement with our two frequencies showing the highest amplitudes.It is possible to estimate the nonradial degree, ℓ , of the dominant pulsation mode fromthe available photometry (for a recent application see Lenz et al. 2007). From the v and y passbands we derive a value of φ ( v ) − φ ( y ) = + 3.3 ± ◦ . In this temperature domain,such positive values generally indicate radial pulsation. Indeed, preliminary pulsation modelcalculations for EE Cam identify a unique value of ℓ = 0, i.e., radial pulsation.The frequency ratio f /f = 0.946. Such a frequency ratio cannot be identified withradial modes (e.g., see Suarez, Garrido & Goupil 2006), so that f has to be nonradial. Wealso note that f and f form a close frequency pair. Such close frequencies are not unusualin Delta Scuti stars (e.g., see Breger & Pamyatnykh 2006). In the case of EE Cam, however,we cannot yet exclude the possibility that the close-frequency pair could be an artifact ofstrong amplitude variability of the dominant mode. 5 –
4. Spectroscopy
EE Cam certainly deserves a thorough spectroscopic study. Here we present new resultswhich shed light on the subject of the rotation of the star. Two spectra of EE Cam andone spectrum of a standard star, HD 89449 (40 Leo, F6IV), were obtained with the DavidDunlop Observatory 1.88m telescope on Feb. 14, 2006. For EE Cam, the UT start timeswere 05:15:19 (1220 s exposure time) and 06:14:02 (1803 s exposure time), while for HD89449 the values were 06:52:16 and 200s.The spectra were centred at the Mg I 5184 ˚A triplet and covered the range 5070 to5306 ˚A with an effective spectral resolution of about 0.35 ˚A. A full technical description isgiven in Rucinski (2002). The spectra were rectified and then processed using the broadeningfunction (BF) formalism (as described in the same paper) and subsequently improved duringthe DDO binary-star program (for the last paper of the series, see Pribulla et al. (2007)).The BF’s were determined over the span of 61 points at the 6.7 km s − spacing thus covering ±
150 km s − . With such processing, a BF of a very sharp-line spectrum has a half-width atthe base of 19.5 km s − . The broken line in the figure (Figure 3) shows the rotational profilecalculated for the limb darkening of u = 0 . − respectively) can be used to estimate v sin i . The two BF’s, whencorrected for the intrinsic broadening introduced by the formalism and for v sin i ≃
17 of thetemplate itself, give v sin i = 40 km s − . The real uncertainty is larger than one determinedfrom the difference of the two spectra and is about 3 km s − as based on results for similarstars observed in the DDO programme. Note that the depression of the baseline around theBF peak is of no importance; it is a characteristic feature for BF’s of stars with rotationallybroadenened lines as this reflects the uncertainty of the pseudo-continuum placement in thespectrum rectification step. At the time of observations, the star appeared to have the meanheliocentric velocity of +11 ± − , on the assumption that the radial velocity of thetemplate star HD 89449 is +6 km s − . This assumed the fit by the rotationally broadenedprofile, as shown in Figure 3; note that the standard/template star in the BF technique isused to determine the broadening profile for the program star as shown in this figure (andused for the v sin i determination) as well as the relative radial velocities. The mean radialvelocity of EE Cam was estimated at +14 . − in Nordstrom et al. (2004). 6 –The intensity of the BF can be used as an indication of the spectral match of thetemplate; an integral of unity indicates a perfect match and an identical spectral type (ormore exactly, an identically strong Mg I 5184 ˚A triplet). The two spectra gave the BFintegrals of 0.91 and 0.90 which means that the lines are weaker than in the F6IV standardHD 89449 indicating a spectral type close to F5. This is confirmed by the data in the Tycho-2 Catalog (Høg et al. 2000) (star number GSC 4098-123) where the mean magnitudes givea well defined color index B − V = 0 .
427 which correponds to the spectral type F5 on theMain Sequence.
5. Conclusion
Extensive photometric measurements at the millimag level covering several months werecarried out. The frequency analysis has revealed 15 significant pulsation frequencies. Theresiduals show that many additional modes in the 0 to 15 cd − are present with small ampli-tudes. The dominant pulsation at 4.934 cd − was identified as a radial mode by examiningthe phase shifts of the light curves at different wavelengths. The second most dominant modeat 5.214 cd − was found to be nonradial. This star, therefore, is an excellent example of astar showing both the properties of the HADS and the common small-amplitude pulsators,in which the radial modes are either absent or very weak.This picture of a star in the astrophysical transition region is supported by new measure-ments of the projected rotational velocity: two medium-dispersion spectra yielded a v sin i value of 40 ± − . This value is higher than the upper limit of 30 km s − for the HADS,but lower than the rotational velocity of the typical low-amplitude Delta Scuti star.Due to the relatively high amplitudes and the rich pulsation spectrum, EE Cam isideal for further detailed studies of mode identification in order to compare to asteroseismicmodels.It is a pleasure to thank Heide DeBond and Jim Thomson for assistance with thespectroscopic observations. It is a pleasure to thank Patrick Lenz for computing a pre-liminary pulsation model. This investigation has been supported by the Austrian Fondszur F¨orderung der wissenschaftlichen Forschung and the Natural Sciences and EngineeringCouncil (NSERC) of Canada. 7 – REFERENCES
Antoci, V., Breger, M., Rodler, F., Bischof, K., & Garrido, R. 2007, A&A, 463, 225Breger, M., Stich, J., Garrido, R., et al. 1993, A&A, 271, 482Breger, M., Pamyatnykh, A. A. 2006, MNRAS, 368, 571ESA, 1997, in ’The Hipparcos and Tycho Catalogues’, ESA SP-1200. ESA PublicationsDivision, NoordwijkGranzer, T., Reegen, P., Strassmeier, K. G. 2001, AN, 322, 325Høg, E., Fabricius, C., Makarov, V. V., Urban, S., Corbin, T., Wycoff, G., Bastian, U.,Schwekendiek, P., & Wicenec, A. 2000, A&A, 355L, 27Koen, C. 2001, MNRAS, 321, 44Lenz, P., & Breger, M., 2005, CoAst, 146, 53Lenz, P., Pamyatmykh, A. A., Breger, M., Antoci, V. 2007, A&A, in pressNordstrom B., Mayor M., Andersen J., Holmberg J., Pont F., Jorgensen B.R., Olsen E.H.,Udry S., Mowlavi N. 2004, A&A, 418, 989Olson E. H. 1980, A&A Suppl. 39, 205Pribulla, T., Rucinski, S. M., Conidis, G., DeBond, H., Thomson, J. R., Gazeas, K., Ogloza,W. 2007, AJ, 133, 1977Reegen, P. 2007, A&A, 467, 1353Rucinski, S. M. 2002, AJ, 124, 1746Rucinski , S. M., Pych, W., Ogloza, W., et al. 2005, AJ, 130, 767Strassmeier, K. G., Granzer, T., Boyd, L. J., Epand, D. H. 1997, PASP, 109, 157Suarez, J. C., Garrido, R., Goupil, M. J. 2006, A&A, 447, 649Zima, W., Lehmann, H., St¨utz, Ch, Ilyin, I. V., Breger, M. 2007, A&A, 471, 237
This preprint was prepared with the AAS L A TEX macros v5.2. y and v are shown. 9 – -2 0 2 P o w e r ( m illi m ag ) SpectralWindow
Data f1020
Data - 4f solution f12 f10f2 f7010
Data - 5f solution f15f13f11 f4f80510
Data - 8f solution f14 f30 5 10 1505
Data - 11f solution
Frequency (cycles per day)
Data - 15f solution
Data - 2f solution
Fig. 2.— Power spectra of EE Cam for the 2005 and 2006 photometry. The panels showthe power spectra after the inclusion of additional frequencies into the multiple-frequencysolution. Note the 1 cd − alias patterns (spectral-window insert of the top panel). Thelowest panel clearly shows the power spectrum of the residuals from the 15-frequency solu-tion: the excess power in the 5 to 15 cd − range shows additional pulsation frequencies anddemonstrates the rich pulsation spectrum of EE Cam. 10 –Fig. 3.— The Broadening Functions for two spectra of EE Cam, as explained in the text.The rotational profile with v sin i = 40 km s − , centered at +11 km s − , is shown by a brokenline. 11 –Table 1. Journal of the photometric observations of EE CamStart Length Start LengthHJD hours HJD hours245 0000+ 245 0000+3791.5925 3.30 4079.6626 1.783796.6821 0.80 4080.6584 2.283797.6170 1.18 4081.6584 7.603798.6337 1.82 4084.9154 0.483799.5965 2.78 4086.6439 6.643803.6372 1.51 4090.6314 6.143805.5997 1.28 4093.6188 5.043808.6153 1.60 4094.6146 6.863810.6021 1.82 4095.6139 3.133997.8792 3.14 4100.5988 6.884000.9181 2.24 4101.5946 5.054003.8632 3.61 4102.5953 6.814005.8595 3.77 4103.5930 6.814010.8476 3.61 4104.5869 6.964023.9142 2.54 4105.5876 6.874024.8081 5.19 4108.5755 6.954025.8054 5.21 4116.5703 6.484028.7963 5.51 4117.5707 6.484029.7944 5.51 4124.5788 5.754030.7936 5.52 4127.5763 5.584031.7896 5.67 4128.5810 5.394035.7800 6.00 4134.5845 4.944038.8807 3.66 4135.6248 3.964048.7434 2.33 4136.5857 4.844049.7408 2.33 4140.5878 4.554050.7387 2.33 4143.6649 2.394054.7279 2.33 4146.6432 2.824055.7273 2.17 4147.6938 1.444056.7237 2.33 4152.5903 3.67 12 –Table 1—ContinuedStart Length Start LengthHJD hours HJD hours245 0000+ 245 0000+4057.7199 2.33 4153.5906 2.244058.7168 2.33 4154.5913 3.514059.7159 2.17 4156.5923 3.354060.7150 2.17 4157.5928 3.274061.7102 2.33 4158.5935 3.244062.7057 2.33 4160.5943 3.034064.7010 2.33 4161.6335 2.084067.6962 2.18 4169.6321 1.604069.6876 2.33 4170.5992 2.244070.6872 2.18 4171.6000 2.244071.6826 2.34 4172.6004 2.084072.6826 2.24 4173.6007 2.084074.6737 2.34 4174.6013 1.924077.6648 2.34 4175.6017 1.924178.6033 1.60 13 –Table 2. Detected pulsation frequencies of EE CamFrequency Detection Amplitude NotesSignificance y filtercd − Ampl. S/N mag ± ≥ ∼ −1