- Email: [email protected]
Evidence for the pulsational origin of the Long Secondary Periods: The red supergiant star V424 Lac (HD 216946)
New Astronomy 12 (2007) 556–561 www.elsevier.com/locate/newast
Evidence for the pulsational origin of the Long Secondary Periods: The red supergiant star V424 Lac (HD 216946) q Sergio Messina
*
INAF – Catania Astrophysical Observatory, via S. Sofia 78, I-95123 Catania, Italy Received 29 January 2007; received in revised form 26 February 2007; accepted 2 April 2007 Available online 7 April 2007 Communicated by W. Soon
Abstract The results of a long-term UBV photometric monitoring of the red supergiant (RSG) star V424 Lac are presented. V424 Lac shows multiperiodic brightness variations which can be attributed to pulsational oscillations. A much longer period (P = 1601 d), that allows us to classify this star as a long secondary period variable star (LSPV) has been also detected. The B V and U B color variations related to the long secondary period (LSP) are similar to those related to the shorter periods, supporting the pulsational nature of LSP. The long period brightness variation of V424 Lac is accompanied by a near-UV (NUV) excess, which was spectroscopically detected in a previous study [Massey, P., Plez, B., Levesque, E.M., et al., 2005. ApJ 634, 1286] and which is now found to be variable from photometry. On the basis of the results found for V424 Lac, the NUV excess recently found in a number of RSGs may be due not solely to circumstellar dust but may also have a contribution from a still undetected LSP variability. Ó 2007 Elsevier B.V. All rights reserved. PACS: 97.20.Pm; 97.10.Sj; 97.20.Jg; 97.20. w Keywords: Stars: supergiants; Stars: oscillations; Stars: late-type; Stars: individual: V424 Lac
1. Introduction Red supergiants (RSG) are evolved stars characterized by brightness variations, mainly arising from radial pulsations, which represent the periodical component of their variability (Guo and Li, 2002), as well from huge convection cells, which interplay with the oscillations and can determine an additional stochastic component of variability (e.g. Tuthill et al., 1997). Measuring pulsations in RSGs is a time-demanding task since models predict pulsational instability with fundamental periods as long as 4000 days. However, their study is particularly interesting since the q Based on observations collected at INAF-Catania Astrophysical Observatory, Italy. * Tel.: +39 095 7332230; fax: +39 095 330592. E-mail addresses: [email protected], [email protected]
1384-1076/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.newast.2007.04.002
pulsational modes of RSGs allows us to check the values of fundamental stellar parameters such as the stellar radius derived from evolutionary models (Levesque et al., 2005). Moreover, RSGs show their own period–luminosity (P– L) relation which makes them useful as extragalactic distance indicators (e.g. Pierce et al., 2000). It is known from a number of studies (Kiss et al., 2006; Derekas et al., 2006; Wood et al., 2004) that a significant fraction (25%) of pulsating RSGs and of asymptotic giant branch (AGB) stars show periodic brightness changes characterized by two distinct time scales. The short-period variations manifest on a time scale of about a few hundreds days and can be attributed to first and possibly second overtone mode pulsations, which are also expected from theoretical models. The long-period variations manifest on a time scale greater than about 1000 days. Indeed, these stars characterized by long-period variations are better
S. Messina / New Astronomy 12 (2007) 556–561
known as long secondary period variables (LSPV). The origin of the long secondary period is not understood yet. As discussed by Kiss et al. (2006), these long secondary periods cannot be explained by radial pulsations, nor by metallicity effects. Maeder (1980) suggested that the long periods observed in blue-yellow supergiants can be due to non-radial oscillations of gravity modes. Despite their different internal structures and global properties, however, the presence of low-degree g modes, also proposed by Wood et al. (2004), seems to be the most likely explanation of the existence of long secondary periods of both AGB and RSG stars. Unfortunately, the LSPs remain beyond the limits of the models. The presence of circumstellar dust around red supergiants makes these stellar objects further interesting. Recently, Massey et al. (2005) have found that previous broadband studies of RSGs have underestimated the effect of extinction by circumstellar dust on the properties of RSGs, such us the luminosity when derived from the observed V magnitude. RSG stars with the highest amount of extra visual extinction also show significant near-UV (NUV) excesses compared to the stellar models reddened according to the standard reddening law. This NUV excess is likely to be due to the scattering of the star’s light by dust and/or an average grain size larger than that typical of grains found in the diffuse interstellar medium. Similar excesses have been attributed to circumstellar dust around R Coronae Borealis stars. The presence of circumstellar dust shells was first revealed by ground-based IR photometry, while Infrared Astronomical Satellite (IRAS) two-color diagrams established that such dust shells are a common phenomenon for RSGs (Stencel et al., 1989). V424 Lac (V424 Lac, HD 216946, Vmin = 4.87, B Vmin = 1.68) is a bright galactic supergiant belonging to the Lac OB1 association. It was discovered to be variable in the optical band by the Hipparcos mission (Perryman and The Hipparcos Science Team, 1997) and designed as variable star in the 74th Special Name-list of Variable Stars (Kazarovets et al., 1999). On the basis of moderate-resolution optical spectrophotometry and using new MARCS stellar atmosphere models, Levesque et al. (2005) classified V424 Lac as an M0 I star with Teff = 3800 K, log g = 0.7, R/Rx = 260, MV = 4.27, Mbol = 5.50, assuming, for the Lac OB1 association, a distance modulus (m M)0 = 8.9 mag and an interstellar reddening E(B V) = 0.11 mag. Interestingly, V424 Lac is one of the RSG stars analysed by Massey et al. (2005) for which NUV ˚ region has been measured and excess in the 3500–4000 A attributed to the presence of circumstellar dust. The multiband UBV photometric observations analysed in this paper reveal that V424 Lac has multiperiodic brightness variations and, in particular, a long secondary period that allows us to classify it as a long secondary period variable star. The nearly simultaneous observations in the U, B and V bands, which are very rarely collected for these stars, allow us to better characterize their variability, providing additional information to address the origin of
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long secondary periods and the effect of circumstellar extinction. 2. Observations The photometric observations analysed in the present study were collected with the 80-cm automated photometric telescope (APT-80), located at the M.G. Fracastoro station of INAF-Catania Astrophysical Observatory on Mt. Etna (Italy). This telescope feeds a single channel charge-integration photometer, equipped with an uncooled Hamamatsu R1414 SbCs photomultiplier and standard UBV filters (Rodono` et al., 2001). V424 Lac was observed differentially compared to the comparison star BD+46 3969 (c) and the check stars HD 218949 (ck1) and HD 218452 (ck2). Originally, V424 Lac was included in the telescope schedule to serve as a bright navigation star (n), i.e., the first star of a group that the APT-80 hunts, to make long-term differential observations of the BY Dra-type variable star KZ And (v). The integration time in U, B and V filters was set to 15, 10 and 10 s, respectively, and the observing sequence was n-c-ck1-c-vv-v-c-v-v-v-c-ck2-c-n. The sky background was measured at a fixed position near each star. Differential magnitudes were corrected for atmospheric extinction and transformed into the standard UBV system. The transformation coefficients were determined quarterly by observing selected samples of standard stars. Due to the relatively short duration of an observing sequence (.30 min), the v c, ck1 c, ck2 c and n c values were finally averaged to obtain one single data point for each night. The transformation into the standard system is made with an accuracy of the order of 0.01, 0.01 and 0.02 mag in the V magnitude, B V and U B color indices, respectively. A comparison between the standard deviations of ck c and v c differential magnitudes shows that the comparison star has remained constant within the observation accuracy. V424 Lac has been observed for 8 years from August 20, 1993 to October 29, 2001 for a total of 232 nights. In order to extend the data time series the Hipparcos photometry was also retrieved (Perryman and The Hipparcos Science Team, 1997). V424 Lac has been observed by Hipparcos from 1989 to 1993. Hp magnitudes were transformed into Johnson V magnitudes by applying the correction V = Hp 0.09 mag using the Hp V versus V I relation taken from Perryman and The Hipparcos Science Team (1997). Ten additional visual observations of V424 Lac were found in the database of the American Association of Variable Star Observers (AAVSO). However, since such observations are provided in the instrumental magnitude and, therefore, not transformed into the standard system and since they have not been scrutinized for ‘validation’, according to the AAVSO rules (Malatesta et al., 2005), they are not used in the following analysis. Summarizing, the dataset analysed in the present paper represents to date the most complete time series of photometric observations of V424 Lac. In Fig. 1, the
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Fig. 2. Top panel: power spectrum from Scargle periodogram analysis. The dotted line indicates the 0.1% false alarm probability. Bottom panel: the observational window function.
Fig. 1. Time sequence of U, B, and V magnitudes, U B and B V colors of V424 Lac. Filled circles represent the APT-80 observations, whereas crosses (top panel) represent the V-band Hipparcos photometry. The solid line represents the sinusoidal fit with the longest period P = 1601 days (see text).
UBV magnitudes, U B and B V colors are plotted versus time as filled circles, whereas the V-band Hipparcos photometry is plotted as crosses (top panel of Fig. 1). V424 Lac shows clear evidence of brightness variations versus time. The amplitude of variation increases towards shorter wavelengths, from about 0.08 mag in the V-band to 0.11 in the B-band and 0.33 in the U-band. The variation of B V and U B colors is of about 0.04 and 0.23 mag, respectively.
PN is set to be the fraction of simulated non-variable light curves which have the highest peak power exceeding PN. In the present case the power related to a 0.1% FAP is that which was exceeded in 10 simulations and corresponded to PN = 11. Although several periods were detected with a confidence level larger that 99.9%, the four periods with the largest power (see Table 1) were considered in the following analysis. A following analysis of the B and V magnitudes time series also confirmed the same periods with a similar confidence level. It must be noted that due to the quasi-periodical and not strictly stationary nature of the pulsational modes of RSGs, some of the listed short periods may be just numerical artifacts. In fact, the assumption of the Fourier analysis that the observed variation results from the superposition of distinct stationary signals is not fully applicable in this class of variable stars (see, e.g., Kiss et al., 2006).
3. Fourier analysis 3.2. CLEAN periodogram 3.1. Scargle periodogram In order to search for significant periodicities, the Scargle-Press periodogram search routine (Scargle, 1982; Horne and Baliunas, 1986) was applied to the whole sequence of U magnitudes. The U magnitude was selected for the period search because it showed the largest amplitude variations, thus making the periodicity detection more reliable. Several periods were detected (see top panel of Fig. 2) with a false alarm probability (FAP) smaller than 0.1% (corresponding to a confidence level larger than 99.9%). The FAP is the probability that a peak of given height is due to simply statistical variations, i.e. to white Gaussian noise. In order to determine the FAP, the Scargle periodogram was computed for 10,000 simulated light curves. Such curves were created with a Monte Carlo algorithm and with a time sampling equal to that actually observed, and the cumulative distribution of the power of the highest peaks was determined. The FAP related to a given power
The Scargle technique does not take into account the observational window function (see bottom panel of Fig. 2). As a consequence, some of the peaks in the power spectrum can be the result of the data sampling. This effect is called aliasing and even the highest peaks may be artifacts. In order to remove the effect due to the data sampling, the Clean periodogram technique (Roberts et al., Table 1 Most significant periods derived from Scargle periodogram and CLEAN analysis along with uncertainty, corresponding peak power and peak power related to a 0.1% FAP PScargle (d)
PN
PN (FAP = 0.1%)
PCLEAN (d)
Padopted (d)
DP (d)
1601 490 305 422
95 65 50 22
11 11 11 11
1600 526 312 412
1601 490 305 422
278 2 1 1
As discussed in the text, some of the shorter periods may be numerical artifacts.
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Fig. 3. Power spectrum from CLEAN analysis. In the second panel from top, the highest peak is out of plot to better show the smaller peaks. For a detailed description see Roberts et al. (1987) and Bailer-Jones and Mundt (2001).
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the MACHO database (Wood, 2000; Derekas et al., 2006). It also falls in the lower end of the long-period sequence of galactic RSG variables (see Fig. 7 of Kiss et al., 2006). According to the calculations of Guo and Li (2002), the shortest period P = 305 days results to be the pulsational fundamental mode. The values of the pulsation constants Q = P(M/Mx)1/2(R/Rx) 3/2 and W = P(M/Mx)(R/ Rx) 2 which represent, respectively, the classical period– density relation and the natural form of the pulsation constant if the oscillations are confined to the upper layers of the envelope (Gough et al., 1965), are found to be in good agreement with the values typical of RSG variables (see Fig. 8 of Kiss et al., 2006), giving further support to the pulsational nature of short periods and to the classification of V424 Lac as LSP star. According to the evolutionary calculations of Levesque et al. (2005), a mass value log M/Mx = 0.89 is used in the previous relations. Being the faintest LSP galactic RSGs to date, the newly discovered long period of V424 Lac is particularly significant since it allows us to extend and, therefore, to improve the P L relation for galactic LSP variable stars and to better calibrate the P L relation (‘‘D’’ sequence) of LMC red giant variables from the MACHO database (see Kiss et al., 2006). As already mentioned, the origin of the long secondary periods of RSGs is not well understood. The V magnitude and color variations showed by V424 Lac allow us to confirm that they cannot be ascribed either to the rotational modulation of the visibility or to the evolution of dark spots on the stellar photosphere. In fact, the presence of dark spots on the stellar photosphere gives rise to light curves whose amplitude increases towards shorter wavelengths. As shown in Fig. 4, in the black body approximation
1987; Bailer-Jones and Mundt, 2001) was applied to the U magnitude time series (see Fig. 3). As shown in Table 1, the periods independently detected by Scargle and CLEAN methods are in good agreement. The finally adopted periods are those giving the smallest residuals of the sinusoidal fit to data, which in the present case are the periods from the Scargle technique. In Fig. 1, the sinusoidal fit with the longest period of P = 1601 days is plotted as a solid line, whereas in Fig. 5 all four periods are used to fit the U-band data series. 4. Discussion V424 Lac has a K-band absolute magnitude MK = 8.23 which is derived from the OB Lac1 distance modulus (m M)0 = 8.9, the 2MASS dereddened K-band magnitude K = 0.67 (Cutri et al., 2003), adopting an interstellar reddening E(B V) = 0.11 mag. A RV = 4.2 ratio was used to determine the K-band extinction (AK) according to the results of Massey et al. (2005). In the period-K-band magnitude diagram, the longest period P = 1601 days clearly reveals V424 Lac to be a long secondary period variable. Specifically, this period falls in the upper end of the ‘‘D’’ sequence outlined by RSGs from
Fig. 4. An example of model variations of light curve amplitudes vs. wavelength arising from spots. Solid and dashed lines connect the light ˚ curve amplitude values obtained at three different wavelengths (5500 A ˚ B-band and 3600 A ˚ U-band), for two different spots V-band, 4500 A temperatures Tspot = 3500 K and Tspot = 3000 K, respectively, and for three values of area (f = 0.2, 0.3 and 0.5) which is expressed as fraction of the visible disk. The model effective temperature is Teff = 3800 K. The solid heavy line represents the observed light curve amplitudes of V424 Lac which show a variation vs. wavelength not explainable in terms of spots.
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Fig. 5. Time sequence of U magnitudes. Filled circles represent the APT80 observations, whereas the two diamonds mark the epochs of the spectrophotometry by Massey et al. (2005) and Levesque et al. (2005).
the light curve amplitude varies approximately linearly vs. wavelength for different combinations of spot temperatures (solid lines refer to Tspot = 3500 K, whereas dashed lines to Tspot = 3000 K) and spot covering factors. This dependence is clearly different from the one observed in V424 Lac (solid heavy line in Fig. 4). Although we cannot completely rule out a possible partial contribution from spots to the observed long-term variability, we can state that spots are not the main cause in the case of V424 Lac. Such a result is in agreement with the previous mentioned studies. As anticipated, Massey et al. (2005) observed V424 Lac spectroscopically at two different epochs. They detected NUV excess but no evidence for significant time variation. However, by chance they observed V424 Lac when it was at the same light level as shown by the open diamonds in Fig. 5. On the contrary, the U magnitude variations found in the present analysis may indicate a likely presence of variable NUV excess. Specifically, the flux in the U-band at the star’s brightness maximum is up to 35% larger than the flux at the brightness minimum. Assuming that such NUV excess is due, as proposed by Massey et al. (2005), to the star’s light scattering by a dust shell and/or to the grain size, typically larger than the grains found in the diffuse interstellar medium, this should imply the presence of
either (periodical) variations of the dust shell depth and/or variations of the grain size. However, the color variations related to the long secondary period are similar to those related to the short-period pulsational oscillations. In fact, after having removed the periodic component of variability related to the longest period (P = 1601 d), it has been found that V424 Lac gets brighter in the V-band when it is brighter in the B and U bands, which is the same behaviour shown by the long secondary period. In Fig. 6, the relation between U, B and V magnitudes are plotted. For each pair of these magnitudes the linear correlation coefficient is computed, which, in all three cases, has a very high significance level (a < 0.001). On the basis of the result found for V424 Lac, it can be stated that the NUV excess observed by Massey et al. (2005) in RSGs may also arise from the presence of still undetected LSP variability and, therefore, may be caused by pulsation effects and not solely by circumstellar dust shells. 5. Conclusions Long-term UBV photometry is a powerful observational approach to detect and investigate the nature of long-term secondary periods in RSGs. Eight years of high precision UBV observations of V424 Lac have allowed us to discover the existence of short-period brightness variations related to pulsational modes and to classify this star as a LSPV star thanks to the discovery of a long secondary period. The analysis of multicolor observations has allowed us to conclude that the color variations related to the long secondary period are similar to those ascribed to shorterperiod pulsational oscillations. Multicolor observations also indicate that the NUV excess recently found in a number of RSGs and attributed to circumstellar dust, can be variable and partly due to still undetected LSP variability. Acknowledgement The author thanks the anonymous referee for helpful comments. The acquisition of photometric data over so many years with the Catania APT has been possible thanks to the dedicated and highly competent technical assistance of a number of people, notably P. Bruno, E. Martinetti and
Fig. 6. Magnitude–magnitude relations after removing the fit to the long-term component of variability due to the long secondary period. Solid lines are the liner fit to the data. The label ‘r’ is the linear correlation coefficient.
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S. Sardone. Active star research at the INAF-Catania Astrophysical Observatory is funded by MUR (Ministero dell’Universita` e della Ricerca), and the Regione Sicilia, whose financial support is gratefully acknowledged. The extensive use of the SIMBAD and ADS databases, operated by the CDS center, (Strasbourg, France), is also gratefully acknowledged. The author thanks Luigia Santagati, of the INAF-Catania Astrophysical Observatory, for the English revision of the text. References Bailer-Jones, C.A.L., Mundt, R., 2001. A&A 367, 218. Cutri, R.M., Skrutskie, M.F., van Dyk, S., et al., 2003. The IRSA 2MASS all-sky point source catalog. NASA/IPAC Infrared Science Archive. Derekas, A., Kiss, L.L., Bedding, T.R., et al., 2006. ApJ 650, L55. Gough, D.O., Ostriker, J.P., Stobie, R.S., 1965. ApJ 142, 1649. Guo, J.H., Li, Y., 2002. ApJ 565, 559.
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Horne, J.H., Baliunas, S.L., 1986. ApJ 302, 757. Kazarovets, A.V., Samus, N.N., Durlevich, O.V., et al., 1999. IBVS, 4659. Kiss, L.L., Szabo´, Gy. M., Bedding, T.R., 2006. MNRAS 372, 1721. Levesque, E.M., Massey, P., Olsen, K.A.G., et al., 2005. ApJ 628, 973. Maeder, A., 1980. A&A 90, 311. Malatesta, K.H., Beck, S.J., Menali, G., Waagen, E.O., 2005. JAAVSO 34, 1. Massey, P., Plez, B., Levesque, E.M., et al., 2005. ApJ 634, 1286. Perryman, M.C.A., The Hipparcos Science Team, 1997ESA SP-1200, vol. 1–12. ESA Publ. Division, c/o ESTEC, Nordwijk, The Netherlands. Pierce, M.J., Jurcevic, J.S., Crabtree, D., 2000. MNRAS 313, 271. Roberts, D.H., Lehar, J., Dreher, J.W., 1987. AJ 93, 978. Rodono`, M., Cutispoto, G., Lanza, A.F., Messina, S., 2001. AN 322, 333. Scargle, J.D., 1982. ApJ 263, 835. Stencel, R.E., Pesce, J.E., Bauer, W.H., 1989. AJ 97, 1120. Tuthill, P.G., Haniff, C.A., Baldwin, J.E., 1997. MNRAS 285, 529. Wood, P.R., 2000. PASA 17, 18. Wood, P.R., Olivier, E.A., Kawaler, S.D., 2004. ApJ 604, 800.
Evidence for the pulsational origin of the Long Secondary Periods: The red supergiant star V424 Lac (HD 216946) q Sergio Messina
*
INAF – Catania Astrophysical Observatory, via S. Sofia 78, I-95123 Catania, Italy Received 29 January 2007; received in revised form 26 February 2007; accepted 2 April 2007 Available online 7 April 2007 Communicated by W. Soon
Abstract The results of a long-term UBV photometric monitoring of the red supergiant (RSG) star V424 Lac are presented. V424 Lac shows multiperiodic brightness variations which can be attributed to pulsational oscillations. A much longer period (P = 1601 d), that allows us to classify this star as a long secondary period variable star (LSPV) has been also detected. The B V and U B color variations related to the long secondary period (LSP) are similar to those related to the shorter periods, supporting the pulsational nature of LSP. The long period brightness variation of V424 Lac is accompanied by a near-UV (NUV) excess, which was spectroscopically detected in a previous study [Massey, P., Plez, B., Levesque, E.M., et al., 2005. ApJ 634, 1286] and which is now found to be variable from photometry. On the basis of the results found for V424 Lac, the NUV excess recently found in a number of RSGs may be due not solely to circumstellar dust but may also have a contribution from a still undetected LSP variability. Ó 2007 Elsevier B.V. All rights reserved. PACS: 97.20.Pm; 97.10.Sj; 97.20.Jg; 97.20. w Keywords: Stars: supergiants; Stars: oscillations; Stars: late-type; Stars: individual: V424 Lac
1. Introduction Red supergiants (RSG) are evolved stars characterized by brightness variations, mainly arising from radial pulsations, which represent the periodical component of their variability (Guo and Li, 2002), as well from huge convection cells, which interplay with the oscillations and can determine an additional stochastic component of variability (e.g. Tuthill et al., 1997). Measuring pulsations in RSGs is a time-demanding task since models predict pulsational instability with fundamental periods as long as 4000 days. However, their study is particularly interesting since the q Based on observations collected at INAF-Catania Astrophysical Observatory, Italy. * Tel.: +39 095 7332230; fax: +39 095 330592. E-mail addresses: [email protected], [email protected]
1384-1076/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.newast.2007.04.002
pulsational modes of RSGs allows us to check the values of fundamental stellar parameters such as the stellar radius derived from evolutionary models (Levesque et al., 2005). Moreover, RSGs show their own period–luminosity (P– L) relation which makes them useful as extragalactic distance indicators (e.g. Pierce et al., 2000). It is known from a number of studies (Kiss et al., 2006; Derekas et al., 2006; Wood et al., 2004) that a significant fraction (25%) of pulsating RSGs and of asymptotic giant branch (AGB) stars show periodic brightness changes characterized by two distinct time scales. The short-period variations manifest on a time scale of about a few hundreds days and can be attributed to first and possibly second overtone mode pulsations, which are also expected from theoretical models. The long-period variations manifest on a time scale greater than about 1000 days. Indeed, these stars characterized by long-period variations are better
S. Messina / New Astronomy 12 (2007) 556–561
known as long secondary period variables (LSPV). The origin of the long secondary period is not understood yet. As discussed by Kiss et al. (2006), these long secondary periods cannot be explained by radial pulsations, nor by metallicity effects. Maeder (1980) suggested that the long periods observed in blue-yellow supergiants can be due to non-radial oscillations of gravity modes. Despite their different internal structures and global properties, however, the presence of low-degree g modes, also proposed by Wood et al. (2004), seems to be the most likely explanation of the existence of long secondary periods of both AGB and RSG stars. Unfortunately, the LSPs remain beyond the limits of the models. The presence of circumstellar dust around red supergiants makes these stellar objects further interesting. Recently, Massey et al. (2005) have found that previous broadband studies of RSGs have underestimated the effect of extinction by circumstellar dust on the properties of RSGs, such us the luminosity when derived from the observed V magnitude. RSG stars with the highest amount of extra visual extinction also show significant near-UV (NUV) excesses compared to the stellar models reddened according to the standard reddening law. This NUV excess is likely to be due to the scattering of the star’s light by dust and/or an average grain size larger than that typical of grains found in the diffuse interstellar medium. Similar excesses have been attributed to circumstellar dust around R Coronae Borealis stars. The presence of circumstellar dust shells was first revealed by ground-based IR photometry, while Infrared Astronomical Satellite (IRAS) two-color diagrams established that such dust shells are a common phenomenon for RSGs (Stencel et al., 1989). V424 Lac (V424 Lac, HD 216946, Vmin = 4.87, B Vmin = 1.68) is a bright galactic supergiant belonging to the Lac OB1 association. It was discovered to be variable in the optical band by the Hipparcos mission (Perryman and The Hipparcos Science Team, 1997) and designed as variable star in the 74th Special Name-list of Variable Stars (Kazarovets et al., 1999). On the basis of moderate-resolution optical spectrophotometry and using new MARCS stellar atmosphere models, Levesque et al. (2005) classified V424 Lac as an M0 I star with Teff = 3800 K, log g = 0.7, R/Rx = 260, MV = 4.27, Mbol = 5.50, assuming, for the Lac OB1 association, a distance modulus (m M)0 = 8.9 mag and an interstellar reddening E(B V) = 0.11 mag. Interestingly, V424 Lac is one of the RSG stars analysed by Massey et al. (2005) for which NUV ˚ region has been measured and excess in the 3500–4000 A attributed to the presence of circumstellar dust. The multiband UBV photometric observations analysed in this paper reveal that V424 Lac has multiperiodic brightness variations and, in particular, a long secondary period that allows us to classify it as a long secondary period variable star. The nearly simultaneous observations in the U, B and V bands, which are very rarely collected for these stars, allow us to better characterize their variability, providing additional information to address the origin of
557
long secondary periods and the effect of circumstellar extinction. 2. Observations The photometric observations analysed in the present study were collected with the 80-cm automated photometric telescope (APT-80), located at the M.G. Fracastoro station of INAF-Catania Astrophysical Observatory on Mt. Etna (Italy). This telescope feeds a single channel charge-integration photometer, equipped with an uncooled Hamamatsu R1414 SbCs photomultiplier and standard UBV filters (Rodono` et al., 2001). V424 Lac was observed differentially compared to the comparison star BD+46 3969 (c) and the check stars HD 218949 (ck1) and HD 218452 (ck2). Originally, V424 Lac was included in the telescope schedule to serve as a bright navigation star (n), i.e., the first star of a group that the APT-80 hunts, to make long-term differential observations of the BY Dra-type variable star KZ And (v). The integration time in U, B and V filters was set to 15, 10 and 10 s, respectively, and the observing sequence was n-c-ck1-c-vv-v-c-v-v-v-c-ck2-c-n. The sky background was measured at a fixed position near each star. Differential magnitudes were corrected for atmospheric extinction and transformed into the standard UBV system. The transformation coefficients were determined quarterly by observing selected samples of standard stars. Due to the relatively short duration of an observing sequence (.30 min), the v c, ck1 c, ck2 c and n c values were finally averaged to obtain one single data point for each night. The transformation into the standard system is made with an accuracy of the order of 0.01, 0.01 and 0.02 mag in the V magnitude, B V and U B color indices, respectively. A comparison between the standard deviations of ck c and v c differential magnitudes shows that the comparison star has remained constant within the observation accuracy. V424 Lac has been observed for 8 years from August 20, 1993 to October 29, 2001 for a total of 232 nights. In order to extend the data time series the Hipparcos photometry was also retrieved (Perryman and The Hipparcos Science Team, 1997). V424 Lac has been observed by Hipparcos from 1989 to 1993. Hp magnitudes were transformed into Johnson V magnitudes by applying the correction V = Hp 0.09 mag using the Hp V versus V I relation taken from Perryman and The Hipparcos Science Team (1997). Ten additional visual observations of V424 Lac were found in the database of the American Association of Variable Star Observers (AAVSO). However, since such observations are provided in the instrumental magnitude and, therefore, not transformed into the standard system and since they have not been scrutinized for ‘validation’, according to the AAVSO rules (Malatesta et al., 2005), they are not used in the following analysis. Summarizing, the dataset analysed in the present paper represents to date the most complete time series of photometric observations of V424 Lac. In Fig. 1, the
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Fig. 2. Top panel: power spectrum from Scargle periodogram analysis. The dotted line indicates the 0.1% false alarm probability. Bottom panel: the observational window function.
Fig. 1. Time sequence of U, B, and V magnitudes, U B and B V colors of V424 Lac. Filled circles represent the APT-80 observations, whereas crosses (top panel) represent the V-band Hipparcos photometry. The solid line represents the sinusoidal fit with the longest period P = 1601 days (see text).
UBV magnitudes, U B and B V colors are plotted versus time as filled circles, whereas the V-band Hipparcos photometry is plotted as crosses (top panel of Fig. 1). V424 Lac shows clear evidence of brightness variations versus time. The amplitude of variation increases towards shorter wavelengths, from about 0.08 mag in the V-band to 0.11 in the B-band and 0.33 in the U-band. The variation of B V and U B colors is of about 0.04 and 0.23 mag, respectively.
PN is set to be the fraction of simulated non-variable light curves which have the highest peak power exceeding PN. In the present case the power related to a 0.1% FAP is that which was exceeded in 10 simulations and corresponded to PN = 11. Although several periods were detected with a confidence level larger that 99.9%, the four periods with the largest power (see Table 1) were considered in the following analysis. A following analysis of the B and V magnitudes time series also confirmed the same periods with a similar confidence level. It must be noted that due to the quasi-periodical and not strictly stationary nature of the pulsational modes of RSGs, some of the listed short periods may be just numerical artifacts. In fact, the assumption of the Fourier analysis that the observed variation results from the superposition of distinct stationary signals is not fully applicable in this class of variable stars (see, e.g., Kiss et al., 2006).
3. Fourier analysis 3.2. CLEAN periodogram 3.1. Scargle periodogram In order to search for significant periodicities, the Scargle-Press periodogram search routine (Scargle, 1982; Horne and Baliunas, 1986) was applied to the whole sequence of U magnitudes. The U magnitude was selected for the period search because it showed the largest amplitude variations, thus making the periodicity detection more reliable. Several periods were detected (see top panel of Fig. 2) with a false alarm probability (FAP) smaller than 0.1% (corresponding to a confidence level larger than 99.9%). The FAP is the probability that a peak of given height is due to simply statistical variations, i.e. to white Gaussian noise. In order to determine the FAP, the Scargle periodogram was computed for 10,000 simulated light curves. Such curves were created with a Monte Carlo algorithm and with a time sampling equal to that actually observed, and the cumulative distribution of the power of the highest peaks was determined. The FAP related to a given power
The Scargle technique does not take into account the observational window function (see bottom panel of Fig. 2). As a consequence, some of the peaks in the power spectrum can be the result of the data sampling. This effect is called aliasing and even the highest peaks may be artifacts. In order to remove the effect due to the data sampling, the Clean periodogram technique (Roberts et al., Table 1 Most significant periods derived from Scargle periodogram and CLEAN analysis along with uncertainty, corresponding peak power and peak power related to a 0.1% FAP PScargle (d)
PN
PN (FAP = 0.1%)
PCLEAN (d)
Padopted (d)
DP (d)
1601 490 305 422
95 65 50 22
11 11 11 11
1600 526 312 412
1601 490 305 422
278 2 1 1
As discussed in the text, some of the shorter periods may be numerical artifacts.
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Fig. 3. Power spectrum from CLEAN analysis. In the second panel from top, the highest peak is out of plot to better show the smaller peaks. For a detailed description see Roberts et al. (1987) and Bailer-Jones and Mundt (2001).
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the MACHO database (Wood, 2000; Derekas et al., 2006). It also falls in the lower end of the long-period sequence of galactic RSG variables (see Fig. 7 of Kiss et al., 2006). According to the calculations of Guo and Li (2002), the shortest period P = 305 days results to be the pulsational fundamental mode. The values of the pulsation constants Q = P(M/Mx)1/2(R/Rx) 3/2 and W = P(M/Mx)(R/ Rx) 2 which represent, respectively, the classical period– density relation and the natural form of the pulsation constant if the oscillations are confined to the upper layers of the envelope (Gough et al., 1965), are found to be in good agreement with the values typical of RSG variables (see Fig. 8 of Kiss et al., 2006), giving further support to the pulsational nature of short periods and to the classification of V424 Lac as LSP star. According to the evolutionary calculations of Levesque et al. (2005), a mass value log M/Mx = 0.89 is used in the previous relations. Being the faintest LSP galactic RSGs to date, the newly discovered long period of V424 Lac is particularly significant since it allows us to extend and, therefore, to improve the P L relation for galactic LSP variable stars and to better calibrate the P L relation (‘‘D’’ sequence) of LMC red giant variables from the MACHO database (see Kiss et al., 2006). As already mentioned, the origin of the long secondary periods of RSGs is not well understood. The V magnitude and color variations showed by V424 Lac allow us to confirm that they cannot be ascribed either to the rotational modulation of the visibility or to the evolution of dark spots on the stellar photosphere. In fact, the presence of dark spots on the stellar photosphere gives rise to light curves whose amplitude increases towards shorter wavelengths. As shown in Fig. 4, in the black body approximation
1987; Bailer-Jones and Mundt, 2001) was applied to the U magnitude time series (see Fig. 3). As shown in Table 1, the periods independently detected by Scargle and CLEAN methods are in good agreement. The finally adopted periods are those giving the smallest residuals of the sinusoidal fit to data, which in the present case are the periods from the Scargle technique. In Fig. 1, the sinusoidal fit with the longest period of P = 1601 days is plotted as a solid line, whereas in Fig. 5 all four periods are used to fit the U-band data series. 4. Discussion V424 Lac has a K-band absolute magnitude MK = 8.23 which is derived from the OB Lac1 distance modulus (m M)0 = 8.9, the 2MASS dereddened K-band magnitude K = 0.67 (Cutri et al., 2003), adopting an interstellar reddening E(B V) = 0.11 mag. A RV = 4.2 ratio was used to determine the K-band extinction (AK) according to the results of Massey et al. (2005). In the period-K-band magnitude diagram, the longest period P = 1601 days clearly reveals V424 Lac to be a long secondary period variable. Specifically, this period falls in the upper end of the ‘‘D’’ sequence outlined by RSGs from
Fig. 4. An example of model variations of light curve amplitudes vs. wavelength arising from spots. Solid and dashed lines connect the light ˚ curve amplitude values obtained at three different wavelengths (5500 A ˚ B-band and 3600 A ˚ U-band), for two different spots V-band, 4500 A temperatures Tspot = 3500 K and Tspot = 3000 K, respectively, and for three values of area (f = 0.2, 0.3 and 0.5) which is expressed as fraction of the visible disk. The model effective temperature is Teff = 3800 K. The solid heavy line represents the observed light curve amplitudes of V424 Lac which show a variation vs. wavelength not explainable in terms of spots.
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Fig. 5. Time sequence of U magnitudes. Filled circles represent the APT80 observations, whereas the two diamonds mark the epochs of the spectrophotometry by Massey et al. (2005) and Levesque et al. (2005).
the light curve amplitude varies approximately linearly vs. wavelength for different combinations of spot temperatures (solid lines refer to Tspot = 3500 K, whereas dashed lines to Tspot = 3000 K) and spot covering factors. This dependence is clearly different from the one observed in V424 Lac (solid heavy line in Fig. 4). Although we cannot completely rule out a possible partial contribution from spots to the observed long-term variability, we can state that spots are not the main cause in the case of V424 Lac. Such a result is in agreement with the previous mentioned studies. As anticipated, Massey et al. (2005) observed V424 Lac spectroscopically at two different epochs. They detected NUV excess but no evidence for significant time variation. However, by chance they observed V424 Lac when it was at the same light level as shown by the open diamonds in Fig. 5. On the contrary, the U magnitude variations found in the present analysis may indicate a likely presence of variable NUV excess. Specifically, the flux in the U-band at the star’s brightness maximum is up to 35% larger than the flux at the brightness minimum. Assuming that such NUV excess is due, as proposed by Massey et al. (2005), to the star’s light scattering by a dust shell and/or to the grain size, typically larger than the grains found in the diffuse interstellar medium, this should imply the presence of
either (periodical) variations of the dust shell depth and/or variations of the grain size. However, the color variations related to the long secondary period are similar to those related to the short-period pulsational oscillations. In fact, after having removed the periodic component of variability related to the longest period (P = 1601 d), it has been found that V424 Lac gets brighter in the V-band when it is brighter in the B and U bands, which is the same behaviour shown by the long secondary period. In Fig. 6, the relation between U, B and V magnitudes are plotted. For each pair of these magnitudes the linear correlation coefficient is computed, which, in all three cases, has a very high significance level (a < 0.001). On the basis of the result found for V424 Lac, it can be stated that the NUV excess observed by Massey et al. (2005) in RSGs may also arise from the presence of still undetected LSP variability and, therefore, may be caused by pulsation effects and not solely by circumstellar dust shells. 5. Conclusions Long-term UBV photometry is a powerful observational approach to detect and investigate the nature of long-term secondary periods in RSGs. Eight years of high precision UBV observations of V424 Lac have allowed us to discover the existence of short-period brightness variations related to pulsational modes and to classify this star as a LSPV star thanks to the discovery of a long secondary period. The analysis of multicolor observations has allowed us to conclude that the color variations related to the long secondary period are similar to those ascribed to shorterperiod pulsational oscillations. Multicolor observations also indicate that the NUV excess recently found in a number of RSGs and attributed to circumstellar dust, can be variable and partly due to still undetected LSP variability. Acknowledgement The author thanks the anonymous referee for helpful comments. The acquisition of photometric data over so many years with the Catania APT has been possible thanks to the dedicated and highly competent technical assistance of a number of people, notably P. Bruno, E. Martinetti and
Fig. 6. Magnitude–magnitude relations after removing the fit to the long-term component of variability due to the long secondary period. Solid lines are the liner fit to the data. The label ‘r’ is the linear correlation coefficient.
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