Period luminosity relation for M-type semiregular variables from Hipparcos parallaxes

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1 Mon. Not. R. Astron. Soc. 355, (2004) doi: /j x Period luminosity relation for M-type semiregular variables from Hipparcos parallaxes C. Yeşilyaprak 1 and Z. Aslan 1,2 1 Akdeniz University, Physics Department, Antalya, Turkey 2 TÜBİTAK National Observatory, Akdeniz University Campus, Antalya, Turkey Accepted 2004 August 19. Received 2004 July 29; in original form 2004 February 16 1 INTRODUCTION In the words of Wood (2000), red giants are probably the least understood of all variable stars, even the mode of pulsation of these stars has remained a topic of controversy. This is especially true of semiregular (SR) variables. The General Catalogue of Variable Stars (GCVS) defines the SR variables as giants or supergiants of intermediate or late spectral types showing noticeable periodicity of light changes, with time-scales of 20 to 2000 d or more, accompanied or sometimes interrupted by different irregularities, or even light constancy (GCVS4, Kholopov et al. 1988). The shapes of light curves are often different and variable. The visual light amplitude is, as a rule, less than 2.5 mag. SR variables are not a homogeneous group: four subtypes are defined, classification into which is not always unique. SRa variables are late-type giants (M, C, S) with persistent periodicity. Many of these differ from Mira variables only by the smaller light amplitude, less than 2.5 mag in V. According to Kerschbaum & Hron (1992, 1994), SRa variables are not a distinct class, but probably a mixture of SRb and Mira variables, the former being late-type giants (M, C, S) with poorly expressed periodicity. Many of the SRb as well as SRa variables show multiple periodicity (Mattei et al. 1998; Kiss et al. 1999). SR variables are pulsating variables located in about the same region of the H R diagram as Mira variables, which are believed to be at the tip of the asymptotic giant branch (AGB), but the evolutionary link is not clear. On a study based on mean motions and velocity dispersions, Aslan (1981) argued that the sequence Lb cahity@akdeniz.edu.tr (CY); aslan@akdeniz.edu.tr (ZA) ABSTRACT We have studied the period luminosity (P L) relationships of oxygen-rich semiregular (SR) variables in several wavelength bands using Hipparcos parallaxes with an accuracy of better than 10 per cent. We have shown that there is a clear dependence on period of absolute magnitude in the U, B, V, R, I C, J, H, K, L, M, N, [12], [25], [60] and [100] bands, and that the slope of the linear M λ logp relation is a smooth function of wavelength. We point out that this relation can in principle be used to derive absolute bolometric magnitude as a function of period. The behaviour of the second periods of SR variables in the P L relation in the V and K bands is also discussed. Keywords: stars: distances stars: fundamental parameters stars: late-type stars: oscillations. SR (non-emission) SR (emission) Mira may indicate the direction of evolution. Kerschbaum, Olofsson & Hron (1996b) and Ivezić & Knapp (1999) suggested that SR variables might really oscillate between the Mira and SR phases. Having found that the Whitelock evolutionary track from clusters (Whitelock 1986) fits the Hipparcos data for nearby SR variables, Bedding & Zijlstra (1998) concluded that SR variables are Mira progenitors. The aim of this paper is to investigate the P L relationship for various wavelength bands for M-type (O-rich) SR variables in the solar neighbourhood using Hipparcos parallaxes (ESA 1997), with a view to obtaining information on wavelength dependence. Absolute magnitudes of SR variables in the solar vicinity have been determined in the past from statistical parallaxes (Wilson 1942; Aslan 1973), from membership in stellar groups (Aslan 1976), and more recently, from membership in clusters (Whitelock 1986). After the publication of the Hipparcos Catalogues (ESA 1997), a number of papers discussed the P L relationship for long-period variables (LPVs), including SR variables (van Leeuwen et al. 1997; Bedding & Zijlstra 1998; Barthès et al. 1999; Aslan & Yeşilyaprak 2000; Whitelock & Feast 2000; Yeşilyaprak 2003), based on Hipparcos parallaxes. However, there are few LPVs with good parallaxes, and it is not easy to make good use of, and allow for any bias that may be introduced by, the less certain parallaxes (see e.g. Arenou & Luri 1999). As a result, different authors have taken different approaches in treating the parallaxes. In order to avoid statistical biases, it is advocated that the so-called reduced parallax, or astrometry-based luminosity, should be used (e.g. Arenou & Luri 1999; Feast 2002; Knapp et al. 2003). van Leeuwen et al. (1997), Bedding & Zijlstra (1998), and Whitelock & Feast (2000) adopted the slope of the P L relation derived from the LMC and determined the zero-point from C 2004 RAS

2 602 C. Yeşilyaprak and Z. Aslan Hipparcos parallaxes. Barthès et al. (1999) used parallaxes (without any imposed limits, i.e. including negative parallaxes) and proper motions from the Hipparcos Catalogue to calibrate the absolute K magnitudes. For reasons given in Section 2, we think that the information content in the not-well-determined or negative parallaxes, even if due allowance is made for statistical biases, will not contribute significantly to a mean P L relationship for SR variables, nor to the existence of any dependence of the slope of a linear M λ logp relationship on wavelength obtainable from good parallaxes. In fact, anticipating the results of this paper, we see that our P L relation in the K band agrees very well with that obtained by Knapp et al. (2003) using reduced parallaxes. In this paper, we will therefore use the best available parallaxes directly to calculate the absolute magnitudes to study the P L relation of the type M = α logp + β for the O-rich SR variables in various wavelength bands, leaving the inclusion of all the parallaxes into the solution using reduced parallaxes for a later paper. 2 THE DATA AND SELECTION OF THE SAMPLE 2.1 Spectral type We selected all M-type SR variables that have a period determined with designation SR, SRa or SRb from the General Catalogue of Variable Stars (GCVS4, Kholopov et al. 1988), Hipparcos Catalogue (ESA 1997), New Catalogues of Suspected Variable Stars I (NSV I, Kukarkin et al. 1982) and II (NSV II, Kazarovets, Durlevich & Samus 1998). We then identified these SR variables in the SIM- BAD data base. We have of course included all the new discoveries by Hipparcos. 2.2 Johnson s magnitudes It is known that the magnitudes in the GCVS4 are heterogeneous and may contain large random and systematic errors. On the other hand, Hipparcos photometry is a homogeneous and uniformly calibrated system (HIP Vol. I, van Leeuwen et al. 1997). Although time baselines in Hipparcos are generally shorter than in GCVS4 and there are some discussions about the calibration of V I C (Cousins I) colours for red variables in Hipparcos photometry (Platais et al. 2003; Pourbaix et al. 2003), the amplitudes of the stars are small so that a mean Hipparcos magnitude is not expected to deviate much from the true mean (e.g. Knapp et al. 2003). We therefore adopted V, I C magnitudes and B V colours from the Hipparcos Catalogue (ESA 1997); they refer to the mean of the light cycle. Other magnitudes (U, R, J, K, L, M, N) onthe Johnson system (Johnson 1965) and the H magnitude were taken from the SIMBAD data base. The H band appeared in 1967 as part of the Arizona system (Moro & Munari 2000), and all 11 magnitudes (U, B, V, R, I, J, H, K, L, M, N) (Moro & Munari 2000) are often called the Johnson photometric system and are abbreviated to JP11 in the SIMBAD data base. The U, the red, and the infrared magnitudes are also the means of all the available magnitudes given in the SIMBAD data base. 2.3 IRAS magnitudes The infrared fluxes of IRAS F 12, F 25, F 60, F 100 (Beichman et al. 1988) were taken from the SIMBAD data base. IRAS m 12, m 25, m 60 and m 100 magnitudes were calculated from [12] = logf 12, [25] = logf 25, [60] = logf 60 and [100] = logf 100,asgiven in the IRAS-PSC (1988) and Walker & Cohen (1988). 2.4 Periods and parallaxes The periods given in the Hipparcos Catalogue are mostly based on Hipparcos measurements only (ESA 1997), and this apparently resulted in many known SR variables being designated as unclassified with no period. We have therefore taken the periods from the GCVS4 (Kholopov et al. 1988) as the main source as well as using Hipparcos periods if available. We have also used the SIMBAD data base. Some periods were taken from the studies of Houk (1963), Kerschbaum, Lazaro & Habison (1996a), Percy et al. (1996), Bedding et al. (1998), Bedding & Zijlstra (1998), Groenewegen & de Jong (1998), Mattei et al. (1998), Percy & Parkes (1998), Kiss et al. (1999), Koen & Laney (2000), Whitelock & Feast (2000), Percy et al. (2001) and Hinkle et al. (2002). From the master list thus obtained, we selected our sample for studying the luminosities according to the following criteria. (i) Parallaxes better than 10 per cent with the aim of studying the P L relation. The mean absolute magnitude of a sample selected on the basis of relative parallax error, ɛ π /π, will be affected by the so-called Lutz Kelker (LK) bias (Lutz & Kelker 1973), in the sense that for a given (approximately constant) measuring error we favour stars for which measuring parallax is too large. The LK bias is generally considered to depend on ɛ π /π and the luminosity function of the sample, but there seems to be no consensus on how to assess it and different authors have used different approaches (Turon & Crézé 1977; Hanson 1979; Lutz 1979; Smith 1987a, 1987b; Ratnatunga & Casertano 1991; Koen 1992; Oudmaijer, Groenewegen & Schrijver 1998; Arenou & Luri 1999; Groenewegen & Oudmaijer 2000; Smith 2003). Individual absolute magnitudes are not affected by the LK bias (Arenou & Luri 1999; Aslan 2000; Groenewegen & Oudmaijer 2000; Feast 2002). If we use Koen s calculations (Koen 1992), the most probable correction to the mean absolute magnitude for a sample of small size, 20 say, with ɛ π /π 0.10 is smaller than 0.1 mag (in absolute value); see also Bedding & Zijlstra (1998) and Groenewegen & Oudmaijer (2000). The formal error of an individual absolute magnitude calculated from the parallax π with a standard error ɛ π is, to first approximation, ɛ M ±2.17 ɛ π /π, which gives ɛ M ±0.22 mag at ɛ π /π = 0.10 as the error of the absolute magnitude. If, however, no limit is imposed, any P L relation with its intrinsic dispersion will be blurred by the dispersion in absolute magnitude at a given period due to the errors of individual absolute magnitudes, and any correction to the mean absolute magnitude arising from the LK bias is unlikely to improve the picture. In this paper, we do not aim at obtaining a universally valid P L relationship for SR variables, but rather we wish to determine whether there are any P L relations at all and whether any such relation is wavelength-dependent. Indeed, such P L relations, even if not definitive, can be used to examine both theoretical and observational aspects while the answer is sought to the question Are the P L relations of SR variables obtained universal or is there a valid relationship at all? We will therefore limit our sample to ɛ π /π 0.10 in order to keep the statistical errors and the bias due to the nonlinearity of the transformation from parallax to absolute magnitudes (e.g. Brown et al. 1998) as small as possible, keeping in mind that it is essential to use the best parallaxes available of a statistically reasonable number of stars. We note in passing that, as our sample is not selected according to apparent magnitude, there will be no need to consider Malmquist bias (Malmquist 1936). (ii) Periods between 20 and 500 d. Periods smaller than 20 d fall below the classical definition of SR designation and we exclude them from our present discussion as their nature is still uncertain (see, for example, Bedding et al. 1998; Groenewegen & de Jong

3 P L relation for M-type semiregular variables 603 Table 1. SR variables with P 20 d and ɛ π /π Name Spec. Var. V K P 1 P 2 P 3 π ɛ π M V M K Period a Type Type (mag) (mag) (d) (d) (d) (mas) (mas) (mag) (mag) References θ Aps M7 III SRb VZ Cam M4 III SR V1070 Cyg M7 III SRb ,7,7 R Dor M8e III SRb ,1 WZ Dor M3 III SRb Dra M3 III SRb DM Eri M4 III SRb g Her M6 III SRb ,1,10 X Her M6e SRb ,11, Her M1 III SR II Hya M4 III SRb RX Lep M6 III SRb ,13 σ Lib M3 III SRb RLyr M5III SRb ,14,15 ɛ Mus M5 III SRb ɛ Oct M6 III SRb SX Pav M7 III SRb ρ Per M4 III SRb ,15,15 ψ Phe M4 III SR L 2 Pup M5e III SRb γ Ret M4 III SR RR UMi M5 III SRb ,16 a References: (1) Kholopov et al. (1988) (GCVS4); (2)ESA (1997) (Hipparcos); (3) SIMBAD Data base; (4) Koen & Laney (2000); (5) Groenewegen & de Jong (1998); (6) Kerschbaum et al. (1996b); (7) Percy et al. (2001); (8) Bedding et al. (1998); (9) Percy & Parkes (1998); (10) Mattei et al. (1998); (11) Kiss et al. (1999); (12) Houk (1963); (13) Bedding & Zijlstra (1998); (14) Whitelock & Feast (2000); (15) Percy et al. (1996); (16) Hinkle et al. (2002). 1998; Mattei et al. 1998; Kiss et al. 1999; Koen & Laney 2000; Whitelock & Feast 2000; Percy et al. 2001; Hinkle et al. 2002). It is likely that longer periods will be more contaminated with non-pulsational variations (see, for example, Barnbaum, Morris & Kahane 1995; Kiss et al. 2000). 3 PERIOD LUMINOSITY RELATION We have calculated the nominal absolute magnitudes of the SR variables in our sample for Johnson, Cousins, and IRAS bands (U, B, V, R, I C, K, [12], [25], and [60]). 1 We have estimated the interstellar absorption using the model of Arenou et al. (1992) for the V band: the corrections, not more than about 0.15 mag even in the U band, are small for the present purpose and have not been applied. The corrections in the red and infrared bands are even smaller (Kerschbaum & Hron 1994; Pierce, Jurcevic & Crabtree 2000; Alard et al. 2001). 3.1 P L relations for SR variables SR variables with relative parallax errors better than 10 per cent are listed in Table 1. We have plotted the P L relations for these variables for the V and [25] bands in Fig. 1, and for the K band in Fig. 2. The diagrams for other wavelength bands (Yeşilyaprak 2003) are similar, with different slopes, and are not given here. The coefficients of the P L relation, M = α logp + β, calculated by least squares, for the U, B, V, R, I C, J, H, K, L, M, N, [12], [25], [60], and [100] bands are listed in Table 2. The last three columns give the number of stars involved, the dispersion about the solution, and the correlation coefficient, respectively. 1 See Section 2 for references to the photometry. Figure 1. The P L relations of SR variables with P 20 d and ɛ π /π 0.10 in the V and [25] bands. The solid lines are the linear least-squares fits through the points (see Table 2). The following factors contribute to the total dispersion in absolute magnitude in all bands in Table 2: (i) errors in the observed parallaxes (ɛ M ±0.22 mag at ɛ π /π = 0.10); (ii) intrinsic dispersion in absolute magnitude at a given period; (iii) intrinsic dispersion in period at a given absolute magnitude (probably due to a mixture of pulsation modes, multiperiods, and the semiregular nature of the periods, see Section 3.2); (iv) observational errors in apparent magnitudes; (v) uncertainty in the mean apparent magnitude of each star due to the lack of observational coverage over the period and the fact that the star is not truly periodic;

4 604 C. Yeşilyaprak and Z. Aslan Table 2. Coefficients of the equation M = α logp + β for SR variables with P 20 d and ɛ π /π 0.10 in various bands. N is the number of stars involved, σ is the dispersion about the solution and ρ is the correlation coefficient. System Band Wavelength a α ± ɛ α β ± ɛ β N σ ρ λ 0 (µm) (Slope) U ± ± B ± ± V ± ± R ± ± I C ± ± Johnson J ± ± & Cousins H ± ± K ± ± L ± ± M ± ± N ± ± [12] ± ± IRAS [25] ± ± [60] ± ± [100] ± ± a Moro & Munari (2000). Figure 2. The P L relations in the K band and the second periods of SR variables with P 1 20 d and ɛ π /π The solid line is the linear least-squares fit through the points with P 1,excluding 69 Dra (see Section 3.1). The dotted line is the relation for Mira variables (Whitelock & Feast 2000). (vi) uncertainties in interstellar absorption (especially in bands bluer than R); (vii) dependence on colour. It is probably safe to say that the first three causes dominate the dispersion about the mean relation. It can be seen from Fig. 1 that there is a clear dependence of absolute magnitude on period, but this dependence is not very convincing in the case of Fig. 2. The reason lies in the fact that the slope of the P L relation is a function of wavelength and flattens near 1 µm (see below). We also note that the solid line in Fig. 2 agrees very well with the P L relation in the K band obtained by Knapp et al. (2003) (see their equation 7) using reduced parallaxes from revised Hipparcos parallaxes for galactic SR variables. The variable 69 Dra has a faint absolute magnitude in the K band and stands below the mean relation in Fig. 2 by more than 4σ and is not included in the least-squares solution. L 2 Pup and 106 Her also fall below the line but they are within 2σ and are included in the solution. We note that the absolute magnitudes of 69 Dra in B and V, aswell as those of 106 Her and L 2 Pup, agree well (within 1σ ) with the mean relations. Moreover, 106 Her and 69 Dra have the earliest spectral types (see Table 1). This suggests that the latter variables may be intrinsically faint in the infrared. There may also be evolutionary differences as 69 Dra and L 2 Pup lie in the tails of the distributions of the space velocity components (Yeşilyaprak 2003). It is seen clearly from Table 2 and Fig. 3 that the slope (α)ofthe linear P L relation is a relatively smooth function of wavelength.

5 The absolute magnitude at short wavelengths becomes fainter for the longer periods. It is flat near 1 µm, after which the luminosity increases with period. This is reflected in the variation of the correlation coefficient with wavelength in the last column of Table 2. For comparison, the slopes of P L relations at mean light in the J, H and K bands for O-rich Mira variables in the LMC given by Feast et al. (1989) are plotted in Fig. 3 as open triangles. They fall systematically below the curve for SR variables, hinting at a similar dependence on wavelength but we lack information on other wavelengths. The number of galactic Mira variables with good parallaxes is too small to make a similar study and compare with the SR variables. Fig. 3 implies that it is in principle possible to derive the bolometric absolute magnitude at a given period, but before that is done it is necessary to evaluate, if possible, the effects of multiperiodicity in the P L relationships (see Section 3.2) and the probable bias introduced by the less accurate parallaxes. The implications of Fig. 3 and its usefulness in the study of LPVs are the subject of a different paper, but it suffices here to remark that the variation of the slope with wavelength mimics the variation of the energy flux of an individual M star: see the observed flux of the M1 star HD given by Fluks et al. (1994). 3.2 P L relations and SR variables with second periods We designate the multiple periods of SR variables as P i, with P 1 < P 2 < P 3, where P 1 is referred to as the first and P 2 as the second period. To see how the second periods behave in the P L relation, we have plotted the P 1,2 L relation for the K band in Fig. 2 (filled circles and solid line) together with P 2 (open circles). The P L relation of Mira-type stars (Whitelock & Feast 2000) (dotted line) is also shown. It is seen from Fig. 2 that the SR variables with second periods fall on the extension of the P 1 L relation. This behaviour of SR variables with multiperiods must be related to the pulsation-mode changes of SR variables (Fox & Wood 1982; Cadmus et al. 1991; Feast 1996; Wood & Sebo 1996; Percy & Desjardins 1996; Percy P L relation for M-type semiregular variables 605 Figure 4. The visual P L relation from Fig. 1 and the second periods of SR variables (labelled) with ɛ π /π et al. 1996; Bedding et al. 1997; van Leeuwen et al. 1997; Barthès 1998; Bedding et al. 1998; Kiss et al. 1999), or to changes in stellar structure (Bedding & Zijlstra 1998), but it is not clear whether these multiperiods are the result of mode switching between Mira-like and SR-like pulsation modes (Knapp et al. 2003) or an indication of an evolutionary change into the Mira stage (Whitelock 1986; Bedding & Zijlstra 1998; Wood 2000). The behaviour of the second periods of SR variables in the visual P L relation is also shown in Fig. 4, where the stars involved are labelled. Although these stars fall over the entire luminosity range, it is seen that ρ Per, R Lyr, and RR UMi are well separated from the P 1 L relation, hinting at a separate sequence. This is to be expected as they are known to change pulsation mode (Little, Little-Marenin & Bauer 1987; Percy et al. 1996; Whitelock & Feast 2000), but the implied period ratios, P 2 /P 1, for R Lyr and RR UMi (8.2 and 17.3 respectively) are too high to be attributed to pulsational connection. On the other hand, as far as the dispersion about the mean P 1 L relation (solid line) is concerned, the other five stars with P 2 Figure 3. Variation of the slope of the linear P L relation as a function of wavelength for SR variables with P 20 d and ɛ π /π 0.10 (see Table 2). Triangles denote Mira variables at mean light in the LMC taken from Feast et al. (1989).

6 606 C. Yeşilyaprak and Z. Aslan (g Her, RX Lep, X Her, V1070 Cyg, and R Dor) obey the P 1 L relation. We note that four of the five stars fall to the right of the P 1 L line, their period ratios P 2 /P 1 being in the range 1.49 (g Her) to 1.93 (R Dor). It is known that R Dor with its second period behaves like a Mira and alternates between the two periods (Bedding & Zijlstra 1998; Bedding et al. 1998) (see Figs 2 and 4). Furthermore, g Her, RX Lep, V1070 Cyg, and R Dor all have visual light amplitudes significantly larger (about 2 mag) than the average amplitude of SR variables. If these stars with their second periods really form a sequence displaced from the P 1 L relation in Fig. 4 and pulsate in the same mode as Mira variables, then the second periods of ρ Per, R Lyr, and RR UMi are probably the galactic counterpart of Wood s long secondary period sequence (see Fig. 1, Wood 2000), the nature of variability of which is still in question. 4 CONCLUSIONS We have investigated the P L relationships of O-rich SR variables in several wavelength bands using Hipparcos parallaxes with an accuracy of better than 10 per cent. We have found that SR variables obey well-defined P L relations in the U, B, V, R, I C, J, H, K, L, M, N, [12], [25], [60] and [100] bands. Possible sources of dispersion about the mean relations are discussed. We have also found that the slope of the linear M λ logp relation is a smooth function of wavelength. 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