CDROM/AJ/V108/P0222 Pop. II Variable Stars (Nemec+ 1994) ================================================================================ Period-Luminosity-Metallicity Relations, Pulsation Modes, Absolute Magnitudes, and Distances for Population II Variable Stars James M. Nemec, Amanda F. Linnell Nemec, Thomas E. Lutz <1994, AJ, 108, 222> =1994AJ....108..222N ================================================================================ Abstract: Period-luminosity-metallicity (P-L-[Fe/H]) relations are presented for RR Lyrae stars, Pop. II Cepheids, anomalous Cepheids and SX Phe stars pulsating in the fundamental (F) and first-overtone (H) modes. The relations were derived by fitting regression lines to the observed pulsation periods and mean B, V, and K magnitudes of over 1200 stars in ~40 stellar systems. Analysis of covariance methods, which allow the simultaneous computation of more than one P-L-[Fe/H] relation, were used to estimate the slopes and intercepts. Of the 24 possible P-L-[Fe/H] relations for the four kind of stars, two pulsation modes, and three passbands considered here, 18 relations have been derived -- the others could not be derived because of a lack of photometry in one or more of the three passbands. The slopes for the F and H pulsators were tested for departures from equality for all types of stars and passbands; the results suggest that the observations are consistent with the assumption that, for each kind of star (except possibly the Pop. II Cepheids), the P-L-[Fe/H] relations for the F and H pulsation modes are parallel but vertically offset, with a family of lines corresponding to a range of metallicities. Pulsation modes and absolute magnitudes are presented for the non-RR Lyrae variable stars considered in the analysis, and distances are estimated for the program clusters. It is well established from previous studies that the P-L relations for RR Lyrae stars are approximately flat for the B passband, and have a slope Delta M(K)/Delta log P ~ -2.4 for the K passband. We recover these slopes, and find that the P-L-[Fe/H] relation in V has an intermediate slope, Delta M(V)/Delta log P = -0.52 +/- 0.11. A similar dependence of slope on passband is seen for classical Cepheids [see Madore & Freedman, PASP, 103, 933 (1991)]. The available B,V photometry for ~40 of the known globular cluster Cepheids are found to be consistent with Arp's [AJ, 60, 1 (1955)] assumption that Pop. II Cepheids pulsate in the F and H modes (and not in the F mode only, as has often been assumed). The estimated slopes of the corresponding P-L-[Fe/H] relations are Delta M(B)/Delta log P = -1.69 +/- 0.05 and Delta M(V)/Delta log P = -1.93 +/- 0.05, with a separation between the F and H modes of 0.59 mag in B, and 0.45 mag in V. As in the case of the RR Lyrae stars the redder passband has the steeper slope. We find that 15 of the 21 short-period BL Her Cepheids (P <= 8 days) appear to be H pulsators, while 15 of the 19 W Cir Cepheids (12 <= P <= 30 days) appear to be F pulsators. The period-amplitude (P-A(B)) diagram suggests that at a given period the first-overtone pulsators have larger amplitudes than the fundamental mode pulsators. For the Anomalous Cepheids the estimated P-L-[Fe/H] relations have slopes Delta M(B)/Delta log P = -3.20 +/- 0.18, and Delta M(V)/Delta log P = -3.13 +/- 0.28. The offsets between the F and H mode relations are 0.68 and 0.66 mag in B and V, respectively. The estimated P-L-[Fe/H] relations in B and V for the SX Phe stars have slopes Delta M(B)/Delta log P = -2.66 +/- 0.52 and Delta M(V)/Delta log P = -2.56 +/- 0.54, and the F and H relations are separated by 0.34 and 0.29 mag in B and V, respectively. These relations are consistent with the observed period ratio for the double-mode star SX Phe. In a period-amplitude diagram the longest period SX Phe stars have the largest amplitudes, with no dependence on metallicity. The (B-V)0 color range of the SX Phe stars is from 0.12 to 0.29. File Summary: -------------------------------------------------------------------------------- File Name Lrecl Records Explanations -------------------------------------------------------------------------------- table4.dat 137 50 Pop. II Cepheids in galactic globular clusters table4.tex 106 315 TeX version of table4.dat table4.txt 79 167 Plain text version of table4.tex table5.dat 157 24 Anomalous Cepheids: puls. modes and abs. mags table5.tex 89 235 TeX version of table5.dat table5.txt 80 105 Plain text version of table5.tex table6.dat 154 21 SX Phe Stars: pulsation modes and abs. mags table6.tex 109 239 TeX version of table6.dat table6.txt 78 103 Plain text version of table6.tex -------------------------------------------------------------------------------- Byte-by-byte Description of file: table4.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1-11 A11 --- Name *Star name 12-17 F6.2 --- Fe_H []? Assumed metal abundance 18-22 F5.2 --- E_B-V []? Assumed reddening 23-32 F10.6 day P []? Pulsation period 33-40 F8.4 --- logP []? Log base 10 of P 41 1X --- --- Blank 42-45 A4 --- Type *Type of Cepheid and pulsation mode 46-50 F5.2 --- A_B Blue amplitude of the Cepheid 51-56 F6.2 mag B Assumed mean B magnitude 57-62 F6.2 mag B0 Dereddened B magnitude 63-68 F6.2 mag V []? Assumed mean V magnitude 69-74 F6.2 mag V0 []? Dereddened V magnitude 75-79 F5.2 mag B-V []? B-V color 80-84 F5.2 mag B-V_0 []? Dereddened B-V color 85-90 F6.2 mag o_B0_M15 *Observed M15-normalized apparent B mag 91-96 F6.2 mag p_B0_M15 *Predicted M15-normalized apparent B mag 97-102 F6.2 mag o_V0_M15 *[]? Observed M15-normalized apparent V mag 103-108 F6.2 mag p_V0_M15 *[]? Predicted M15-normalized apparent V mag 109-114 F6.2 mag o_M_B Observed absolute B magnitude 115-120 F6.2 mag p_M_B Predicted absolute B magnitude 121-126 F6.2 mag o_M_V []? Observed absolute V magnitude 127-132 F6.2 mag p_M_V []? Predicted absolute V magnitude 133 1X --- --- Blank 134-137 A4 --- Ref *Reference for source of data -------------------------------------------------------------------------------- Notes for file: table4.dat -------------------------------------------------------------------------------- Type: Cepheid Types: BL=BL Her WV=W Vir RV=RV Tau Pulsation Modes: F = fundamental mode H = first-overtone mode o_B0_M15, p_B0_M15, o_V0_M15, p_V0_M15: Observed and predicted apparent B and V magnitudes after correcting and normalizing the metallicity and distance to that of M15 (i.e., the magnitudes are the values that the stars would have if they were all at the distance of M15 and had the metallicity [Fe/H] = -2.15). See equation 5 in the printed paper. Ref: C88 = Clement, Sawyer Hogg & Yee 1988, AJ, 96, 1642 CS78 = Clement & Sawyer Hogg 1978, AJ, 83, 167 D69 = Demers 1969, AJ, 74, 926 DH74 = Demers & Harris 1974, AJ, 79, 627 DC67 = Dickens & Carey 1967, Roy. Obs. Bull. no. 129, p. E335 E72 = Eggen 1972, ApJ, 172, 639 G93 = Gonzalez 1993, Ph.D. thesis, U. of Washington, Seattle, WA H85 = Harris 1985, in Cepheids: Theory and Observations. IAU Colloquim No. 82, edited by B. F. Madore (Cambridge University Press, Cambridge), p. 232 K68 = Kwee 1968, Bulletin Astron. Inst. Netherlands, 19, 374 L74 = Lee 1974, Observatory, 94, 74 PM77 = Pike & Meston 1977, MNRAS, 180, 613 PR77 = Pinto & Rosino 1977, A&AS, 28, 427 W86 = Wehlau et al. 1986, AJ, 91, 1340 WS84 = Wehlau & Sawyer Hogg 1984, AJ, 89, 1005 WS85 = Wehlau & Sawyer Hogg 1985, AJ, 90, 2514 W92 = Wehlau 1992, private communication -------------------------------------------------------------------------------- Byte-by-byte Description of file: table5.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1-14 A14 --- Name Star name 15-20 F6.2 --- Fe_H Assumed metal abundance 21-25 F5.2 --- E_B-V Assumed reddening 26-34 F9.5 h Ph Pulsation period (hours) 35-43 F9.6 day Pd Pulsation period (day) 44-51 F8.4 --- logP Log base 10 of P (day) 52 1X --- --- Blank 53 A1 --- Mode *Pulsation mode 54-59 F6.2 mag B Assumed mean B magnitude 60-65 F6.2 mag B0 Dereddened B magnitude 66-70 F5.2 --- A_B []? B pulsation amplitude 71-76 F6.2 mag V []? Assumed mean V magnitude 77-82 F6.2 mag V0 []? Dereddened V magnitude 83-87 F5.2 --- A_V []? V pulsation amplitude 88-92 F5.2 mag B-V []? B-V color 93-97 F5.2 mag B-V_0 []? Dereddened B-V color 98-103 F6.2 mag o_B0_M15 Observed M15-normalized apparent B mag 104-109 F6.2 mag p_B0_M15 Predicted M15-normalized apparent B mag 110-115 F6.2 mag d_B0_M15 Difference between o_B0(M15)-p_B0(M15) 116-121 F6.2 mag o_V0_M15 []? Observed M15-normalized apparent V mag 122-127 F6.2 mag p_V0_M15 []? Predicted M15-normalized apparent V mag 128-133 F6.2 mag d_B0_M15 []? Difference between o_V0(M15)-p_V0(M15) 134-139 F6.2 mag o_M_B Observed absolute B magnitude 140-145 F6.2 mag p_M_B Predicted absolute B magnitude 146-151 F6.2 mag o_M_V []? Observed absolute V magnitude 152-157 F6.2 mag p_M_V []? Predicted absolute V magnitude -------------------------------------------------------------------------------- Notes for file: table5.dat -------------------------------------------------------------------------------- Mode: Pulsation Modes: F = fundamental mode H = first-overtone mode -------------------------------------------------------------------------------- Byte-by-byte Description of file: table6.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1-14 A14 --- Name Star name 15-20 F6.2 --- Fe_H Assumed metal abundance 21 1X --- --- Blank 22-24 A3 --- r_Fe_H *Source of metal abundance 25-29 F5.2 --- E_B-V Assumed reddening 30 1X --- --- Blank 31-33 A3 --- r_E_B-V *Source of reddening 34-40 F7.2 min Pm Pulsation period (minutes) 41-47 F7.4 day Pd Pulsation period (day) 48-54 F7.4 --- logP Log base 10 of P (day) 55 1X --- --- Blank 56 A1 --- Mode *Pulsation mode 57-62 F6.2 mag B Assumed mean B magnitude 63-68 F6.2 mag B0 Dereddened B magnitude 69-74 F6.2 mag V Assumed mean V magnitude 75-80 F6.2 mag V0 Dereddened V magnitude 81-85 F5.2 --- A_V V pulsation amplitude 86-90 F5.2 mag B-V B-V color 91-95 F5.2 mag B-V_0 Dereddened B-V color 96-101 F6.2 mag o_B0_M15 Observed M15-normalized apparent B mag 102-107 F6.2 mag p_B0_M15 []? Predicted M15-normalized apparent B mag 108-113 F6.2 mag d_B0_M15 []? Difference between o_B0(M15)-p_B0(M15) 114-119 F6.2 mag o_V0_M15 Observed M15-normalized apparent V mag 120-125 F6.2 mag p_V0_M15 []? Predicted M15-normalized apparent V mag 126-131 F6.2 mag d_B0_M15 []? Difference between o_V0(M15)-p_V0(M15) 132-136 F5.2 mag o_M_B Observed absolute B magnitude 137-141 F5.2 mag p_M_B []? Predicted absolute B magnitude 142-146 F5.2 mag o_M_V Observed absolute V magnitude 147-151 F5.2 mag p_M_V []? Predicted absolute V magnitude -------------------------------------------------------------------------------- Notes for file: table6.dat -------------------------------------------------------------------------------- r_Fe_H: ADZ = Armandroff, Demarque & Zinn 1993, BM = Burki & Meylan 1986, A&A, 159, 261 EI = Eggen & Iben 1989, AJ, 97, 431 GMC = Geisler, Minniti & Claria 1992, AJ, 104, 627 KK = Kaluzny & Krzeminski 1993, MNRAS, 264, 785 MB = McNamara & Budge 1985, PASP, 97, 322 MF = McNamara & Feltz 1980, PASP, 90, 275 ZW = Zinn & West 1984, ApJS, 55, 45 r_E_B-V: FRN = Fahlman, Richer & Nemec 1991, ApJ, 380, 124 RF = Richer & Fahlman 1988, ApJ, 325, 218 Z85 = Zinn 1985a, ApJ, 293, 424 Mode: Pulsation Modes: F = fundamental mode H = first-overtone mode -------------------------------------------------------------------------------- ================================================================================ (End) Lee Brotzman [ADS] 10-Oct-1994