J/ApJ/919/85   Field RR Lyrae as Gal. probes. V. RVC templates   (Braga+, 2021)

On the use of field RR Lyrae as Galactic probes. V. Optical and radial velocity curve templates. Braga V.F., Crestani J., Fabrizio M., Bono G., Sneden C., Preston G.W., Storm J., Kamann S., Latour M., Lala H., Lemasle B., Prudil Z., Altavilla G., Chaboyer B., Dall'Ora M., Ferraro I., Gilligan C.K., Fiorentino G., Iannicola G., Inno L., Kwak S., Marengo M., Marinoni S., Marrese P.M., Martinez-Vazquez C.E., Monelli M., Mullen J.P., Matsunaga N., Neeley J., Stetson P.B., Valenti E., Zoccali M. <Astrophys. J., 919, 85 (2021)> =2021ApJ...919...85B 2021ApJ...919...85B
ADC_Keywords: Stars, variable; Spectroscopy; Radial velocities; Photometry, UBV Keywords: RR Lyrae variable stars ; Atomic spectroscopy ; Radial velocity ; Globular star clusters Abstract: We collected the largest spectroscopic catalog of RR Lyrae (RRLs) including ∼20000 high-, medium-, and low-resolution spectra for ∼10000 RRLs. We provide the analytical forms of radial velocity curve (RVC) templates. These were built using 36 RRLs (31 fundamental-split into three period bins-and five first-overtone pulsators) with well-sampled RVCs based on three groups of metallic lines (Fe, Mg, Na) and four Balmer lines (Hα, Hβ, Hγ, Hδ). We tackled the long-standing problem of the reference epoch to anchor light-curve and RVC templates. For the V-band, we found that the residuals of the templates anchored to the phase of the mean magnitude along the rising branch are ∼35% to ∼45% smaller than those anchored to the phase of maximum light. For the RVC, we used two independent reference epochs for metallic and Balmer lines and we verified that the residuals of the RVC templates anchored to the phase of mean RV are from 30% (metallic lines) up to 45% (Balmer lines) smaller than those anchored to the phase of minimum RV. We validated our RVC templates by using both the single-point and the three phase point approaches. We found that barycentric velocities based on our RVC templates are two to three times more accurate than those available in the literature. We applied the current RVC templates to Balmer lines RVs of RRLs in the globular NGC 3201 collected with MUSE at VLT. We found the cluster barycentric RV of Vγ=496.89±8.37(error) ±3.43 (standard deviation) km/s, which agrees well with literature estimates. Description: To provide new radial velocity curve (RVC) templates, we performed a large spectroscopic campaign aimed at providing RV measurements for both field and cluster RR Lyrae (RRLs). We reduced and analyzed a large sample of high-, medium-, and low-resolution (HR, MR, and LR) spectra. We have collected the largest spectroscopic data set --both proprietary and public-- for RRLs. Preliminary versions of this spectroscopic catalog have already been used in studies focused on chemical abundances (Fabrizio+ 2019ApJ...882..169F 2019ApJ...882..169F ; Crestani+ 2021, J/ApJ/908/20 and J/ApJ/914/10) and RV (Bono+ 2020ApJ...896L..15B 2020ApJ...896L..15B). In this investigation, we have added new spectroscopic data and will discuss in detail the spectra used for RV measurements. Our data set comprises a total of 23865 spectra for 10413 RRLs. The HR sample mainly includes spectra collected with the Las Campanas Observatory du Pont echelle spectrograph (du Pont, 6208 spectra), plus HR spectra collected from ESO telescopes (277 from UVES@VLT, 320 from HARPS@3.6m, and 55 from FEROS@2.2m MPG). We also have 100 HR spectra from SES@STELLA, 81 from HRS@SALT, 10 from HARPS-N@TNG, and 34 from We collected MR spectra from both X-Shooter@VLT (121 spectra) and the LAMOST MR survey (1271 spectra). Finally, our spectroscopic data set includes LR spectra from the LAMOST (9099 spectra) and from the SDSS-SEGUE (6289 spectra) surveys. See section 3. File Summary: -------------------------------------------------------------------------------- FileName Lrecl Records Explanations -------------------------------------------------------------------------------- ReadMe 80 . This file table1.dat 65 57 Photometric properties of the RRLs adopted to evaluate the optical light-curve template table2.dat 246 8 Coefficients and standard deviations of the PEGASUS fits to the V-band light curve template table7.dat 62 31665 Individual radial velocity measurements for the 36 calibrating RRLs table8.dat 117 35 Barycentric radial velocities and RV amplitudes based on Balmer lines table9.dat 117 36 Barycentric radial velocities and RV amplitudes based on metallic lines table10.dat 230 28 Coefficients and standard deviations of the PEGASUS fits to the CNRVCs table14.dat 79 7 Properties of the RRLs observed by MUSE in NGC 3201 table15.dat 33 281 Radial velocity measurements for the 7 RRLs in NGC 3201 table16.dat 39 10 Systemic velocities of the RRLs in NGC 3201 based on the RVC templates table17.dat 58 5 Coefficients of the Amp(RV)-Amp(V) relations table18.dat 18 2828 Phase-gridded radial velocity curve (RVC) templates -------------------------------------------------------------------------------- See also: III/176 : RR Lyrae Metallicities (Layden 1994) J/AJ/108/1016 : Kinematics of local RR lyrae stars. I. (Layden, 1994) J/AJ/110/2288 : Kinematics of local RR Lyrae stars. II. (Layden 1995) J/ApJ/678/851 : RR Lyrae survey in the Galactic Halo (Keller+, 2008) J/ApJ/696/870 : Catalina Real-time Transient Survey (CRTS) (Drake+, 2009) J/AJ/137/4377 : List of SEGUE plate pairs (Yanny+, 2009) J/ApJ/708/717 : Light curve templates of RR Lyrae stars (Sesar+, 2010) J/ApJS/197/29 : Chemical compositions of 11 RR Lyrae (For+, 2011) J/ApJ/731/4 : Galactic halo as seen by the CFHTLS (Sesar+, 2011) J/MNRAS/422/2116 : BHB and RR Lyrae towards Anticentre and NGP (Kinman+, 2012) J/AJ/144/114 : Radial velocities of 6 field RR Lyrae (Sesar+, 2012) J/ApJ/797/43 : Blue stragglers in ω Cen (Mucciarelli+, 2014) J/PASP/126/521 : UBVRIJHK photometry of RR Lyrae in M4 (Stetson+, 2014) J/A+A/576/A30 : NIR LC templates for classical Cepheids (Inno+, 2015) J/AJ/152/170 : RRLs in globulars. IV. UBVRI in Omega Cen (Braga+, 2016) J/MNRAS/469/3688 : CSS Periodic Variable Star Catalogue (Drake+, 2017) J/AJ/153/204 : RR Lyrae stars from the PS1 3π survey (Sesar+, 2017) J/ApJ/848/68 : Abund. & RVs of stable and Blazhko RRc stars (Sneden+, 2017) J/A+A/619/A51 : Type II Cepheids in the Galactic bulge (Braga+, 2018) J/MNRAS/478/4513 : GALAH Survey DR2 (Buder+, 2018) J/ApJ/864/57 : Abund. of field & GC RR Lyrae. I. NGC3201 (Magurno+, 2018) J/A+A/625/A1 : RR Lyrae variables NIR light-curve templates (Braga+, 2019) J/A+A/622/A60 : Gaia DR2 misclassified RR Lyrae list (Clementini+, 2019) J/A+A/632/A3 : MUSE binaries in NGC 3201 (Giesers+, 2019) J/A+A/623/A117 : Gal. Cepheids & RR Lyrae multiplicity. II (Kervella+, 2019) J/ApJ/876/85 : HST observations for LMC Cepheids (Riess+, 2019) J/AJ/158/16 : RR Lyrae stars from the DES (Stringer+, 2019) J/MNRAS/484/2832 : Proper motions of MW globular clusters (Vasiliev, 2019) J/A+A/644/A95 : omega Cen RR Lyrae and Type II Cepheids (Braga+, 2020) J/ApJ/908/20 : On use of field RRL as Gal. probes. II. (Crestani+, 2021) J/ApJ/912/144 : Metallicity of Gal. RRL from opt. & IR LCs (Mullen+, 2021) Byte-by-byte Description of file: table1.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 5 A5 --- Tpl Optical (V-band) light curve template bin 7- 20 A14 --- Name Star name 22- 30 F9.7 d Per [0.28/0.85] Pulsation period 32- 37 F6.3 mag Vmag [9.9/16.1] Mean V-band magnitude 39- 43 F5.3 mag AmpV [0.4/1.3] Mean V-band amplitude 45- 54 F10.4 d Tmean [43689.8/55715.9] Mean optical epoch; HJD-2400000 56- 65 F10.4 d Tmax [30950.5/55715.9] Maximum optical epoch; HJD-2400000 -------------------------------------------------------------------------------- Byte-by-byte Description of file: table2.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 5 A5 --- Tpl Optical (V-band) light curve template bin 7- 11 A5 --- Epoch Reference Epoch, Tmean or Tmax 13- 17 I5 --- N [8387/26029] Number of phase points 19- 25 F7.4 --- ZP [-4.8/0.5] Zeropoint 27- 33 F7.4 --- Amp1 [-0.7/1.6] 1st Gaussian amplitude 35- 40 F6.4 --- phi1 [0.5/8.1] 1st Gaussian center 42- 48 F7.4 --- sig1 [-0.4/2.3] 1st Gaussian width 50- 56 F7.4 --- Amp2 [-1.4/0.2] 2nd Gaussian amplitude 58- 64 F7.4 --- phi2 [-0.05/0.9] 2nd Gaussian center 66- 72 F7.4 --- sig2 [-0.2/2.5] 2nd Gaussian width 74- 80 F7.4 --- Amp3 [-3.1/3.6] 3rd Gaussian amplitude 82- 88 F7.4 --- phi3 [-0.02/1] 3rd Gaussian center 90- 95 F6.4 --- sig3 [0.06/0.5] 3rd Gaussian width 97-103 F7.4 --- Amp4 [-3.93/1.9] 4th Gaussian amplitude 105-110 F6.4 --- phi4 [0.5/1.1] 4th Gaussian center 112-117 F6.4 --- sig4 [0.3/1.8] 4th Gaussian width 119-125 F7.4 --- Amp5 [-0.3/5.5] 5th Gaussian amplitude 127-133 F7.4 --- phi5 [-0.4/1.4] 5th Gaussian center 135-141 F7.4 --- sig5 [-0.2/3.1] 5th Gaussian width 143-152 F10.4 --- Amp6 [-0.5/2.9]?=-9999 6th Gaussian amplitude 154-163 F10.4 --- phi6 [-1.1/0.03]?=-9999 6th Gaussian center 165-174 F10.4 --- sig6 [-0.2/1.6]?=-9999 6th Gaussian width 176-185 F10.4 --- Amp7 [-0.5/1.4]?=-9999 7th Gaussian amplitude 187-196 F10.4 --- phi7 [-0.2/1.1]?=-9999 7th Gaussian center 198-207 F10.4 --- sig7 [-1.4/0.3]?=-9999 7th Gaussian width 209-218 F10.4 --- Amp8 [-0.3/-0.2]?=-9999 8th Gaussian amplitude 220-229 F10.4 --- phi8 [0.14/0.15]?=-9999 8th Gaussian center 231-240 F10.4 --- sig8 [0.3674]?=-9999 8th Gaussian width 242-246 F5.3 --- sigma [0.028/0.07] Total standard deviation -------------------------------------------------------------------------------- Byte-by-byte Description of file: table7.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 19 A19 --- Name Variable star name 21- 22 A2 --- Sp Spectroscopic diagnostic (1) 24- 35 F12.4 d HJD Heliocentric Julian date 37- 44 F8.3 km/s RVel [-903/2012] Radial velocity (2) 46- 52 F7.3 km/s e_RVel [0.006/126] Uncertainty in RVel (3) 54- 62 A9 --- Inst Spectrograph used (4) -------------------------------------------------------------------------------- Note (1): Fe, Mg and Na indicate the average of [Fe1, Fe2, Fe3, Sr], [Mg2, Mg3] and [Na1, Na2] lines, respectively (see Section 5.1). In contrast, Balmer lines radial velocity measurements are single. Note (2): Velocity plus heliocentric velocity and diurnal velocity correction. Note (3): Uncertainty on the radial velocity measurements. For the Balmer lines, it is the uncertainty from spectroscopic data reduction. For Fe, Mg and Na, it is the standard deviation of the RVs from different lines. Note (4): Instrument as follows: DuPont = Las Campanas Observatory du Pont echelle spectrograph (29265 occurrences) BW = literature observations for RRLs with Baade-Wesselink (BW) analysis (Braga+ 2019, J/A+A/625/A1 and references therein; 1277 occurrences) HARPS = HARPS on ESO 3.6m telescope (846 occurrences) XSHOOTER = X-Shooter on VLT (102 occurrences) SALT = HRS on the Southern African Large Telescope (87 occurrences) UVES = UVES on ESO VLT (33 occurrences) UVES.p95 = (12 occurrences) SubaruHDS = The High Dispersion Spectrograph (HDS) on Subaru (25 occurrences) FEROS = FEROS on ESO 2.2m MPG (18 occurrences) -------------------------------------------------------------------------------- Byte-by-byte Description of file: table8.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 19 A19 --- Name Variable star name (1) 21- 27 F7.2 km/s BRVHa [-377/303] Barycentric Radial Velocity, Hα 29- 32 F4.2 km/s e_BRVHa [0.8/2] Uncertainty in BRV-Ha 34- 39 F6.2 km/s AmpRVHa [30/115] Radial velocity amplitude, Hα 41- 45 F5.2 km/s e_AmpRVHa [2/11] Uncertainty in AmpRV-Ha 47- 53 F7.2 km/s BRVHb [-377/304] Barycentric Radial Velocity, HΒ 55- 58 F4.2 km/s e_BRVHb [0.7/2] Uncertainty in BRV-Hb 60- 64 F5.2 km/s AmpRVHb [25/95] Radial velocity amplitude, HΒ 66- 69 F4.2 km/s e_AmpRVHb [1.9/10] Uncertainty in AmpRV-Hb 71- 77 F7.2 km/s BRVHg [-380/304] Barycentric Radial Velocity, Hγ 79- 82 F4.2 km/s e_BRVHg [0.9/2.4] Uncertainty in BRV-Hg 84- 88 F5.2 km/s AmpRVHg [25/89] Radial velocity amplitude, Hγ 90- 93 F4.2 km/s e_AmpRVHg [1.9/8.2] Uncertainty in AmpRV-Hg 95-101 F7.2 km/s BRVHd [-374/304] Barycentric Radial Velocity, Hδ 103-106 F4.2 km/s e_BRVHd [0.8/2.2] Uncertainty in BRV-Hd 108-112 F5.2 km/s AmpRVHd [21/76] Radial velocity amplitude, Hδ 114-117 F4.2 km/s e_AmpRVHd [1.8/7] Uncertainty in AmpRV-Hd -------------------------------------------------------------------------------- Note (1): Cl* NGC 6341 SAW V1 does not appear because the Balmer RV measurements for this star are not accurate. -------------------------------------------------------------------------------- Byte-by-byte Description of file: table9.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 19 A19 --- Name Variable star name 21 A1 --- f_Name Flag on Name (1) 23- 29 F7.2 km/s BRVFe [-376/306] Barycentric Radial Velocity, Fe 31- 34 F4.2 km/s e_BRVFe [0.1/1.2] Uncertainty in BRV-Fe 36- 40 F5.2 km/s AmpRVFe [22.7/69.3] Radial velocity amplitude, Fe 42- 45 F4.2 km/s e_AmpRVFe [0.7/5] Uncertainty in AmpRV-Fe 47- 54 F8.2 km/s BRVMg [-375/305]?=-9999 Barycentric Radial Velocity, Mg 56- 63 F8.2 km/s e_BRVMg [0.16/1.2]?=-9999 Uncertainty in BRV-Mg 65- 72 F8.2 km/s AmpRVMg [22/72]?=-9999 Radial velocity amplitude, Mg 74- 81 F8.2 km/s e_AmpRVMg [1.2/4.3]?=-9999 Uncertainty in AmpRV-Mg 83- 90 F8.2 km/s BRVNa [-376/306]?=-9999 Barycentric Radial Velocity, Na 92- 99 F8.2 km/s e_BRVNa [0.3/1.7]?=-9999 Uncertainty in BRV-Na 101-108 F8.2 km/s AmpRVNa [23/96]?=-9999 Radial velocity amplitude, Na 110-117 F8.2 km/s e_AmpRVNa [1.3/9.1]?=-9999 Uncertainty in AmpRV-Na -------------------------------------------------------------------------------- Note (1): Flag as follows: a = DR Cap is also ASAS J203145-2158.7 b = V0384 Tel is also ASAS J181215-5206.9 c = Cl* NGC 6341 SAW V1 does not appear in Table 8 because the Balmer RV measurements for this star are not accurate. -------------------------------------------------------------------------------- Byte-by-byte Description of file: table10.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 2 A2 --- Line Radial velocity curve (RVC) template diagnostic 4- 8 A5 --- Tpl Optical (V-band) light curve template bin 10- 13 I4 --- N [150/2325] Number of phase points 15- 21 F7.4 --- ZP [-2.6/1.6] Zeropoint 23- 29 F7.4 --- Amp1 [-1.4/2.1] 1st Gaussian amplitude 31- 36 F6.4 --- phi1 [0.95/3.7] 1st Gaussian center 38- 44 F7.4 --- sig1 [-1.05/1.11] 1st Gaussian width 46- 52 F7.4 --- Amp2 [-7.96/-0.02] 2nd Gaussian amplitude 54- 59 F6.4 --- phi2 [0.007/0.4] 2nd Gaussian center 61- 66 F6.4 --- sig2 [0.1/1.8] 2nd Gaussian width 68- 74 F7.4 --- Amp3 [-3.2/-0.08] 3rd Gaussian amplitude 76- 82 F7.4 --- phi3 [-0.009/0.2] 3rd Gaussian center 84- 89 F6.4 --- sig3 [0.04/0.9] 3rd Gaussian width 91- 96 F6.4 --- Amp4 [0.15/8.3] 4th Gaussian amplitude 98-103 F6.4 --- phi4 [0.58/1.01] 4th Gaussian center 105-110 F6.4 --- sig4 [0.23/2.3] 4th Gaussian width 112-118 F7.4 --- Amp5 [-9.8/3] 5th Gaussian amplitude 120-126 F7.4 --- phi5 [-0.09/0.04] 5th Gaussian center 128-134 F7.4 --- sig5 [-0.23/0.4] 5th Gaussian width 136-142 F7.4 --- Amp6 [0.09/10.2] 6th Gaussian amplitude 144-150 F7.4 --- phi6 [-0.22/0.5] 6th Gaussian center 152-157 F6.4 --- sig6 [0.069/1.04] 6th Gaussian width 159-168 F10.4 --- Amp7 [-2.95/-0.04]?=-9999. 7th Gaussian amplitude 170-179 F10.4 --- phi7 [-0.23/1.06]?=-9999. 7th Gaussian center 181-190 F10.4 --- sig7 [0.13/1.5]?=-9999. 7th Gaussian width 192-201 F10.4 --- Amp8 [-1.94/-0.017]?=-9999. 8th Gaussian amplitude 203-212 F10.4 --- phi8 [-0.15/1.52]?=-9999. 8th Gaussian center 214-223 F10.4 --- sig8 [0.17/0.61]?=-9999. 8th Gaussian width 225-230 F6.4 --- sigma [0.02/0.09] Total standard deviation -------------------------------------------------------------------------------- Byte-by-byte Description of file: table14.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 4 A4 --- Name Variable star name (<Cl* NGC 3201 SAW VNN> in Simbad) 6- 9 A4 --- Type Variable star type (always "RRab") 11- 18 F8.6 d Per [0.5/0.61] Period 20- 25 F6.3 mag Vmag [14.67/14.8] V-band mean magnitude 27- 35 F9.3 mag AmpV [0.74/1.05]?=-9999 Amplitude V-band 37- 47 F11.5 d tmean ?=-9999 Reference epoch, mean, HJD-2,400,000 49- 59 F11.5 d tmax ?=-9999 Reference epoch, max, HJD-2,400,000 61- 65 F5.1 km/s BRVHa [483/501] Barycentric Radial Velocity, Hα 67- 69 F3.1 km/s e_BRVHa [3/3.8] Uncertainty in BRV-Ha 71- 75 F5.1 km/s BRVHb [488/501.6] Barycentric Radial velocity, HΒ 77- 79 F3.1 km/s e_BRVHb [2.8/3.4] Uncertainty in BRV-Hb -------------------------------------------------------------------------------- Byte-by-byte Description of file: table15.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 4 A4 --- Name Variable Star name 6- 7 A2 --- Sp Spectroscopic diagnostic 9- 20 F12.4 d HJD Heliocentric Julian date 22- 27 F6.2 km/s RVel [439/567] Radial velocity (1) 29- 33 F5.2 km/s e_RVel [0.9/23] Uncertainty in RVel (2) -------------------------------------------------------------------------------- Note (1): Velocity plus heliocentric velocity and diurnal velocity correction. Note (2): Uncertainty on the radial velocity measurements. For the Balmer lines, it is the uncertainty from spectroscopic data reduction. For Fe, Mg and Na, it is the standard deviation of the RVs from different lines. -------------------------------------------------------------------------------- Byte-by-byte Description of file: table16.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 3 A3 --- Ref Templates (S12=Sesar+ 2012, J/AJ/144/114) 5- 7 A3 --- Name Variable Star name 9- 13 F5.1 km/s BRVHa [486/501] Systemic BRV, Hα template 15- 18 F4.1 km/s e_BRVHa [5/19] Uncertainty in BRV-Ha 20- 23 F4.1 km/s dBRVHa [-5/5.1] Median systematic BRV offset, Hα 25- 29 F5.1 km/s BRVHb [488/500] Systemic BRV, Hβ template 31- 34 F4.1 km/s e_BRVHb [5/23] Uncertainty in BRV-Hb 36- 39 F4.1 km/s dBRVHb [-3.2/5] Median systematic BRV offset, Hβ -------------------------------------------------------------------------------- Byte-by-byte Description of file: table17.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 2 A2 --- Line Line 4- 8 F5.2 km/s aRRc [-9.18/3.85] Coefficient "a", RRc variables 10- 13 F4.2 km/s e_aRRc [4.92/9.36] Uncertainty in aRRc 15- 20 F6.2 km/s/mag bRRc [45/107] Coefficient "b", RRc variables 22- 26 F5.2 km/s/mag e_bRRc [12/25] Uncertainty in bRRc 28- 31 F4.2 --- sigRRc [3.5/7] Standard deviation of the AmpRV and AmpV relation for RRc 33- 37 F5.2 km/s aRRab [38/78] Coefficient "a", RRab variables 39- 42 F4.2 km/s e_aRRab [2.9/7] Uncertainty in aRRab 44- 48 F5.2 km/s/mag bRRab [14/23] Coefficient "b", RRab variables 50- 53 F4.2 km/s/mag e_bRRab [3/7] Uncertainty in bRRab 55- 58 F4.2 --- sigRRab [4/9] Standard deviation of the AmpRV and AmpV relation for RRab -------------------------------------------------------------------------------- Byte-by-byte Description of file: table18.dat -------------------------------------------------------------------------------- Bytes Format Units Label Explanations -------------------------------------------------------------------------------- 1- 2 A2 --- Sp Spectroscopic diagnostic 4- 4 I1 --- Bin [0/3] Template bin 6- 10 F5.3 --- Phase [0/1] Phase 12- 18 F7.4 --- Template [-0.63/0.51] Template value (1) -------------------------------------------------------------------------------- Note (1): Calculated at the given phase by using Equation 1: P(φ)=A0iAiexp(-sin([π(φ-φi)]/σi)2) where A0 and Ai are the zero points and the amplitudes of the Gaussians, while φi and σi are the centers and the σ of the Gaussians. and the coefficients provided in Table 10. -------------------------------------------------------------------------------- History: From electronic version of the journal
(End) Prepared by [AAS], Emmanuelle Perret [CDS] 30-Jan-2023
The document above follows the rules of the Standard Description for Astronomical Catalogues; from this documentation it is possible to generate f77 program to load files into arrays or line by line