J/A+A/709/A151 Reconstruction of Cepheid radial velocity curves (Hocde+. 2026)
Reconstruction of Cepheid radial velocity curves from the shape of the V-band
light curves.
Hocde V., Moskalik P., Nardetto N., Kervella P., Pilecki B., Smolec R.,
PietrzyNski G., Gieren W., Hajdu G., Gallenne A., Bailleul M.C., Bras G.,
Wielgorski P., Breuval L., Merand A., Rathour R.S., Espinoza-Arancibia F.,
Kiviaho W., Apostolova B., Sivkova K.
<Astron. Astrophys. 709, A151 (2026)>
=2026A&A...709A.151H 2026A&A...709A.151H (SIMBAD/NED BibCode)
ADC_Keywords: Stars, variable ; Photometry ; Optical ; Radial velocities
Keywords: methods: data analysis - methods: statistical -
techniques : photometric - techniques: radial velocities -
stars: variables: Cepheids
Abstract:
Radial velocity (RV) curves of Cepheids are essential for studying
their pulsation properties and also for measuring their distance via
the parallax-of-pulsation method. Although precise RV curves are
available for hundreds of Cepheids, it is still not possible to
predict the complete RV curve from other observables such as their
pulsation period or metallicity.
This paper aims to develop the first method of reconstructing the
shape of the RV curves of short-period fundamental-mode Cepheids,
based exclusively on their pulsation period and the morphology of
their V-band light curves (LCs).
We compiled a dataset of high-quality spectroscopic and photometric
measurements from the literature for 81 short-period fundamental-mode
Galactic Cepheids up to a pulsation period of 8 days, enabling the
precise determination of the Fourier parameters and their
uncertainties. By performing a detailed comparative analysis of their
shapes, we investigated correlations between LC and RV Fourier
parameters and used these relations to reconstruct the RV curves. We
further assessed the accuracy of these reconstructions by examining
potential metallicity effects with an additional dataset of 24
metal-poor Cepheids.
For pulsation periods between 3.5 and 7.0 days, we found tight
correlations between different combinations of LC and RV Fourier
parameters up to order 7. In particular, we discovered that the ratios
R21(RV)/R21(LC) and R31(RV)/R31(LC) are tightly correlated
with the pulsation period. These relationships enable the
reconstruction of RV curves of Cepheids with their LC. The
reconstructed curve has an uncertainty of about 0.60km/s relative to
the Fourier fit of true spectroscopic RV measurements. For individual
Cepheids, the reconstructed RV curves integrated along the pulsation
cycle (i.e. the linear radius variations) are accurate to less than 1%
and precise to within 4.16% in comparison to the integrated true
spectroscopic RV curves. Last, our sample of metal-poor Cepheids shows
a good agreement with the empirical relations calibrated on Galactic
pulsators, indicating that the method of reconstruction is weakly
dependent on metallicity.
For the first time, we present a method of reconstructing the shape of
the RV curves of Cepheids using solely the V-band LC and the pulsation
period. This approach provides a valuable tool for the reconstruction
of RV curves for extragalactic Cepheids through photometric data
alone. It opens the road to a purely photometric parallax-of-pulsation
method in the context of photometric surveys, such as the Vera Rubin
Telescope. Further calibration in different photometric bands and for
a larger metallicity baseline will be useful to improve the method.
Description:
We present a method to reconstruct the shape of the RV curves of
Cepheids using solely the V-band LC and the pulsation period. This
approach provides a valuable tool for the reconstruction of RV curves
for extragalactic Cepheids through photometric data alone. We compiled
a dataset of high-quality spectroscopic and photometric measurements
from the literature for 81 fundamental-mode Galactic Cepheids up to a
pulsation period of 8 days, enabling precise determination of the
Fourier parameters and their uncertainties. By performing a detailed
comparative analysis of their shapes, we investigated correlations
between LC and RV Fourier parameters and used these relations to
reconstruct the RV curves.ta For pulsation periods between 3.5 and 7.0
days (59 stars), we found tight correlations between different
combinations of LC and RV Fourier parameters up to order 7. In
particular, we discovered that the ratios R21(RV) to R21(LC) and
R31(RV) to R31(LC) are tightly correlated with the pulsation period.
These relationships enable the reconstruction of RV curves of Cepheids
with their LC. The reconstructed curve has an uncertainty of about
0.60 km.s-1 when compared to the Fourier fit of true spectroscopic RV
measurements. For individual Cepheids, the reconstructed RV curves
integrated along the pulsation cycle (i.e. the linear radius
variations) are accurate to less than 1% and precise to within 4.16%
when compared to the integrated true spectroscopic RV curves. Last,
our sample of metal-poor Cepheids shows a good agreement with the
empirical relations calibrated on Galactic pulsators, indicating that
the method of reconstruction is weakly dependent on metallicity.
We present the Fourier parameters of Cepheids and their uncertainties
for the calibrating sample of light-curves and radial velocity curves
(59 stars with P < 7.0day) and the metal-poor sample (24 stars) up to
order 7.
File Summary:
--------------------------------------------------------------------------------
FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
table_rv.dat 195 83 Fourier parameters of RV curves for the
calibrating sample (table A4)
table_lc.dat 200 83 Fourier parameters of V-band LC curves for the
calibrating sample (table A3)
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table_rv.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 17 A17 --- Star Cepheid identifier
19- 22 A4 --- Order Order of the Fourier fit
24- 26 I3 --- Ndat [20/355] Number of data points (1)
28- 35 F8.6 d Period Pulsation period
37- 40 F4.2 km/s sigma Fit residual scatter
42- 46 F5.2 km/s A1 Fourier amplitude of first harmonic
48- 51 F4.2 km/s e_A1 Error of A1
53- 57 F5.3 --- R21 Fourier amplitude ratio R21 = A2/A1
59- 63 F5.3 --- e_R21 Error of R21
65- 69 F5.3 --- phi21 Fourier phase phi21 = phi2 - 2*phi1
71- 75 F5.3 --- e_phi21 Error of phi21
77- 81 F5.3 --- R31 Fourier amplitude ratio R31 = A3/A1
83- 87 F5.3 --- e_R31 Error of R31
89- 93 F5.3 --- phi31 Fourier phase phi31 = phi3 - 3*phi1
95- 99 F5.3 --- e_phi31 Error of phi31
101-105 F5.3 --- R41 ?=- Fourier amplitude ratio R41 = A4/A1
107-111 F5.3 --- e_R41 ?=- Error of R41
113-117 F5.3 --- phi41 ?=- Fourier phase phi41 = phi4 - 4*phi1
119-123 F5.3 --- e_phi41 ?=- Error of phi41
125-129 F5.3 --- R51 ?=- Fourier amplitude ratio R51 = A5/A1
131-135 F5.3 --- e_R51 ?=- Error of R51
137-141 F5.3 --- phi51 ?=- Fourier phase phi51 = phi5 - 5*phi1
143-147 F5.3 --- e_phi51 ?=- Error of phi51
149-153 F5.3 --- R61 ?=- Fourier amplitude ratio R61 = A6/A1
155-159 F5.3 --- e_R61 ?=- Error of R61
161-165 F5.3 --- phi61 ?=- Fourier phase phi61 = phi6 - 6*phi1
167-171 F5.3 --- e_phi61 ?=- Error of phi61
173-177 F5.3 --- R71 ?=- Fourier amplitude ratio R71 = A7/A1
179-183 F5.3 --- e_R71 ?=- Error of R71
185-189 F5.3 --- phi71 ?=- Fourier phase phi71 = phi7 - 7*phi1
191-195 F5.3 --- e_phi71 ?=- Error of phi71
--------------------------------------------------------------------------------
Note (1): The order ndat is additionally supplemented with an orbital motion
correction or a trend t.
--------------------------------------------------------------------------------
Byte-by-byte Description of file: table_lc.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 17 A17 --- Star Cepheid identifier
19- 22 A4 --- Order Order of the Fourier fit
24- 27 I4 --- Ndat [20/1909] Number of data points (1)
29- 36 F8.6 d Period Pulsation period
38- 42 F5.3 mag sigma Fit residual scatter
44- 49 F6.4 mag A1 Fourier amplitude of first harmonic
51- 56 F6.4 mag e_A1 Error of A1
58- 62 F5.3 --- R21 Fourier amplitude ratio R21 = A2=- /A1
64- 68 F5.3 --- e_R21 Error of R21
70- 74 F5.3 --- phi21 Fourier phase phi21 = phi2 - 2*phi1
76- 80 F5.3 --- e_phi21 Error of phi21
82- 86 F5.3 --- R31 ?=- Fourier amplitude ratio R31 = A3=- /A1
88- 92 F5.3 --- e_R31 ?=- Error of R31
94- 98 F5.3 --- phi31 ?=- Fourier phase phi31 = phi3 - 3*phi1
100-104 F5.3 --- e_phi31 ?=- Error of phi31
106-110 F5.3 --- R41 ?=- Fourier amplitude ratio R41 = A4=- /A1
112-116 F5.3 --- e_R41 ?=- Error of R41
118-122 F5.3 --- phi41 ?=- Fourier phase phi41 = phi4 - 4*phi1
124-128 F5.3 --- e_phi41 ?=- Error of phi41
130-134 F5.3 --- R51 ?=- Fourier amplitude ratio R51 = A5=- /A1
136-140 F5.3 --- e_R51 ?=- Error of R51
142-146 F5.3 --- phi51 ?=- Fourier phase phi51 = phi5 - 5*phi1
148-152 F5.3 --- e_phi51 ?=- Error of phi51
154-158 F5.3 --- R61 ?=- Fourier amplitude ratio R61 = A6=- /A1
160-164 F5.3 --- e_R61 ?=- Error of R61
166-170 F5.3 --- phi61 ?=- Fourier phase phi61 = phi6 - 6*phi1
172-176 F5.3 --- e_phi61 ?=- Error of phi61
178-182 F5.3 --- R71 ?=- Fourier amplitude ratio R71 = A7=- /A1
184-188 F5.3 --- e_R71 ?=- Error of R71
190-194 F5.3 --- phi71 ?=- Fourier phase phi71 = phi7 - 7*phi1
196-200 F5.3 --- e_phi71 ?=- Error of phi71
--------------------------------------------------------------------------------
Note (1): The order ndat is additionally supplemented with trend correction t.
--------------------------------------------------------------------------------
Acknowledgements:
Vincent Hocde, vincent.hocde(at)oca.eu
License: CC-BY-4.0
(End) Patricia Vannier [CDS] 17-Apr-2026