different synthetic spectra for every star in the Gaia RVS cross-correlation
pipeline (Katz et al. 2023). For stars brighter than $g_{\rm{RVS}}\leq 12$ mag
(Sartoretti et al. 2023), the choice of template is decided automatically in
favor of the spectral template that consistently yields the highest
correlation peaks. This approach is well adapted for dealing with the enormous
number and diversity of objects observed by Gaia. However, when comparing RVs
of a group of similar objects, such as Cepheids, it is advantageous to adopt
the same correlation mask for all stars in the group and their spectra in
order to ensure consistent RV zero-points. Choosing different templates either
from Cepheid to Cepheid, or as a function of phase for the same Cepheid, may
complicate the interpretation of the results because different correlation
templates assign different weights to the same spectral lines.

####  5.4.2 Comparison of Gaia RVS Fourier fit results to VELOCE

Figure 31: Difference $\Delta v_{\gamma}=$$v_{\gamma,{\rm
GDR3}}$$-v_{\gamma,\texttt{VELOCE}}$ between parameter average_rv from
gaiadr3.vari_cepheid and $v_{\gamma}$ from VELOCE for 71 well-behaved non-SB1
Cepheids as a function of the Gaia correlation template parameters and the
number of Gaia time series observations, num_clean_epochs_rv. Orange points
highlight the 33 Cepheids whose Gaia RVs were measured using the most suitable
template parameter range $5000\leq T_{\rm eff}\leq 6500$, $\log{g}\leq 2$, and
$-0.75\leq$ [Fe/H] $\leq 0.75$. The green point in the right-most panel is RW
Cas, for which the template parameters are not known. Trends appear among all
template parameters, with cooler templates or higher-$\log{g}$ templates
yielding larger positive offset. RVs measured using adequate template
parameters show significantly improved scatter. Figure 32: Ratio of the peak-
to-peak RV amplitudes from Gaia DR3 (peak_to_peak_rv from table
gaiadr3.vari_cepheid) to the VELOCE peak-to-peak RV amplitudes as a function
of the template parameters, analogous to Fig. 31. The amplitude ratios exhibit
large scatter. However, no clear trends emerge.

We considered the parameters average_rv and peak_to_peak_rv from table
gaiadr3.vari_cepheid to investigate the impact of template parameters on the
offset between Gaia and VELOCE. The spectral template parameters
rv_template_teff, rv_template_logg, and rv_template_fe_h were taken from table
gaiadr3.source_id, and are available for the majority of stars with Gaia RV
time series measurements or average_rv values, but not all (exceptions include
RW Cas, SS CMa, and BM Per). We considered the range $5000<T_{\rm
eff}\mathrm{[K]}<6500$, $\log{g}\leq 2.0$, and $-0.75\leq{\rm[Fe/H]}\leq 0.75$
to be particularly adequate for Cepheids and distinguish Gaia results based on
this range in the following as orange points.

Figure 31 shows $\Delta$$v_{\gamma,{\rm GDR3}}$$=$ $v_{\gamma,{\rm
GDR3}}$$-v_{\gamma,\texttt{VELOCE}}$ against the correlation template
parameters for $71$ stars, $33$ of which were processed using the most
adequate range of template parameters. Trends can be seen among all three
template parameters, although their relative contributions are not immediately
distinguished. The most obvious trend in Fig. 31 is that $v_{\gamma,{\rm
GDR3}}$ is much more consistent with VELOCE when the adequate template
parameter range is considered. In this case, just over $\gtrsim 10$
measurements suffice to find a similar result ($\pm 2\,$ km s-1). When the
full parameter range is considered, a larger number of observations is
required. Figure 31 also suggests that the automated identification of the
appropriate parameter range works best when a larger number of observations
are available ($\gtrsim 25$).

Figure 32 shows the ratio between the peak-to-peak RV amplitudes from Gaia and
VELOCE as a function of the Gaia correlation template parameters and
$N_{\mathrm{obs,GDR3}}$. Interestingly, neither the number of observations,
nor the choice of template parameters appears to significantly affect this
comparison. We did not find significant evidence of biased amplitudes,
although there is a noticeable dispersion of $\sim 16\%$ between the
amplitudes. For the time being, it remained unclear whether this is a physical
effect related to the amplitudes of near-IR lines, or the precision of Gaia
peak-to-peak amplitudes, since the number of harmonics used to fit Gaia RV
curves was likely low ($2-3$; G. Clementini, priv. comm.) and is not reported
in the vari_cepheids table. Larger number of observations in the next Gaia DR4
will allow for a more detailed comparison of amplitudes. In the meantime, we
caution that inferences sensitive to RV amplitudes, such as BW-type distances
or $p-$factor calibrations, will be limited by the dispersion seen in Fig.32.

Figure 33 illustrates the differences shown in Fig. 31 and 32 as a function of
$\log{P}$. At a pivot period of $P_{\mathrm{puls}}$$=10$ d ($\log{P}$$=1$),
the median offset if $0.51\pm 0.13$ km s-1, consistent with the offset
determined using template fitting. Additionally, a trend of $1.03\pm 0.29$ km
s-1$/\log{P}$ ($3.5\sigma$) trend is found. A larger offset of $1.6\pm 0.2$ km
s-1 and steeper trend of $1.69\pm 0.44$ km s-1$/\log{P}$ ($3.8\sigma$) is
found among the stars whose template parameters were outside the most adequate
range (blue points). As seen in Fig. 32, the amplitude ratio appears very
stable across the full range of periods. We tentatively note better agreement
for short-period Cepheids processed with the adequate template parameters
($\log{P}$$\lesssim 0.7$), although a cleaner comparison would required a
larger number of stars.

Figure 33: $v_{\gamma}$ (left) and peak-to-peak RV amplitude (right)
determined by Gaia SOS compared to VELOCE as a function of logarithmic
pulsation period. $v_{\gamma,{\rm GDR3}}$ and $A_{\rm p2p,GDR3}$ are the
values published in table gaiadr3.vari_cepheid as parameters average_rv and
peak_to_peak_rv, respectively. Orange points highlight Cepheids for which Gaia
used the most adequate template parameters. Blue points show measurements
processed using template parameters outside this range. Blue and orange solid
lines show linear fits to the respective points; green solid lines show linear
fits to the combined data sets. At $\log{P}$$=1$, we find $\Delta
v_{\gamma}=0.51\pm 0.13\,$ km s-1, and a slight trend of $1.03\pm 0.29$ km
s-1/$\log{P}$ for the orange points. The blue points exhibit a much more
significant offset of $1.6\pm 0.2\,$ km s-1 and trend $1.69\pm 0.44$ km
s-1$/\log{P}$. Peak-to-peak amplitudes are generally consistent with a
dispersion of approximately $16\%$ and do not exhibit a trend with $\log{P}$.

##  6 Summary and conclusions

We present the first data release (DR1) of the VELOCE project, which comprises
more than 18 225 high-precision radial velocity measurements of 253 classical
Cepheids located on both hemispheres, as well as 1161 observations of 164
stars that are not classical Cepheids. This data set provides an unprecedented
combination of RV precision (median uncertainty of $0.037$ m s-1), sample
size, and temporal baselines of up to $11$ yr featuring well-characterized RV
zero-points based on RV standard stars. VELOCE extends the number of Cepheid
RV time series at magnitudes fainter than $G\gtrsim 10$ mag, where previous
catalogs contained relatively few observations. Systematic zero-point changes
following instrumental upgrades ($\sim 26$ m s-1 on Coralie, $<75$ m s-1 on
Hermes) have been characterized.

We performed Fourier decomposition of RV curves with an emphasis on model
selection and to determine ephemerides from the RV data directly. Contrary to
common practice, we define $\phi=0$ at minimum radius, since this phase is
most precisely measurable. The fitted Fourier series models provide the most
detailed view of the Hertzsprung (1926) progression of MW Cepheids to date and
revealed a second bump feature on the descending RV branch of approximately
half of the observed Cepheids with periods between $9-18$ d. These double
bumps are likely to further inform mode resonances (Simon & Lee 1981; Buchler
et al. 1990; Antonello & Morelli 1996), and further investigation of this
feature is required to understand their potential for informing the evolution
and pulsation physics of Cepheids.

Approximately $30\%$ of the Cepheids studied here exhibit changes in the
pulsation-averaged velocity, $v_{\gamma}$, due to orbital motion. A systematic
study of spectroscopic binaries is presented in paper II of this series
(Shetye et al., in prep.).

Thirty-six Cepheids were found to exhibit various forms of modulated
variability, that is, variability signals beyond the dominant pulsation mode
or orbital motion (not counting double-mode Cepheids). The dichotomy of long-
timescale modulations among overtone Cepheids and cycle-to-cycle variations
for long-period Cepheids reported by Anderson (2014) is confirmed. Modulated
variability becomes ubiquitous for given sufficient RV precision ($20-40$ m
s-1 per epoch), and the diversity of phenomena suggests that multiple
astrophysical mechanisms are at play. High-precision RV observations of
Cepheids thus hold great promise to cast open an asteroseismic window for
studying this advanced evolutionary stage of intermediate-mass stars in
unprecedented detail. Future work will systematically study this “modulation
zoo,” starting with the discovery of non-radial pulsation in Cepheid time
series spectra (Netzel et al. 2024).

We investigated the linear radius variations and found striking differences in
the RV curve integrals ($\Delta R/p$) between Cepheids with
$P_{\mathrm{puls}}$ above and below $10$ d. We noted at least two, possibly
three, distinct sequences of long-period Cepheids ($P>10$ d) in the $\Delta
R/p$ vs. $\log{P}$ diagram, which we conjecture are at the origin of the
difficulties encountered when calibrating BW-type projection factors. Although
no obvious physical explanation for these sequences was identified, we noticed
mild preference for the sample of $11$ Cepheids exhibiting the smallest linear
radius variations (the low-$\Delta R/p$ sequence) to reside not far from the
blue edge of the instability strip (Fig. 21).

The VELOCE project provides a legacy dataset of high-quality Cepheid RVs that
will enable further study and allow for future datasets to be combined with
existing ones from the literature. All RV time series measurements and the
results from Fourier series modeling of single-mode bona fide Cepheids are
made publicly available in this data release (DR1). To facilitate accurate
comparisons with the literature, we have determined RV zero-point offsets
relative to the VELOCE zero-point for 31 literature sources using a template
fitting approach. This also allowed us to measure secular (linear) period
changes of 80 Cepheids based on RV measurements alone. We found good agreement
with photometrically measured linear period changes from the literature as
well as stellar model predictions.

Comparing our template fitting results to recently published Gaia DR3 time
series measurements, we find an average offset from VELOCE of $0.65\pm 0.12$
km s-1. Systematic offsets of a few to several km s-1 were found for stars
whose RVs were measured using inadequate template parameters. The published RV
amplitudes of Cepheids in Gaia DR3 exhibit significant ($16\%$) scatter around
the closely mapped VELOCE amplitudes. As Gaia continues its unprecedented
survey of the MW, the number of published RV time series measurements are set
to skyrocket. To ensure consistency among the measurements for specific
variable star classes, we recommend using predefined sets of correlation
template parameters for classes of large-amplitude variables, such as
Cepheids. The accuracy of RV peak-to-peak amplitudes is likely to improve as
more epochs are being collected. Ensuring the consistency of RV amplitudes
measured by Gaia’s RVS instrument with angular diameter variations will be
paramount to achieving accurate BW projection factor calibrations based on
hundreds, if not thousands, of Cepheids.

###### Acknowledgements.

This work would not have been possible without a great deal of help from a
large number of people. Useful with discussions with the following people are
acknowledged (in alphabetical order): Gisella Clementini, Xavier Dumusque,
Nancy R. Evans, Michel Grenon, Martin Groenewegen, Pierre Kervella, Christophe
Lovis, Antoine Mérand, Francesco Pepe, Vincenzo Ripepi, Damien Ségransan,
Jesper Storm, Laszlo Szabados, Stéphane Udry. We especially thank the support
staff at Euler, Mercator, La Silla Observatory, the Observatorio del Roque de
los Muchachos, at the University of Geneva, KU Leuven, and ESO for their
excellence and dedication to operating and maintaining these facilities. This
notably includes Luc J.M. Weber, René Debusson, Michel Fleury, Michel Crausaz,
Gregory Lambert, Vincent and Denis Mégevand, Gaspare Lo Curto, Emmanuela
Pompei, Jesus Dalgado, Florian Merges, among others. We also warmly thank the
following people for contributing observations on Euler and/or Mercator:
Maxime Spano, Pierre Dubath, Thierry Semaan, Maria Süveges, Mihaly Varadi,
Janis Hagelberg, Nicolas Cantale, Sarah Gebruers, Maddalena Bugatti, Amaury M.
J. Triaud, Abigail Frost, Marion Cointepas, Monika Lendl, Dominique Naef,
Matthias Fabry, Sébastien Peretti, Uriel Conod, Julia Seidel, Siemen Burssens,
Raine Karjalainen, Azzurra Bigioli, Federica Cersullo, Ga el Ottoni, Thibault
Merle, Olivier Verhamme, Akke Corporaal, Bruno Chazelas, Fatemeh Motalebi,
Javiera Rey Cerda, Rosemary Mardling, Nicolas Lodieu, Tinne Pauwels, Lea
Planquart, Steven Bloemen, Beatriz Gonzalez Merino, Oliver Turner, and Sara
Mancino, among others. While we sought to include everyone who contributed, we
are likely to have forgotten some, and we apologize to those we failed to
mention. Your contributions were nonetheless valuable!
We thank the anonymous referee for a constructive report that helped to
improve the manuscript. This research has received support from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme (Grant Agreement No. 947660). RIA and SK are funded by
the SNSF Swiss National Science Foundation Eccellenza Professorial Fellowship
(award PCEFP2_194638). RIA acknowledges funding and support from several
sources over the 11 year duration of the project, including the Swiss National
Science Foundation early Postdoc.Mobility fellowship (grant No. 155687) and
the ESO fellowship program in Garching. AT is a Research Associate at the
Belgian Scientific Research Fund (F.R.S.-F.N.R.S.). MP is supported by BEKKER
fellowship BPN/BEK/2022/1/00106 from the Polish National Agency for Academic
Exchange. The Euler telescope is funded by the Swiss National Science
Foundation (SNSF). Early VELOCE observations ($2010-2016$) were enabled by
SNSF project funding from grant Nos. 119778, 130295, and 140893. MM
acknowledges the support of the Swiss National Science Foundation (SNSF) under
grant P500PT_203114. This research is based on observations made with the
Mercator Telescope, operated on the island of La Palma by the Flemish
Community, at the Spanish Observatorio del Roque de los Muchachos of the
Instituto de Astrofísica de Canarias. Hermes is supported by the Fund for
Scientific Research of Flanders (FWO), Belgium, the Research Council of K.U.
Leuven, Belgium, the Fonds National de la Recherche Scientifique
(F.R.S.-FNRS), Belgium, the Royal Observatory of Belgium, the Observatoire de
Geneève, Switzerland, and the Thüringer Landessternwarte, Tautenburg, Germany.
This research was supported by the International Space Science Institute
(ISSI) in Bern, through ISSI International Team project #490, SHoT: The
Stellar Path to the Ho Tension in the Gaia, TESS, LSST and JWST Era. This
research has made use of NASA’s Astrophysics Data System; the SIMBAD database
and the VizieR catalog access tool provided by CDS, Strasbourg; Astropy, a
community-developed core Python package for Astronomy (Astropy Collaboration
et al. 2013, 2018).

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##  Appendix A Classical Cepheids in VELOCE

Here, we report the list of classical Cepheids in this first VELOCE data
release. Table LABEL:tab:Cepheidcatalog lists identifiers, coordinates, Gaia
DR3 information (source ids, mean $G-$band magnitudes, mean $G_{Bp}-G_{Rp}$
color, and pulsation modes), whether the star exhibits orbital motion based on
VELOCE data alone (not considering literature information, which is included
in paper II), the number of VELOCE observations, the number of Fourier
harmonics used in the modeling, $N_{\mathrm{FS}}$, the pulsation period
$P_{\mathrm{puls}}$, its uncertainty (squared sum of statistical and
systematic error), and the epoch of minimum radius $E$ with its uncertainty
(squared sum of statistical and systematic error). All information presented
in Tab. LABEL:tab:Cepheidcatalog is contained within the data files provided
via Zenodo in FITS format, cf. App. C.

Additionally, Tab. LABEL:app:table:RVglobal lists information from the Fourier
modeling, including the degree of the polynomial used to determine
$P_{\mathrm{puls}}$ and $E$, the number of degrees of freedom of the fit,
$N_{\rm DOF}$, the $\chi^{2}$ of the fit (often $\gg N_{\rm DOF}$ due to
unmodeled signals, cf. Sect. 4.3), the pulsation-averaged velocity
$v_{\gamma}$, peak-to-peak RV amplitude, the first Fourier harmonic’s
amplitude and phase, as well as the Fourier amplitude ratios and Fourier phase
differences for higher harmonics relative to the first harmonic. The full
Fourier models for every star are provided in the data tables described in
App. C. Tables LABEL:tab:Cepheidcatalog and LABEL:app:table:RVglobal are made
available in machine-readable form via the CDS.

###  A.1 Corner plots of Fourier parameters

Figures 34 and 35 illustrate the Fourier phase differences and amplitude
ratios up to the 5th harmonic for all combinations191919These corner plots
were inspired by Taylor (2024). While we here do not plot uncertainties for
clarity, we note that uncertainties of the Fourier parameters can be obtained
from the FITS files delivered as part of this data release. The color scheme
applied follows Sect. 4.4 and is intended to help identify the specific groups
of stars discussed therein. A few observations can be made at this time:

  1. 1.

At $P\leq 10$ d, the trend between amplitude ratio $R_{i1}$ and $\log{P}$
increasingly disappears towards higher harmonic $i=2,3,4$. By $R_{41}$, a
previously clean trend with $\log{P}$ turns into a rather continuous
distribution.

  2. 2.

At $P\leq 10$ d, the range of $R_{21}$ clearly exceeds that of long-P
Cepheids. Amplitude ratios of higher harmonics, e.g., $R_{41}$, are more
similar among long-and short-period Cepheids.

  3. 3.

At $P>10$ d the trends of phase differences $\phi_{21}$ and $\phi_{31}$ vs
$\log{P}$ in Fig. 34 appear “delayed” (follow the same trend at higher
$\log{P}$) for orange and green points compared to yellow points.

  4. 4.

At $P>10$ d, the orange points identified in Sect. 4.4 have consistently lower
$A_{1}$ than other long-period Cepheids. The amplitudes of their higher
harmonics (2,3,4) are also lower than those of other long-period Cepheids, cf.
left column of Fig. 35. Apparently, all harmonics contribute to the overall
smaller peak-to-peak amplitude seen in low-$\Delta R/p$ stars.

  5. 5.

Low-amplitude short-period (purple) and low-$\Delta R/p$ long-period (orange)
Cepheids occupy the same region in the plot of $R_{41}$ vs $R_{21}$ in Fig.
35, indicating similar ratio of $A_{4}/A_{2}$ for these stars.

  6. 6.

High-amplitude $P>10$ d Cepheids (yellow) feature higher values of $R_{41}$
and $R_{51}$ across the same range of $R_{21}$.

Table 7: Bona fide classical Cepheids observed as part of the VELOCE project (excerpt) Name | RA (J2000) | DEC (J2000) | GDR3 source_id | $G$ | $G_{\rm Bp}-G_{\rm Rp}$ | Mode | SB1 | $N_{\mathrm{obs}}$ | $N_{\mathrm{FS}}$ | $P$ | $\sigma_{P}$ | $E$ | $\sigma_{E}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (h:m:s) | (d:am:as) |  | (mag) | (mag) |  |  |  |  | (d) | (d) | (d) | (d)
AA Gem | 06:06:34 | +26:19:45 | 3430067092837622272 | 9.4 | 1.4 | FU | F | 68 | 12 | 11.303705 | 1.9e-05 | 58011.537774 | 6.0e-09
AB Cam | 03:46:08 | +58:47:02 | 473239154746762112 | 11.4 | 1.7 | FU | F | 28 | 6 | 5.787585 | 6.4e-05 | 57060.317069 | 4.1e-10
AC Mon | 07:00:59 | -08:42:32 | 3050050207554658048 | 9.6 | 1.6 | FU | F | 61 | 6 | 8.014995 | 4.8e-06 | 56894.022100 | 2.1e-09
AD Pup | 07:48:03 | -25:34:40 | 5614312705966204288 | 9.5 | 1.4 | FU | T | 125 | 13 | 13.597599 | 1.3e-05 | 58269.802393 | 2.4e-12
AH Vel | 08:11:59 | -46:38:39 | 5519380081746387328 | 5.6 | 0.8 | FO | T | 70 | 5 | 4.227158 | 5.6e-06 | 58326.793961 | 6.3e-09
AK Cep | 22:28:50 | +58:12:39 | 2007997408188526336 | 10.6 | 1.8 | FU | F | 18 | 5 | 7.232608 | 5.3e-03 | 57417.918474 | 8.1e-09
AN Aur | 04:59:41 | +40:50:09 | 201574982848108416 | 9.9 | 1.6 | FU | F | 40 | 7 | 10.288512 | 1.1e-04 | 58077.184797 | 5.1e-09
…
202020 $G$ lists the intensity-averaged Gaia DR3 $G-$band magnitude (int_average_g) from table gaiadr3.vari_cepheids unless preceded by a $\dagger$, in which case phot_g_mean_mag from table gaiadr3.source was adopted because these stars were not included in the SOS processing (Ripepi et al. 2023). This was the case for ASAS J082710-3825.9, BB Gem, BB Sgr, FM Aql, RT Aur, SZ Aql, T Mon, TT Aql, TZ Mon, U Sgr, $\beta$ Dor, and $\zeta$ Gem. Analogously, $G_{Bp}-G_{Rp}$ is the intensity averaged Gaia DR3 color obtained from gaiadr3.vari_cepheids, or from gaiadr3.gaia_source. Column ‘Mode’ lists pulsation mode assignments according to gaiadr3.vari_cepheids. Column ‘SB1’ is ‘T’ for ‘True’ if the star exhibits clear signs of orbital motion either over the VELOCE baseline or in the template fitting analysis including literature data, ‘U’ for ‘Unsure’ if the signal is tentative, and ‘F’ for ‘False’ otherwise. Note that very long-period binaries may thus be labeled as ‘F’. Columns $N_{\rm{obs}}$ and $N_{\rm{FS}}$ list the number of VELOCE observations and the number of Fourier harmonics used to represent the pulsational RV variability. Columns $P$ and $\sigma_{P}$ specify the pulsation period and its total uncertainty. Analogously for the epoch $E$ and $\sigma_{E}$, which is defined so that pulsation phase $phi=0$ at $v_{\gamma}$ on the descending RV branch (minimum radius), cf. Sect. 3.1. Stars for which no models were fitted for various reasons are listed separately as labeled. Time-series RV measurements are published as part of this data release, even if no Fourier models were fitted. The full table is available at the CDS.  Table 8: Fourier parameters of single-mode Cepheids (excerpt) Name | poly |  NDOF | $\chi^{2}$ | $v_{\gamma}$ | $A_{\rm{p2p}}$ | $A_{1}$ | $\phi_{1}$ | $R_{21}$ | $\Phi_{21}$ | $R_{31}$ | $\Phi_{31}$ | $R_{41}$ | $\Phi_{41}$ | $R_{51}$ | $\Phi_{51}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  |  |  [ km s-1] |  [ km s-1] |  [ km s-1] | [rad] |  | [rad] |  | [rad] |  | [rad] |  | [rad]
AA Gem | - | 42 | 137.5 | 19.608 | 39.880 | 17.355 | -1.317 | 0.0511 | 0.72 | 0.1444 | 5.81 | 0.0759 | 3.94 | 0.0170 | 1.54
AB Cam | - | 14 | 999.7 | -43.980 | 47.204 | 16.814 | -1.524 | 0.4957 | 4.71 | 0.2981 | 3.37 | 0.1551 | 1.93 | 0.0810 | 0.38
AC Mon | - | 47 | 1420.7 | 60.494 | 38.814 | 14.542 | -1.355 | 0.5818 | 5.32 | 0.1397 | 3.95 | 0.1185 | 2.80 | 0.0223 | 1.83
AD Pup | 4 | 93 | 2359.3 | 72.908 | 52.429 | 22.918 | -1.337 | 0.0936 | 4.77 | 0.1075 | 5.82 | 0.1000 | 4.16 | 0.0449 | 2.67
AH Vel | 1 | 57 | 17218.1 | 26.815 | 16.852 | 8.467 | -1.544 | 0.1301 | 5.04 | 0.0436 | 3.23 | 0.0085 | 1.69 | 0.0181 | 5.89
AK Cep | - | 6 | 143.5 | -53.950 | 36.077 | 14.119 | -1.517 | 0.4548 | 4.72 | 0.2124 | 3.60 | 0.0810 | 2.18 | 0.0410 | 0.45
AN Aur | - | 24 | 205.6 | 4.094 | 33.243 | 13.759 | -1.230 | 0.5051 | 5.88 | 0.1796 | 4.14 | 0.0890 | 3.70 | 0.0573 | 1.74
…
212121Fourier parameters were determined as explained in Sect. 3.1, and
Fourier ratios are computed as described in Sect. 3.2. Stars exhibiting long-
term trends of $v_{\gamma}$ were modeled using polynomials, and column ‘poly’
states its degree. $N_{\rm{DOF}}=N_{\rm{obs}}-1-N_{\rm{model}}$ states the
number of degrees of freedom of the fit, i.e., with $N_{\rm{model}}=1+2\cdot
N_{\rm{FS}}+{\rm poly}$ the number of model parameters. $\chi^{2}$ has the
usual meaning; high values of $\chi^{2}$ indicate unmodeled signals, cf. Sect.
4.3. $v_{\gamma}$ is the constant term of the fitted Fourier series, cf. Eqs.
2 and 3. Note that $v_{\gamma}$ does not correspond to the barycentric
velocity for SB1 Cepheids. $A_{\rm{p2p}}$ is the peak-to-peak RV curve
amplitude determined from the Fourier fit. $A_{1}$ and $\phi_{1}$ are the
semi-amplitude and Fourier phase of the first harmonic, respectively. $R_{i1}$
and $\Phi_{i1}$ are the amplitudes and phase ratios of the $i-$th harmonic
relative to the first (Simon & Lee 1981). Uncertainties for all parameters are
provided in the data files as explained in App. C. The full table is available
via the CDS.  Figure 34: Fourier phase differences and the amplitude of the
first harmonic shown against one another up to the 5th harmonic. The color
scheme adopted in Sect. 4.4 is applied to identify specific groups. Figure 35:
Fourier amplitude ratios shown against one another up to the 5th harmonic. The
color scheme adopted in Sect. 4.4 is applied to identify specific groups.

##  Appendix B Stars other than classical Cepheids

In an early phase (mostly between $2011-2012$), VELOCE targeted candidate
type-I Cepheids reported by different photometric surveys, including ASAS
(Pojmanski 2002, 2003; Pojmanski & Maciejewski 2004; Pojmanski et al. 2005;
Pojmanski & Maciejewski 2005), NSVS (Woźniak et al. 2004), ROTSE (Akerlof et
al. 2000), as well as other stars previously classified as Cepheids in order
to determine cluster membership (Anderson et al. 2013). A large number of
these candidate Cepheids were found not to be Cepheids based on the observed
CCFs or, since then, by other variability classification studies (e.g.,
Johnson 2016). Additionally, a few RR Lyrae stars and type-II Cepheids were
observed to fill time during observing runs.

CCFs provide sensitive checks of variable star classifications based on four
observational features that allow us to identify bona fide classical Cepheids
with only a few observations (Anderson 2013, Sect. 2.4) thanks to the enhanced
S/N compared to ordinary spectra and thanks to spectroscopic features.
Firstly, classical Cepheids produce noticeable correlation peaks at any phase
when cross-correlated with a G2 correlation mask, since their spectral types
vary between mid F to early K, cf. Fig. 1. Stars that fail to produce
noticeable correlation peaks are thus outside the spectral type range of
interest. Cepheid CCFs computed using the G2 masks do not usually exhibit
strong rotational broadening, virtually always exhibit a single correlation
peak, and virtually never exhibit emission features. However, Cepheid CCFs do
generally exhibit phase-dependent displacement in velocity space, phase-
dependent line broadening, phase-dependent line asymmetry, and phase-dependent
line depth; these parameter are traced by RV, FWHM, BIS, and CCF contrast.
Hence, stars that do not exhibit all four types of variations are very likely
not classical Cepheids. Johnson (2016).

We have visually inspected the CCFs and their measured parameters of all stars
observed for VELOCE. Table LABEL:tab:noncep lists the 164 stars that are not
classical Cepheids that have been observed as part of VELOCE, including 4 RR
Lyrae stars, 12 type-II Cepheids, and 33 (candidate) multi-lined spectroscopic
binaries. The table provides qualitative notes on whether the CCF showed a
significant correlation peak, whether this peak appeared atypical for
Cepheids, whether multiple components were apparent, whether the CCF showed
signs of emission features, and whether RV, FWHM, BIS, and Contrast exhibited
variability. We also included a brief note concerning the CCF in the hopes
that this will be useful in the future. Finally, the table includes the Gaia
DR3 source identifier and classifiers assigned by the Gaia DR3 variability
analysis (Eyer et al. 2023) and by a literature meta-study of variable stars
(Gavras et al. 2023). A detailed reclassification of the stars listed in Tab.
LABEL:tab:noncep is out of scope of this work. However, we consider that stars
can be effectively shown not to be classical Cepheids if they a) exhibit no
CCF peaks ($N_{RV}$), b) exhibit multiple peaks or emission features, or c) do
not exhibit all four types of variability despite having been observed more
than $4-5$ times. It is thus possible that a few classical Cepheids remain in
Tab. LABEL:tab:noncep in case there were only one or two good observations
available.

The RV measurements of the stars in Tab. LABEL:tab:noncep is published as part
of this data release. However, we stress that these RVs have not been vetted,
that is, no further quality control was applied. In particular, RVs of SB2
systems need to be considered with caution because it is not always clear that
the same CCF peak was measured. Further information on these stars will be
published as part of the second data release and is available upon request to
the lead author.

Table 9: Stars previously misclassified as Cepheid (candidates) observed as part of VELOCE and later found out to not be classical Cepheids (excerpt)  Name |  NRV | Peak | odd? |  Ncomp | Emi? | vRV | vFWHM | vAsy | vCont | CCF note |  Gaia DR3 source_id | GDR3 class | G22
---|---|---|---|---|---|---|---|---|---|---|---|---|---
RR Lyrae stars
ASAS J165126-2434.9 | 10 | y | n |  |  | y | y | y | y |  | 6046836528519375232 | RR | RRAB
GP Aqr | 2 | y | y |  |  | y | y | y | y | Noisy CCF | 2622261225664677120 | RR | EA
RR Lyr | 146 | y |  |  |  | y | y | y | y | RRAB | 2125982599343482624 | RR | RRAB
V1319 Sco | 19 | y | y |  |  | y | y | y | y | Low contrast variable CCF and noisy | 6246499215814759936 | RR | RRC
Type-II Cepheids
AM Vel | 6 | y | n |  |  | y | y | y | y |  | 5521425379537360896 | T2CEP | DCEP
AL Vir | 15 | y | n |  |  | y | y | y | y |  | 6303152720661307648 | CEP | CW
…
222222$N_{\rm RV}$ lists the number of RV measurements reported here; this
number is $0$ if no observation produced a CCF peak. Peak specifies whether at
least one observation produced a CCF peak. ‘odd?’ specifies whether the CCFs
looked significantly different than those of classical Cepheids.
$N_{\rm{comp}}$ specifies if more than a single absorption component was
noticed, ‘Emi’ whether any observation exhibited signs of emission features.
‘vRV’, ‘vFWHM’, ‘vAsy’ and ‘vCont’ specify whether the object is variable in
RV, line width, line asymmetry, and line depth, respectively. Column ‘CCF
note’ provides qualitative information. Gaia DR3 source IDs are provided for
cross-matching. ‘GDR3 class’ lists the best classifiers from Gaia DR3
classifier_best_class_name, where ‘DSCT++’ abbreviates DSCT—GDOR—SXPHE, and
“ACV++” abbreviates ACV—CP—MCP—ROAM—ROAP—SXARI. Column ‘G22’ lists the
primary_var_type from Gavras et al. (2023). ‘y’ indicates ‘yes’, ‘n’ means
‘no’, ‘NA’ indicates ‘not applicable’ (typically because only one observation
was available). ‘WVir?’ indicates a tentative signature of emission in the
blue part of the CCF analogous to what is seen in W Vir, cf. Fig 1. Question
marks indicate tentative assessments. The full table is available via the CDS.

##  Appendix C VELOCE DR1 data structure

The data published as part of this first VELOCE date release (DR1) are stored
in multiple FITS (Flexible Image Transport System) files. Each FITS file
contains all the quantities and properties used or derived in the present
paper and/or paper II dedicated to spectroscopic binaries (Shetye et al. in
prep.), and one FITS file is used per stars.

The FITS files are organized using a Header-Data Unit (HDU) list, consisting
of a PrimaryHDU and multiple BinTableHDU232323A detailed description of this
kind of files and how to handle them is given in the astropy.io.fits library
documentation at https://docs.astropy.org/en/stable/io/fits/index.html. The
HDU contains the header with all the metadata, whereas the BinTableHDU contain
the data and results derived in tabular form.

As mentioned above, we applied different parts of our analysis to different
stars according to the available data and signal complexity. Hence, the
content and number of HDUs vary among the FITS files. However, the file
structure consistently follows the different phases of the analysis presented
in the two papers.

The most complex file structure is used for stars that underwent all possible
stages of the analysis. In this case, the structure of the HDU list is as
follows:

  1. 0.

Primary HDU \- Header containing all the metadata (see keys at 10, 11, 12, 13
and 14)

  2. 1.

DATA - BinTableHDU \- Table containing the observational data 15)

  3. 2.

FIT - BinTableHDU \- Coefficients of the model fitted to the RV data (see
column names at 17)

  4. 3.

RVTF_CLUSTER - BinTableHDU \- Results of the template fitting analysis per
cluster (see column names at 18)

  5. 4.

ZP_CORRECTED - BinTableHDU \- Results of the template fitting analysis per
observation and zero-point offsets determined for each instrument/source (see
column names at 19)

  6. 5.

VL_KEPLER - BinTableHDU \- Results of the fitted Keplerian orbit after
combining VELOCE and literature data (see column names at 20)

  7. 6.

VL_CIRCULAR - BinTableHDU \- Results of the fitted circular orbit after
combining VELOCE and literature data (see column names at 21)

The first table, DATA - BinTableHDU, is published for all stars for which RVs
were measured from CCFs, including stars not modeled and non-Cepheids. The
subsequent BinTableHDUs are published only if the corresponding analysis was
carried out for a given star. However, the order of the binary tables follows
the stream of the analysis so that the order and hierarchy of the HDU are
always respected.

All barycentric Julian dates (BJDs) are reported minus $2,400,000$ for
brevity.

Table 10: General keys present in the FITS file headers

Header - PrimaryHDU
---
KEY |  DESCRIPTION
NAME |  Name of the star
GAIA_DR3_SOURCE_ID |  Gaia DR3 source_id of the target
RA |  Right Ascension in h:m:s (J2000)
DEC |  Declination in d:am:as (J2000)
USED_SOURCES |  List of instruments used to take the RV measurements
OBSERVED_WITH_CORALIE07 |  Flag - The star was observed with the Coralie instrument BEFORE the 2014 upgrade
OBSERVED_WITH_CORALIE14 |  Flag - The star was observed with the Coralie instrument AFTER the 2014 upgrade
OBSERVED_WITH_HERMES |  Flag - The star was observed with the Hermes instrument
N_RV |  Number of RV measurements
N_RV_CORALIE07 |  Number of RV measurements taken with the Coralie instrument BEFORE the 2014 upgrade
N_RV_CORALIE14 |  Number of RV measurements taken with the Coralie instrument AFTER the 2014 upgrade
N_RV_HERMES |  Number of RV measurements taken with the Hermes instrument
BJD_MIN |  Minimum value of BJD (Barycentric Julian Date) among the RV measurements for the target
BJD_MAX |  Maximum value of BJD (Barycentric Julian Date) among the RV measurements for the target
BASELINE |  Baseline of the RV measurements (BJD_MAX - BJD_MIN) $\mathrm{[d]}$
BOOL_CLASSICAL_CEPHEID |  Flag - Set to True for targets identified as bona-fide classical Cepheids, set to False for the rest.
BOOL_DOUBLE_BUMP |  Flag - Target show a double bump feature (see Sect. 4.2)
BOOL_SB1 |  Flag - Star is identified as an SB1
BOOL_FIT_AVAILABLE |  Flag - A model of the pulsation curve was fitted and is available
BOOL_INTERPOLATED |  Flag - If True, interpolated points were used to determine the best parameters that fit the pulsation curve (only VX Cyg, see Sect. 3.3)
BOOL_TEMPLATE_FITTING_ANALYSIS |  Flag - The template fitting analysis was performed
BOOL_KEPLERIAN_VL |  Flag - VELOCE and Literature data were combined to estimate orbital parameters
BOOL_CIRCULAR_VL |  Flag - VELOCE and Literature data were combined to estimate orbital parameters assuming a circular orbit
242424The word ‘Flag’ indicates a Boolean variable. The word ‘Optional’
indicates that the key is present only if it is relevant for the specific
science case.

Table 11: Additional FITS header keys when a Fourier series model was fitted
to VELOCE data

Optional Header Fit - Added to PrimaryHDU
---
KEY |  DESCRIPTION
P |  Pulsation Period $P_{\mathrm{puls}}$ $\mathrm{[d]}$
P_ERR_SYST |  Systematic uncertainty on $P_{\mathrm{puls}}$ related to the choice of the number of harmonics ($N_{\rm FS}$) $\mathrm{[d]}$
P_ERR_STAT |  Statistical uncertainty on $P_{\mathrm{puls}}$ determined via Monte-Carlo (fixed number of harmonics $N_{\rm FS}$) $\mathrm{[d]}$
P_ERR |  Total uncertainty on the pulsation period $P_{\mathrm{puls}}$ (combination of P_ERR_SYST and P_ERR_STAT) $\mathrm{[d]}$
E |  Epoch ($\mathrm{BJD}-2400000.0$) at which $\phi=0$ (determined using Fourier fit)
E_ERR_SYST |  Systematic uncertainty on E related to the choice of the number of harmonics ($N_{\rm FS}$)
E_ERR_STAT |  Statistical uncertainty on E determined via Monte-Carlo (fixed number of harmonics $N_{\rm FS}$)
E_ERR |  Total uncertainty on the epoch E (combination of E_ERR_SYST and E_ERR_STAT)
N_DOF |  Degrees of freedom of the fit
CHISQ |  Chi-squared statistics
NORMALIZED_CHISQ |  Normalized chi-squared
STDDEV |  Standard deviation of the residuals (weighted) [ km s-1]
STDMER |  Standard error of the mean of the residuals (STDDEV/sqrt(N_DOF)) [ km s-1]
N_TERMS_FS |  Number of harmonics (terms) used for the Fourier Series model ($N_{\rm FS}$ in the text)
BOOL_POLYNOMIAL |  Flag - True if a polynomial was used as a nuisance parameter for determining the best-fit Fourier Series model and the pulsation period
BOOL_KEPLERIAN |  Flag - True if a Keplerian orbit was used to represent orbital motion, see Table 12 for the best-fit parameters of the Keplerian model.
VGAMMA_0 |  Systemic heliocentric velocity [ km s-1] (When no polynomial is used for the fit, VGAMMA_0 is equal to the pulsation averaged RV which is determined by the constant term of the fit ($v_{\gamma}$in Eq. 2). In case a polynomial was also adopted for the fit, either no value is reported or we estimate the VGAMMA_0 from the fit that combined the Fourier series with a Keplerian or from the Keplerian fit over VELOCE and literature data (V+L).)
VGAMMA_0_ERR |  Uncertainty on VGAMMA_0 [ km s-1]
DELTA_RADIUS_OVER_P |  Difference in the star’s radius between its most contracted and expanded configuration $\Delta R/p$ $\mathrm{[R_{\odot}]}$
INTERCEPT_PHASE |  Phase at which the ascending branch cross the mean value of the Fourier series
PEAK2PEAK |  Peak-to-peak amplitude ($A_{p2p}$) of the pulsation [ km s-1]
MIN_RV |  Minimum RV during the pulsation cycle [ km s-1]
MIN_RV_PHASE |  Phase of minimum RV
MAX_RV |  Maximum RV during the pulsation cycle [ km s-1]
MAX_RV_PHASE |  Phase of maximum RV
R$n$1 |  Amplitude ratio between the $n$-th and the first harmonics (A$n$/ A1) (up to $n=7$)
R$n$1_ERR |  Uncertainty on the amplitude ratio between the $n$-th and the first harmonics
PHI$n$1 |  Phase difference between the $n$-th and the first harmonics (PHI$n$ \- $n$ PHI1) (up to $n=7$)
PHI$n$1_ERR |  Uncertainty on the phase difference between the $n$-th and the first harmonics
POLYDEG |  Optional - Degree of the polynomial used to improve the fit the pulsation curve, if applied (key exists only if BOOL_POLYNOMIAL is True)
252525Only present if BOOL_FIT_AVAILABLE in Table 10 is True. Fourier
amplitude ratios, R$n1$, and phase differences, PHI$n1$ are reported up to the
7th order via the integer $2\leq n\leq 7$. Higher-order Fourier parameters can
be computed from the Fourier series fit coefficients, cf. Tab. 17.

Table 12: Additional FITS header keys if a Keplerian orbit was fitted to
VELOCE data

Optional Header Keplerian Orbit - Added to PrimaryHDU
---
KEY |  DESCRIPTION
P_ORB |  Orbital period $\mathrm{[d]}$
P_ORB_ERR |  Uncertainty on the orbital period $\mathrm{[d]}$
ECCENTRICITY |  Eccentricity of the orbit
ECCENTRICITY_ERR |  Uncertainty on the eccentricity of the orbit
T0 |  Time of periastron passage ($\mathrm{BJD}-2400000.0$)
T0_ERR |  Uncertainty on the time of periastron passage
ARGPERI |  Argument of periastron $\omega$ $\mathrm{[deg]}$
ARGPERI_ERR |  Uncertainty on the argument of periastron $\mathrm{[deg]}$
K |  Semi-amplitude of the velocity curve (orbital signal) $\mathrm{[km\,s^{-1}]}$
K_ERR |  Uncertainty on the semi-amplitude of the orbital signal $\mathrm{[km\,s^{-1}]}$
A_SINI |  Projected semi-major axis of the orbit $\mathrm{[au]}$
A_SINI_ERR |  Uncertainty on the projected semi-major axis $\mathrm{[au]}$
F_MASS |  Mass function of the binary system $\mathrm{[M_{\odot}]}$
F_MASS_ERR |  Uncertainty on the mass function $\mathrm{[M_{\odot}]}$
262626These keys are present only if BOOL_KEPLERIAN of Table 11 is True.

Table 13: Additional FITS header keys if both VELOCE and literature data were
used to fit a Keplerian orbit using the MCMC method

Optional Header Keplerian Orbit V+L - Added to PrimaryHDU
---
KEY |  DESCRIPTION
KP_VL_N_ITERATIONS |  Number of iterations of the MCMC for the VL Keplerian model
KP_VL_N_WALKERS |  Number of walkers used in the MCMC for the VL Keplerian model
KP_VL_ACCEPTANCE_RATIO |  Mean of the acceptance fraction for each walker of the MCMC chain for the VL Keplerian model
KP_VL_N_CHAIN |  Number of independent samples MCMC
KP_VL_N_DOF |  Degrees of freedom of the VL Keplerian fit
KP_VL_CHISQ |  Chi-squared statistics
KP_VL_NORMALIZED_CHISQ |  Normalized chi-squared statistics
KP_VL_STDDEV |  Standard deviation of the residuals (weighted)[ km s-1]
KP_VL_STDMER |  Standard error of the mean of the residuals (STDDEV/sqrt(N_DOF))[ km s-1]
KP_VL_PORB |  Orbital period of the VL Keplerian model (mean) $\mathrm{[d]}$
KP_VL_PORB_ERR |  Uncertainty on the orbital period of the VL Keplerian model (standard deviation) $\mathrm{[d]}$
KP_VL_PORB_Q50 |  50th percentile of the orbital period $\mathrm{[d]}$
KP_VL_PORB_Q16 |  16th percentile of the orbital period $\mathrm{[d]}$
KP_VL_PORB_Q84 |  84th percentile of the orbital period $\mathrm{[d]}$
KP_VL_K |  Semi-amplitude of the radial velocity curve of the VL Keplerian model (mean) [ km s-1]
KP_VL_K_ERR |  Uncertainty on the semi-amplitude of the radial velocity curve of the VL Keplerian model (standard deviation) [ km s-1]
KP_VL_K_Q50 |  50th percentile of the semi-amplitude of the radial velocity curve [ km s-1]
KP_VL_K_Q16 |  16th percentile of the semi-amplitude of the radial velocity curve [ km s-1]
KP_VL_K_Q84 |  84th percentile of the semi-amplitude of the radial velocity curve [ km s-1]
KP_VL_ECCENTRICITY |  Eccentricity of the orbit for the VL Keplerian model
KP_VL_ECCENTRICITY_ERR |  Uncertainty on the eccentricity of the orbit for the VL Keplerian model
KP_VL_ARGPERI |  Argument of periastron $\omega$ for the VL Keplerian model $\mathrm{[deg]}$
KP_VL_ARGPERI_ERR |  Uncertainty on the argument of periastron $\omega$ $\mathrm{[deg]}$
KP_VL_T0 |  Time of periastron passage for the VL Keplerian model ($\mathrm{BJD}-2400000.0$)
KP_VL_T0_ERR |  Uncertainty on the time of periastron passage for the VL Keplerian model
KP_VL_A_SINI |  Projected semi-major axis of the orbit for the VL Keplerian model $\mathrm{[au]}$
KP_VL_A_SINI_ERR |  Uncertainty on the projected semi-major axis of the orbit for the VL Keplerian model $\mathrm{[au]}$
KP_VL_F_MASS |  Mass function of the binary system for the VL Keplerian model $\mathrm{[M_{\odot}]}$
KP_VL_F_MASS_ERR |  Uncertainty on the mass function $\mathrm{[M_{\odot}]}$
272727Only present if BOOL_KEPLERIAN_VL is True, cf. Table 10. The prefix
‘KP_VL’ identifies orbital solutions involing both VELOCE and Literature (VL)
data from those based purely on VELOCE data, cf. Table 12.

Table 14: Additional FITS header keys if both VELOCE and literature data were
used to fit a circular orbit using the MCMC method

Optional Header Circular Orbit V+L - Added to PrimaryHDU
---
KEY |  DESCRIPTION
KC_VL_N_ITERATIONS |  Number of iterations of the MCMC for the VL circular model
KC_VL_N_WALKERS |  Number of walkers for the VL circular model
KC_VL_ACCEPTANCE_RATIO |  Mean of the acceptance fraction for each walker of the MCMC chain for the VL circular model
KC_VL_N_CHAIN |  Number of independent samples MCMC
KC_VL_N_DOF |  Degrees of freedom of the VL circular fit
KC_VL_CHISQ |  Chi-squared statistics
KC_VL_NORMALIZED_CHISQ |  Normalized chi-squared statistics
KC_VL_STDDEV |  Standard deviation of the residuals (weighted) [ km s-1]
KC_VL_STDMER |  Standard error of the mean of the residuals (STDDEV/sqrt(N_DOF)) [ km s-1]
KC_VL_PORB |  Orbital period of the VL circular model (mean) $\mathrm{[d]}$
KC_VL_PORB_ERR |  Uncertainty on the orbital period of the VL circular model (standard deviation) $\mathrm{[d]}$
KC_VL_PORB_Q50 |  50th percentile of the orbital period $\mathrm{[d]}$
KC_VL_PORB_Q16 |  16th percentile of the orbital period $\mathrm{[d]}$
KC_VL_PORB_Q84 |  84th percentile of the orbital period $\mathrm{[d]}$
KC_VL_K |  Semi-amplitude of the radial velocity curve of the VL circular model (mean) [ km s-1]
KC_VL_K_ERR |  Uncertainty on the semi-amplitude of the radial velocity curve of the VL circular model (standard deviation) [ km s-1]
KC_VL_K_Q50 |  50th percentile of the semi-amplitude of the radial velocity curve [ km s-1]
KC_VL_K_Q16 |  16th percentile of the semi-amplitude of the radial velocity curve [ km s-1]
KC_VL_K_Q84 |  84th percentile of the semi-amplitude of the radial velocity curve [ km s-1]
KC_VL_A_SINI |  Projected semi-major axis of the orbit for the VL circular model $\mathrm{[au]}$
KC_VL_A_SINI_ERR |  Uncertainty on the projected semi-major axis of the orbit for the VL circular model $\mathrm{[au]}$
KC_VL_F_MASS |  Mass function of the binary system for the VL circular model $\mathrm{[M_{\odot}]}$
KC_VL_F_MASS_ERR |  Uncertainty on the mass function $\mathrm{[M_{\odot}]}$
282828Only present if BOOL_CIRCULAR_VL is True, cf. Table 10. The prefix
‘KC_VL’ identifies all keys corresponding to a circular orbital solution
involing both VELOCE and Literature (VL) data from those based purely on
VELOCE data, cf. Table 12.

Table 15: Content of the first BinTableHDU containing the VELOCE radial
velocity measurements DATA - BinTableHDU
---
COLUMN |  DESCRIPTION
RV |  Radial velocities measurements [ km s-1]
RV_ERR |  Uncertainties on the RV measurements [ km s-1]
BJD |  Barycentric Julian Date (2400000.0 was subtracted to the values)
SOURCE |  Instrument used to take the RV measurement
UNIQUE_ID |  Unique identifier of the observation
SN_60 |  Signal-to-Noise ratio per pixel near $6000$Å
MASK |  Boolean array that flags if a data point was used to fit the model. TRUE indicates that the data point was used, FALSE otherwise.
Table 16: Content of the BinTableHDU containing the model fitted to the RV
curve FIT - Optional BinTableHDU
---
COLUMN |  DESCRIPTION
COEFF |  Coefficients of the fitted model
COEFF_COV_MATRIX |  Covariance matrix of the fitted coefficients
COEFF_ERR |  Uncertainties on the fitted coefficients
Table 17: The coefficients are arranged in correspondence with their
appearance in Eq. 2. In cases where a polynomial was also fitted to the data,
the $c_{i}$ coefficients (see Eq. 3) are added after the Fourier series. Note
this table is present only if BOOL_FIT_AVAILABLE in Table 10 is set to True.
Table 18: Per-cluster results of the template fitting analysis

RVTF_CLUSTER- Optional BinTableHDU
---
COLUMN |  DESCRIPTION
REFERENCE |  Name of the instrument (for VELOCE measurement) or source in the literature
BIBCODE |  Bibcode of the reference (Set to NULL if reference is an instrument)
CLUSTER_ID |  Identification number of the (KDE) data cluster
N_OBS_CLUSTERED |  Number of RV measurements in the cluster
MEAN_BJD |  Mean BJD of the RV measurements in the cluster
MIN_BJD |  Minimum BJD of the RV measurements in the cluster
MAX_BJD |  Maximum BJD of the RV measurements in the cluster
VGAMMA_CLUSTER |  Radial velocity offset of the pulsation for the cluster ($v_{\gamma}$) [ km s-1]
VGAMMA_CLUSTER_ERR |  Uncertainty on VGAMMA_CLUSTER [ km s-1]
DELTA_PHI |  Phase difference between the cluster and the initial template model
DELTA_PHI_ERR |  Uncertainty on DELTA_PHI
292929Only present if BOOL_TEMPLATE_FITTING_ANALYSIS is True, cf. Table 10).
Each line corresponds to a temporal data cluster composed of multiple
observations.

Table 19: Epoch results of the template fitting analysis

ZP_CORRECTED - Optional BinTableHDU
---
COLUMN |  DESCRIPTION
REFERENCE |  Name of the instrument (for VELOCE measurement) or source in the literature
BIBCODE |  Bibcode of the reference (Set to NULL if reference is an instrument)
CLUSTER_ID |  Identification number of the data cluster that the measurement belongs to
BJD |  Barycentric Julian Date of the observation
EPOCH_RESIDUALS |  Residuals between the measurement and the VELOCE template (shifted accordingly to the phase shift of the epoch and without offset) [ km s-1]
EPOCH_RESIDUALS_ERR |  Uncertainty on EPOCH_RESIDUALS [ km s-1]
EPOCH_RESIDUALS_ZPC |  Residuals between the measurement and the VELOCE template (shifted accordingly to the phase shift of the epoch and without offset) after applying the zero-point correction to the measurement [ km s-1]
EPOCH_RESIDUALS_ZPC_ERR |  Uncertainty on EPOCH_RESIDUALS_ZPC [ km s-1]
ZP_CORRECTION_USED |  Zero-point offset correction of the instrument/source in the literature [ km s-1]
ZP_CORRECTION_USED_ERR |  Uncertainty on ZP_CORRECTION_USED [ km s-1]
303030Only present if BOOL_TEMPLATE_FITTING_ANALYSIS is True, cf. Table 10.
Each line corresponds to a single RV measurement. Zero-point offset
corrections could not be determined for some references. In such cases, the
last four columns contain a NULL value.

Table 20: Keplerian fit results based on both VELOCE and literature data using
the MCMC method

VL_KEPLER - Optional BinTableHDU
---
COLUMN |  DESCRIPTION
VAR_NAMES |  Names of the variables of the Keplerian model
MEAN |  Mean of the MCMC chain fitted parameters
STD |  Standard deviation of the MCMC chain fitted parameters
Q50 |  50th percentile of the MCMC chain fitted parameters
Q16 |  16th percentile of the MCMC chain fitted parameters
Q84 |  84th percentile of the MCMC chain fitted parameters
313131Only present if BOOL_KEPLERIAN_VL is True, cf. Table 10).

Table 21: Circular Keplerian fit results based on both VELOCE and literature
data using the MCMC method

VL_CIRCULAR - Optional BinTableHDU
---
COLUMN |  DESCRIPTION
VAR_NAMES |  Name of the variables of the circular model
MEAN |  Mean of the MCMC chain fitted parameters
STD |  Standard deviation of the MCMC chain fitted parameters
Q50 |  50th percentile of the MCMC chain fitted parameters
Q16 |  16th percentile of the MCMC chain fitted parameters
Q84 |  84th percentile of the MCMC chain fitted parameters
323232Only present if BOOL_CIRCULAR_VL is True, cf. Table 10).