Gaia/GSP-spec spectroscopic properties of gamma Doradus pulsators
P. de Laverny A. Recio-Blanco C. Aerts P. A. Palicio
 

   
   

    

   
   Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Bd de l'Observatoire, CS 34229, 06304 Nice cedex 4, France  
   Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, 3001, Leuven, Belgium
      Department of Astrophysics, IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
      Max Planck Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
   

   

   
   The third Data Release of the ESA  mission has provided 
   a large sample of new gravity-mode pulsators, among which more than 11,600 are  stars.
   The goal of the present work is to present  the spectroscopic parameters of these  pulsators estimated by the the  module that analysed millions of  spectra. Such a parametrisation could help to confirm their  nature and provide their chemo-physical properties.
   The Galactic positions, kinematics, and orbital properties of these new  pulsators were examined in order to define a sub-sample belonging to the Milky Way thin disc, in which these young stars should preferentially be found. The stellar luminosities, radii, and astrometric surface gravities were estimated without adopting any priors from uncertain stellar evolution models. These parameters, combined with the  effective temperatures, spectroscopic gravities, and metallicities were then validated by comparison with recent literature studies.
   Most stars are found to belong to the Galactic thin disc, as expected. It is also found that the derived luminosities, radii, and astrometric surface gravities are of high quality and have values typical of genuine  pulsators. Moreover, we have shown that  and  of pulsators with high enough  spectra or slow to moderate rotation rates are robust. This allowed to define a sub-sample of genuine slow-rotating    pulsators. Their  are found between ∼6,500 and  
∼7,800 K,  around 4.2 and luminosities and stellar radii peak at ∼5 L_⊙ and ∼1.7 L_⊙, The median metallicity is close to the Solar value, although 0.5 dex more metal-poor and metal-rich  are identified.
   The  content  is fully consistent with the chemical properties of the Galactic  disc.
   /DR3 spectroscopic properties of  stars therefore confirm the nature of these pulsators and allow to chemo-physically parametrise a new large sample of such stars. 
   Moreover, future  data releases should drastically increase the number of  stars with 
   good-precision spectroscopically derived parameters.
      
   /GSP-spec spectroscopic properties of γ Doradus 

pulsators
    P. de Laverny 1
          A. Recio-Blanco1
          C. Aerts 2,3,4
          P.A. Palicio1
    
    
          
    Received ?? ; accepted ??
====================================================================================================================



§ INTRODUCTION



The European Space Agency  mission with the release of its third catalogue <cit.> has already revolutionised different fields of astrophysics. In particular our view of the Milky Way stellar populations
is being upgraded substantially <cit.>.
Regarding stellar physics and variable stars, 
<cit.> assessed the  fundamental parameters and mode properties of 15,602 newly found /DR3 gravity-mode 
(g-mode hereafter)
pulsator candidates, among the more than 100,000 new pulsators along the main sequence identified from their  photometric light-curves 
by <cit.>.
These g-mode pulsators are low- and intermediate-mass main-sequence stars (masses between 
1.3 and 9 M_) and are ideal laboratories for 
asteroseismology, within the broad landscape of such modern studies
<cit.>.

Meanwhile <cit.> extracted light curves assembled with the Transiting Exoplanet Survey Satellite <cit.> for more than 60,000 of the candidate pulsators discovered by <cit.>. They confirmed the pulsational nature for the large majority and found them to be multiperiodic, with about 70% of them even sharing the same dominant frequency in the totally independent  DR3 and TESS data. By comparing the astrophysical 
properties of the  g-mode pulsators with those studied 
asteroseismically from Kepler data by 
<cit.> and by 
<cit.>, <cit.> classified them either as 
Slowly Pulsating B (SPB) or γ Doradus () candidate stars. 
Our current work is focused on this last category of pulsating F-type dwarfs, covering masses
1.3M_⊙ M 1.9 M_⊙. In the Hertzsprung-Russell diagram (HRD), they are
found in a rather small main-sequence area
<cit.>,
close to the cool limit of δ Scuti instability strip <cit.>.
However, we do point out that many of the  stars actually turn out to be hybrid pulsators when observed in high-cadence space photometry. Indeed a good fraction of these pulsators exhibit not only high-order g modes, but also acoustic waves known as  pressure (or p) modes <cit.>. This makes their instability strip overlap with the one of the δ Scuti stars <cit.>.  


One of the new products published with /DR3 are the stellar atmospheric parameters 

derived from the analysis of the /Radial Velocity Spectrometer (RVS) spectra by the DPAC/ module <cit.>. 
 RVS spectra cover the Ca II IR domain   (846–870 nm) and have a resolution around 11,500.
By automatically analysing these spectra, <cit.> parametrised about 5.6 million single low-rotating stars
belonging to the FGKM-spectral type. Hotter stars (>8000 K)  or highly-rotating stars (more than ∼30-50 km.s^-1, depending on the stellar type) were disregarded for the /DR3 (this will be updated for the next  Data Releases). These limitations come from the adopted reference grids upon which rely the parametrisation algorithms of .
The derived stellar atmospheric parameters are: the effective temperature , the surface gravity , the global metallicity , and the enrichment in α-element with respect to iron . Moreover, up to 13 individual chemical abundances were also estimated for most of these stars. This analysis led to the first all-sky spectroscopic catalogue and the largest compilation of stellar chemo-physical parameters ever published. Moreover, radial velocities () of about 33 millions stars were published in the DR3 catalogue <cit.>. All these data allow to study the Galactic kinematics and orbital properties 
of this huge number of stars, along
with their atmospheric and chemical characteristics, 
keeping in mind that they belong
to various populations in the Milky Way. This multitude of data also facilitates constraining stellar evolution models for 
a broad range of masses. In particular, the  spectroscopic data give us the opportunity to unravel the properties of different kinds of variable stars, among which the g-mode pulsators
characterised photometrically by <cit.>.

One of the main goals of the present study is to apply 
spectroscopic techniques to characterise the g-mode 
and hybrid
pulsators identified in <cit.>
and <cit.>.
This perspective adds to their photometrically-deduced properties and may help future asteroseismic modelling of the most promising pulsators.
Some contamination by other or additional 
variability could also occur, such as 
rotational modulation.  This is expected since 
<cit.> and <cit.> 
could infer only one secure frequency  for many of these 15,602 candidates. Moreover, <cit.> found
a fraction of the g-mode 
and hybrid
pulsators to reveal Ap/Bp characteristics in addition to their pulsational behaviour. 
Therefore, some of them might be Ap/Bp pulsators with anomalous chemical abundances from spots, as previously found from Kepler space photometry <cit.>.
/ spectroscopic parameters could therefore help to confirm the nature of these pulsators and facilitate to build sub-catalogues of g-mode 
and hybrid
pulsating stars with respect to their chemical properties.
In addition, the main properties of these stars can be constrained from the  spectroscopy and compared with the values deduced from the photometry, such as their effective temperature, surface gravity, luminosities, radius, etc.

Another goal is to explore the metallicity (and, possibly, chemical abundances)  of genuine   g-mode 
and hybrid
pulsators. This is an important input for asteroseismic modelling, once a sufficient number of oscillation frequencies has been identified<cit.>.
Aside from the Kepler sample of  pulsators modelled by <cit.>, the confirmed g-mode 
and hybrid
pulsators from <cit.> are currently  under study 
to derive their global parameters
(mass, convective core mass, radius, and evolutionary stage; 
Mombarg et al., submitted), as well as 
all their significant oscillation mode frequencies from high-cadence 
TESS photometry. Future studies will point  out whether their TESS data allow us to find period spacing patterns to assess their suitability for asteroseismology, as has been possible for  stars in the TESS Continuous Viewing Zones <cit.>.

We note that the present work focuses only on the  stars 
or hybrid pulsators with dominant g modes
in the catalogue by <cit.>, for several reasons.
First, only ∼12% of the SPB candidates 
in that paper have a DR3 radial
velocity () and, when available, the associated  uncertainties are quite large,
suggesting possible problems in their RVS spectra.
Moreover, most of the SPB candidates
are too faint to have a high enough  to be analysed meaningfully with
. Finally, we remind that  
was initially constructed to achieve proper parametrisation of slowly-rotating rather cool stars. In particular,
the reference training grid does not contain model spectra for stars
hotter than ∼8000 K and the lines identified in the stellar spectra are assumed not to be too broadened. These restrictions led to the rejection of A-type or hotter stars and/or to lower quality parametrisation for the 
fastest
rotators, as indicated by specific quality flags (and even rejection for the extreme cases). This is confirmed by examining the few SPB 
stars with available  parameters: most of them are indeed flagged as doubtful. We therefore postpone the spectroscopic study of these SPB to the next  Data Releases in which the spectral parametrisation of hotter and/or fast rotators, such as many of the  and SPB pulsators <cit.>,
will be optimised.

This article is structured as follows.
In Sect. <ref>, we present the sample of  pulsators with available  spectroscopic data and we study their spatial distribution, kinematics, and orbital properties in the Milky Way. This led to the definition of a sub-sample of stars with very-high probability of being genuine  stars belonging to the Galactic thin disc.
Subsequently, we present in Sect. <ref> the physical parameters of the  candidates analysed by the  module and discuss their properties in Sect. <ref>.
Our conclusions are summarised in Sect. <ref>.








§ THE /DR3 SPECTROSCOPIC SAMPLE OF  STARS



Among the 11,636  pulsator candidates presented in <cit.>, 4,383 stars (38%) have a published /DR3 radial velocity <cit.> and only 650 of them are found in the  catalogue. 
These numbers can be explained by taking into account that (i) 58% of these pulsating stars are too faint for having a high enough  spectrum,
necessary to estimate their  and/or to be parametrised by  (G13.5 mag for this later case) and (ii) many of them are too hot,  preventing their  parametrisation (see the limitation caused by the reference grid hot boundary, described in the introduction).
In the following, we will discuss the Galactic properties of these candidate stars, derived from their available distances and , in order to 
define a sub-sample of bona-fide  stars based only on kinematic and dynamical criteria.



 §.§ Spatial distribution, kinematics, and Galactic orbits


We derived the spatial (Cartesian coordinates) and kinematic properties of all the 4,383  candidate stars from their  coordinates, proper motions and ,  adopting the 
distances of <cit.>. Their Galactic orbital properties (eccentricity) were computed as described in <cit.> using the Solar Galactic constants presented in <cit.>. 
We also adopted for the LSR velocity of the Sun V_ LSR=238.5 km/s.

Among all these stars with Galactic data, 560 were parametrised by . We note that the parametrisation is available for 90 more stars (see Sect. <ref>) because  parametrised some spectra whose  was finally not published within /DR3, hence their Galactic properties were not computed.

The following quality selections were then applied to define a sub-sample of 2,721 stars (405 of them with  parameters) with high-quality Galactic parameters. (1) The best astrometric data were selected thanks to the ruwe parameter (ruwe < 1.4) and the identification of the non-spurious
solutions <cit.>.
This filters out 521 stars.
(2) We then rejected 152 stars having a distance uncertainty larger than 10%.

(3) The  determination of several of these  candidates was found to be of poor quality, mostly because of the low  of their spectra. We therefore disregarded 1,258 stars having a relative  error larger than 50%. 

The Galactic location of this high-quality sub-sample of 2,721  candidates with astrometric and  information is presented in Fig.<ref>. The colour-code of the middle and right panels represents their rotational velocity in the Galactic plane (V_ϕ, whose typical value for thin disc stars in the Solar vicinity is around ∼240 km/s). In the following, we will adopt for this last quantity the  
velocity of the LSR at the Sun's position.
The location of the same stars in a Toomre diagram, colour-coded with their Galactic orbit  eccentricity is shown in Fig.<ref>. The regions enclosed by the circular dotted lines 
denote those populated by stars with thin disc kinematics, i.e. typical total velocity found within ±40-50 km/s around the LSR value
<cit.>.
From these figures,
it is clear that most stars have thin disc kinematics as expected, although some  candidates belong actually to the Galactic thick disc or halo (low V_ϕ-values, high Galactic latitudes, large eccentricities or total velocities). 
Among those having a total velocity larger than ±50 km/s compared with the LSR value (i.e. too large velocities for belonging to the thin disc, first dotted line in Fig. <ref>), very few have published  atmospheric parameters. Their spectra  is indeed low
(around 25) leading to rather large  uncertainty. Moreover,  their rotational rate is high, and their metallicity could be too low for thin disc stars; but, more importantly, the associated  uncertainties are very large. All of this reveals that their spectra were probably not properly analysed by .
In any case, the fact of not belonging kinematically to the thin disc is contradictory to our understanding of the evolutionary stage of this class of variable stars and they will be rejected from the studied sample (see below).
On the contrary, most of the brightest candidates with  parameters (i.e. with the highest  spectra) are found closer to the Galactic plane with  kinematics and orbital properties typical of thin disc stars (circular orbits, V_ϕ∼ 215-260 km/s and/or abs(V_ Tot-V_ LSR)25 km/s. 



 §.§  candidates belonging to the thin disc


 stars are known to be late A- to early F-type stars, located on the main-sequence below the 
classical
instability 
strip. 
As already mentioned, they
have masses between ∼1.3 and ∼1.9 M_⊙ <cit.> and have therefore rather young ages. We refer to
<cit.> who deduced the ages of the 37 best characterised   stars from asteroseismic modelling of their identified oscillation modes and found ages ranging from ∼0.15 up to 2 Gyr.
Similarly, <cit.> also report asteroseismic ages for 490  that are always smaller than 3.0 Gyr, their mean age being close to 1.5 Gyr with a dispersion of 0.5 Gyr. 
On the contrary, thick disc stars are older than ∼8 Gyr <cit.> whereas halo stars are even older. Therefore, most of the Galactic  stars are expected to belong to the thin disc of the Milky Way. 

One can thus use the above described kinematic and orbital properties of the candidates from <cit.> to select those with the highest probability of being bona-fide  pulsators. 
This is an entirely complementary and independent selection to the one based on the DR3 or TESS light curves.
We have therefore selected all the above candidates having a high probability to belong to the thin disc, i.e. those having close to circular orbits (eccentricity lower than 0.2)

and (V_ Tot-V_ LSR)<25 km/s. These kinematic criteria[Adding a filter based on the distance from the Galactic Plane did not modify this selection.] led to the selection of 
2,245  candidates belonging to the Galactic thin disc (i.e. 83% of the stars with high-quality Galactic parameters), 385 of them having  parameters. This sub-sample, called the Thin Disc-sample hereafter, is discussed below. We can therefore conclude that most stars of the initial sample are thin disc members.




§ PHYSICAL PARAMETERS OF THE  PULSATORS

 

All the 650  pulsators with parameters from  have a published effective temperature () and  a surface gravity (). In addition, one can also access their global metallicity () and abundances in -elements with respect to iron () for 602 and 595 of them, respectively. We remind that, within ,  is estimated from all the available atomic lines in the RVS spectra and is a good proxy of . Similarly, -element abundances are derived from all the available lines of any α-elements. The  abundance ratio is, however, strongly dominated by the huge  infrared lines that are present in the /RVS wavelength domain and is thus strongly correlated to .
Moreover, because of the complex analysis of these rather hot and, usually, 
fast-rotating stars, very few other atomic lines are present in their RVS spectra. Therefore,  individual chemical abundances were derived for only very few tens of them. Only 20 stars have an estimate of their  and the number of stars with other published chemical abundances is even lower. As a consequence, we will only consider hereafter the  abundance ratio for this  sample.
We calibrated all the above mentioned atmospheric parameters and abundances as a function of , adopting the prescriptions recommended in <cit.>.
In addition, we remind that, associated to the  parameters, there are several quality flags () that have to be considered to assess the quality of this parametrisation. 

We also adopted other parameters derived from the analysis of the RVS spectra. For example, 
we partially used the /DR3 spectral type provided by the spectraltype_esphs parameters. In addition,
409 of the   candidates have a published line-broadening measurement <cit.>, confirming the fast-rotating nature for most of them. We refer to <cit.> for a detailed study of the  vbroad properties of the g-mode pulsators.
Even if vbroad was in the end not published for most stars in /DR3,
 has published three quality flags <cit.> that depend directly on vbroad (internally delivered within DPAC for the spectra analysis). The possible biases in the  parameters that could be induced by rotational line-broadening can therefore be explored by future users thanks to these three vbroadTGM flags. 
Contrarily to vbroad, 
these flags are available for the whole sample and are used below to complement the rotational broadening information, when necessary. In the following and for convenience, all these line-broadening quantities will be referred to as rotational velocities.

Finally, we remind that the /DR3 spectroscopic  parameters were derived by the  module by assuming that the rotation rate of the analysed stars are rather low. Therefore, highly rotating stars were rejected: depending on the
stellar type, vbroad limitations are around ∼30-40 km.s^-1, and the parametrisation quality degrades quickly above ∼25 km.s^-1.
Because of this parametrisation limitation, we warn the reader that the  candidates parametrised by  have thus lower rotational velocities than typical values for these variable stars. 
Indeed, the vbroad distribution of our stars has a mean value around ∼25 km.s^-1, associated to a standard deviation equal to ∼10 km.s^-1, and a maximum value of 58 km.s^-1. As a comparison, 
these stars are known to rotate at 40-100 km.s^-1 and some can reach up to ∼150 km.s^-1, see for instance <cit.>. This rotational velocity of the stellar atmosphere is related to the internal rotation rate, as discussed for instance by <cit.>. As a consequence, we are conscious that our sample is biased towards  with rather low rotation rate, and should therefore not be fully representative of these specific class of variable stars. 


Stellar luminosities and radii:
To complement this spectral parametrisation, we computed the luminosity (L_⋆) and radius (R_⋆)

for each star.
For that purpose, we first estimated the extinction E(B_P-R_p) in the  bands by subtracting the observed (B_P-R_p) colour from a theoretical one. The latter was calculated from the  ,  and , inverting the <cit.> relation that predicts stellar colour from atmospheric parameters <cit.>. This procedure did not converge for a few stars, hence these were rejected hereafter.
We then estimated the coefficients k_TGMA =  A_G / E(B_P-R_p), A_G being the absorption in the G-band. These coefficients depend on the four atmospheric parameters and have been estimated thanks to the tables provided with the  stellar parameters[https://www.cosmos.esa.int/web/gaia/dr3-astrophysical-parameter-inference]. The value of A_G then allows to deduce the absolute magnitude in the G-band
from the  DR3 G-magnitude and the <cit.> geometric distances.
We derived the luminosities, adopting the bolometric corrections (BC) from <cit.>. We note that the considered relations to estimate k_TGMA
and BC do not depend on . When available, we adopted the relation of <cit.> to include the α-element content into the global metallicity.
Finally, thanks to the    one directly obtains the stellar radius. The quality of these radii simply computed from  photometry, distances and spectroscopic parameters is excellent.
We refer to de Laverny et al. (2024, to be submitted) and <cit.> for a detailed comparison with interferometric and/or asteroseismic radii, that confirmed the high-quality of our R_⋆ estimates.
One could then also get the stellar mass (M_⋆) from the surface gravities, but we favoured to fix this quantity thanks to the known typical masses of  (see below the discussion on the adopted ). For all these parameters, the uncertainties were estimated by performing 1000 Monte-Carlo
realisations, propagating the uncertainties on each atmospheric parameters (that reflect the  spectra), distance
and  magnitudes. 



Effective temperatures:
Since  stars are known to be early-F spectral type and in order to define a sub-sample of 
high-quality parametrised stars, we first checked their spectral type provided by the /DR3.
Among the 650 candidates parametrised by , 562, 82 and 6 were found by the DPAC/ESP-HS module to belong to the 'F', 'A' or 'B' spectral types, respectively. The   also confirmed the too hot temperature with respect to typical  stars of a few other stars <cit.>, hence they were filtered out. 
Moreover, we also found that ∼6% of the candidates have a   much cooler and not compatible with an early spectral type. All the spectra of these outliers suffer from large  uncertainties and/or very large rotational velocities and/or low  that may lead to an erroneous parametrisation. Therefore, all these too cool stars were also rejected. The remaining 598 spectroscopic candidates have a  (B_p-R_p)_0 colour (corrected from extinction by us) fully compatible with
their . The median of their (B_p-R_p)_0 colour is 0.5 and the associated dispersion is found to be extremely small (0.04 mag.), confirming their early F-type nature.
These 598 stars will be called F-type  sample, hereafter.


Stellar surface gravities: Knowing the stellar luminosity, the  effective temperature and adopting a  typical mass,
the surface gravity can simply be estimated for almost all the  pulsators (called _ Lum, hereafter). Practically, we randomly chose the mass of each star within the  mass range 1.3 to 1.9 M_⊙ <cit.>, assuming an uniform distribution. The associated mass uncertainty has been fixed to half of this range (±0.3 M_⊙).
We note that varying the mass over the entire range covered by genuine  stars changes our  _ Lum estimates by about 0.1 dex and, thus, do not affect our conclusions. The _ Lum uncertainties were computed from 1000 Monte-Carlo realisations, propagating the uncertainties on L_⋆,  and M_⋆.
 We finally point out that 30 stars (among the 650) have no _ Lum because no extinction was available for them (see above). 
 
 It was found that most of these _ Lum are in very good agreement with the   for stars with a rather low rotational velocity (vbroad15-20 km/s) or for stars with slightly larger rotational rate but with high  spectra (100). 
However, larger discrepancies between the two surface gravity estimates are found for the highest rotators and/or stars with low  spectra (mean difference of log(g_/g_ Lum)∼0.35 dex, with a standard deviation of 0.4 dex). This results from the DR3  pipeline that is optimised for non-rotating stars and some parameter biases could exist for stars with large rotation rates[This will be addressed for /DR4.]

In the following and in order to avoid surface gravities potentially affected by the stellar rotation,
we adopted these _ Lum and their associated uncertainties. Thanks to this procedure, we have a sub-sample of about 600  pulsators with rather accurate surface gravity (found in the range from ∼3.5 to ∼4.5) and effective temperatures typical of  stars, according to <cit.>. We emphasize that all the above derived quantities do not rely on any stellar isochrones, but only on  astrometric and photometric data and RVS spectra.






Global metallicities: We simply adopted the  calibrated metallicities for all the  pulsators having a  and a _ Lum, as defined above.


Parameter uncertainties: The RVS spectra of all these  pulsators belonging to the
 F-type  sample
have rather low  ratios. The median of these  is 34 and only 9% of the spectra have a >100. 
The resulting median uncertainties[Estimated by propagating the RVS spectra flux errors on the parameter determination through Monte-Carlo realisations <cit.>.] on (, , , L_⋆, R_⋆) are therefore rather high (182 K, 0.13 dex, 0.21 dex, 0.13 L_⊙, 0.11 R_⊙) with a dispersion although still reasonable of (62 K, 0.02 dex, 0.07 dex, 0.07 L_⊙, 0.04 R_⊙).




§ PROPERTIES OF THE   PULSATORS


The distribution of the main stellar parameters derived above ,  (both derived from the spectrum analysis and from the luminosity), , L_⋆, and R_⋆ are shown in Fig. <ref>. 
In the different panels of this figure, we considered the sub-sample of 371 slowly-rotating stars belonging to both the F-type  and Thin Disc samples, that is those having effective temperature typical of  stars and having typical thin disc kinematics as defined in Sect. <ref>. This sub-sample will be called F-type Thin Disc (FTD) hereafter. It is shown as light-blue histograms in Fig. <ref> and should contain good   candidate stars.

For comparison purposes, we have over-plotted in Fig. <ref> the parameter distributions derived by three recent studies that provide parameters for large numbers of  stars. First, <cit.> report ,  and  
estimated from the analysis of high-resolution spectra (R ∼ 85,000)
for 77 bona-fide  stars with asteroseismic modelling from Kepler observations. None of these stars were found in the  F-type  sample. Secondly, <cit.> published luminosities and asteroseismic radii of 490  derived from  and Kepler observations. 
Their parameter distributions are shown as green lines in Fig. <ref>. There is only one star of <cit.> that was parametrised by , but it is not included in the  F-type  sample because of its too large rotational broadening and associated low-quality flags.
Finally, we also show the , , L_⋆ and R_⋆ distributions of the  candidates of <cit.> as another comparison. Some of their stars suffer from rather large uncertainties on their parameters and we therefore filtered out the stars with  and  errors larger than 100 K and 0.2 dex, respectively, before constructing the black histograms. Moreover,  stars with relative uncertainties in L_⋆ and R_⋆ larger than 25% and 50% were also rejected. 


Some other  stars were also analysed by high-resolution spectroscopy as, for instance, in <cit.>. The spectra collected by these authors have a resolution of 32 000, 85 000, and 25 000/45 000, respectively, but their sample are much smaller than ours. None of our stars are found in these samples but one discusses below the atmospheric parameter properties derived by these studies with respect to the  ones (see also the discussion about Fig. <ref>).











Regarding the effective temperatures, it can be seen in Fig. <ref> that 
our  distribution is nearly compatible with the estimates reported in the literature.
We do report a large number of cooler  stars than <cit.> and <cit.>. We checked that  most of these cooler stars had bad quality  vbroadTGM flags,
meaning that their parametrisation was not optimal because of the broadened lines in their spectra. Moreover, we remind that most RVS  spectra are of rather low-quality, leading to large  uncertainties. As a consequence, if one selects only
the 151 stars belonging to the F-type  sample and having a  error less than 200 K (the mean  ratio of the selected spectra is then around 60) plus their three vbroadTGM flags strictly smaller than 2, we then obtain a  distribution fully compatible with the two comparison ones. This High-Quality (HQ) sub-sample of  stars is shown as dark-blue histograms in Fig. <ref>. Our  distribution is also fully compatible with the ones derived from high-resolution spectroscopy (see above cited references), if one excludes binaries and/or hybrid stars: their  are always found in the ∼6700 – ∼8000 K range. 


Our stellar luminosity distributions (FTD and HQ sub-samples) are peaked around 5 L_⊙ with few bright stars up to ∼25 L_⊙. They are close to the distribution of the two comparison samples (similar peak in L_⋆) although <cit.> and <cit.> report a larger number of more luminous stars. We have checked that considering only stars with good  astrometric ruwe parameters (ruwe < 1.4) in the different comparison samples
(about 10% stars would be rejected) does not modify these distributions. Moreover, we remind that these two other studies computed their stellar luminosity adopting a /DR3 interstellar reddening 
that could differ from our own absorption estimate. Since we did not find any
specific differences between these two reddening flavours, the lack of high-luminosity stars in our sample could be due to selection bias effects: either a lack of too hot and, hence more luminous  stars, not parametrised by ; and/or a lack of low surface gravity stars, hence with high-radius and luminosity, as seen in the  and radius panels of Fig. <ref>. 




The  FTD and <cit.> spectroscopic surface gravities are
in good agreement (left panel, second row in Fig.<ref>).  surface gravities derived 
by other analysis of high-resolution spectra studies also agree, although we note that the samples of <cit.> have  within ∼3.6–∼4.0, i.e. surface gravities slightly smaller than ours and those of <cit.> that reach up to =4.4. However, more numerous lower gravity values are seen in Fig. <ref> compared to <cit.>. Such stars with a surface gravity lower than ∼3.5 should have left the main sequence (or are close to this evolutionary stage).
The agreement between the HQ spectroscopic gravities and those of <cit.> is however excellent, confirming again that low-quality and line-broadened spectra are more difficult to parametrise.
Moreover, the results from <cit.> are also in good agreement with our surface gravities estimated from the stellar luminosity (_ Lum shown in the right panel, second row) and assuming  masses in the range 1.3-1.9 M_⊙. This is quite normal since the <cit.>  values were estimated by the DPAC GSP-phot module <cit.> from the luminosity,  and stellar isochrones, a rather similar method to ours, except for using isochrones. From these different comparisons, we conclude that  surface gravities derived from the stellar luminosity and assuming typical  masses should be preferred over the spectroscopic ones because of the difficulty to analyse spectra of fast-rotating stars, except if one considers the HQ stars for which the spectroscopic gravities are excellent. 




As for the  stars' mean metallicities, our FTD sample covers a larger range in  than the comparison samples. More importantly, it reveals an excess of low-stars  with respect to the spectroscopic sample of <cit.>. The latter peaks around -0.2 dex, whereas ours peaks at about -0.7 dex.
We note that the confirmed  of <cit.> with parameters derived from high-resolution spectra have  that cover a distribution close to the one of <cit.>.

We remind that such low-metallicities are not expected to be numerous for thin disc stars. This shift towards lower metallicities could again be partially explained by the stellar rotation and/or low-quality RVS spectra, as it might induce a bias in the parametrisation. 
Again, rejecting such complex spectra and considering HQ sub-sample stars with a   uncertainty less than 0.25 dex leads to a metallicity distribution that is more compatible with <cit.>.
We still have however more stars with higher and lower metallicities than them by about ±0.5dex. They could be present since our sample has a larger spatial coverage in the Milky Way.



Finally, the compared stellar radius FTD and HQ distributions are in very good agreement with the asteroseismic radii determined by <cit.>, which are expected to be the most accurate ones. 
The spectroscopic radii, whatever the sample considered, are indeed very well representative of those expected for  stars.
Our radius median value is close to 1.7 R_⊙ and 90% of the sample is found in the range
1.35 – 2.35 R_⊙. The largest stars in our sample have R∼3.5-4 R_⊙, so they must be rather close to leave the main-sequence, which is confirmed by their 

effective temperatures and high luminosities (≃7000 K and L ≃25 L_⊙).






In summary, our reported , , , L_⋆ and R_⋆ are in very good agreement with recent literature values, in particular when considering the High-Quality sub-sample defined by selecting high-quality spectra or low-rotating stars. Furthermore, our L_⋆, 
_ Lum, and R_⋆ values are trustworthy, even without considering the membership of the Galactic thin disc as an extra good measure of the star being a genuine  pulsator and/or their spectra properties. 

Moreover, since we have shown that the agreement on the effective temperature and mean metallicity is improved by
selecting high-quality  stellar spectra or stars without large rotational broadening velocities, 
we show these HQ  stars 
in a luminosity - effective temperature  diagram (Fig. <ref>), 
colour-coded with their metallicity.
This figure is similar to those found in the literature, as for example in <cit.>. Excluding binaries and hybrid stars, all our  stars are very well concentrated in the same small region of the L- diagram (or -, in some of the above cited works).
We note that there is no  stars in this figure with   hotter than ∼7750 K[A few hotter  can be found in the literature <cit.>]. This bias is caused by the  parametrisation that was optimised for 
FGKM-type stars (we recall that the reference grid 
is based on spectra models cooler than 8000 K).
We therefore cannot exclude that hotter  could exist but they were rejected during the parameterisation (this will be updated for /DR4).
Finally, it can be seen in Fig.<ref> that more metal-rich   are found at higher , whatever their luminosity is. This could be partly due to some possible parametrisation biases: for instance, metal-poor hot star spectra show very few lines and are thus more difficult to parameterise particularly when their rotation rate is high, explaining probably the absence of such stars in the present sample. But this could also be real and could be a signature of the different evolution of stars with slightly different masses and metallicity. For instance, by exploring BaSTI evolutionary tracks <cit.>, it can be seen that metal-rich  stars with masses around 1.6-1.9 M_⊙ appear hotter than lower mass (∼1.3 M_⊙) more metal-poor stars. More specifically, we have estimated that a difference of ∼0.3 M_⊙ implies a shift in  of similar amplitude as a difference of ∼0.7 dex in metallicity. This rather well corresponds to what is seen in Fig.<ref>. 

The same HQ sub-sample but filtering out stars with  uncertainty greater than 0.15 dex is plotted in an  versus  diagram in Fig. <ref>. Such  a filtering again reduces the number of stars
but reveals more accurate chemo-physical properties of  pulsators.
We remind that only the global  abundances (which is a good indicator of [Ca/Fe] for RVS spectra) of these  stars parametrised by   are available in the DR3 catalogue because of too low statistics of individual chemical abundances (see above). Fig. <ref>
confirms that the selected sample has chemical properties consistent with the Galactic disc population, that is a constant decrease of  with the metallicity for >-1.0 dex. Moreover, since the membership
of most of these stars to the thin disc was based on purely kinematics and dynamical criteria, such a  versus  trend is an independent proof that the chemo-physical  properties of the  pulsators can be safely adopted.

Thus, the /DR3 analysis of  pulsators provides useful physical and/or chemical parameters once an optimized filtering of the poorly parametrised spectra (low  or too fast rotating stars) is performed. The parameters of these HQ  stars are provided in an electronic table which content is presented in Table. <ref>.

















§ CONCLUSIONS



We have studied the /DR3 spectroscopic parameters derived from the analysis of the RVS spectra for the large sample of  candidate pulsators composed by <cit.> and confirmed in <cit.>. About 38% of these stars have a published radial velocity and ∼6% of them were actually analysed by the  module in charge to analyse their  spectra.

Thanks to the available  and astrometric  information, we have been able to compute kinematics and orbital information for all these stars. This allowed us to identify that  2,245 of them (i.e. most of the candidates with high-quality kinematics) belong to the thin disc of the Milky Way, which is expected since these gravity mode pulsator should have typical ages lower than 2-3 Gyr.

We then computed their luminosity and stellar radius from  astrometric and photometric data, adopting the  effective temperature
and without considering any stellar evolutionary models or isochrone priors.
A comparison with recently published values of well studied  stars reveals
that the derived luminosities, stellar surface gravities derived from L_⋆ and
assuming typical  masses, as well as the stellar radii, are of high quality.
Moreover, a strict filtering rejecting stars with large  uncertainty 
(caused by too low  RVS spectra) or high rotational velocity led to pulsators 
with the best derived parameters, including , , and . All of these observables were found to be fully consistent with typical values of genuine slowly-rotating  pulsators. Indeed, the  High-Quality  stars have effective temperatures between ∼6,500 and  
∼7,800 K and surface gravities around 4.2.
Their luminosities and stellar radii peak at ∼5 L_⊙ and ∼1.7 L_⊙, whereas their metallicity distribution is centered close to the Solar value, covering the range [-0.5, +0.5] dex. 
Their  properties 
 is consistent with the chemical properties of the Galactic disc population. We note that the final number
of parametrised stars is smaller compared to the initial sample because of the low  spectra of many of  them, together with the fact that most of them 
are fast rotator for which the  analysis pipeline was not optimised for the /DR3. Anyway, the number of newly spectroscopically parametrised  presented in this work is about a factor two larger than in previous studies. 






Finally, it can be concluded that the  analysis of  stars provides a significant added value to the study of these gravity-mode pulsators, delivering their physical and chemical properties.
This will be even more important with the future  data releases for which the RVS spectra  values and the number of analysed stars will be significantly increased. 
Indeed, it is expected that the  increase between DR3 spectra and those released in DR4 and DR5 will correspond to a factor
√(2) and 2, respectively.
Moreover, it is also anticipated that the analysis of fast-rotating stars by the  module will be improved by considering reference grids of synthetic spectra representative of a wide variety of stellar rotational values, contrarily to the present study that is  biased towards slowly-rotating . Finally, hot star spectra will also be considered for reference, allowing a better  parametrisation for stars with high . These anticipated future improved analyses of gravity-mode pulsators performed by the  module will therefore be 
of prime interest as input for asteroseismology of such stars. They will indeed allow to define a much larger and thus more statistically significant number of bona-fide  stars with physical and chemical properties. Furthermore, they will also allow to study the  spectroscopic parameters of hotter gravity-mode pulsator, such as the Slowly Pulsating B stars with the aim to improve their asteroseismic modelling <cit.>.


This work has made use of data from the European Space Agency (ESA)
mission  (https://www.cosmos.esa.int/gaia), processed by the  Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the  Multilateral Agreement.

This work has also made use of the SIMBAD database, operated at CDS, Strasbourg, France  <cit.>, the IPython package <cit.>, NumPy <cit.>, Matplotlib <cit.>, Pandas and TOPCAT <cit.>.
PdL and ARB acknowledge funding from the European
Union’s Horizon 2020 research and innovation program under SPACE-H2020
grant agreement number 101004214: EXPLORE project.
CA acknowledges funding 
from the European Research Council (ERC)
under the Horizon Europe programme (Synergy Grant agreement
number 101071505: 4D-STAR project).  While partially funded by the European
Union, views and opinions expressed are however those of the authors
only and do not necessarily reflect those of the European Union or the
European Research Council. Neither the European Union nor the granting
authority can be held responsible for them.

Finally, we are
grateful to the anonymous referee for their constructive
remarks.


aa 


