Gaia Data Release 3: Hot-star radial velocities

The second Gaia data release, DR2, contained radial velocities of stars with effective temperatures up to Teff = 6900 K. The third data release, Gaia DR3, extends this up to Teff = 14,500 K. We derive the radial velocities for hot stars (i.e. in the Teff = 6900 - 14,500 K range) from data obtained with the Radial Velocity Spectrometer (RVS) on board Gaia. The radial velocities were determined by the standard technique of measuring the Doppler shift of a template spectrum that was compared to the observed spectrum. The RVS wavelength range is very limited. The proximity to and systematic blueward offset of the calcium infrared triplet to the hydrogen Paschen lines in hot stars can result in a systematic offset in radial velocity. For the hot stars, we developed a specific code to improve the selection of the template spectrum, thereby avoiding this systematic offset. With the improved code, and with the correction we propose to the DR3 archive radial velocities, we obtain values that agree with reference values to within 3 km/s (in median). Because of the required S/N for applying the improved code, the hot star radial velocities in DR3 are mostly limited to stars with a magnitude in the RVS wavelength band<= 12 mag.


Introduction
The Gaia satellite (Gaia Collaboration et al. 2016b) was launched in December 2013. By continuously scanning the sky, it is collecting astrometric, photometric, and spectroscopic information on a large number of stars. A number of data releases have made part of this wealth of information public (DR1 by Gaia Collaboration et al. 2016a;DR2 by Gaia Collaboration et al. 2018;EDR3 by Gaia Collaboration et al. 2021). Now the third data release (Gaia DR3, Gaia Collaboration et al. 2022a) is available, which not only updates the previous releases, but also adds substantially new information, such as BP/RP spectra (De Angeli et al. 2022), astrophysical parameters (Creevey et al. 2022), and variability classification (Eyer et al. 2022). This new information also includes the radial velocities for almost 34 million stars (Katz et al. 2022), and Radial Velocity Spectrometer (RVS) spectra for almost one million stars (Seabroke et al. 2022).
The Gaia data are processed by the Data Processing and Analysis Consortium (DPAC; see Gaia Collaboration et al. 2016a, for details). Within DPAC, the Coordination Unit 6 (CU6) is responsible for handling the RVS spectra. Its main tasks are the reduction of the RVS data for use by other Coordination Units and for publication in the data releases, as well as the determination of the radial velocity from these spectra. A secondary task is measuring the broadening of the spectral lines. This broadening is mainly due to the (projected) rotational velocity of the star, but may also include other effects, such as macroturbulence (Frémat et al. 2022). For this reason, we use the e-mail: Ronny.Blomme@oma.be term 'broadening velocity' rather than rotational velocity. Other uses of the spectra, such as astrophysical parameter determination, are within the remit of other DPAC Coordination Units.
This paper is one of four presenting the radial velocity results in DR3. Katz et al. (2022) present the DR3 radial velocity content in general, Gosset et al. (2022) describe the processing and performance for SB1 binary stars in detail, and Damerdji et al. (2022) does the same for SB2 binaries. The present paper focusses on the radial velocity performances of hot stars. For a scientific application in which the radial velocities play an important role, we refer to Gaia Collaboration et al. (2022b).
Data release 3 is the first data release to contain radial velocities for stars with effective temperatures above 6900 K, extending the range up to 14 500 K. The previous data release DR2 did not include these, as the quality of the results could not be guaranteed. The present paper describes how these hot-star radial velocities were derived, and the caveats that have to be taken into account in their use. For stars even hotter than 14 500 K, there remain challenges that could not be solved in DR3 and will therefore be handled in the next release, DR4.
Determining radial velocities for hot stars with the Gaia RVS is quite challenging. The instrument is described in detail in Cropper et al. (2018). It is a medium-resolution spectrograph (R ≈ 11 500) covering the wavelength range 846 -870 nm. This rather small wavelength range has been chosen to optimise radial velocity determination for cool stars. Figure 1 shows two examples of the RVS spectrum of a hot star. The hotter star (right panel) is dominated by the hydrogen Paschen lines, with no other substantial spectral lines that can be used for radial velocity determination. The somewhat cooler star (left panel) has, in addi- Fig. 1. Two examples of RVS spectra of hot stars (https://www.cosmos.esa.int/web/gaia/iow_20141124). Both stars have Paschen hydrogen lines, and the cooler star (left panel) also shows the calcium infrared triplet lines. A spectrum of the cooler star with a much higher S/N is available in the DR3 archive (Gaia DR3 1053778957742409984). tion to the Paschen lines, also the lines from the calcium infrared triplet. While these sharper calcium lines are useful for radial velocity measurements, their proximity to the Paschen lines complicates matters.
The focal plane of Gaia contains four rows of three CCDs each that are dedicated to the RVS instrument. During a single transit of a star across the focal plane, three spectra are therefore taken. The integration time for a single spectrum is ∼ 4.4 s. During the 34 months of observations covered by DR3 each star has 22 of these transits on average. The information from these 22 transits can be combined to improve the signal-to-noise ratio (S/N) and thus the precision of the radial velocity determination.
In Sect. 2 we present the part of the pipeline that determines the radial velocity, and discuss the resulting hot-star radial velocities from a preliminary run of the code. Section 3 presents the specific method we implemented to improve the handling of the hot stars. In Sect. 4 we show the improvement in the resulting hot-star radial velocities. Section 5 presents the conclusions and the caveats for the user of the Gaia DR3 hot-star radial velocities.

Method
This section describes the method we used to derive the radial velocities and presents the results of a preliminary run (Sect. 2.2). As the results of this preliminary run were not satisfactory for the hot stars, an improved method was developed. This is described in Sect. 3.

STA and MTA
The processing of the RVS data consists of six pipelines (Sartoretti et al. 2022a); the four main pipelines take care of the spectrum extraction, the determination of the wavelength calibration and the background correction, and the radial velocity determination. The pipeline we are concerned with consists of two parts: single-transit analysis (STA) and multi-transit analysis (MTA). These are described in detail for DR2 in Sartoretti et al. (2018), and the description is updated for DR3 in Sartoretti et al. (2022a). Here we provide a summary of the points that are relevant for this paper. Figure 2 also provides an overview.

STA input
The STA part of the pipeline uses the observed spectra as input that have been wavelength-calibrated and normalised, and it uses the astrophysical parameters of the most appropriate synthetic time needed for the processing and the validation of the results means that it is not feasible to iterate between the CU6 and CU8 processing. CU6 therefore used parameters from the preliminary CU8 run. This CU8 run used an earlier version of the GSP-Phot (Andrae et al. 2022) and GSP-Spec (Recio-Blanco et al. 2022) pipelines. GSP-Phot used DR2 photometric data instead of the better-quality and more detailed DR3 BP/RP data, while GSP-Spec used RVS spectra from the preliminary CU6 run (discussed in Sect. 2.2). These initial sets of parameters are thus intrinsically not optimal, and CU6 supplemented these data by other (non-Gaia) sources of parameters (Sartoretti et al. 2022a, their Table 6.4). The input astrophysical parameters for the choice of the synthetic spectrum are determined as follows, in order of priority: 1. Parameters from the literature (Sartoretti et al. 2022a, their  The percentages listed above are applicable for all stars that turn out to have a rv_template_teff 2 ≥ 7000 K after the improved method detailed in Sect. 3 was applied. Based on the astrophysical parameters, the nearest synthetic spectrum is selected. The list of available synthetic spectra is given in Blomme et al. (2017). The astrophysical parameters of the synthetic spectrum (which we call template parameters from here on) are therefore usually slightly different from the true astrophysical parameters, and in the remainder of this paper, we are mainly concerned with the template parameters. Figure 3 shows the fraction of the hot stars (rv_template_teff ≥ 7000 K) that obtained their template parameters from each of the above possibilities. GSP-Phot is the dominant contributor. GSP-Spec, which uses the RVS spectra, does not cover the higher temperatures. This is highly relevant for this paper. The figure also shows information for hot stars with grvs_mag fainter than magnitude 12, but for reasons explained in Sect. 3, a cut-off magnitude 12 is applied for the DR3 archive.

STA processing
For a given transit, the selected synthetic spectrum is converted into a template by convolving it with the instrumental profile, and possibly with a broadening profile. For the latter, a rotational broadening kernel is used (Gray 2005), with the caveat that the line-broadening velocity can include other broadening mechanisms as well. The template is then normalised, so that it can be compared to the normalised observed spectrum.
The radial velocity and its corresponding uncertainty are then determined using three different techniques: crosscorrelation by Fourier transform, Pearson correlation, and a χ 2 minimum distance (David et al. 2014). The spectra from the three CCDs that cover this single transit are processed separately (because the instrumental profile is different for the three CCDs) to derive a cross-correlation function (CCF) or a χ 2 function for each spectrum. These three functions are then combined, and the radial velocity is derived from the maximum of the combined CCF and the minimum of the combined χ 2 function. For the brighter stars, the broadening velocity is also determined; for details, we refer to Frémat et al. (2022).
The final value for the transit radial velocity is the median of the three determinations. During this processing, the spectra are also checked for the possible presence of two components and, if they are detected, the corresponding radial velocities are determined following a dedicated channel described in Damerdji et al. (2022).

MTA processing
In the MTA part of the pipeline, the information of all transits for a given star (with a supposed single-line spectrum) is combined. This combination is done in a different way for bright stars than for faint stars. The switch between bright and faint occurs at grvs_mag = 12 mag, where grvs_mag is the magnitude over the RVS bandpass (Sartoretti et al. 2022b).
For the bright stars (grvs_mag ≤ 12 mag), MTA corrects the STA radial velocities for the barycentric velocity and takes the median; this quantity is stored in the DR3 archive as radial_velocity. The corresponding uncertainty radial_velocity_error is derived from the uncertainty on the median (with a floor value of 0.113 km s −1 ); for details, see Sartoretti et al. (2022a, Sect. 6.4.9).
For the faint stars (grvs_mag = 12 − 14 mag), MTA uses the STA cross-correlation functions determined by Fourier transform, shifts them for the barycentric velocity correction, and averages them to obtain the source cross-correlation function. From the maximum of this function, the radial_velocity is determined. The radial_velocity_error is calculated using the formula of Zucker (2003, Sect. 2.3).
In both cases, the MTA processing also provides the spectrum combined over all transits. This combined spectrum is shifted by MTA to its rest wavelength. . Preliminary radial velocities compared to their reference values as a function of the template effective temperature. ReDetermineApHotStars was not applied to these data. The left panel shows the bias of the radial velocity of the stars (RVS value minus reference value). Each point on the plot presents the median of the bias of all stars having this T eff value (the template effective temperatures take on only discrete values). The coloured bar around it gives the uncertainty on the median; in most cases, this uncertainty is smaller than the symbol. The results for cooler stars are also included in this figure to show the difference in quality of the radial velocity determination. The dashed blue lines indicate ±3 km s −1 . The numbers at the top show how many stars correspond to this temperature. The right panel shows the precision. The blue symbols give the external uncertainty (dispersion of RVS value minus reference value), while the red symbols give the internal precision, i.e. the intrinsic uncertainty as derived by the code. The uncertainties on these values are given by the coloured bars; for the higher T eff values, they have been offset slightly in temperature to avoid overlap. The plots include only stars with grvs_mag ≤ 12 mag.

Preliminary radial velocities
A preliminary run of the RVS processing pipeline revealed that the radial velocities of hot stars show a systematic offset with respect to the reference stars. The reference stars we use in this comparison are those from the literature listed in Katz et al. (2019). We also use values that were derived for cluster members using Gaia DR2. Although Gaia DR2 contains radial velocities only for cooler stars (T eff ≤ 6900 K), these were used by Soubiran et al. (2018) to determine the cluster radial velocity, and the hotter stars that are members of the cluster are assigned the same velocity as the cluster.
In Fig. 4 we plot the difference between the preliminary RVS radial velocities and the reference values as a function of the template T eff . As there are a large number of stars, we condense the information by grouping the stars according to their template T eff (which takes on only discrete values). For each template T eff , we calculate the median and the uncertainty on the median of the radial velocity difference, giving us a point and an uncertainty on the plot. The number of stars corresponding to each T eff is listed at the top of the left panel in Fig. 4. Figure 4 shows a clear offset of about −20 km s −1 for T eff > 7000 K. The reason for this offset is a mismatch between the template and the observed spectrum. For the T eff range we consider here, the spectra have a mixture of the calcium infrared triplet and hydrogen Paschen lines. Fig. 1 shows that three of the Paschen lines have a calcium line on their blueward side. If the template does not have the correct relative intensities of the calcium and Paschen lines, the radial velocity determination techniques will attempt to shift the theoretical Paschen lines towards the position of the observed calcium lines, leading to an incorrect, blue-shifted, velocity. A template without template mismatch would not have this problem, and the correct radial velocity would be obtained.
The right panel of Fig. 4 shows two versions of the precision. The blue symbols give the external precision: this is the half-range between the 15.85 and 84.15 percentile of the distribution of the radial velocity differences (see Katz et al. 2019, their Eqs. 4-6). The red symbols give the internal precision: this is the median value (and its uncertainty) of the radial velocity uncertainty (radial_velocity_error) as derived in the MTA processing (Sec. 2.1.3). The precision of stars hotter than 6500 K is considerably worse than the precision for stars at lower temperatures. The internal precision is lower than the external one, indicating that the radial velocity uncertainty is underestimated for these stars. We also checked the influence of the uncertainty of the reference values on the external precision, but this is negligible compared to the difference between external and internal precision.

Improved method
Because of the unsatisfactory results of the preliminary run for hot stars, we decided on a new approach, implemented as the module ReDetermineApHotStars. This module does an exhaustive brute-force search among the combination of many templates and broadening velocities to find the combination that best fits (in χ 2 sense) all transit spectra of a given star. As part of the procedure, ReDetermineApHotStars also shifts the template being explored in velocity space, and it thus also determines the transit radial velocities. However, only the updated template parameters and the broadening velocity are output from ReDeter-mineApHotStars; the radial velocity determination is left to the three radial velocity modules (Sect. 2.1.2).
The way the ReDetermineApHotStars module is included in the STA part of the pipeline is shown in Fig. 2. ReDe-termineApHotStars is called for stars with a template T eff ≥ 7000 K. It is also called for 6500 ≤ T eff < 7000 K when the atmospheric parameters are not from literature data (see Sect. 2.1.1). We apply this procedure only to stars that are bright enough (G RVS ≤ 12 mag) so that we have a sufficient S/N in the spectra.
The G RVS value used in this procedure is not exactly the same as the grvs_mag available in the DR3 archive. The latter value is determined in the MTA part of the pipeline as the median of all valid transit G RVS values (Sartoretti et al. 2022b). During the run of STA, this median value was not yet available, therefore STA used the first valid value from the list of transits. The bottom panel shows the templates derived from these synthetic spectra: they have been convolved with a broadening velocity of 100 km s −1 (blue curve), and 80 km s −1 (red curve), and with the instrumental profile. They are compared with the observed spectrum of Gaia DR3 51853419339515136 (grey curve). All spectra are at their vacuum rest wavelength, except for the blue curves, which are shifted by −60.9 km s −1 ; this is the offset we found between the case when ReDetermineApHotStars was applied or was left unused. The template selected by ReDetermineApHotStars (red curve) clearly provides a better fit to the observed spectrum and therefore also gives a more correct radial velocity. Because of the requirement for bright enough stars for Re-DetermineApHotStars, the hot-star radial velocities in the DR3 archive are mostly limited to grvs_mag ≤ 12 mag. The few stars that are fainter than this are due to the difference between the value used by STA and MTA, as explained above.
Because the brute-force grid search in ReDetermineApHot-Stars is computing-time intensive, various optimisations are in-troduced in that module. We combine the observed spectra from the three CCDs into a single spectrum, so that we have to handle fewer spectra. For the combination, we use a wavelength grid with a constant step in log λ, so that the radial velocity shifts can be made by simple index manipulation. The templates we compare with have been pre-calculated. We base them on the synthetic spectra used in the RVS processing (Blomme et al. 2017;Sartoretti et al. 2022a), selecting all those that have a T eff ≥ 6500 K. The parameter ranges of the synthetic spectra we use are listed in Table 1. We convolve each synthetic spectrum with a pre-specified grid of rotational velocities and with the instrumental profile consisting of a Gaussian with the nominal RVS resolving power of 11 500. The templates are also on a wavelength grid with a constant step in log λ.
ReDetermineApHotStars has a main loop over the set of the pre-calculated templates and an inner loop over all transits of a given star. In the inner loop, it determines the best radial velocity for each transit. It does so by exploring a range of radial velocities and calculating the χ 2 between observed spectrum and template. As part of this procedure, the normalisation of the observed spectrum is also slightly adapted to agree as well as possible with the normalisation of the template. Again, for optimisation purposes, we first use a coarse velocity grid to obtain an approximate radial velocity from the minimum χ 2 . The velocity grid is then refined around this approximate result to obtain a better value, which is then even further refined by parabolic interpolation. In this way, we obtain the best radial velocity for a specific combination of pre-calculated template and transit. The inner loop then loops over all transits, and the best-fitting precalculated template for the star is then determined by the minimum of the χ 2 summed over all transits of that star.
As a further optimisation, we ordered the pre-calculated templates in such a way that we first explore the templates that show the highest difference among themselves (the difference between the templates is measured by the sum of the square of the flux differences). In this way, we quickly determine a template with a reasonably good χ 2 value for the star. When we proceed with the set of pre-calculated templates, we find many templates with a much higher χ 2 than the best χ 2 obtained thus far. It therefore frequently happens that as we loop over the transits, we already arrive at a summed χ 2 that is too large before we have processed all the transits of that star. We can therefore break off further processing of this specific template in the inner loop, and in this way reduce the required computing time.
An example of applying ReDetermineApHotStars is shown in Fig. 5. ReDetermineApHotStars works on the separate transit spectra, but for the example, we chose an RVS spectrum from the Gaia DR3 archive, which is a combination of all its transit spectra. As for all archive spectra, this spectrum was shifted to its rest wavelength, in this case, using the radial velocity based on the processing by ReDetermineApHotStars. The observed spectrum (shown in grey in the bottom panel) contains a mixture of Paschen and calcium lines. This spectrum was then compared to two templates that were derived from the synthetic spectra shown in the top panel. The template used in the preliminary run has a relatively high effective temperature (T eff = 11 500 K) and therefore shows only weak calcium lines. When fitting such a template (blue curve) to the observed spectrum, the theoretical Paschen lines are blue-shifted in attempting to partially fit the observed calcium lines. This gives an incorrect, blue-shifted, radial velocity of −60.9 km s −1 . The bottom panel shows that the blue curve fits the region around Pa13 and Pa15 reasonably well, but clearly fails around Pa14, Pa16, and Pa17. ReDeter-mineApHotStars finds a much cooler template that has the ap-  propriate mixture of Paschen and calcium lines, and therefore fits the observed spectrum much better. Using this template results in a more correct radial velocity. This radial velocity was used to place the DR3 archive spectrum (shown in Fig. 5) at its rest wavelength.

Improved radial velocities
The top left panel of Fig. 6 shows the improvement in the bias of the radial velocities (RVS radial velocity minus the reference value). The offset of about −20 km s −1 shown in Fig. 4 is reduced to about −5 km s −1 for most of the effective temperature range.
The remaining −5 km s −1 offset can be further reduced by considering the plot in the top right panel of Fig. 6. When we plot the bias of the radial velocities (for T eff = 8500 − 14 500 K stars) as a function of magnitude (grvs_mag), a clear dependence on magnitude is seen. We approximate this dependence with a linear fit, After we apply Eq. 1 to correct the radial velocities, we can again plot their bias (Fig. 6, bottom-left panel). Now, almost all points show a bias lower than 3 km s −1 . The only exception is T eff = 12 000 K; we were unable to determine why this temperature behaves somewhat differently. It is important to realise that the radial_velocity listed in the DR3 archive does not include this correction. It is up to the user of the DR3 hot-star radial velocities to decide whether they wish to apply this correction. As an example, we refer to Gaia Collaboration et al. (2022b), where this correction is applied.
The magnitude-dependent effect (Fig. 6, top right panel) is due to the difference in normalisation between the template and the observed spectrum. The normalisation consists of repeatedly fitting a second-degree polynomial to the fluxes and rejecting flux values that deviate too much from the polynomial. A stricter cutoff is used for fluxes below the polynomial than for those above it. Although the same technique is used for both the template and the observation, the presence of noise in the observation leads to a polynomial with a somewhat different slope than that of the noise-free template. With increasing effective temperature, the wider Paschen lines start to dominate, and radial velocity measurements become more sensitive to this slope mismatch, leading to a systematic offset. The effect becomes larger for the fainter stars because they have noisier observed spectra. For DR4 we are exploring a different normalisation technique where the normalised template is used as a reference for the normalisation of the observed spectrum. Preliminary indications are that this substantially reduces the magnitude-dependent effect described here.
The bottom right panel of Fig. 6 shows the two versions of the precision in the same way as for Fig. 4. With the improved method, both curves are now lower, indicating the improved precision. Furthermore, the internal precision (red curve) is now much closer to the external one. As for Fig. 4, we examined the influence of the uncertainty of the reference values on the external precision and found that it is negligible compared to the difference between external and internal precision. From the comparison of the two curves, we deduce that the radial_velocity_error is underestimated in the T eff = 8000 − 10 000 K range by ∼ 30%. For higher temperatures (T eff = 10 500 − 13 000 K), the radial_velocity_error is slightly overestimated (though the uncertainty regions of the two precisions partially overlap). Figure 6 does not plot results for stars hotter than 14 500 K. These stars still present a considerable offset that could not be solved in DR3 and will be handled in DR4.
A further test of the hot-star radial velocities is provided by the CU8 processing to determine the astrophysical parameters from the spectra delivered by CU6. As part of the astrophysical parameter determination performed by the Extended Stellar Parameterizer -Hot Stars (ESP-HS; Creevey et al. 2022), the spectra are compared to synthetic spectra. When RVS data are available, the ESP-HS performs a first estimation of the astrophysical parameters of hot stars from the analysis of BP/RP data and then applies a cross-correlation technique in Fourier space to measure any remaining radial velocity offset of the RVS spectrum relative to the corresponding interpolated theoretical one. The RVS spectra used by CU8 were shifted to their rest wavelength by the CU6 processing (Sect. 2.1.3), therefore no offset should remain in principle. This CU6 shift is based on the combination of the transit radial velocities, however, while the ESP-HS test looks at the single combined spectrum for the source. This can result in a somewhat different radial velocity, and thus the ESP-HS test provides an independent way of validating the correctness of the CU6 radial velocity determination.
The ESP-HS module applies the radial velocity offset it measures to proceed further with the astrophysical parameter determination by fitting both BP/RP and RVS data. While the value of this CU8 offset shift is not published in DR3, it is kept for validation purposes and provides an a posteriori check on the CU6 results. An interesting point of this test is that it can be applied to a much larger number of stars, as we do not need a reference value for the radial velocity. Figure 7 shows the variation in required shift with the effective temperature measured by  ESP-HS. Its median computed between 7500 K and 14 500 K is +1.7 km s −1 , with a half interquantile dispersion of 5.9 km s −1 . These values are low and are consistent with the results found from the comparison with the reference values (Fig. 6). The CU8 results thus confirm that the combined spectra are in the rest frame and that the CU6 determined radial velocities are accurate to within the claimed ±3 km s −1 . The median here has the opposite sign from that in Fig. 6 because this test measures the  required shift of theoretical spectrum to align it to the observed spectrum.

Astrophysical versus template parameters
The improved selection of the best template does not necessarily mean that the DR3 template parameters (rv_template_teff, rv_template_logg, and rv_template_fe_h in the archive) describe the spectral type well. One effect that is responsible for this is the degeneracy between T eff and metallicity in the very short wavelength range covered by RVS.
As an example of this degeneracy, Fig. 8  A further illustration of the difference between the template parameters as used in the radial velocity determination and the astrophysical parameters is shown in Fig. 9. The astrophysical parameters used for this figure are the input parameters discussed in Sect. 2.1.1. The colour scale shows the number of stars having a specific combination of astrophysical and template T eff . Many stars lie close to the diagonal, and the two temperatures agree well. Some stars have a high astrophysical T eff , however, where ReDetermineApHotStars has assigned a low template T eff . Conversely, for stars with an astrophysical T eff ≈ 10 000 K, ReDeter-mineApHotStars sometimes finds a higher T eff . We stress again that the sole purpose of the template T eff is to obtain the best possible radial velocity; it does not necessarily describe the astrophysical properties of the star well.

Hot stars with cool templates
As mentioned in Sect. 2.1.1, we were only able to use a preliminary version of the CU8 astrophysical parameters as input data. However, towards the end of the validation phase of the CU6 results, the CU8 results were available to us. These include the astrophysical parameters determined by the ESP-HS (Creevey et al. 2022). In these data, we found a number of stars for which we used a cool-star template for a star that is now classified by CU8 as a hot star. This can again lead to a systematic offset because the calcium lines in the cool-star template try to fit the Paschen lines in the hot-star observed spectrum. We therefore carefully examined these cases again to determine which provided incorrect radial velocities. On the basis of this, the radial velocities of 20 470 hot stars (i.e. 3.8 % of all hot stars) with cool templates were removed from the DR3 archive.

Number of hot stars
The important difference between DR2 and DR3 discussed in this paper is the extension to 14 500 K of the effective temperature range for which radial velocities are determined. Of the total number of 33 812 183 of stars with radial velocities in DR3, 543 017 lie in the range rv_template_teff = 7000 -14 500 K. The distribution of these hot stars with rv_template_teff, grvs_mag and G magnitude (phot_g_mean_mag) is shown in Fig. 10.
As expected, most of these stars are in the cooler, fainter part of the diagram. We introduced a formal cutoff in magnitude of grvs_mag = 12 mag, so that the S/N of the spectra is high enough for ReDetermineApHotStars to give good results. Some stars that are fainter than this cutoff are shown: this is due to the (sometimes) different value that was used by STA or MTA (see Sect. 3). Figure 10 has no stars with a template of 12 500 K because our list does not contain a synthetic spectrum with this T eff . Figure 11 shows the distribution on the sky of the hot stars whose radial velocity is listed in DR3. As expected, the approximately half a million stars are concentrated in the disk of our Galaxy.

Conclusions
The third Gaia data release (Gaia DR3) is the first data release to contain radial velocities of stars with a template T eff (rv_template_teff) between 7000 and 14 500 K. The archive contains 543 017 stars in this range.
A preliminary run of the pipeline deriving these hot-star radial velocities from the spectra of the Radial Velocity Spectrometer gave unsatisfactory results. The problem is due to the proximity to and systematic blueward offset of the calcium infrared triplet lines to the Paschen hydrogen lines. This leads to a systematic offset in radial velocity if the template does not describe the observed spectrum correctly. For this reason, a specific module was developed that improves the choice of the template. Using this module leads to a much better agreement between the Gaia radial velocities and the reference data. As a sufficiently high S/N is required for the module to be applied, the DR3 archive mostly contains only hot stars with grvs_mag ≤ 12 mag.
The user of the Gaia DR3 hot-star radial velocities should be aware of the following caveats. The template parameters T eff , log g, and [M/H] used by CU6 (rv_template_teff, rv_template_logg, and rv_template_fe_h in the archive) are not necessarily a good description of the spectral type of the star. A magnitude-dependent effect is still present in the hot-star radial velocities of the Gaia DR3 archive. For stars with 8500 ≤ rv_template_teff ≤ 14 500 K and 6 ≤ grvs_mag ≤ 12 mag, this effect can be corrected for as follows: RV corrected = radial_velocity − 7.98 + 1.135 * grvs_mag, where rv_template_teff, grvs_mag, and radial_velocity are the quantities listed in the DR3 archive. This correction has been derived based on the median offsets of the DR3 radial velocities and the reference data. Individual stars can behave quite differently.

Appendix A:
This work presents results from the European Space Agency (ESA) space mission Gaia. Gaia data are being processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC is provided by national institutions, in particular the institutions participating in the Gaia MultiLateral Agreement (MLA). The Gaia mission website is https: //www.cosmos.esa.int/gaia. The Gaia archive website is https://archives.esac.esa.int/gaia.
The Gaia mission and data processing have financially been supported by, in alphabetical order by country: