# 11.3.8 Extended Stellar Parametrizer for Hot Stars (ESP-HS)

Author(s): Yves Frémat

## Goal

ESP-HS aims to derive the astrophysical parameters of stars hotter than 7500 K, by applying assumptions and methods not adopted by GSP-Phot and GSP-Spec. Assuming a Solar chemical composition ([Fe/H] = 0), it derives $T_{\rm eff}$, $\log g$, $A_{\rm G}$, $A_{\rm 0}$, $E(G_{\rm BP}-G_{\rm RP})$, as well as $v\sin i$ when RVS data of sufficient quality is available.

## Inputs

ESP-HS processes targets brighter than magnitude G=17.65. The module input is made of the BP and RP spectra sampled over 120 samples per pass-band prepared by SMSgen, then resampled to 40 wavelength bins by ESP-HS. The data are only considered when it results from the co-addition of more than 5 transits in both pass-bands, and that the SNR integrated over BP and RP is sufficiently high. RVS spectra supposedly in rest frame are taken into account once the SNR per bin (derived by the module) is greater than 10.

In the Apsis workflow, ESP-HS is run after ESP-ELS as it makes use of its output during the target selection. To only process candidate A-, B-, and O-type stars, the target selection is indeed based on the spectral type tag (spectraltype_esphs) provided by the ESP-ELS module (Note that the algorithm used to derive the spectral type tag was initially launched by ESP-HS but it was moved to the upstream module ESP-ELS, while the field name remained.). Also, all suspected emission-line stars, except for Be stars, are not selected based on the value found in the field classlabel_espels. If the target is a Be star, only the BP/RP data is processed.

## Outputs

All the module results are stored in the astrophysical_parameters tables. The parameters/uncertainties and corresponding field names are

A flag, stored in the first digit of field flags_esphs, informs the user about the processing mode adopted to derive the APs. It has value 0 when BP/RP & RVS spectra were used, 1 if only BP/RP was available, 9 if no parameters were derived (e.g. cooler stars).

## Method

The module is working in two modes: RVS+BP/RP and BP/RP-only mode. In the BP/RP-only mode, the astrophysical parameters ($T_{\rm eff}$, $\log g$, $A_{\rm G}$, $A_{\rm 0}$, $E(G_{\rm BP}-G_{\rm RP})$) are inferred by minimizing the weighted squared residuals

 $\chi^{2}=\sum_{k=1}^{n}\frac{(F^{obs.}_{k}-F^{sim.}_{k})^{2}}{\sigma^{2}_{k}}$ (11.29)

where $F^{obs.}_{k}$ and $\sigma_{k}$ are the observed flux and corresponding uncertainties provided by SMSgen for the sample k, and $F^{sim.}_{k}$ is the flux from the simulations obtained by processing the BP/RP spectrum simulator and SMSgen on the A (7000 to 15 000 K) and OB (15 000 to 50 000 K) synthetic spectra libraries.

One minimisation trial is done in 2 consecutive steps. The first step is based on the use of a Nelder-Mead approach (Press et al. 2007) and provides a first estimate of the location of the $\chi^{2}$ minimum in APs space. The second step consists in the use of a Levenberg-Marquardt algorithm (Press et al. 2007) aimed to finalize the minimisation around the local minimum and to derive the covariance matrix. Eight minimisation trials are performed starting from different initial $T_{\rm eff}$ estimates ranging from 7500 to 45 000 K ($\log g$ starting value is 4). They provide eight different estimates of the astrophysical parameters, of which only the AP set that obtained the lowest $\chi^{2}$ is kept. The uncertainty on the parameters is provided by the diagonal of the covariance matrix. At all steps, the correlations between flux samples are ignored.

When RVS spectra of sufficient quality is available (SNR${}_{\mathrm{RVS}}>$10, where the signal-to-noise ratio is computed by the module on the mean spectrum.) the weighted squared residuals of the RVS spectrum is added to the $\chi^{2}$ expression given by Equation 11.3.8. Before starting the minimisation, a parameter determination is performed in BP/RP-only mode. The resulting parameters set is used to perform a first re-normalisation of the RVS spectrum to the corresponding grid-interpolated simulation. Because we may expect that the spectra of hot stars are set to the rest frame (Blomme et al. 2022b) with a lower accuracy than at lower $T_{\rm eff}$, the same APs and simulations are used to estimate the remaining RV offset, as well as the $v\sin i$. Both values are then used to put the spectrum in the star’s rest frame and to perform a final re-normalisation. As for the BP/RP-only mode, the minimisation is performed in two steps, by combining the Nelder-Mead and Levenberg-Marquardt algorithms to provide the final APs and corresponding uncertainties. The APs obtained during the BP/RP-only mode determination are used as a first guess.

Because of the systematics we have noted between the observed and simulated BP/RP spectra above 10 000 K, a temperature dependent median correction was introduced in the simulations. Discrepancies noted in the Bracket continuum were however difficult to compensate. Further, during the same comparisons, we estimated that the uncertainties provided by the SMSgen module for the BP/RP are underestimated by a factor of 5. Therefore, the ESP-HS module only uses the BP/RP spectra between 340 and 800 nm, and rescales the flux uncertainties by a factor of 5.

## Scope

All results were obtained assuming a Solar chemical composition (Asplund et al. 2009). They are provided for stars with spectral type tag (spectraltype_esphs) A, B, or O, brighter than magnitude G=17.65, with BP and RP spectra obtained over more than 5 transits, and with a sufficiently low noise level. During the post-processing, outlying results were filtered out based on processing flags, goodness-of-fit, and uncertainties.

## Results

Not all A,B, and O stars having BP/RP data and being brighter than G=17.65 have astrophysical parameters derived by ESP-HS in Gaia DR3. Due to the post-processing, a fraction of the results have been discarded in an attempt to remove the most outlying estimates. From a comparison with the LAMOST OBA (DR6) astrophysical parameters catalogue, 62 percent of the Galactic A- & B-type stars are expected to be present. On the other hand, from the 612 Galactic O-type stars present in GOSC (Galactic O-type Stars Catalogue Maíz Apellániz et al. 2013), only 186 O-type star APs are published (further considerations on the OBA sample completeness and purity are provided in Creevey et al. 2022). This is a direct consequence of the remaining difficulty to accurately derive astrophysical parameters of hot stars from the analysis of BP/RP data. The almost featureless nature of the spectra makes the AP determination more sensitive to observed vs. synthetic spectra mismatches, and to AP degeneracy. The empirical correction of the simulations and the masking of the Brackett continuum allowed to significantly correct for the temperature bias (still present in GSP-Phot results). However, the trend to systematically underestimate the effective temperature is still present especially above 25 000 K (see $T_{\rm eff}$ and $\log g$ residuals in the corresponding figure in Fouesneau et al. 2022b). At cooler temperatures, the AP determinations are usually consistent with what is expected (see Figure 11.43). We provide a more detailed overview of the observed residuals (off.) and of the half interquantile dispersion (hdisp.) in Table 11.31 (the number of targets under consideration is given in the last column). Comparisons with various catalogue data as well as with isochrones show that the uncertainties provided in the BP/RP-only mode are of the correct order of magnitude, while those obtained in the BP/RP +RVS mode are underestimated by a factor 5 to 10.

## Uses and limitations

We expect that two thirds of the Gaia B and A type stars of the Galaxy have published ESP-HS astrophysical parameters, while only one third belonging to O-type stars survived the post-processing (a more detailed analysis of the completeness is given in Gaia Collaboration et al. 2022c). The spectral type tag (spectraltype_esphs) should however enable the user to get a list of all the candidate OBA stars brighter than G=17.65.

In BP/RP +RVS mode, the module also provides an estimate of the projected rotational velocity. These values were obtained on co-added spectra obtained with known RV offsets for OB stars. While the true RVS LSF is expected to vary (Section 11.2.4), we adopted a Gaussian LSF with median R=11 500. Therefore, the value found in vsini_esphs should be interpreted carefully as it also includes the impact on line broadening of astrophysical and instrumental phenomena not related to stellar rotation. The measurement suffers from similar limitations as those noted for the vbroad estimate made by the CU6 pipeline (Frémat et al. 2022).