# GSPSpec metallicity/logg calibration - Gaia

# Gaia DR3 GSP-spec metallicity/logG calibration

## Calibration of the GSP-spec and ANN atmospheric parameters and chemical abundances

- Calibration of the GSP-Spec atmospheric parameters
- Calibration of the GSP-Spec chemical abundances
- Calibration of the Artificial Neural Networks (ANN) atmospheric parameters
- Downloadable files
- References

### 1. Calibration of the GSP-spec atmospheric parameters

The General Stellar Parametrizer-spectroscopy module (**GSP-Spec)** estimates the chemo-physical parameters from combined RVS spectra of single stars, without additional inputs from astrometric, photometric or spectro-photometric BP/RP data. It provides, among other data, the stellar parameters and the individual chemical abundances of thirteen elements (N, Mg, Si, S, Ca, Ti, Cr, FeI, FeII, Ni, Zr, Ce and Nd). Another workflow, ANN (Artificial Neural Networks), based on a neural network, provides a second set of atmospheric parameters, useful for classification control.

Published **Gaia DR3 GSP-Spec** data are deliberately uncalibrated. Thanks to this, users are free to

- use the data as they come from the GSP-Spec processing
- apply, whenever suggested, the calibrations presented in Recio-Blanco et al. 2022 or
- perform a new calibration tailored to their scientific analysis.

The observed biases with respect to the literature can be partially due to mismatches between observations and reference synthetic spectra if some physical aspects (e.g. stellar rotation, macroturbulence, departures from local thermodynamic and hydrostatic equilibria...) not considered in the modeling become non negligible for some parameters of certain types of stars. This has been partially taken into account in the definition of the quality flags (e.g. *vbroadT*, *vbroadG*, *vbroadM* flags, see Recio-Blanco et al. 2022). It is worth noting that the biases with respect to the literature can be a consequence of the different in methodologies and theoretical assumptions considered in our work as, for instance, different atmosphere models, atomic data or reference Solar abundances. Furthermore, it is important to recall that reference catalogues have their own biases which, although they are generally calibrated (in contrast to the Gaia Archive data), this calibration does not remove all the existent trends.

As a consequence of all the above mentioned points, the results of the bias analysis presented in the following have to be cautiously and thoroughly considered. We recommend that the user to adapt any bias correction to the targeted scientific goal and selected sample. For more details about the GSP-Spec parameter offsets and recommended solutions, we refer to Section 9 in Recio-Blanco et al. 2022. As a summary, we provide the polynomial calibrations associated with Tables 3, 4 and 5 of Recio-Blanco et al. 2022.

NOTE: the information presented in this page is extracted from Recio-Blanco et al. 2022. Therefore, if used, the correspondent citation to this work should be included in your paper.

#### 1.1 Calibration of the surface gravity

The comparison of the surface gravities estimated by GSP-Spec with these of APOGEE-DR17 (Abdurro’uf et al. 2022), GALAH-DR3 (Buder et al. 2021) and RAVE-DR6 (Steinmetz et al. 2020) reveals a median offset of -0.3 dex. In order to minimise this bias, we propose the following polynomial correction for logg:

*log(g)*

_{calibrated}= log(g) + 0.4496 -0.0036 log(g) -0.0224 log(g)^{2}(Eq. 1)where the coefficients of the correction were extracted from *Table 3* of Recio-Blanco et al. 2022 and can be found downloaded below:

#### Download the calibration coefficients here.

#### 1.2 Calibration of the metallicity

Although the best quality sample of GSP-Spec shows almost no median offset in metallicity when compared to the Literature, there are some trends in *[M/H]* with *log(g)* that should be corrected. For instance, giant stars (*log(g)*<3.5) dex show lower metallicities with respect to the Literature while dwarfs (*log(g)*>4) have over-estimated values of *[M/H]*. The modelling of this trend with *log(g)* leads to the following correction for *[M/H]*:

*[M/H]*

_{calibrated}= [M/H] + 0.274 -0.1373 log(g) -0.0050 log(g)^{2}+ 0.0048 log(g)^{3}(Eq. 2)where we recall that the left-hand term depends on the **uncalibrated** surface gravity *log(g)*.

Similarly, for stars in open clusters the following correction is proposed:

*[M/H]*

_{calibrated}= [M/H] -0.7541 + 1.8108 log(g) -1.1779 log(g)^{2}+ 0.2809 log(g)^{3}-0.0222 log(g)^{4}(Eq. 3)

### 2. Calibration of the GSP-spec individual abundances

The calibration of the chemical abundances is similar to that proposed for the metallicity. The abundance of the element X_{1} relative to X_{2} has assigned certain coefficients p_{i} such that the correction reads:

*[X _{1}/X_{2}]_{calibrated} = [X_{1}/X_{2}] + p_{0} + p_{1} log(g) + p_{2} log(g)^{2} + p_{3} log(g)^{3} + p_{4} log(g)^{4} (Eq. 4)*

where the coefficients p_{i} can be found in *Table 4* of Recio-Blanco et al. 2022. In order to avoid extrapolations, a recommended validity interval [log(g)_{min}, log(g)_{max}] is provided in the seventh and eighth columns of *Table 4*. For values of *log(g)* out of this interval, we propose either to exclude this stars from the sample or correct using the values of Eq. 4 evaluated at [*log(g) _{min}, log(g)_{max}*]; that is

- If
*log(g)*<*log(g)*_{min}: use Eq. 4 for*log(g)*_{min} - If
*log(g)*_{min}<*log(g)*<*log(g)*_{max}: use Eq. 4 for*log(g)* - If
*log(g)*>*log(g)*_{max}: use Eq. 4 for*log(g)*_{max}

For *[α/Fe]*, *[Ca/Fe]* and *[S/Fe]* an alternative correction based on the rescaled effective temperature (*t=T _{eff}/5750K*):

*[X*

_{1}/X_{2}]_{calibrated}= [X_{1}/X_{2}] + p_{0}+ p_{1}t + p_{2}t^{2}+ p_{3}t^{3}(Eq. 5)whose coefficients are in the last three rows of *Table 4*. Analogously, a validity interval for the correction with T_{eff} is provided.

#### 2.1 Example of python code for abundance calibrations

See this file for a full python example of the calibration in [Ca/Fe] and [α/Fe] for a sample of stars within 500 pc from the Sun. The query for this test dataset satisfies the criteria for the Calcium abundance sample described in Appendix B of Gaia Collaboration & Recio-Blanco et al.(2022), imposing an additional condition in the maximum geometric distance (Bailer-Jones et al., 2021) of 500 pc, with a relative error lower than 10%.

For a short example of abundance calibration with python see the code below.

from pandas import read_csv import numpy as np #import your libraries #Code to read the astrophysical parameters and abudances #... #------------------------------------------------- #This function is useful to apply the corrections: def AbundanceCal(logg, coeffs, limits): # Impose maximum and minimum in logg logg = limits[0]*(logg<limits[0]) + limits[1]*(logg>limits[1]) + logg*(logg>=limits[0])*(logg<=limits[1]) # Apply the correction correction = np.poly1d(np.flip(coeffs))(logg)# Note the flip function return(correction) #------------------------------------------------- #Read Table 4 data = read_csv("CalibCoeffs_logg.csv", sep=",") # Compute the correction: index_elm = list(data["Elm"]).index("CaFe") # Example for Calcium coeffs = data[["p%i"%i for i in range(5)]].values[index_elm,:] # Read the coefficients. limits = data[["Minlogg", "Maxlogg"]].values[index_elm,:] # Read the validity limits. CaFe_cal = CaFe_unc + AbundanceCal(logg, coeffs, limits)

### 3. Calibration of the ANN atmospheric parameters

The calibration of the *ANN* parameters depends on the signal-to-noise defined for *ANN*; hereafter, S/N_{ANN} (see next section for the conversion table). As in the case of *GSP-Spec*, the corrections for *ANN* parameters have the form:

*X*

_{calibrated}= X_{uncalibrated}+ ∑ p_{i}X^{i}*X*∈

*{T*and the coefficients

_{eff}, log(g), [M/H], [α/Fe]}*p*are summarised in

_{i}*Table 5*and

*Appendix F*in Recio-Blanco et al. 2022. Also, it is recommended not to apply the correction for stars hotter than

*T*>6000 K.

_{eff}

#### 3.1 Equivalence table between RVS and ANN signal-to-noise ratios

ANN | 25 | 30 | 35 | 40 | 50 |
---|---|---|---|---|---|

RVS | [20-24] | (24-40] | (40-68] | (68-108] | (108-∞) |

### 4. Downloadable files

- Coefficients of Tables 3 and 4 for calibrations based on log(g): CalibCoeffs_logg.csv
- Coefficients of Table 4 for calibrations based on T
_{eff}: CalibCoeffs_teff.csv - Coefficients in Table 5 and F.3 for ANN calibrations: CalibCoeffs_ANN.csv
- Example in python: CalibrationExample.py
- Dataset used in the python example: Good_Ca_SolarN.csv

All downloadable from this ZIP file

#### Download Files Here

### 5. References:

- Abdurro'uf, Accetta, K., Aerts, C., Silva Aguirre, V. et al. 2022. April 2022, The Astrophysical Journal Supplement Series, 259, 2, 35.
- Bailer-Jones, C. A. L., Rybizki1, J., Fouesneau1, M., Demleitner, M. et al. 2021. February 2021, The Astronomical Journal, Volume 161, Issue 3, id.147, 24 pp.
- Buder, S., Sharma, S., Koz, J., Amarsi, A. M. et al. 2022. September 2021, Monthly Notices of the Royal Astronomical Society, 506,1,150-201.
- Gaia Collaboration & Recio-Blanco, A., Kordopatis, G., de Laverny, P., Palicio, P.A. et al. 2022. June 2022. Astronomy and Astrophysics, accepted.
- Recio-Blanco, A., de Laverny, P., Palicio, P.A., Kordopatis, G. et al. 2022. June 2022, Astronomy and Astrophysics, in press.
- Steinmetz, M., Guiglion, G., McMillan, P. J. et al. 2022. August 2020, the Astronomical Journal, 160, 2, 83.

When using any of the calibrations provided in this page, we ask you to cite the paper Gaia Data Release 3: Analysis of RVS spectra by the General Stellar Parametrizer from spectroscopy by Recio-Blanco et al. (2022) (Arxiv)