Retrieving stellar parameters and dynamics of AGB stars with Gaia parallax measurements and CO5BOLD RHD simulations
E. Béguin A. Chiavassa A. Ahmad B. Freytag S. Uttenthaler
 

   
 
   

   Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Lagrange, CS 34229, Nice,  France 

              elysabeth.beguin@oca.eu
            Theoretical Astrophysics, Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden
            Institute of Applied Physics, TU Wien, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria

   

   
   The complex dynamics of asymptotic giant branch (AGB) stars and the resulting stellar winds have a significant impact on the measurements of stellar parameters and amplify their uncertainties. Three-dimensional (3D) radiative hydrodynamic (RHD) simulations of convection suggest that convection-related structures at the surface of AGB star affect the photocentre displacement and the parallax uncertainty measured by Gaia.
  
   We explore the impact of the convection on the photocentre variability and aim to establish analytical laws between the photocentre displacement and stellar parameters to retrieve such parameters from the parallax uncertainty.
  
   We used a selection of 31 RHD simulations with CO^5BOLD and the post-processing radiative transfer code Optim3D to compute intensity maps in the Gaia G band [320–1050 nm]. From these maps, we calculated the photocentre position and temporal fluctuations. We then compared the synthetic standard deviation to the parallax uncertainty of a sample of 53 Mira stars observed with Gaia.
  
   The simulations show a displacement of the photocentre across the surface ranging from 4 to 13 % of the corresponding stellar radius, in agreement with previous studies. We provide an analytical law relating the pulsation period of the simulations and the photocentre displacement as well as the pulsation period and stellar parameters. By combining these laws, we retrieve the surface gravity, the effective temperature, and the radius for the stars in our sample.
  
   Our analysis highlights an original procedure to retrieve stellar parameters by using both state-of-the-art 3D numerical simulations of AGB stellar convection and parallax observations of AGB stars. This will help us refine our understanding of these giants.

   

   Gaia parallax uncertainties and RHD simulations

   Retrieving stellar parameters and dynamics of AGB stars 
 
   with Gaia parallax measurements and CO^5BOLD RHD simulations
    E. Béguin
          1
          A. Chiavassa1
          A. Ahmad2
          B. Freytag2
          S. Uttenthaler3
          
          
          
    Received April 4, 2024; accepted July 16, 2024
======================================================================================================================================================




 


§ INTRODUCTION


Low- to intermediate-mass stars (0.8-8 M_⊙) evolve into the asymptotic giant branch (AGB), in which they undergo complex dynamics characterised by several processes including convection, pulsations, and shockwaves. These processes trigger strong stellar winds <cit.> that significantly enrich the interstellar medium with various chemical elements <cit.>. These processes and stellar winds also amplify uncertainties of stellar parameter determinations with spectro-photometric techniques, like the effective temperature, which in turn impacts the determination of mass-loss rates <cit.>. In particular, Mira stars are peculiar AGB stars, showing extreme magnitude variability (larger than 2.5 mag in the visible) due to pulsations over periods of 100 to 1000 days <cit.>.

In <cit.>, 3D radiative hydrodynamics (RHD) simulations of convection computed with CO^5BOLD <cit.> reveal the AGB photosphere morphology to be made of a few large-scale, long-lived convective cells and some short-lived and small-scale structures that cause temporal fluctuations on the emerging intensity in the Gaia G band [320–1050 nm]. The authors suggest that the temporal convective-related photocentre variability should substantially impact the photometric measurements of Gaia, and thus the parallax uncertainty. In this work, we use 31 recent simulations to establish analytical laws between the photocentre displacement and the pulsation period and then between the pulsation period and stellar parameters. We combine these laws and apply them to a sample of 53 Mira stars from <cit.> to retrieve their effective stellar gravity, effective temperature, and radius thanks to their parallax uncertainty from Gaia Data Release 3[GDR3 website: https://www.cosmos.esa.int/web/gaia/data-release-3] (GDR3) <cit.>.



§ OVERVIEW OF THE RADIATIVE HYDRODYNAMICS SIMULATIONS


In this section, we present the simulations and the theoretical relations between the stellar parameters and the pulsation period. We also present how we compute the standard deviation of the photocentre displacement and its correlation with the pulsation period.



 §.§ Methods


We used RHD simulations of AGB stars computed with the code CO^5BOLD <cit.>. It solves the coupled non-linear equations of compressible hydrodynamics and non-local radiative energy transfer, assuming solar abundances, which is appropriate for M-type AGB stars. The configuration is ‘star-in-a-box’, which takes into account the dynamics of the outer convective envelope and the inner atmosphere. Convection and pulsations in the stellar interior trigger shocks in the outer atmosphere, giving a direct insight into the stellar stratification. Material can levitate towards layers where it can condensate into dust grains <cit.>. However, models used in this work do not include dust. 



We then post-processed a set of temporal snapshots from the RHD simulations using the radiative transfer code Optim3D <cit.>, which takes into account the Doppler shifts, partly due to convection, in order to compute intensity maps integrated over the Gaia G band [320–1050 nm]. The radiative transfer is computed using pre-tabulated extinction coefficients from MARCS models <cit.> and solar abundance tables <cit.>. 



 §.§ Characterising the AGB stellar grid


We used a selection of simulations from <cit.>, <cit.> [abbreviation: F17+C18], <cit.> [abbreviation: A23] and some new models [abbreviation: This work], in order to cover the 2000–10000 L_⊙ range. The updated simulation parameters are reported in Table <ref>. 

In particular, 24 simulations have a stellar mass equal to 1.0  M_⊙, and seven simulations have one equal to 1.5  M_⊙. In the rest of this work, we denote by a 1.0 subscript the laws or the results obtained from the analysis of the 1.0  M_⊙ simulations; and by a 1.5 subscript those obtained from the analysis of the 1.5  M_⊙ simulations. 

The pressure scale height is defined as H_p  =  k_B T_eff/μ g, with k_B the Boltzmann constant, T_eff the effective surface temperature, μ the mean molecular mass, and g the local surface gravity. The lower the surface gravity is, the larger the pressure scale height becomes, and so the larger the convective cells can grow (see Fig. <ref> and <cit.>). 





Moreover, <cit.> estimated that the characteristic granule size scales linearly with H_P. Interplay between large-scale convection and radial pulsations results in the formation of giant and bright convective cells at the surface. The resulting intensity asymmetries directly cause temporal and spatial fluctuations of the photocentre. The larger the cells, the larger the photocentre displacement. This results in a linear relation between the photocentre displacement and the pressure scale height <cit.>.
However, <cit.> found it is no longer true for H_p greater than 2.24 × 10^10cm for both interferometric observations of red supergiant stars and 3D simulations, suggesting that the relation for evolved stars is more complex and depends on H_p (Fig. 18 in the aforementioned article).

Concerning the pulsation period, <cit.> performed a fast Fourier transform on spherically averaged mass flows of the CO^5BOLD snapshots to derive the radial pulsation periods. The derived bolometric luminosity–period relation suggests good agreement between the pulsation periods obtained from the RHD simulations and from available observations. They are reported in columns 9 and 10 in Table <ref>. 

<cit.> found a correlation between the pulsation period and the surface gravity (g∝M_⋆/R_⋆^2, see Eq. (4) in the aforementioned article). Thus, the pulsation period increases when the surface gravity decreases. In agreement with this study, we found a linear relation between log(P_puls) and log(g), see Fig. <ref>. By minimising the sum of the squares of the residuals between the data and a linear function as in the non-linear least-squares problem, we computed the most suitable parameters of the linear law. We also computed the reduced χ̅^2 for the 1.0  M_⊙ simulations and for the 1.5  M_⊙ simulations: χ̅_1.0^2  =  2.2 and χ̅_1.5^2  =  0.4. The linear law found in each case is expressed as follows:  


    log(P_puls)  =  -0.84 ·log(g) + 2.14,  for M_⋆  =  1.0  M_⊙



    log(P_puls)  =  -0.78 ·log(g) + 2.20,  for M_⋆  =  1.5  M_⊙
    .


It is important to note that the χ̅_1.5^2 value is lower than χ̅_1.0^2 because there are only seven points to fit (i.e. seven RHD simulations at 1.5  M_⊙) and they are less scattered.





We compared the pulsation period, P_puls, with the effective temperature, T_eff. <cit.> showed that the pulsation period decreases when the temperature increases. A linear correlation is confirmed with our simulations, as is displayed in Fig. <ref>. However, we do not see any clear differentiation between the law found from the 1.0  M_⊙ simulations and the law from the 1.5  M_⊙ simulations so we chose to use all simulations to infer a law between P_puls and T_eff (Eq. (<ref>) and the black curve in Fig. <ref>). We computed the reduced χ̅^2  =  77 and the parameters of the linear law are expressed as follows: 


    log(P_puls)  =  -5.92 ·log(T_eff) + 23.02
        
    .



<cit.> found a correlation between the pulsation period and the inverse square root of the stellar mean-density (M_⋆/R_⋆^3, see Eq. (4) in the aforementioned article). In agreement with this study, we found a linear correlation between log(P_puls) and log(R_⋆), with R_⋆ the stellar radius (Fig. <ref>). We computed with the least-squares method χ̅_1.0^2  =  2.0 and χ̅_1.5^2  =  0.4 and the parameters of the linear law are expressed as follows:


    log(P_puls)  =  1.68 ·log(R_⋆) - 1.59,  for M_⋆  =  1.0  M_⊙



    log(P_puls)  =  1.54 ·log(R_⋆) - 1.36,  for M_⋆  =  1.5  M_⊙
    .




We compared our results with the relation found by <cit.> — log(P_puls)  =  -2.07 + 1.94 log(R_⋆/R_⊙) - 0.9 log(M_⋆/M_⊙) — and with the fundamental mode of long-period variables, Eq. (12), found by <cit.> (see Figs. <ref> and <ref>). We used the solar metallicity and helium mass function from <cit.> and the reference carbon-to-oxygen ratio from <cit.>. Overall, we have the same trends, but we notice that the laws we obtained are less steep than the relation from <cit.> and the fundamental mode from <cit.>, meaning that the pulsation periods of our simulations are shorter than expected.









 §.§ Photocentre variability of the RHD simulations in the Gaia G band


For each intensity map computed (for example, Fig. <ref>), we calculated the position of the photocentre as the intensity-weighted mean of the x-y positions of all emitting points tiling the visible stellar surface according to


    P_x  =  ∑ ^N _i=1∑ ^N _j=1 I(i,j) · x(i,j)/∑ ^N _i=1∑ ^N _j=1 I(i,j)



    P_y  =  ∑ ^N _i=1∑ ^N _j=1 I(i,j) · y(i,j)/∑ ^N _i=1∑ ^N _j=1 I(i,j)
    ,


where I(i,j) is the emerging intensity for the grid point (i,j) with co-ordinates x(i,j),y(i,j) and N the number of points in each co-ordinate of the simulated box.

Large-scale convective cells drag hot plasma from the core towards the surface, where it cools down and sinks <cit.>. Coupled with pulsations, this causes optical depth and brightness temporal and spatial variability, moving the photocentre position <cit.>. Thus, in the presence of brightness asymmetries, the photocentre will not coincide with the barycentre of the star. Figure <ref> displays the time variability of the photocentre position (blue star) for three snapshots of the simulation st28gm05n028. The dashed lines intersect at the geometric centre of the image.

We computed the time-averaged photocentre position, ⟨ P_x ⟩ and ⟨ P_y ⟩, for each Cartesian co-ordinate in astronomical units, [AU], the time-averaged radial photocentre position, ⟨ P ⟩ as ⟨ P ⟩  =  (⟨ P_x ⟩ ^2+⟨ P_y ⟩^2)^1/2, and its standard deviation, σ_P, in AU and as a percentage of the corresponding stellar radius, R_⋆ [% of R_⋆] (see Table <ref>). 

Figure <ref> displays the photocentre displacement over the total duration for the simulation st28gm05n028, with the average position as the red dot and σ_P as the red circle radius (see additional simulations in Figs. B1 to B21, available on Zenodo[https://zenodo.org/records/12802110]).






We also computed the histogram of the radial position of the photocentre for every snapshot available of every simulation (Fig. <ref>). The radial position is defined as P=(P_x^2+P_y^2)^1/2 in % of R_⋆. We notice that the photocentre is mainly situated between 0.05 and 0.15 of the stellar radius.





 §.§ Correlation between the photocentre displacement and the stellar parameters


After the correlations between P_puls and the stellar parameters (log(g), T_eff and R_⋆), we studied correlations between P_puls and the photocentre displacement, σ_P, displayed in Fig. <ref>. The pulsation period increases when the surface gravity decreases (Fig. <ref>); in other words, when the stellar radius increases. The photocentre gets displaced across larger distances <cit.>. We notice a correlation for each sub-group that we approximated with a power law, whose parameters were determined with a non-linear least-squares method (see Eq. (<ref>) and (<ref>)):




    log(P_puls)  =  3.38 · x^0.12,  with x  = σ_P or x  =  σ_ϖ



    log(P_puls)  =  3.44 · x^0.13,  with x  = σ_P or x  =  σ_ϖ
    .


The resulting reduced χ̅^2 are χ̅_1.0^2∼ 161 and χ̅_1.5^2∼ 2. As before, we note a stark difference because there are fewer 1.5   M_⊙ simulations and they are less scattered.



§ COMPARISON WITH OBSERVATIONS FROM THE GAIA MISSION


From the RHD simulations, we found analytical laws between the pulsation period and stellar parameters and between the pulsation period and the photocentre displacement, which were used to estimate the uncertainties of the results. We used these laws with the parallax uncertainty, σ_ϖ, measured by Gaia to derive the stellar parameters of observed stars. 



 §.§ Selection of the sample


To compare the analytical laws with observational data, the parameters of the observed stars need to match the parameters of the simulations. <cit.> investigated the interplay between mass-loss and third dredge-up (3DUP) of a sample of variable stars in the solar neighbourhood, which we further constrained to select suitable stars for our analysis by following these conditions: (i) Mira stars with an assumed solar metallicity, (ii) a luminosity, L_⋆, lower than 10000 L_⊙, and σ_L_⋆ / L_⋆ < 50 %, σ_L_⋆ being the uncertainty on the luminosity, and (iii) the GDR3 parallax uncertainty, σ_ϖ, lower than 0.14 mas. We also selected stars whose (iv) renormalised unit weight error (RUWE) is lower than 1.4 <cit.>. This operation resulted in a sample of 53 Mira stars (Table <ref>).

The pulsation periods were taken mainly from <cit.> where available, or were also collected from VizieR. Preference was given to sources with available light curves that allowed for a critical evaluation of the period, such as the All Sky Automated Survey <cit.>. Since some Miras have pulsation periods that change significantly in time <cit.>, we also analysed visual photometry from the AAVSO[https://www.aavso.org/] database and determined present-day periods with the program Period04[http://period04.net/] <cit.>.
The analysis of <cit.> provided a period variability of the order of 2.4 % of the respective pulsation period for Miras in the solar neighbourhood.

The luminosities were determined from a numerical integration under the photometric spectral energy distribution between the B-band at the short end and the IRAS 60 μ m band or, if available, the Akari 90 μ m band. A linear extrapolation to λ=0 and ν=0 was taken into account. The photometry was corrected for interstellar extinction using the map of <cit.>. We adopted the GEDR3 parallaxes and applied the average zero-point offset of quasars found by <cit.>: -21  mas.
Two main sources of uncertainty on the luminosity are the parallax uncertainty and the intrinsic variability of the stars. The uncertainty on interstellar extinction and on the parallax zero-point were neglected. 

The RUWE[https://gea.esac.esa.int/archive/documentation/GDR2/, Part V, Chapter 14.1.2] is expected to be around 1.0 for sources where the single-star model provides a good fit to the astrometric observations. Following <cit.>, we rejected stars whose RUWE is above 1.4 as their astrometric solution is expected to be poorly reliable and may indicate unresolved binaries. 


Figure <ref> displays the location of stars in a pulsation period-luminosity diagram with the colour scale indicating the number of good along-scan observations — that is, astrometric_n_good_obs_al data from GDR3 (top panel) — or indicating the RUWE (bottom panel).
We investigated whether the number of times a star is observed, N_obs, or the number of observed periods, N_per, is correlated with RUWE. We do not see improvements of the astrometric solution when more observations are used to compute it. 



Information about the third dredge-up activity of the stars is available from spectroscopic observations of the absorption lines of technetium <cit.>. Tc-rich stars have undergone a third dredge-up event and are thus more evolved and/or more massive than Tc-poor stars. Also, since ^12C is dredged up along with Tc, the C/O ratio could be somewhat enhanced in the Tc-rich compared to the Tc-poor stars. However, as our subsequent analysis showed, we do not find significant differences between Tc-poor and Tc-rich stars with respect to their astrometric characteristics; hence, this does not impact our results.



 §.§ Origins of the parallax uncertainty


The uncertainty in Gaia parallax measurements has multiple origins: (i) instrumental <cit.>, (ii) distance <cit.>, and (iii) convection-related <cit.>. This makes the error budget difficult to estimate. In particular, only with time-dependent parallaxes with Gaia Data Release 4 will the convection-related part be definitively characterised <cit.>. 
Concerning the distance and instrumental parts, <cit.> investigated the bias of the parallax versus magnitude, colour, and position and developed an analytic method to correct the parallax of these biases. For comparison, the parallax and the corrected parallax are displayed in Table <ref>, columns 8 and 9, respectively.
In this work, we assume that convective-related variability is the main contributor to the parallax uncertainty budget, which is already hinted at in observations; thus, σ_P is equivalent to σ_ϖ. 

Indeed, optical interferometric observations of an AGB star showed the presence of large convective cells that affected the photocentre position. It has been shown for the same star that the convection-related variability accounts for a substantial part of the Gaia Data Release 2 parallax error <cit.>. 



 §.§ Retrieval of the surface gravity based on the analytical laws


In Section <ref>, we established an analytical law, Eq. (<ref>),  between σ_P and P_puls with the 1.0  M_⊙ simulations. We used it to calculate the pulsation period, P_1.0, of the stars from observed σ_ϖ. We defined Δ P_1.0, the relative difference between the observed pulsation period, P_obs, and our results as Δ P_1.0  =  P_obs-P_1.0/P_obs. This intermediate step gives an estimation of the error when computing the pulsation period and comparing it with observations. This error can then be used as a guideline to estimate the uncertainties of the final results; in other words, of the effective temperature, the surface gravity, and the radius of the stars in our sample.

The top panel of Figure <ref> displays  P_obs versus σ_ϖ as dots and P_1.0 versus σ_ϖ as the dashed red curve. 
The bottom panel displays the histogram of the relative difference, Δ P_1.0, and the cumulative percentage of the observed sample. The same colour scale is used in both panels: for example, light yellow represents a relative difference between P_1.0 and P_obs of less than 5 %, while purple represents a relative difference greater than 60 % (column 3 in Table <ref>). 

Δ P_1.0 ranges from 0.4 % to 72 %, with a median of 16 % (i.e. from 1 to 68 days' difference). For 85 % of the sample stars, Δ P_1.0 is ≤ 30 %, and for 57 %, it is ≤ 20 %, suggesting we statistically have a good agreement between our model results and the observations.






We then combined Eqs. (<ref>) and (<ref>) to derive the surface gravity (log(g_1.0)) directly from σ_ϖ (column 6 in Table <ref>). The top left panel of Figure <ref> displays log(P_obs) versus log(g_1.0) and Eq. (<ref>) as the dashed red curve. We notice that the calculated log(g_1.0) values follow the same trend as log(g) from the simulations and are the most accurate when closest to the line.

We performed the same analysis with the analytical laws from the 1.5  M_⊙ simulations. The top panel of Figure <ref> displays the calculated P_1.5 versus σ_ϖ and the bottom panel displays a histogram of the relative difference between P_1.5 and P_obs defined as Δ P_1.5 (column 5 in Table <ref>). The same colour code is used in both panels. We combined Eqs. (<ref>) and (<ref>) to compute log(g_1.5). Fig. <ref> displays log(P_obs) from the simulations versus log(g_1.5).

For the 1.5  M_⊙ simulations, Δ P_1.5 ranges from 0.6 % to 62 %, with a median of 16 % (i.e. from 1 to 76 days' difference). For 81 % of the sample stars, Δ P_1.5 is ≤ 30 %, and for 70 %, it is ≤ 20 %.

Qualitatively, we observe two different analytical laws depending on the mass of the models used to infer the laws. However, a larger grid of simulations, covering the mass range of AGB stars, would help to confirm this trend, tailor the analytical laws to specific stars, and predict more precise stellar parameters.






 §.§ Retrieval of the other stellar parameters


We repeated the same procedure to retrieve the stellar radius, R_1.0, and the effective temperature, T_1.0 (columns 8 and 10 in Table <ref>). Combining Eqs. (<ref>) and (<ref>), we computed the radius, R_1.0. The top central panel of Figure <ref> displays log(P_obs) versus log(R_1.0). 
Combining the Eqs. (<ref>) and (<ref>), we computed the effective temperature, T_1.0 (Fig. <ref>, top right panel). 
As in Section <ref> for log(g_1.0), the calculated log(R_1.0) follow the Eq. <ref> derived from the simulations, and log(R_1.0) follow Eq. <ref>.

We repeated the same procedure for the 1.5  M_⊙ simulations to retrieve R_1.5 and T_1.5 (columns 9 and 11 in Table <ref>). The results are displayed in the bottom central and right panels of Fig. <ref>.



For comparison, R Peg has been observed with the interferometric instrument GRAVITY/VLTI in 2017, which provided a direct estimation of its radius: R_Ross  =  351^+38_-31 R_⊙ <cit.>. From our study, R_1.0,RPeg  =  321^+5_-15 R_⊙ and R_1.5,RPeg  =  373^+5_-14 R_⊙, which is in good agreement with the results of <cit.>. With future interferometric observations, we shall be able to further validate our results. 



§ SUMMARY AND CONCLUSIONS


We computed intensity maps in the Gaia band from the snapshots of 31 RHD simulations of AGB stars computed with CO^5BOLD. The standard deviation of the photocentre displacement, σ_P, due to the presence of large convective cells on the surface, ranges from about 4 % to 13 % of its corresponding stellar radius, which is coherent with previous studies and is non-negligible in photometric data analysis. It becomes the main contributor to the Gaia parallax uncertainty σ_ϖ budget. The dynamics and winds of the AGB stars also affect the determination of stellar parameters and amplify their uncertainties. It becomes worth exploring the correlations between all these aspects to eventually retrieve such parameters from the parallax uncertainty.

We provided correlations between the photocentre displacement and the pulsation period as well as between the pulsation period and stellar parameters: the effective surface gravity, log(g), the effective temperature, T_eff, and the radius, R_⋆. We separated the simulations into two sub-groups based on whether their mass is equal to 1.0 or 1.5  M_⊙. Indeed, the laws we provided, and the final results, are sensitive to the mass. A grid of simulations covering a larger range of masses, with a meaningful number of simulations for each, would help confirm this observation and establish laws that are suitable for varied stars. This will be done in the future.

We then applied these laws to a sample of 53 Mira stars matching the simulations' parameters. We first compared the pulsation period with the literature: we obtained a relative error of less than 30 % for 85 % of the stars in the sample for the first case and 81 % for the second, which indicates reasonable results from a statistical point of view. This error can then be used as a guideline to estimate the uncertainties of the final results. We then computed log(g), T_eff and R_⋆ by combining the analytical laws (Table <ref>). 

While mass loss from red giant branch stars should be mainly independent of metallicity, it has been suggested that this is less true for AGB stars <cit.>. Photocentre displacement and stellar parameters may be dependent on metallicity and this question needs to be further studied.

We argue that the method used for Mira stars presented in this article, based on RHD simulations, can be generalised to any AGB stars whose luminosity is in the 2000–10000 L_⊙ range and that have a Gaia parallax uncertainty below 0.14 mas. Figure <ref> sums up the analytical laws found in this work that can be used to calculate the stellar parameters.

Overall, we have demonstrated the feasibility of retrieving stellar parameters for AGB stars using their uncertainty on the parallax, thanks to the employment of state-of-the-art 3D RHD simulations of stellar convection. The future Gaia Data Release 4 will provide time-dependent parallax measurements, allowing one to quantitatively determine the photocentre-related impact on the parallax error budget and to directly compare the convection cycle, refining our understanding of AGB dynamics. 


This work is funded by the French National Research Agency (ANR) project PEPPER (ANR-20-CE31-0002). BF acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme Grant agreement No. 883867, project EXWINGS. The computations were enabled by resources provided by the Swedish National Infrastructure for Computing (SNIC). This work was granted access to the HPC resources of Observatoire de la Côte d’Azur - Mésocentre SIGAMM.


aa 
 


 


§ TABLES













  


§ APPENDIX C: M DWARFS VERSUS AGB STARS PARALLAX UNCERTAINTY


Our key assumption is that the parallax uncertainty budget in the Mira sample is dominated by the photocentre shift due to the huge AGB convection cells. To test this assumption, one would need a comparison sample of stars with similar properties such as apparent G magnitude, distance, G_BP-G_RP colour, etc., but ideally without surface brightness inhomogeneities. M-type dwarfs could be useful for a comparison because they have similar G_BP-G_RP colour as our Miras. Therefore, we searched the SIMBAD database for M5 dwarfs with G<15 mag, which yielded a sample of 240 objects. The list was cross-matched with the Gaia DR3 catalogue. Obvious misidentifications between SIMBAD and Gaia with G>15 were culled from the list. A Hertzsprung-Russell diagram based on M_G vs. G_BP-G_RP revealed that the sample still contained several misclassified M-type giant stars. Removing them retained a sample of 99 dwarf stars that have comparable G_BP-G_RP colour to the Miras sample. However, as M dwarfs are intrinsically much fainter than Miras, the dwarf stars are much closer to the sun than the Miras: their distances vary between ∼7 and 160 pc, whereas our Mira sample stars are located between 300 and over 5000 pc from the sun. Furthermore, we noticed that a significant fraction of the dwarfs have surprisingly large parallax uncertainties. These could be related to strong magnetic fields on the surfaces of these dwarfs that are the cause of bright flares or large, dark spots, creating surface brightness variations similar to those expected in the AGB stars. A detailed investigations into the reasons for their large parallax uncertainties is beyond the scope of this paper. We therefore decided to not do the comparison with the M dwarfs.

Luckily, the contaminant, misclassified (normal) M giants in the Simbad search appear to be a much better comparison sample. They have overlap with the Mira stars in G magnitude and are at fairly similar distances, between ∼260 and 1700 pc. The only drawbacks are that the normal M giants are somewhat bluer in G_BP-G_RP colour than the Miras, and we found only ten suitable M giants in our limited search. Fig. <ref> illustrates the location of the M giants together with the Mira sample and the M dwarfs in an HR diagram.

Importantly, we note that the parallax uncertainties of the M giants are all smaller than those of the Miras. This is shown in Fig. <ref>, where the logarithmic value of the parallax uncertainty is plotted as a function of the logarithm of the distance (here simply taken as the inverse of the parallax). On average, the M giants have parallax uncertainties that are smaller by a factor of 3.5 than those of the Miras. As the M giants are more compact than the Miras and have smaller pressure scale heights, it is plausible that the larger parallax uncertainties of the Miras indeed result from their surface convection cells. We therefore conclude that our key assumption is correct.







