Revisiting the stellar characterisation of CoRoT planet hosts with Gaia

Matthias Ammler-von Eiff 1 , Daniel Sebastian 2 , Jie Yu 3 , Chen Jiang 1 , Eike Guenther 4

  • 1 Max Planck Institute for Solar System Research, Göttingen
  • 2 School of Physics and Astronomy, University of Birmingham, Birmingham
  • 3 School of Computing, Australian National University, Canberra
  • 4 Thuringian State Observatory, Tautenburg

Abstract

The accurate determination of the host star parameters is essential to characterise their orbiting planets. In the PLATO mission, the P5 sample consists of stars with V <= 13 mag, many of which may be too faint for the full characterisation via asteroseismology and ground-based spectroscopy, as planned for the P1 sample. Additionally, these stars tend to be distant, making extinction a more significant factor compared to other PLATO samples.



To assess the limitations of the stellar characterisation and to explore possible solutions in preparation for PLATO, we reviewed the stellar parameters of all 36 CoRoT planet hosts. These are typically faint (V=12-16 mag) and can be as distant as 1 kpc and more.



We identified independent constraints that do no rely on details of stellar modelling, in particular stellar density based on transit light curves and distance from Gaia astrometry. We compared those to published estimates of extinction and effective temperature for CoRoT targets with planets. This way, we can determine how accurate stellar parameters are and reassess extinction. We found that published estimates of extinction and effective temperature do not match the constraints in several cases.



After constraining extinction and effective temperature, we can compute the radii of the host stars from stellar density and Gaia distance in a homogeneous way. To our knowledge, this is the first comprehensive characterisation of the full set of CoRoT host stars using precise distances from Gaia. These findings provide a framework for improving stellar characterisation in the PLATO mission, particularly for faint planet host stars.

Background: Stellar parameters from transit light curves and stellar models

Seager & Mallén-Ornelas (2003)

It is a common approach to derive stellar mass and radius by comparing observed quantities to expectations from stellar evolutionary models. Here, the observed quantities are the stellar density from the transit light curve (above) and the effective temperature obtained from spectroscopy.


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Stellar density can be directly determined from the transit geometry and timing encoded in the observed light curve (Seager & Mallén-Ornelas 2003, Sandford & Kipping 2017). It does not depend on details of stellar modelling.

\rho_\star=\frac{M_\star}{R^3_\star}=\left(\frac{4\pi^2}{P^2G}\right)\left(\frac{(1+\sqrt{F})^2-b^2[1-sin^2(t_{\rm T}\pi/P]}{sin^2(t_{\rm T}/P)}\right)^\frac{3}{2}

Effective temperature is defined by the Stefan-Boltzmann law:

\frac{L}{L_\odot}=\left(\frac{R}{R_\odot}\right)^2\left(\frac{T_{\rm eff}}{T_{\rm eff, \odot}}\right)

The stellar evolutionary models predict values for these quantities at different age and mass. These evolutionary tracks (solid lines in the figure below) are compared to the error bars of observations (open rectangle). Then, the radius can be computed from the density and the constrained mass.

Deleuil et al. (2008)

The caveat is that not only the evolutionary tracks are affected by uncertainties in stellar modeling but also the derived effective temperature depends on details of modelling stellar spectra lines. Thus, an independent prior on effective temperature is important.

Interstellar extinction - a challenge for characterising distant planet hosts

Zucker et al. (2022)

  1. Our main interest is Sun-like stars with planets as far as about 1kpc. They are particularly interesting because we can study planetary systems in Galactic regions beyond the Local Bubble.
  2. This set of stars overlaps with the PLATO P5 sample (as faint as V=13).
  3. Obviously, these distant stars will be affected by extinction by interstellar dust and gas and thus be reddened. This way, extinction mimicks a cool effective temperature of the star.



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Clearing the haze in the near-infrared...

Extinction is about 0.078 times the V band extinction (Wang & Chen, 2019). Therefore, the use of near-infrared photometry mitigates the impact of interstellar extinction on the determination of stellar parameters.


Reaching out with Gaia

Ammler-von Eiff et al. in prep.

  1. In the presence of extinction, a stars appears more distant and cooler than its true radius and effective temperature would suggest.
  2. Nowadays, the distances are well-known from Gaia for stars as distant as 1 kpc and more.
  3. The Gaia astrometric distance can be used to validate effective temperature and other stellar parameters by a comparison to the spectroscopic distance which is computed from these parameters:


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\newcommand{\BCV}{B.C._{\rm V}} \newcommand{\Mbolsun}{M_{{\rm bol},\odot}} {\log}d=\frac{1}{5}(V-A_{\rm V}-\BCV-\Mbolsun+5)+\frac{1}{3}\left( {\log}\frac{M}{M_{\odot}}-{\log}\frac{\rho}{\rho_{\odot}} \right)+2{\log}\frac{T_{\rm eff}}{T_{\mathrm{eff},{\odot}}}
Towards lifting the degeneracy

This comparison is very sensitive to errors in effective temperature. However, it cannot be used to constrain effective temperature since the sensitivity to errors in the absorption coefficient is high as well:

In the near-infrared, the effect of interstellar extinction and thus the absorption coefficient is much reduced. Therefore, we can essentially compute effective temperature form distance in the near-infrared since AKs will be very small.

\newcommand{\Ks}{{\rm K}_{\rm s}} \newcommand{\AKs}{A_{\Ks}} \newcommand{\Ksmag}{K_{\rm s}} \newcommand{\BCKs}{B.C._{\rm K_s}} \newcommand{\Mbolsun}{M_{{\rm bol},\odot}} {\log}d=\frac{1}{5}(\Ksmag-A_{\Ksmag}-\BCKs-\Mbolsun+5)+\frac{1}{3}\left( {\log}\frac{M}{M_{\odot}}-{\log}\frac{\rho}{\rho_{\odot}} \right)+2{\log}\frac{T_{\rm eff}}{T_{\mathrm{eff},{\odot}}}

Results: Updates on CoRoT-2!

The computation has been exercised for the case of CoRoT-2. Effective temperature is computed from distance in the near-infrared. The other parameters are well-known (Ks band magnitude, stellar density) or a rough estimate is sufficient (absorption coefficient, bolometric correction, mass).

\newcommand{\Ks}{{\rm K}_{\rm s}} \newcommand{\AKs}{A_{\Ks}} \newcommand{\Ksmag}{K_{\rm s}} \newcommand{\BCKs}{B.C._{\rm K_s}} \newcommand{\Mbolsun}{M_{{\rm bol},\odot}} {\log}d=\frac{1}{5}(\Ksmag-A_{\Ksmag}-\BCKs-\Mbolsun+5)+\frac{1}{3}\left( {\log}\frac{M}{M_{\odot}}-{\log}\frac{\rho}{\rho_{\odot}} \right)+2{\log}\frac{T_{\rm eff}}{T_{\mathrm{eff},{\odot}}}

gives for CoRoT-2: 5560+-180K

compares to published value (Alonso et al., 2008): 5625+-120K


An independent proxy for the (small) absorption coefficient in the Ks band has been adopted from extinction maps. Bolometric correction is used from SED fitting but allowing for large range of possible values. Also, a large range in mass is sampled. Because of low sensitivity to these parameters, the distribution of resulting effective temperature values remains narrow. MCMC is used to sample the distributions of parameters and obtain a likely range of effective temperature.

The resulting value for effective temperature enters the computation in the V band to obtain a range for the absorption coefficient:

\newcommand{\BCV}{B.C._{\rm V}} \newcommand{\Mbolsun}{M_{{\rm bol},\odot}} {\log}d=\frac{1}{5}(V-A_{\rm V}-\BCV-\Mbolsun+5)+\frac{1}{3}\left( {\log}\frac{M}{M_{\odot}}-{\log}\frac{\rho}{\rho_{\odot}} \right)+2{\log}\frac{T_{\rm eff}}{T_{\mathrm{eff},{\odot}}}

tentatively for CoRoT-2: AV=0.93+-0.13

compares to published value (e.g. Schroeter et al., 2011): 0.5

Eventually, mass and radius can be computed from the Stefan-Boltzmann law and mass from stellar density:

V band radius & mass in solar units:

  1. radius: 0.91+-0.08
  2. mass: 1.0+-0.3

Ks band radius & mass in solar units:

  1. radius: 0.93+-0.06
  2. mass: 1.1+-0.2

Published values (Alonso et al., 2008):

  1. radius: 0.90+-0.02
  2. mass: 0.97+-0.06

The resulting effective temperature, mass, and radius agree well with previously published values while the absorption coefficient differs significantly. This is a major outcome for the example of CoRoT-2.

Goals

Main question: Can we get more accurate parameters for stars with planets?

Where we are...

We know the mass and radius of a transiting exoplanet if we know the mass and radius of the host star.

Challenges

  1. The determination of absolute stellar mass and radius is affected by limitations in stellar modelling.
  2. Distant planetary systems are particularly interesting but spectroscopic, asteroseismic, and other methods work best for host stars in the solar neighbourhood.
  3. The study of distant stars suffers from extinction.

Solution

We get a better constraint on stellar luminosity and radius by combining direct measurements, incl.

  1. accurate distances from Gaia
  2. stellar density from transit light curves
  3. near-infrared and visual photometry

What we are showing here ...

Here, we apply to stars from the CoRoT mission to see if the approach works.

This approach can be particulalry useful for the fainter stars in the PLATO space mission.

Have a look into the image boxes to learn more ...

Conclusions

Summary

Open issues & caveats

Astrometric distances and transit geometry validate parameters of host star.


Inclusion of near-infrared photometry lifts degeneracy of Teff and AV.


Works for CoRoT targets with planets (faint targets, like fainter PLATO targets).


Approach not impacted by limited knowledge of stellar physics -> calibrate/validate stellar models?

Sign/definition of bolometric corrections & how good are they in Ks?


AKs/AV is not uniform and can differ along line of sight!

References & acknowledgments

Alonso et al. (2008), A&A 482L, 21

Deleuil et al. (2008), A&A 491, 889

Schroeter et al. (2011), A&A 532A, 3

Seager & Mallén-Ornelas (2003), ApJ 585, 1038

Sandford & Kipping (2017), AJ 154, 228

Wang & Chen (2019), PASP 111, 63

Zucker et al. (2022), Nature 601, 334

This work was supported in part by DLR (Deutsches Zentrum f\"ur Luft- und Raumfahrt) grants 50OO1501 and 50OP1902 "PLATO Data Center" at the Max Planck Institute for Solar System Research.