Modeling Proxima Centauri b with ReflectX and Picaso/Virga

Can we distinguish Proxima Centauri b atmosphere cases with ELTs like GMT/GMagAO-X?

Known Prox Cen/ Prox Cen b parameters:

Param	Value	Ref
semi-major axis	0.048 au	Faria et al. 2022
period	11.19 d	Faria et al. 2022
eccentricity	0.02	Faria et al. 2022
Mp*sin(incl)	1.07 Mearth	Faria et al. 2022
equil. temp.	230 K	Anglada-Escude et al. 2016
Star Teff	3000 K	Approx value from several refs
Star radius	0.14 Rsun	Faria et al. 2022
Star SpT	M5.5V	Faria et al. 2022
Star log(Luminosity)	-2.8 +0.1/-0.2	Faria et al. 2022
log(g)	5.2 cm s^-2	Faria et al. 2022
metallicity	0.21 dex	Schlaufman and Laughlin 2012

No Atmosphere Models

The first case is an airless rocky planet. In this case, we will simply observe the star’s spectrum reflecting from the surface, with a planet-star contrast determined by the albedo of the planet’s surface composition. We used Eqn 1 from Cahoy et al. 2010 for the contrast of a given Lambertian sphere with albedo \(A_g\) , radius \(R_p\) , separation \(\rho\) , and phase angle \(\alpha\)

\[C(\alpha) = A_g(\lambda) \left( \frac{R_p}{\rho} \right)^2 \left[ \frac{\sin(\alpha) + (\pi - \alpha)\cos(\alpha)}{\pi} \right]\]

Since Prox Cen b is an RV detected planet, the orbital inclination is unconstrained. The value of orbital inclination will affect the true mass of the planet, and consequently the radius, and also the phase angle as a function of orbit phase.

The figure on the left shows the observer’s phase angle as a function of orbital phase (expressed in degrees, where 0 degrees is the inferior conjunction and 360 degrees is one complete orbit) as a function of five values of orbital inclinations.

Each inclination will correspond to a different true mass of the planet and thus different radius. We computed mass/radius for a range of inclinations. To estimate radius we used an emperical mass-radius relation.

Incl (deg)	Mass (Mearth)	Radius (Rearth)
10	6.2	2.1
20	3.1	1.46
30	2.1	1.30
45	1.5	1.15
60	1.2	1.07
70	1.1	1.04
80	1.0	1.0

Placing these four Mass/Radii on a density plot:

The four above estimated mass/radii are plotted as the black triangles. The solid curves represent theoretical density curves from Zeng & Sasselov 2013 (downloaded from Harvard CfA) for airless planets of varying compositions: pure iron (100% Fe), Earth-like rocky (32.5% Fe, 67.5% MgSiO3), pure rock (100% MgSiO3), pure water (100% H2O), and 50% H2O 50% Earth-like rocky core. The red dashed lines show models of an Earth-like rocky planet with varying percent H2 envelope by mass. We see that the three least massive planets fall nicely on the Earth-like density line, while the most massive is consistent with an Earth-like planet with a 1% H2 envelope. We did not estimate uncertainties on the Prox Cen b densnity estimates, so this analysis is used as a rough estimate of what is likely to be found on this planet.

Albedo

We used the wavelength-dependent albedos as a function of surface type for airless rocky planets from Hu et al. 2012 (excluding surfaces unlikely to exist at these temperatures). The plot below shows the relevant surface-type contrast curves for a planet with inclination = 60 deg and viewed at quadrature (phase = 90 deg), with broadband filters \(g^\prime\), \(r^\prime\), \(i^\prime\), \(z^\prime\), \(J\), and \(H\) shown below.

The metal-rich and ice-rich surfaces show the most variation across the observing bands, and will be distinguishable from the rest in color-color space. The filter combinations with the highest distinguishing power involve comparisons between optical and NIR bands. Below shows each surface type in \(J - H\) vs \(i^\prime - H\) color, in which metal-rich and ice-rich are separated from the rest by over half a magnitude.

A color-magnitude diagram provides even more distinguishing power. Below is shown an \(H - i^\prime\) vs \(z^\prime\) contrast CMD in which metal-rich is separated from clay/feldspathic/granitoid by 2 magnitudes, and the rest by over half a magnitude. Clay/feldspathic/granitoid would likely not be distinguishable in CMD or color-color space.

Atmosphere Models