Could we observe exomoons in the beta Pictoris system?

Evangelia Kleisioti ¹ , Dominic Dirkx ² , Marc Rovira-Navarro ^2,3 , Matthew Kenworthy ¹

Abstract

There are more than 200 moons in the Solar System, however no confirmed exomoons have been convincingly detected so far. Extrasolar gas giants are expected to host exomoons, which could scale in mass with their parent planet up to Earth radii. Two of the gas giant planet moon systems are in long-lived mean motion resonances (MMR) and it is expected that the latter would prevail in extrasolar systems as well. Since tidal dissipation depends on the orbital and physical properties of the system, there is a chance that Tidally Heated Exomoons (THEMs; Peters and Turner 2015) are detectable with current instrumentation and/or the JWST in infrared (IR) wavelengths if tidal heating is vigorous enough. β Pictoris is a 23 Myr old star with a distance of 19.44 pc. A ~10 Mj directly imaged planet is orbiting the star at 10.31 AU. The proximity to Earth and the fact that the system is almost edge-on makes β Pictoris b a suitable candidate for the search of THEMs in the IR. Taking the Jovian satellites as an archetype for an exomoon system around β Pictoris b, this would mean that an MMR between two or more exomoons would maintain tidal activity over the lifetime of the system and make them detectable for larger timescales. We explore the parameter space of exomoon orbital and physical properties and conclude which values would make an exomoon around β Pictoris b detectable via photometry. We also investigate the interior structures of the putative exomoon that are consistent with these properties. We use orbital-thermal models that assume a layered, radially symmetric moon, consisting of a silicate mantle and a liquid core. We present our results for different rheology models (Maxwell, Andrade) and heat transfer mechanisms (mantle convection, heat piping) and constrain feasible interior models and orbital parameters for a putative (observed) surface heat flux.

Tidally Heated Exomoons (THEMs)

Opportunity to detect exomoons

*Figure 1: Io in the IR (Credits: NASA/Jet Propulsion Laboratory)*

Since more than 200 moons exist in the Solar System, it is expected that they orbit exoplanets as well. Detecting an exomoon could set the next milestone in observations of exoplanetary systems.

Tidal interactions between planets and their satellites can heat a satellite’s interior. The most evident example is Io (Figure 1), which is the most tidally active body in the Solar System. Since tidal dissipation depends on the orbital and physical properties of the system, if tidal heating is vigorous enough in exoplanetary systems, there is a chance that Tidally Heated Exomoons (THEMs; Peters and Turner 2015) are detectable with current instrumentation and/or the JWST in infrared (IR) wavelengths. Recently, Rovira-Navarro et al. (2021) studied the thermal states of THEMs for different orbital configurations and investigated their longevity. As a direct result of tidal heating, spectral signatures of volcanic activity could also be a method of detecting THEMs (Oza et al. 2019).

Tides and eccentric orbit

Tidal dissipation within the satellite is linked to the eccentricity of the orbit (Figure 2). An eccentric orbit causes periodic deformation of the satellite. The latter combined with the viscous nature of the satellite cause tidal dissipation within its interior.

*Figure 2: An eccentric orbit causes periodic deformation of the satellite's shape.* *P represents the planet and* *M the moon. The tidal bulge that is developed as a result of the interactions between the planet and the moon can be seen in blue.*

Objectives

Constrain parameter space which would make a THEM observable
Identify the interior properties which lead to the above values

Importance to the field

Study the diversity of exoplanetary worlds
Habitable exomoons: detecting a THEM implies the existence of one or more
satellites in MMR retaining the THEM's eccentricity
Place of our Solar System in the Universe
Insight in planet formation theories

Thermal Model

Heat transfer

We use a thermal model that assumes a layered, radially symmetric moon, consisting of a silicate mantle and a liquid core. We assume that heat is transferred via melt advection (Moore 2003) and convection from the interior to the surface (Figure 3) and we obtain equilibrium temperatures.

We explore the parameter space of orbital and physical properties of an exomoon around β Pictoris b by using different rheological models: the widely used Maxwell model and the more realistic Andrade one.

Thermal equilibrium

The thermal equilibrium model depends on the orbital properties of the satellite, since those affect the tidal heat that is generated. When excess heat is generated, the interior structure changes, as more melt is formed in the asthenosphere.

We build a thermal model, in which thermal equilibrium is reached once the heat generated in the interior is equal with the one that gets transported throught the different layers (Figure 4). We force it under different orbital scenarios to find stable thermal points. Notice, however, that the orbit might change in time due to tidal interactions between the planet and moon.

Results and Future Prospects

A super-Io around β Pictoris b

*Figure 5: Equilibrium surface temperatures of a 2R_Io exomoon (Super-Io) around β Pictoris b using Andrade rheology and melt advection. The horizontal line shows Io’s orbital eccentricity.*

We scale up a Galilean satellite system around β Pictoris b in order to investigate which properties make a putative exomoon detectable. This results in an 2 R_Io sized exomoon. Given a semi-major axis and eccentricity for a 2 R_Io exomoon, we obtain the corresponding interior structure and heat flow through the moon, resulting in a calculated effective temperature at the surface. Figure 5 shows the equilibrium temperatures of the above "Super-Io" for the Andrade rheology.

We find that the more realistic Andrade model leads to higher temperatures, compared to the more basic Maxwell one, which is promising for future observations.

Temperature and interior structure of an observable exomoon

At Io’s orbital eccentricity a 2R_Io exomoon would need to be close to the Roche radius of β Pictoris b to reach 550 K and be observed with the JWST (Figure 6), however this limit relaxes for higher eccentricities and bigger moons.

Figure 6: Fluxes at the β Pictoris system. The grey continuous line shows the modeled spectrum of a planet with similar parameters as β Pictoris b (Morley et al. 2015), the dashed black line the blackbody curve of the star and the purple line the one of a Super-Io (2R_Io). The horizontal lines are the 5σ and 10,000s integration time detection limits of MIRI/JWST for various bands (Glasse 2010)).

The aforementioned moon would be in equilibrium. The corresponding interior structure is a function of the mantle temperature that is assumed in the lower convective layer (Figure 7). For a 1900K mantle temperature, the corresponding lithosphere thickness would be 50 km and the one of the asthenosphere 300 km.

*Figure 7: Interior structure of "Super-Io" as a function of mantle temperature. For a 1900K mantle the corresponding layers are: 300km asthenosphere and a 50km lithosphere (red dashed line).*

Future work

Apply to more known close-by exoplanets
Around what planets could we detect exomoons?
Could an exomoon system stably exist around known gas giant exoplanets?
What is the sensitivity required to directly image exomoons with the James Webb Telescope (JWST) or METIS on the ELT?

References:

Glasse (2010) SPIE, 7731, 77310K.

Moore (2001) Icarus, 154, p.548.

Morley et al. (2015) The Astrophysical Journal, 815(2), p.110.

Oza et al. (2019) The Astrophysical Journal, 885(2), p.168.

Peters and Turner (2013) The Astrophysical Journal, 769(2), p.98.

Rovira-Navarro et al. (2021) The Planetary Science Journal, 2(3), p.119.