The shape, internal structure and gravity of the fast spinner β Pictoris b

Abstract

A young extrasolar gas giant planet, β Pictoris b, recently discovered in the β Pictoris system, spins substantially faster than the giant gas planets Jupiter and Saturn. Based on the newly measured parameters – the rotation period of the planet, its mass and radius – together with an assumption that the gas planet β Pictoris b is in hydrostatic equilibrium and made of a fully compressible barotropic gas with a polytropic index of unity, we are able to compute, via a hybrid inverse method, its non-spherical shape, internal density/pressure distribution and gravitational zonal coefficients up to degree 8. Since the mass Mβ for the planet β Pictoris b is highly uncertain, various models with different values of Mβ are studied in this Letter, providing the upper and lower bounds for its shape parameter as well as its gravitational zonal coefficients. If Mβ is assumed to be 6MJ with MJ being Jupiter's mass, we show that the shape of the planet β Pictoris b is approximately described by an oblate spheroid whose eccentricity at the one-bar surface is E β =0.36928 Eβ=0.36928 with the gravitational coefficient (J2)β = +15 375.972 × 10−6. It follows that our results open the possibility of constraining or inferring the mass Mβ of the planet β Pictoris b if its shape can be measured or constrained. By assuming that the planet β Pictoris b will shrink to the size of Jupiter in the process of cooling down and, hence, rotate much faster, we also calculate the future shape and internal structure of the planet β Pictoris b.