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

A young extrasolar gas giant planet, beta Pictoris b, recently discovered in the beta 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 beta 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 M-beta for the planet beta Pictoris b is highly uncertain, various models with different values of M-beta are studied in this Letter, providing the upper and lower bounds for its shape parameter as well as its gravitational zonal coefficients. If M-beta is assumed to be 6M(J) with M-J being Jupiter's mass, we show that the shape of the planet beta Pictoris b is approximately described by an oblate spheroid whose eccentricity at the one-bar surface is <tex-math id="TM0001" notation="LaTeX">$\mathcal {E}_{\beta }=0.369\,28$</tex-math> with the gravitational coefficient (J(2))(beta) = +15 375.972 x 10(-6). It follows that our results open the possibility of constraining or inferring the mass M-beta of the planet beta Pictoris b if its shape can be measured or constrained. By assuming that the planet beta 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 beta Pictoris b.