Convection and differential rotation properties of G and K stars computed with the ASH code

Abstract

The stellar luminosity and depth of the convective envelope vary rapidly with mass for G-and K-type main sequence stars. In order to understand how these properties influence the convective turbulence, differential rotation, and meridional circulation, we have carried out 3D dynamical simulations of the interiors of rotating main sequence stars, using the anelastic spherical harmonic (ASH) code. The stars in our simulations have masses of 0.5, 0.7, 0.9, and 1.1 M , corresponding to spectral types K7 through G0, and rotate at the same angular speed as the Sun. We identify several trends of convection zone properties with stellar mass, exhibited by the simulations. The convective velocities, temperature contrast between up-and downflows, and meridional circulation velocities all increase with stellar luminosity. As a consequence of the trend in convective velocity, the Rossby number (at a fixed rotation rate) increases and the convective turnover timescales decrease significantly with increasing stellar mass. The three lowest mass cases exhibit solar-like differential rotation, in a sense that they show a maximum rotation at the equator and minimum at higher latitudes, but the 1.1 M case exhibits anti-solar rotation. At low mass, the meridional circulation is multi-cellular and aligned with the rotation axis; as the mass increases, the circulation pattern tends toward a unicellular structure covering each hemisphere in the convection zone.

Rotation and magnetism of solar-like stars: from scaling laws to spot-dynamos

“…We generally found that for simulations with Ro < 1, meridional circulations possess many cells in radius and/or latitude per hemisphere. Only for anti-solar differential rotation cases, is the meridional circulation uni-cellular Matt et al (2011). We also find that the amplitude decreases as the rotational influence is increased as shown on Figure 4 right panel.…”

“…The ω-effect is a direct measure of the differential rotation ΔΩ established in the star. It is well known both theoretically and observationally that the differential rotation in the convective envelope of solar-type stars is directly connected to the star's rotation rate Ω 0 (Donahue et al(1996), Barnes et al(2005), Ballot et al (2007), Brown et al (2008), Küker et al(2011), Matt et al (2011), Augustson et al (2012), Gastine et al (2013)). However, the exact scaling exponent n r (i.e.…”

“…The general trend is that the Coriolis force modifies convection such as to establish a large scale differential rotation Ω(r, θ) (Brun & Rempel (2009)). Depending on the influence of the Coriolis force, usually mesured by the turbulent Rossby number Ro = ω conv /2Ω 0 ∼ v conv /2Ω 0 d, or a variant, with ω conv , v conv characteristic vorticity and velocity in the convection zone and d the convection zone depth, the resulting differential rotation can be anti-solar (high Ro > 1, with fast poles-slow equator), solar-like (0.2 < Ro < 0.9, with fast equator, slow poles and some constancy at mid latitude of the isocontours of Ω) or Jupiter-like (Ro < 0.1, with cylindrical profile with alternance of prograde and retrograde jets) Matt et al (2011). On Figure 3 we represent these different profiles in models for various masses (0.5, 0.7 and 1.1 Msol) that also include the coupling to a stably stratified radiative interior, thus possessing a tachocline Matt & Brun (2013).…”

Convection and Differential Rotation in F-Type Stars

“…Such behavior is seen in both simulations of spherical domains and Cartesian domains at various levels of turbulence in both the ASH simulations (Brun & Palacios 2009;Matt et al 2011) and simulations carried out in Cartesian domains (Käpylä et al 2004), as well as in spherical segments (Käpylä et al 2011). We observe that this transition between solar-like and anti-solar-like differential rotations occurs within flows that have a Rossby number of nearly one.…”

“…The Rayleigh numbers at mid-convection zone are about 50 times the critical Rayleigh number (Jones et al 2009) for the Case A simulations and about 25 times for the Case B simulations. These levels of supercriticality are equivalent to ASH simulations of lower mass stars (e.g., Brown et al 2008;Matt et al 2011). The lower level of supercriticality in the 1.3 M simulations is primarily due to the stronger driving of the convection and larger superadiabatic gradient, both of which are in turn due to the higher luminosity and narrower convection zones of the higher mass F-type stars.…”