Differential rotation of stars other than the Sun

Why studying stellar differential rotation?

Gradients in angular rotation caused by angular momentum redistribution within the convective layers of a cool star are expected to be one of the main ingredients for generating the large-scale magnetic field of the Sun and stars, through the magneto-hydrodynamical mechanisms (called dynamo processes) that operate in their outer envelopes. On the Sun (see above picture where red represent faster rotation and blue slower rotation), the study of oscillations revealed that rotation is roughly constant within the whole radiative interior (i.e. the inner 70% of the Sun's radius) and constant with radius (though variable with latitude) within the convective envelope (i.e. the outer 30% of the Sun's radius). The interface between these two regions is where angular rotation gradients are strongest and thus where dynamo processes are expected to be most efficient.
Unfortunately, the Sun is the only star yet for which internal differential rotation is known. Till the first asteroseismology spacecrafts (such as COROT) are launched, Surface differential rotation (i.e. the variation of surface rotation with latitude) remains the only information we can access on cool stars other than the Sun.

Measuring surface differential rotation

By comparing two brightness/magnetic surface images of a rapidly rotating spotted cool star obtained typically one week apart, one can track the relative motion, and thus measure the rotation rates, of starspots at different latitudes over several rotation cycles, just as Galileo and his successors did in the particular case of the Sun.
The two upper panels of the image below are brightness images of the young ultra-fast rotator AB Dor (spinning more than 50 times faster than the Sun), as reconstructed from data recorded at the 4m Anglo-Australian Telescope on 1995 December 07 (upper panel) and December 11 (middle panel), i.e. shifted by 8 rotation cycles. The second half of the rotation cycle (left hand side of both images, or phase range [0.55, 0.95])) was observed continuously at both epochs (phases of observations being depicted with vertical ticks above each image). At first glance, the two images look remarkably similar within the overlap phase range. A closer look reveals however that brightness features close to the equator systematically shifted eastward (i.e. towards smaller rotational phases) between the first and second epoch.


By cross-correlating belts of equal latitude between both images within the overlap phase range, we obtain a cross-correlation image (lower panel) describing the amount of rotational shear as a function of latitude at the surface of AB Dor (negative phase shifts indicating faster rotation). The dashed curve indicates a fit to the data with a sine squared law. It tells us that the surface rotational shear of AB Dor is very similar to that of the Sun, both in sense (with the equator rotating faster than the pole) and amplitude (with a time for the pole to lap the equator by one full rotation cycle of about 120 d), even though this star rotates about 50 times faster than the Sun. Note that this is the first reliable determination of differential rotation (i.e. obtained with a cross-correlation analysis on two close-by Doppler images derived from very dense data sets) in a star other than the Sun.
A small animation shows this effect on AB Dor in December 1996.

Studying the physics of stellar convective zones

Measurements of surface differential rotation for stars with various rotation rates and convective depths are very useful inputs to constrain hydrodynamical models of convective zones. It should help us understand in particular how angular momentum is redistributed within convective envelopes under the effect of convective heat transport, anisotropic turbulence and meridional circulation. As a result, we should obtain a better knowledge on these important (yet poorly known) basic physical processes thought to play a major role for numerous studies in stellar physics (such as those on dynamo field generation) and for stellar evolution in general.
A second obvious goal is to see whether dynamo-induced magnetic fields have a feedback action on the large-scale internal velocity fields that produced them. Zeeman-Doppler imaging results indeed indicate that magnetic fields seem to be produced within the bulk of the convective zones, implying that significant magnetic to kinetic energy transfer (and thus modification of the velocity field) probably occurs within the whole convective envelope. Similarly, the changes in quadrupole moment that rapidly rotating stars in binary systems (detected through the system orbital period fluctuations they generate) undergo also imply significant variation of the internal velocity field. Monitoring surface differential rotation throughout activity cycles should bring us a definite answer to this problem. The very recent discovery that differential rotation indeed varies with time confirms all these ideas.

Related publications

Donati J.-F. , ``Magnetic feedback on stellar convective zones'', in: Trujillo Bueno J., Sanchez Almeida J. (eds.), proceedings of the Solar Polarisation Workshop #3 (2003). ASP Conf. Series (in press).

Donati J.-F., Cameron A.C., Petit P., ``Temporal fluctuations in the differential rotation of cool active stars'' (2003) MNRAS 345, 1187

Donati J.-F. , ``Surface magnetic fields and differential rotation of solar-like stars'', in: Arnaud J., Meunier N. (eds.), Proceedings of the workshop dedicated to Jean-Louis Leroy on ``Magnetism and Activity of the Sun and Stars'' (2003). EDP Sciences, EAS 9, 169

Petit P., Donati J.-F., Cameron A.C., ``Differential rotation of cool active stars: the case of intermediate rotators'' (2002) MNRAS 334, 374

Cameron A.C., Donati J.-F., Semel M., ``Stellar differential rotation from direct starspot tracking'' (2002) MNRAS 330, 699

Cameron A.C., Donati J.-F., ``Doin' the twist: Secular changes in the surface differential rotation on AB Doradus'' (2002) MNRAS 329, L23

Petit P., Donati J.-F. , Wade G.A., et al., ``Differential Rotation of Close Binary Stars: Application to HR 1099'', in: Boffin H., Steeghs D., Cuypers J. (eds.), AstroTomography, Indirect imaging methods in observational astronomy (2001). Springer, Berlin, p. 232

Barnes J.R., Cameron A.C., James D.J., Donati J.-F., ``''Doppler Images from dual-site observations of southern rapidly rotating stars II: differential rotation on Speedy Mic'' (2001) MNRAS 324, 231

Donati J.-F., Mengel M., Carter B.D., Cameron A.C., Wichmann R., ``Surface differential rotation and prominences of the Lupus post T Tauri star RX J1508.6-4423'' (2000) MNRAS 316, 699

Barnes J.R., Cameron A.C., James D.J., Donati J.-F., ``Doppler images from dual-site observations of southern rapidly rotating stars I: differential rotation on PZ Tel'' (2000) MNRAS 314, 162

Donati J.-F. , ``Surface magnetic fields of late-type stars'', in: Butler C.J., Doyle J.G. (eds.), Brendan Byrne memorial workshop on ``Solar and Stellar Activity: Similarities and Differences'' (1999). ASP Conf. Series, vol. 158, p. 27

Donati J.-F., ``Magnetic cycles of HR 1099 and LQ Hydrae'' (1999) MNRAS 302, 457

Donati J.-F., Cameron A.C., Hussain G.A.J., Semel M., ``Magnetic topology and prominence patterns on AB Doradus'' (1999) MNRAS 302, 437

Barnes J.R., Cameron A.C., Unruh Y.C., Donati J.-F., Hussain G.A.J., ``Latitude distributions and lifetimes of starspots on G dwarfs in the Alpha Persei cluster'' (1998) MNRAS 299, 904

Donati J.-F., Cameron A.C., ``Differential rotation and magnetic polarity patterns on AB Doradus'' (1997) MNRAS 291, 1

© Jean-François Donati, last update on 2003 Nov 5