Poynting-Robertson-like Drag at the Sun’s Surface

The Sun’s internal rotation $\mathrm{\Omega }(r,\mathrm{\Theta })$ has previously been measured using helioseismology techniques and found to be a complex function of colatitude $\theta$ and radius $r$. From helioseismology and observations of apparently “rooted” solar magnetic tracers, we know that the surface rotates more slowly than much of the interior. The cause of this slow-down is not understood, but it is important for understanding stellar rotation generally and any plausible theory of the solar interior. A new analysis using 5-min solar $p$-mode limb oscillations as a rotation “tracer” finds an even larger velocity gradient in a thin region at the top of the photosphere. This shear occurs where the solar atmosphere radiates energy and angular momentum. We suggest that the net effect of the photospheric angular momentum loss is similar to Poynting-Robertson “photon braking” on, for example, Sun-orbiting dust. The resultant photospheric torque is readily computed and, over the Sun’s lifetime, is found to be comparable to the apparent angular momentum deficit in the near-surface shear layer.

Figure 1

Measured solar radius variation versus filter wavelength during a 3.5-year-duration observing window. Colors indicate HMI filtergrams, and their nominal central wavelength steps in angstroms are indicated on the right axis. The HMI continuum data are indicated with their observing campaign labels Mercury and Venus.

Figure 2

Limb power spectrum $|\alpha (k,\nu ){|}^2$ for line core filter data. Overplotted open circles show observed global $m=0$ mode frequencies [19]. Grey cross symbols show selected mode leakage calculations of some $m\ne 0$ full-disk modes for the indicated angular ($l$) and radial ($n$) modes into the limb harmonics $k$ indicated on the vertical axis. The color scale legend is indicated on the right in units of fractional brightness fluctuation (squared) per frequency bin.

Figure 3

Example sinusoid fit to limb seasonal rotation ${\mathrm{\Psi }}_i(t)$ temporal variation for the line core filter data. The inset graph shows the residual between the data and sinusoidal rotation model.

Figure 4

Solar angular rotation rate versus depth and latitude on a log-log scale derived from Ref. [4]. The final inverted near-surface rotations from the two major helioseismology experiments, Refs. [3] and [4], are consistent. Limb points (cross symbols) show our observed mean solar rotation shear; mean Doppler points (star symbols) indicate the angle-averaged Doppler rotation over the indicated indeterminate depth range; inversion shows the $p$-mode inversion rotation rates at three latitudes through the interior, with the near-surface and tachocline shear zones annotated. The Sun’s temperature minimum defines the outer reference radius ($R_{\text{Sun}}$) for the horizontal scale.

Figure 5

The rotation deficit from a linear trend in radius in the near-surface shear zone is plotted based on Fig. 4 data for solar latitudes 0, 30, and 60 degrees.