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Stellar Rotation and Line Broadening

What you are seeing: a rotating limb-darkened star and the resulting broadened absorption line. The Doppler shift on each surface element makes the approaching limb blue, the receding limb red, and the line profile is the limb-darkened-weighted sum of every shifted copy. Vary vsin⁡iv\sin i and watch the line widen and hollow out

Figure 1. Rotating star (Doppler-coloured surface) and its broadened absorption line. Method: disk-integral sum of Doppler-shifted Gaussians weighted by quadratic limb darkening.
v sin i (km/s)30
σ (intrinsic)0.012
depth0.70
inclination (°)90

WHAT TO TRY

  • Raise v sin i: the faster a star spins, the more its approaching and receding limbs Doppler-shift the line, broadening it into the rotational profile. The line goes shallow and wide.
  • Tilt the inclination: only the projected rotation v sin i broadens the line, so a pole-on fast rotator looks slow, the degeneracy spectroscopy must live with.
  • Compare the intrinsic width sigma against the rotational width: at high v sin i the rotation dominates and the line shape carries the imprint of the limb-darkened spinning disk.