Main sequence stars of spectral types earlier than ~ F6 (i.e.
stars > 1.5 times the Sun’s mass) are expected to be rapid rotators as their
outermost layers are radiative instead of convective. Stars like the Sun have
convective outermost layers that drive surface magnetic activity, generating
strong stellar winds that with time carry away the star’s angular momentum and
spin down the star. Stars of spectral types earlier than ~ F6 retain their high
angular momentum (i.e. rapid rotation rates) since their radiative outermost
layers do not produce strong stellar winds that sap the star’s angular momentum
with time. Some of these stars are known to spin at near their break-up speeds.
The rapid rotation of ~ F6 type and earlier stars can make
then significantly oblate - flattened at the poles and bulging around the
equator. This causes the star’s surface gravity to exhibit a pole-to-equator
gradient, with the poles having a higher surface gravity, and thus higher temperature
and brightness. The star’s photosphere can be several thousand Kevin hotter at
the poles than at the equator. As a result, the poles are “gravity-brightened”
and the equator “gravity-darkened”. This effect is called gravity darkening and
it was first predicted by von Zeipel (1924).
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Figure 1: Artist’s impression of a gas giant planet. Image
credit: Daniel Mallia.
A study by Ahlers et al. (2014) used precise photometric
data from NASA’s Kepler space telescope to constrain the spin-orbit alignment
of the KOI-368 planetary system. Basically, the spin-orbit alignment is the
inclination of a planet’s orbit normal with respect to its star’s spin axis.
The planet in this system, designated KOI-368.01, is probably an inflated gas
giant 1.83 times the size of Jupiter. The planet’s host star, KOI-368, is a
rapidly rotating early spectral type star that is 2.3 times the size of the Sun
and has an effective temperature of 9257 K. The star’s period of rotation is a
mere 30.73 hours. For comparison, the Sun has a rotation period of 25 days.
Gravity darkening allows the true orientation of a star’s
spin axis to be determined. In turn, this allows the true spin-orbit alignment
of any planet transiting the star to be measured. The planet KOI-368.01
transits its host star every 110 days. Due to the rapid spin of its host star,
the transit light curve is expected to display the effects of gravity darkening.
Using a gravity-darkened stellar model to model the observed light curve when
KOI-368.01 transits its host star, the planet’s true spin-orbit alignment was
found to be 11 ± 3 degrees. The results from this study show that the orbit of
KOI-368.01 is well aligned and might suggest that orbits of objects circling
more massive stars are not more likely to be misaligned, contrary to Winn et
al. (2010).
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Figure 2: Photometry and fits for the KOI-368 light curve
with the gravity-darkened fit in blue. Source: Ahlers et al. (2014).
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Figure 3: Four possible transit geometries of the KOI-368
system. The effects of gravity darkening and limb darkening are illustrated.
All four scenarios produce identical transit light curves; therefore, these
geometries are perfectly degenerate. Source: Ahlers et al. (2014).
References:
- Ahlers et al. (2014), “Spin-Orbit Alignment for 110 Day
Period KOI368.01 from Gravity Darkening”, Astrophysical Journal, Volume 786:131
(5pp)
- von Zeipel (1924), “The radiative equilibrium of a
rotating system of gaseous masses”, Monthly Notices of the Royal Astronomical
Society, Vol. 84, p.665-683
- Winn et al. (2010), “Hot Stars with Hot Jupiters Have High
Obliquities”, Astrophysical Journal Letters, Volume 718, Issue 2, pp. L145-L149