Devloping Effective Communication 2
PHAS2901
Malini Patel
Tutor: J.Mur.Petit
ABSTRACT:
S. Charpinet & G. Fontaine2 & P. Brassard
Seismic evidence for the loss of stellar angular momentum before the
white-dwarf stage (Nature 416, 501, 2009)
Observations of the photospheres of white-dwarf stars show they rotate with longer periods
than expected. It is not known whether this is due to the loss of angular momentum during
evolutionary stages, or if the stars ‘hide’ some of their angular momentum by encompassing
interiors that spin more rapidly than the surface. Using asteroseismology the internal rotation
of a white-dwarf star was profiled for the first time. Period spacings between components of
multiplet structures in principle pulsation modes were used to infer information about the
rotation state of the pulsating PG 1159-035 white dwarf star. After finding the optimum
surface rotation period to be 33.61±0.59h, test stellar models consisting of an outer zone that
rotated rigidly with this period and an inner zone assumed to rotate rigidly with a variable
period, were constructed. The best fit between observed and calculated period spacings, as a
function of inner zone rotation period and outer zone depth was found. Results showed the
best solution at a given depth was for the inner and outer zones to rotate with approximately
the same period. This implies white-dwarfs rotate as solid bodies and favours theories
suggesting angular momentum loss through evolution preceding white-dwarf formation.
SUMMARY:
S. Charpinet & G. Fontaine2 & P. Brassard
Seismic evidence for the loss of stellar angular momentum before the
white-dwarf stage (Nature 416, 501, 2009) #
White-dwarfs represent the remnant form of 95% of all stars. If it is assumed that stars retain
their angular momentum throughout the evolutionary process, then white-dwarfs should
rotate relatively rapidly, owing to their compact nature. However observations of
photospheres show that white-dwarf stars rotate with periods much longer than those
expected. It has not been determined whether this is due to the loss of angular momentum
during evolutionary stages, or if the stars ‘hide’ some of their angular momentum by
encompassing interiors that spin more rapidly than the surface.
This investigation used asteroseismology to profile the internal rotation of a white-dwarf star
for the first time. Hence, it was determined whether the star displays solid body rotation or
contains a rapidly rotating inner core.
PG1159-035 is a white-dwarf star experiencing gravity-wave pulsational instabilities which
causes it to exhibit multi-periodic luminosity variations resulting in a rich pulsation spectrum.
A detailed study of this spectrum revealed that a number of the principle modes display a fine
structure of components that are closely spaced in period. These multiplet structures are
attributed to the phenomenon of rotational splitting, where formerly degenerate modes show
their components due the breaking of spherical symmetry that occurs when rotation is
considered. Period spacings between the components of multiplet structures contain
information about the rotation state of the star. This data was interpreted in this investigation.
The analysis was conducted by making two assumptions that would then be verified: (1) the
star is a slow rotator i.e. its rotation period is much larger than observed pulsation periods and
(2) it rotates as a rigid body.
These assumptions allow for the calculation of the period spacings, using pulsation theory
and applying a perturbation method with the unperturbed reference state being similar to the
seismic spherical model referred to above. The assumed rotation period was varied until the
calculated and observed period spacings displayed the best-fit. In order to judge this a merit
function S2 was used. It represented the weighted sum of the squared differences between 31
observed period spacings and their expected counterparts for a given rotational period. The
optimum surface rotational period, found to be 33.61±0.59h, was much larger than any
observed pulsation periods and hence verified the first assumption.
Stellar test models consisting of an outer zone that rotated rigidly with this optimum rotation
period and an inner zone assumed to rotate rigidly with a variable period, were constructed.
Considering the fact that pulsations in stars are global modes, the values of the calculated
period spacings depend on the rotation of the whole vertical structure. Therefore the values
for the theoretical period spacings would also depend on the depth of the outer layer. The aim
was to then minimise the merit quantity S2 both as a function of the rotational period of the
inner zone and the depth of the outer layer.
Results showed a very well defined solution to the function at a period that was
approximately equal to that expected for solid body rotation. Contours about the optimal
solution were also plotted, and found to flatten out at large depths, indicating the method lost
sensitivity. However the results still support rigid rotation as only 2.5% of the star’s mass is
contained in the region where this technique is ineffective. Other experimental methods used
to construct an inner rotation profile of PG1159-035 produced results which also confirm
solid body rotation. The outcome of this experiment implies momentum loss through
evolution and particularly supports theories which imply a strong coupling that would
transfer angular momentum to the outer-reaches of the star in stages preceding white dwarf
formation.