A number of observed phenomena associated with individual neutron star
systems or neutron star populations find explanations in models in which the
neutron star crust plays an important role. We review recent work examining the
sensitivity to the slope of the symmetry energy L of such models, and
constraints extracted on L from confronting them with observations. We focus
on six sets of observations and proposed explanations: (i) The cooling rate of
the neutron star in Cassiopeia A, confronting cooling models which include
enhanced cooling in the nuclear pasta regions of the inner crust, (ii) the
upper limit of the observed periods of young X-ray pulsars, confronting models
of magnetic field decay in the crust caused by the high resistivity of the
nuclear pasta layer, (iii) glitches from the Vela pulsar, confronting the
paradigm that they arise due to a sudden re-coupling of the crustal neutron
superfluid to the crustal lattice after a period during which they were
decoupled due to vortex pinning, (iv) The frequencies of quasi-periodic
oscillations in the X-ray tail of light curves from giant flares from soft
gamma-ray repeaters, confronting models of torsional crust oscillations, (v)
the upper limit on the frequency to which millisecond pulsars can be spun-up
due to accretion from a binary companion, confronting models of the r-mode
instability arising above a threshold frequency determined in part by the
viscous dissipation timescale at the crust-core boundary, and (vi) the
observations of precursor electromagnetic flares a few seconds before short
gamma-ray bursts, confronting a model of crust shattering caused by resonant
excitation of a crustal oscillation mode by the tidal gravitational field of a
companion neutron star just before merger.Comment: 19 pages, 10 figure and 1 tabl
