Inspiralling compact binaries as standard sirens will soon become an invaluable tool for cosmology when advanced interferometric gravitational-wave detectors begin their observations in the coming years. However, a degeneracy in the information carried by gravitational waves between the total rest-frame mass $M$ and the redshift $z$ of the source implies that neither can be directly extracted from the signal, but only the combination $M(1+z)$, the redshifted mass. Recent work has shown that for binary neutron star systems, a tidal correction to the gravitational-wave phase in the late-inspiral signal that depends on the rest-frame source mass could be used to break the mass-redshift degeneracy. We propose here to use the signature encoded in the post-merger signal to deduce the redshift to the source. This will allow an accurate extraction of the intrinsic rest-frame mass of the source, in turn permitting the determination of source redshift and luminosity distance solely from gravitational-wave observations. This will herald a new era in precision cosmography and astrophysics. Using numerical simulations of binary neutron star mergers of very slightly different mass, we model gravitational-wave signals at different redshifts and use Bayesian parameter estimation to determine the accuracy with which the redshift can be extracted for a source of known mass. We find that the Einstein Telescope can determine the source redshift to $sim 10$--$20%$ at redshifts of $z<0.04$.
We present a timing analysis of the 2009 outburst of the accreting millisecond X-ray pulsar Swift J1756.9-2508, and a re-analysis of the 2007 outburst. The source shows a short recurrence time of only ~2 years between outbursts. Thanks to the approximately 2 year long baseline of data, we can constrain the magnetic field of the neutron star to be 0.4x10^8 G < B < 9x10^8 G, which is within the range of typical accreting millisecond pulsars. The 2009 timing analysis allows us to put constraints on the accretion torque: the spin frequency derivative within the outburst has an upper limit of $|dot{ u}| < 3x10^-13 Hz/s at the 95% confidence level. A study of pulse profiles and their evolution during the outburst is analyzed, suggesting a systematic change of shape that depends on the outburst phase.
