Inferring the population properties of binary neutron stars with gravitational-wave measurements of spin

The recent LIGO-Virgo detection of gravitational waves from a binary neutron star inspiral event GW170817 and the discovery of its accompanying electromagnetic signals mark a new era for multimessenger astronomy. In the coming years, advanced gravitational-wave detectors are likely to detect tens to hundreds of similar events. Neutron stars in binaries can possess significant spin, which is imprinted on the gravitational waveform via the effective spin parameter ${\chi }_{\mathrm{eff}}$. We explore the astrophysical inferences made possible by gravitational-wave measurements of ${\chi }_{\mathrm{eff}}$. First, using a fiducial model informed by radio observations, we estimate that $\approx 15–30\%$ of binary neutron stars should have spins measurable at $\gtrsim 90\%$ confidence level by advanced detectors assuming the spin axis of the recycled neutron star aligns with the total orbital angular momentum of the binary. Second, using Bayesian inference, we show that it is possible to tell whether or not the spin axis of the recycled neutron star tends to be aligned with the binary orbit using $\gtrsim 30$ detections. Finally, interesting constraints can be placed on neutron star magnetic field decay after $\gtrsim 300$ detections, if the spin periods and magnetic field strengths of Galactic binary neutron stars are representative of the merging population.

Figure 1

Probability density distribution of ${\chi }_{\mathrm{eff}}$ expected for a population of BNS inspiral events for four different models (Table 2), as compared to the low-spin prior usually used in gravitational-wave data analysis. The vertical shaded region indicates a plausible range expected for Galactic BNS systems extrapolated at merger (Table 1).

Figure 2

Posterior probability density distribution of ${\chi }_{\mathrm{eff}}$ generated by analyzing Monte-Carlo data using LALInference. The data consist of a BNS signal at 200 Mpc added to Hanford and Livingston design sensitivity noise. The blue curve is the Gaussian distribution with mean and standard deviation determined from posterior samples. The black dash-dotted curve is the prior distribution. The red vertical line marks the true injection value. In each panel we list the pulsar name of the Galactic BNS (see Table 1), standard deviation (${\sigma }_{\chi }$) of posterior samples and $S/N$ of each signal injection.

Figure 3

Marginalized 2-D posterior distributions for ${\chi }_{\mathrm{eff}}$, $q$, $M_c$ and $\tilde{\mathrm{\Lambda }}$ for two signal injections as in Fig. 2: PSR $\mathrm{J}1946+2052$ (left) and PSR $\mathrm{J}1913+1102$ (right). The green and blue contours encompass 50% and 90% credible regions, respectively. The red stars mark true injection values and black dots are posterior samples returned from LALInferenceMCMC analysis.

Figure 4

The standard deviation (${\sigma }_{\chi }$) of posterior distribution of ${\chi }_{\mathrm{eff}}$ as a function of signal to noise ratio ($S/N$). Shown here are measured by running parameter estimation code LALInference on Monte-Carlo data at Advanced LIGO design (black diamonds and red circles) or O2 (red plus symbols) sensitivity. The blue curve is a fit for results found for injections to zero-noise data. Gray dots represent the distribution of simulated ${\chi }_{\mathrm{eff}}$ measurements used in Sec. 4. The green square marks the GW170817 uncertainty under the low-spin prior [3].

Figure 5

A schematic diagram showing the sensitivity of Advanced LIGO to measure ${\chi }_{\mathrm{eff}}$. $d_L$ is the approximate luminosity distance out to which ${\chi }_{\mathrm{eff}}$ is measurable at the 90% ($1.6\text{−}\sigma$) confidence level. Galactic BNS systems (blue circles) are placed at the sky location of GW170817 and assumed to be face-on (which allows the maximum $S/N$). Also shown is the published 90% confidence upper limit for GW170817. A second y-axis shows the spin frequency of the recycled NS.

Figure 6

Bayes Factor (BF) as a function of the number of events between models Standard (the true underlying model), Iso Spin, Diff EOS. The shaded areas correspond to $1\text{−}\sigma$ confidence regions.

Figure 7

The mean posterior distribution (black solid curve) and individual distributions for 100 random noise realizations (blue dotted curves) of the magnetic field decay timescale ${\tau }_B$ recovered using 300 events. The red vertical line marks the true injection value.

Figure 8

Simulated BNS at birth (blue dots), along with known Galactic binary pulsar systems (open circles; only recycled pulsars are shown). Red (green) circles are for binaries that will (will not) merge within a Hubble time. For illustration, yellow arrows indicate plausible evolutionary tracks from the current state towards the initial state at the birth of the second NS for the Double Pulsar.