Neutron stars: smoother than billiard balls – unfortunately – LSC – LIGO Scientific Collaboration

Skip to content

Neutron stars: smoother than billiard balls – unfortunately

Neutron stars are famously smooth. The effects of gravity are crushing on these astonishingly dense stars, which have radii of only about 12 km, but contain more mass than the Sun. The star’s overwhelming gravity tends to anneal, that is, to smooth out any bumps, large or small, that might arise from surface cracking or from accretion of interstellar material.

LIGO-Virgo-KAGRA scientists have carried out searches in recent LIGO data (from the O4a observing run — May 2023 to January 2024) for evidence that this annealing process has worked less than perfectly for some neutron star somewhere in our galaxy. By carrying out all-sky searches for continuous gravitational waves (CWs) over a broad frequency range (20 to 2000 Hz), one can try to spot an unusual neutron star that is “bumpy” enough to swirl the space itself around the star as it spins on its axis.

The frequency of the resulting wave is expected to be twice the rotation frequency of the star. For example, a star spinning on its axis 100 times per second would emit continuous gravitational waves with a signal frequency of 200 Hz. As the star loses energy to this emitted radiation, its spin frequency very slowly decreases, leading to a slowly declining signal frequency. The searches carried out here allow for decreases as large as 3/10 of a Hz per year. The amplitude of a CW is expected to be tiny (much smaller than one part in a trillion-trillion).

How did we search and what did we find?

Three different search methods (PowerFlux, Frequency Hough and SOAP) have been used to look for such unusual neutron stars. These algorithms take various approaches, but all rely upon looking for nearly monochromatic (single-frequency) sinusoid-like signals in LIGO data. Spectra based on Fourier Transforms are computed for thousands of intervals of collected data, with interval durations ranging from 1024 to 16384 seconds. These spectra are then averaged together over the run period, while allowing for small modulations (Doppler shifts) in frequency and signal strength due to the Earth’s motion (i.e., its daily rotation and annual orbital motion around the Sun).

The PowerFlux and Frequency Hough programs look explicitly at a huge number of possible signal patterns for different combinations of assumed sky location, frequency and frequency time derivative, each combination representing a different template waveform, while the SOAP1 program does not carry out such an explicit search for particular patterns. As a result, SOAP has reduced sensitivity for the expected signals from isolated neutron stars in comparison to other approaches, but at the same time, it is many orders of magnitude faster than the other two programs, and it holds the potential to detect unexpected signals with unpredicted frequency evolution.

Unfortunately, no CW signals were seen. Figure 1 shows the resulting limits on dimensionless gravitational strain amplitude. The best sensitivity comes at around 290 Hz where limits are placed on strain values higher than 9.7×10−26.

Figure 1 : Upper limits on continuous gravitational wave strain amplitude vs signal frequency found in these searches, shown in comparison with limits from earlier searches of O3 observing run data. The upper graph shows the full search range from 20 to 2000 Hz. The lower graph shows a zoom-in of the 20-500 Hz range. The many upward spikes correspond to instrumental or environmental contaminations (“lines”). (Figure 2 of the paper)

What do the negative search results mean?

In this paper, LVK scientists have interpreted the negative search results to address three specific astrophysical issues:

The “smoothness” of the population of all neutron stars in our Milky Way galaxy;

The population of millisecond pulsars (i.e., with rotation frequency greater than about 100 Hz) near the galactic center, which are thought to be stars that could contribute significantly to the excess of high-energy gamma rays seen from there (referred to as the “GeV excess”); and

The potential contribution to Dark Matter due to inspiraling binary primordial black hole systems where the black holes have asteroid-scale masses and emit nearly monochromatic signals similar to ‘’bumpy’’ rotating neutron stars.

Figure 2 shows one way to characterize the limits on neutron star smoothness. The horizontal axis is the logarithm (base 10) of the ellipticity, which is a dimensionless measure of non-axisymmetry or roughness (on large or small scales) of the star. The vertical axis is the logarithm of the frequency in Hz. The curves show contours of exclusion of the number of neutron stars having ellipticity above a certain value. The colors of the curves are defined by the color bar at the right side. For example, for an ellipticity threshold of about 10-5 and a frequency of about 200 Hz...