Einstein@Home search for continuous gravitational waves from Cassiopeia A

We report the results of a directed search for continuous gravitational-wave emission in a broad frequency range (between 50 and 1000 Hz) from the central compact object of the supernova remnant Cassiopeia A (Cas A). The data come from the sixth science run of LIGO, and the search is performed on the volunteer distributed computing network Einstein@Home. We find no significant signal candidate and set the most constraining upper limits to date on the gravitational-wave emission from Cas A, which beat the indirect age-based upper limit across the entire search range. At 170 Hz (the most sensitive frequency range), we set 90% confidence upper limits on the gravitational-wave amplitude $h_0$ of $\sim 2.9\times {10}^{-25}$, roughly twice as constraining as the upper limits from previous searches on Cas A. The upper limits can also be expressed as constraints on the ellipticity of Cas A; with a few reasonable assumptions, we show that at gravitational-wave frequencies greater than 300 Hz we can exclude an ellipticity of $\gtrsim {10}^{-5}$.

Figure 1

For this search, the number of templates per 50 mHz search band increases quadratically with $f$. At each value of $f$, the $\dot{f}$ search range is [$-f/{\tau }_{\mathrm{NS}}$, 0], and the $\ddot{f}$ search range is [0, $2f/{\tau }_{\mathrm{NS}}^2$]. In total, $4.99\times 10^{17}$ templates are included in this search.

Figure 2

The maximum density (left) and the mean $2\overline{\mathcal{F}}$ value (right) for the candidates are the two metrics we use to identify potentially disturbed bands. Left: undisturbed bands (an example in the top panels) have a very uniform density of candidates in $f-\dot{f}$, while disturbed bands (an example in the bottom panels) present marked overdensities. The $2\overline{\mathcal{F}}$ values in the $f-\dot{f}$ plane are shown in the 3D plot, while the candidate density is shown in the 2D projections. The maximum density in a disturbed band tends to be much higher (here, more red) than the maximum density in an undisturbed band. Right: The $2\overline{\mathcal{F}}$ distribution in an undisturbed band (top) and in a disturbed band (bottom).

Figure 3

The distributions of maximum toplist density (left) and mean toplist $2\overline{\mathcal{F}}$ (right) are shown for a sample 10 Hz frequency range. Both distributions consist of an undisturbed body with a disturbed tail (hatched). All 50 mHz bands that fall within the hatched areas are marked as potentially disturbed.

Figure 4

For each of the 2000 partitions, we determine the $2\overline{\mathcal{F}}$ of the loudest candidates (top) as well as their CR values (bottom), where CR is defined in Eq. (4).

Figure 5

The p-values for the loudest candidate in each upper limit band is plotted in the blue histogram, and the expectation in Gaussian noise is shown in the black scatter points. We do not find any excess in our search. The small systematic deviation in our data from the expected is caused by a subtle difference in the ${\widehat{O}}_{\mathrm{SGL}}$ and $2\overline{\mathcal{F}}$ rankings.

Figure 6

90% confidence strain amplitude upper limits in each of the 2000 partitions. The results for partitions that contain only undisturbed 50 mHz bands are plotted in the filled red circles, while the results for partitions with disturbed 50 mHz bands are plotted in the open red circles. We also plot the 95% confidence upper limits from two previous searches on Cas A in green and blue. Our upper limits beat the so-called indirect age-based limit [17] across the band.

Figure 7

With a few reasonable assumptions, we can convert the upper limits on the gravitational-wave strain to upper limits on the ellipticity of Cas A. The shaded area denotes the source ellipticities (as a function of signal frequency) that are excluded by this search; ellipticities in this region would have produced signals that this search would have detected. The dashed line marks the spindown ellipticity probed by this search and is set by our choice of $\dot{f}$ search range.