Results of an all-sky high-frequency Einstein@Home search for continuous gravitational waves in LIGO’s fifth science run

We present results of a high-frequency all-sky search for continuous gravitational waves from isolated compact objects in LIGO’s fifth science run (S5) data, using the computing power of the Einstein@Home volunteer computing project. This is the only dedicated continuous gravitational wave search that probes this high-frequency range on S5 data. We find no significant candidate signal, so we set 90% confidence level upper limits on continuous gravitational wave strain amplitudes. At the lower end of the search frequency range, around 1250 Hz, the most constraining upper limit is $5.0\times {10}^{-24}$, while at the higher end, around 1500 Hz, it is $6.2\times {10}^{-24}$. Based on these upper limits, and assuming a fiducial value of the principal moment of inertia of ${10}^{38}\mathrm{kg}{\mathrm{m}}^2$, we can exclude objects with ellipticities higher than roughly $2.8\times {10}^{-7}$ within 100 pc of Earth with rotation periods between 1.3 and 1.6 milliseconds.

Figure 1

Tilling of sky grid for the frequency band 1240–1250 Hz; $d_{\text{sky}}=6.6\times {10}^{-4}$ for this band. In the left panel, we show the sky-grid points on the celestial sphere; the color-code traces the number of sky-grid points, ${\mathrm{N}}_{\delta }$, as a function of equatorial latitude $\delta$. The right panel is a polar plot of the northern equatorial hemisphere of the same sky grid but with density scaled down by a factor of 4 to allow for better viewing. In the polar plot, $\theta =\alpha$ and $r=\cos (\delta )$.

Figure 2

Number of templates searched in 50 mHz bands. The variation in template count arises from the variation is number of sky-grid points every 10 Hz in frequency. Each 50 mHz band contributes roughly $6.3\times 10^7$ templates in frequency and spin-down (on the finer grid refined by refinement factor $\gamma$.)

Figure 3

We plot the color-coded $2\overline{\mathcal{F}}$ values on the $z$ axis in three 50 mHz bands. The top-most band is marked as “disturbed”; the middle band is an example of an “undisturbed” band; the bottom-most band is an example of an undisturbed band but containing a simulated continuous gravitational wave signal.

Figure 4

Highest values of $2\overline{\mathcal{F}}$ in every 0.5 Hz band as a function of starting frequency of the band.

Figure 5

Ratio $\mathcal{R}=N_{\text{trials}}/N_{\text{templates}}$ as a function of frequency in 10 Hz intervals. The error bars represent the $1\text{−}\sigma$ statistical errors from the fitting procedure described in the text.

Figure 6

In the top panel, we plot the significance of the loudest observed candidate in every 0.5 Hz band as a function of starting frequency of the band. In the bottom panel, we show the observed distribution of CR values (top brown histogram bars), and the expected distribution of CR values for pure noise for reference (bottom blue histogram bars with markers). The significance folds in the expected value for the loudest $2\overline{\mathcal{F}}$ and its standard deviation.

Figure 7

Distribution of fill levels of 0.5 Hz bands.

Figure 8

$p$-values for the loudest observed candidates in 0.5 Hz bands in the data (top brown histogram bars), and the expected distribution of $p$-values for pure noise for reference (bottom blue histogram bars with markers).

Figure 9

The 90% confidence upper limits on the gravitational wave amplitude for signals with frequency within 0.5 Hz bands, over the entire sky, and within the spin-down range of the search described in Sec. 3. The empty circular markers denote 0.5 Hz bands where the upper-limit value does not hold for all frequencies in that interval; the list of corresponding excluded frequencies is given in Table 4. For reference, we also plot the upper-limit results (with noncircular markers) from the only other high-frequency search [7], on significantly more sensitive S6 data. It should be noted that the upper limits from the PowerFlux search [7] are set at 95% confidence rather than 90% confidence level as in this search, but refer to 0.25 Hz bands rather than 0.5 Hz bands.

Figure 10

Gravitational wave amplitude upper limits recast as curves in the $(f,x|\dot{f}|)$ plane (left panel) for sources at given distances, where $f$ is the signal frequency and $x|\dot{f}|$ is the gravitational wave spin-down i.e. the fraction of the actual spin-down $|\dot{f}|$ that accounts for the rotational energy loss due to gravitational wave emission. We have superimposed the curves of constant ellipticity $\epsilon$. The dotted line at $|{\dot{f}}_{\max }|$ indicates the maximum magnitude of searched spin-down, namely $2.93\times {10}^{-9}\mathrm{Hz}/\mathrm{s}$. The right panel shows the corresponding $(f,\epsilon )$ upper-limit curves for sources at various distances. The ${\epsilon }_{\max }=41.3\times f^{-5/2}$ curve is the ellipticity corresponding to the highest $|\dot{f}|$ searched.