# Status and Perspectives of Continuous Gravitational Wave Searches

^{1}

^{2}

## Abstract

**:**

## 1. Introduction

## 2. Sources of Continuous GWs

#### 2.1. Neutron Stars

**Ellipticity driven emission:**the GW amplitude for an NS with asymmetries can be expressed in terms of the product between the moment of inertia ${I}_{3}$ along the spin axis and the star’s degree of asymmetry, also known as ellipticity $\epsilon $:

**R-mode emission:**a different emission channel for CW radiation is given by the Rossby (r-)modes oscillations in rotating stars. R-mode emission is provided by the Chandrasekhar–Friedman–Schutz instability, leading to the rapid growth of the r-mode amplitude until a saturation amplitude is reached and the growth of the mode stops [69]. These amplitudes are damped by the viscosity of the star. Given these two opposite effects, where the amplitude increases with the spin of the star and is suppressed by the viscosity, dependent on the temperature, an instability window is defined in the angular velocity-temperature plane [70]. Typically, NSs are unstable to r-modes except at extreme temperatures. At very low temperatures, the shear viscosity dominates the damping, while at very high temperatures, the bulk viscosity takes the lead in the r-mode suppression. Given this strict relation with the inner physics of the NS during the r-mode emission, constraints on the GW observable properties are interesting tools for the study of the EOS [56,71]. A typical parameter constrained in CW searches for r-modes is the r-mode amplitude $\alpha $. Considering a source at a distance r the GW strain ${h}_{0}$ is given by [72]:

#### Strain Amplitude Limits

#### 2.2. Dark Matter Candidates

#### 2.2.1. Boson Clouds

#### 2.2.2. Ultralight Vector Bosons: Dark Photons

#### 2.2.3. Compact Dark Objects and Primordial Black Holes

## 3. Searches for CWs Signals with Earth-Based Detectors

#### 3.1. The Signal at the Detector

#### 3.2. Search Methods

`5-vector`[138,139] method, the

`F/B/G statistic`[140,141,142,143,144] and the time-domain heterodyne-based pipelines (

`Bayesian`and

`Band-Sampled-Data`) [145,146,147].

`FrequencyHough`[151,152,153], the

`SkyHough`[154,155,156], the

`Time-Domain`$\mathcal{F}$-

`statistic`[140,157,158],

`Weave`[159],

`PowerFlux`[160,161], and

`Einstein@Home`, based on the global correlation transform method [162,163,164]. A comparison of methods for the detection of GWs from unknown NSs is given in [165].

`Falcon`pipeline [166,167,168], have been developed to manage the huge computing cost of all-sky searches while keeping the robustness to a wide family of signals, allowing for a loose phase track in the evolution of the signal frequency. A different approach can be used if one wants to go deep with the sensitivity in an all-sky search but keep the focus on a specific narrow frequency band, as described in [169].

`Viterbi`tracker [170,171,172], the

`Sidereal Filter`[173] and cross-correlation based methods such as

`CrossCorr`[174]

`STAMP`[175],

`SOAP`[176] or

`Radiometer`[177]. Some of these methods—CrossCorr method [178], Viterbi/J-statistic method [179], the 5-vector binary method [180] and the method in [81]—have been adapted for the LMXB searches such as Sco-X1, where also the orbital modulation needs to be considered and a stochastic spin wandering, including spin-up, is sometimes taken into account. Methods specifically tailored for all-sky searches for unknown binaries are the BinarySkyHough [181] and TwoSpect [182].

## 4. Recent Results

#### 4.1. Results from Known Sources (Pulsars, LMXBs, Supernova Remnants)

#### 4.1.1. Known Pulsars

#### 4.1.2. Supernova Remnants

#### 4.1.3. Low-Mass X-ray Binaries and Sco-X1

#### 4.2. Results from Unknown Sources (All-Sky, Spotlight Surveys, Dark Matter Candidates)

#### 4.2.1. All-Sky Surveys

#### 4.2.2. Spotlight Surveys: The Galactic Center and Terzan 5

#### 4.2.3. Dark Matter Candidates—Ultralight Bosons and CDOs

^{2}is a vector boson, the dark photon, which directly couples to GW interferometers (see Section 2.2). The latest O3 LIGO-Virgo data all-sky search for the CW signature from this type of system provided in [123]. The boson mass range probed by this search is (2–4) $\times \phantom{\rule{0.166667em}{0ex}}{10}^{-13}$ eV/c

^{2}, corresponding to the detectors frequencies $[10;2000]\mathrm{Hz}$. The search applies two complementary methods. One pipeline is based on a cross-correlation method [106] and already used in a previous dark photon DM O1 search [117]. The second is a semi-coherent method [196] based on the band-sampled-data framework [147] and adapted from the one used in the latest O3 BH-boson cloud search [194,297]. No evidence of DM signatures has been found, and upper limits on the signal strain are derived. These limits can be converted into upper limits on the coupling factor of the interaction between the dark photon and the baryons in the detector. These constraints surpass the ones provided by existing DM experiments, such as the Eöt–Wash torsion balance [299] and MICROSCOPE [300], and improve previous O1 results by a factor $\sim 100$.

## 5. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## Notes

1 | Given the proportionality between ${f}_{\mathrm{gw}}$ and ${f}_{\mathrm{spin}}$, here f can indicate any of the two frequencies. |

2 | for $m=1$ and for $\alpha \ll 0.1$. |

3 | Hence, the time derivative of the time component of ${A}_{\mu}$ is negligible relative to $\overrightarrow{A}$. |

4 | Recycled pulsars are ordinary pulsars that have been spun up by accretion from a companion star in a binary system. |

5 | The ranges are due to fact that the coherence time used in [248] changes in each 10Hz frequency band. |

6 | except for the SOAP pipeline that covers the additional small region $[1000;2048]\mathrm{Hz}$ in frequency and $[{10}^{-9};{10}^{-8}]\mathrm{Hz}/\mathrm{s}$ in spin-up. |

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**Figure 1.**Features of a CW signal without noise. (

**Left**): time series of the signal before removing any modulation, the signal is modulated in amplitude and frequency. (

**Right**): power spectrum after removing the frequency modulations, the five peaks due to the sidereal modulation are clearly visible.

**Figure 2.**Upper limits on ${h}_{0}$ for the 236 pulsars in the targeted search in [222] are relative to the time-domain Bayesian method. The stars show $95\%$ credible upper limits on the amplitudes of ${h}_{0}$. Grey triangles represent the spin-down limits for each pulsar computed as in Equation (11). Pulsars with upper limits surpassing their spin-down limits are marked with yellow circles. The pink curve gives an estimate of the expected strain sensitivity of all three detectors combined during the course of O3. Figure taken from [222].

**Figure 3.**Results taken from the supernova remnant search in LIGO O3a data for Cas A and Vela Jr using Weave [247]. Estimated GW strain amplitude sensitivities are given at the $95\%$ confidence level. Additional results from prior searches for Cas A and Vela Jr. in O1 Einstein@Home $90\%$ C.L. [250] and the O3a model-robust Viterbi method (yellow) and band-sampled-data method (purple) [248]. The solid red horizontal line indicates the age-based upper limit on the Cas A strain amplitude. The dashed (dotted) horizontal blue lines indicate the optimistic (pessimistic) age-based upper limit on Vela Jr. strain amplitude, assuming an age and distance of 700 yr and 0.2 kpc (5100 yr and 1.0 kpc). Figure adapted from [247].

**Figure 4.**GW strain upper limits at $95\%$ confidence as a function of frequency. No assumption on the $\iota $ angle is made for the curves in the figure. The curves are for the CrossCorr O1 search [262] (black line), the CrossCorr O2 search [259] (brown line), the Radiometer O3 search [269] (light pink line), and the O3 hidden Markov model search [263] (green line). The indirect torque-balance upper limits (see Equation (13)), for the ${r}_{m}=R$ case (red solid line) and for ${r}_{m}$ equal to the Alfven radius (dashed red line), are also plotted. Figure taken from [263].

**Figure 5.**Comparison of 95% confidence upper limits on GW amplitude obtained in the O3 all-sky search by the FrequencyHough pipeline (black triangles), the SkyHough pipeline (red squares), the Time-Domain F-statistic pipeline (blue circles), and the SOAP pipeline (magenta diamonds). Population-averaged upper limits obtained in the Powerflux O3a search are marked with dark-green crosses. Figure taken from [161].

**Figure 6.**Maximum distance at which at least $5\%$ of a simulated population of BHs-boson cloud would produce a detectable GW signal in the search described in [297]. The simulated population has a maximum BH mass of $100{M}_{\odot}$. The curve is produced for different markers for systems with ages between ${10}^{3}$ yrs and ${10}^{7}$ yrs, as indicated in the legend. Figure taken from [297].

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Piccinni, O.J.
Status and Perspectives of Continuous Gravitational Wave Searches. *Galaxies* **2022**, *10*, 72.
https://doi.org/10.3390/galaxies10030072

**AMA Style**

Piccinni OJ.
Status and Perspectives of Continuous Gravitational Wave Searches. *Galaxies*. 2022; 10(3):72.
https://doi.org/10.3390/galaxies10030072

**Chicago/Turabian Style**

Piccinni, Ornella Juliana.
2022. "Status and Perspectives of Continuous Gravitational Wave Searches" *Galaxies* 10, no. 3: 72.
https://doi.org/10.3390/galaxies10030072