# How to search for gravitational waves from $r$-modes of known pulsars

## TL;DR

This paper introduces a new method for searching gravitational waves from known pulsars specifically targeting $r$-modes, which oscillate at about four thirds the pulsar's spin frequency, expanding the scope beyond traditional mass quadrupole searches.

## Contribution

It presents the first framework for constructing searches over frequency and spin-down ranges to detect $r$-mode gravitational waves from known pulsars, including sensitivity and computational cost estimates.

## Key findings

- Feasible $r$-mode searches can surpass spin-down limits.
- New search methods for $r$-modes are developed.
- Existing LIGO and Virgo data can be used effectively.

## Abstract

Searches for continuous gravitational waves from known pulsars so far have been targeted at or near the spin frequency or double the spin frequency of each pulsar, appropriate for mass quadrupole emission. But some neutron stars might radiate strongly through current quadrupoles via $r$-modes, which oscillate at about four thirds the spin frequency. We show for the first time how to construct searches over appropriate ranges of frequencies and spin-down parameters to target $r$-modes from known pulsars. We estimate computational costs and sensitivities of realistic $r$-mode searches using the coherent $\mathcal{F}$-statistic, and find that feasible searches for known pulsars can beat spin-down limits on gravitational wave emission even with existing LIGO and Virgo data.