Brian McGloughlin, Jing Ming, Maria Alessandra Papa, Kartikey Sharma, Reinhard Prix, Benjamin Steltner, Heinz-Bernd Eggenstein, Na Wang, Jianping Yuan

We perform a search for continuous gravitational waves from J0435+3233 using LIGO O4a public data. J0435+3233 is unique among millisecond pulsars as it exhibits an exceptionally large spin-down and marks the first pulsar observed to date with a spin-down larger than $10^{-12}$ Hz/s in the sub $10$ ms spin period range, making it a potentially strong source of continuous gravitational waves. We target signals at exactly twice the rotation frequency, a narrow band around this frequency, and also signals corresponding to r-modes. Our results are consistent with a non-detection. Our most stringent upper limit on the intrinsic gravitational wave amplitude is $h_0=\targetedULninetyfive$, at the 95\% confidence level, which is a factor of $\approx14$ times lower than the spin-down limit. With an estimated source distance of $1.2$ kpc our upper limit on the gravitational wave amplitude excludes source ellipticities greater than $\targetedellipULninetyfive$, making this the first source for which the spin-down upper limit is beaten by over an order of magnitude {\it{and}} the ellipticity is constrained to a physically interesting range, in the low $10^{-8}$ region.