arXiv subjects

Sha Wu

Publications and source records attributed to Sha Wu.

7 recordsLinked to original sources

arXiv2026

FAST Discovery of $\mu$Jy Radio Pulsations from PSR J2238+5903, Providing a DM Distance Anchor for the Candidate TeV Halo 1LHAASO J2238+5900

We report the first detection of radio pulsations from PSR J2238+5903, a gamma-ray pulsar spatially coincident with the extended TeV source 1LHAASO J2238+5900. Our 3000 s FAST L-band observation reveals a weak periodic signal at the known Fermi-LAT spin period, with $P=162.76568$ ms and $\mathrm{DM}=247.5\pm3.0~\mathrm{pc~cm^{-3}}$. The signal is independently confirmed by both FFT-based and Fast Folding Algorithm searches. The radiometer equation gives a flux density of $S_{1250}\simeq3\,\mu$Jy, placing PSR J2238+5903 among the faintest radio-detected Fermi pulsars. Interpreting the DM with Galactic electron-density models gives $d_{\rm DM}=7.4\pm3.9$ kpc. At this distance, the LHAASO WCDA 39\% containment radius corresponds to a characteristic diameter of $\sim132$ pc, and the $>1$ TeV luminosity is $L_{\rm TeV}\simeq7.1\times10^{34}$ erg s$^{-1}$, about 8\% of the pulsar's spin-down power. The radio DM thus provides the first pulsar-specific distance constraint for assessing whether 1LHAASO J2238+5900 is a young relic-PWN / TeV-halo transition system.

astro-ph.HE↗

arXiv2025

Spectra for finite unions of line segments

In this paper we study the spectrality of arc-length measures supported on the union of two line segments in the plane. We show that any such spectral measure must admit a line spectrum. Moreover, when the two segments are non-parallel, such spectral measure admits only line spectra. Thus, in this case every spectrum is one dimensional. In addition we show that this property fails for unions of three or more segments in the plane. We construct some arc-length spectral measures supported on the union of at least three line segments such that none of its spectra is contained in a line. Finally, we work in the general framework of arc-length measures supported on finite unions of curves in $\mathbb{R}^d$. We show that the size of any orthogonal set for such a measure inside a ball of radius $R$ grows at most linearly in $R$. We also give an alternative proof of this bound, and in fact obtain a more general result of growth rate of orthogonal sets for Ahlfors--David regular measures in $\mathbb{R}^d$ (not restricted to the one-dimensional setting).

math.CA↗

arXiv2025

Anisotropic Diffusion of $e^\pm$ in Pulsar Halos over Multiple Coherence of Magnetic Fields

The slow particle diffusion in pulsar halos, inferred from TeV gamma-ray surface brightness profiles, is attributed to cross-field diffusion under the anisotropic diffusion model. This model assumes sub-Alfv\'enic interstellar turbulence in the surrounding medium of the pulsar and a rough alignment of the line-of-sight of observers towards the pulsars with the local mean magnetic field direction in the halo. In this model, the expected morphology of a pulsar halo is highly dependent on the properties of the interstellar magnetic field. We investigate the anisotropic diffusion of electron-positron pairs across multiple coherence of magnetic fields in pulsar halos in this work. We focus particularly on their influences on the predicted gamma-ray surface brightness profile and the asymmetry of the halo's morphology, as well as the observational expectations by the Large High Altitude Air Shower Observatory (LHAASO). Our results indicate that the requirement of a specific magnetic field geometry can be alleviated when accounting for a limited (and realistic) coherence length of the magnetic field in the model. Also, the halo's morphology may appear less asymmetric, especially after being smoothed by the point spread function of instruments. It largely relaxes the tension between the asymmetric morphology of halos predicted by the model and lack of apparent asymmetric halos detected so far. Our findings demonstrate the important influence of the coherence length of interstellar magnetic field on the distribution of particles around their accelerators, and the consequence on the measured source morphology.

astro-ph.HE↗

arXiv2025

Spectrality of a measure consisting of two line segments

Take an interval $[t, t+1]$ on the $x$-axis together with the same interval on the $y$-axis and let $\rho$ be the normalized one-dimensional Lebesgue measure on this set of two segments. Continuing the work done by Lai, Liu and Prince (2021) as well as Ai, Lu and Zhou (2023) we examine the spectrality of this measure for all different values of $t$ (being spectral means that there is an orthonormal basis for $L^2(\rho)$ consisting of exponentials $e^{2\pi i (\lambda_1 x + \lambda_2 y)}$). We almost complete the study showing that for $-\frac12<t<0$ and for all $t \notin {\mathbb Q}$ the measure $\rho$ is not spectral. The only remaining undecided case is the case $t=-\frac12$ (plus space). We also observe that in all known cases of spectral instances of this measure the spectrum is contained in a line and we give an easy necessary and sufficient condition for such measures to have a line spectrum.

math.CA↗

arXiv2024

Integer tile and Spectrality of Cantor-Moran measures with equidifferent digit sets

Let $\left\{b_{k}\right\}_{k=1}^{\infty}$ be a sequence of integers with $|b_{k}|\geq2$ and $\left\{D_{k}\right\}_{k=1}^{\infty} $ be a sequence of equidifferent digit sets with $D_{k}=\left\{0,1, \cdots, N-1\right\}t_{k},$ where $N\geq2$ is a prime number and $\{t_{k}\}_{k=1}^{\infty}$ is bounded. In this paper, we study the existence of the Cantor-Moran measure $\mu_{\{b_k\},\{D_k\}}$ and show that $$\mathbf{D}_k:=D_k\oplus b_{k} D_{k-1}\oplus b_{k}b_{k-1} D_{k-2}\oplus\cdots\oplus b_{k}b_{k-1}\cdots b_2D_{1}$$ is an integer tile for all $k\in\mathbb{N}^+$ if and only if $\mathbf{s}_i\neq\mathbf{s}_j$ for all $i\neq j\in\mathbb{N}^{+}$, where $\mathbf{s}_i$ is defined as the numbers of factor $N$ in $\frac{b_1b_2\cdots b_i}{Nt_i}$. Moreover, we prove that $\mathbf{D}_k$ being an integer tile for all $k\in\mathbb{N}^+$ is a necessary condition for the Cantor-Moran measure to be a spectral measure, and we provide an example to demonstrate that it cannot become a sufficient condition. Furthermore, under some additional assumptions, we establish that the Cantor-Moran measure to be a spectral measure is equivalent to $\mathbf{D}_k$ being an integer tile for all $k\in\mathbb{N}^+$.

math.NT↗

arXiv2022

Spectrality of a class of infinite convolutions on $\mathbb{R}$

Given an integer $m\geq1$. Let $\Sigma^{(m)}=\{1,2, \cdots, m\}^{\mathbb{N}}$ be a symbolic space, and let $\{(b_{k},D_{k})\}_{k=1}^{m}:=\{(b_{k}, \{0,1,\cdots, p_{k}-1\}t_{k}) \}_{k=1}^{m}$ be a finite sequence pairs, where integers $| b_{k}| $, $p_{k}\geq2$, $|t_{k}|\geq 1$ and $ p_{k},t_{1},t_{2}, \cdots, t_{m}$ are pairwise coprime integers for all $1\leq k\leq m$. In this paper, we show that for any infinite word $\sigma=\left(\sigma_{n}\right)_{n=1}^{\infty}\in\Sigma^{(m)}$, the infinite convolution $$ \mu_{\sigma}=\delta_{b_{\sigma_{1}}^{-1} D_{\sigma_{1}}} * \delta_{\left(b_{\sigma_{1}} b_{\sigma_{2}}\right)^{-1} D_{\sigma_{2}}} * \delta_{\left(b_{\sigma_{1}} b_{\sigma_{2}} b_{\sigma_{3}}\right)^{-1}D_{\sigma_{3}}} * \cdots $$ is a spectral measure if and only if $p_{\sigma_n}\mid b_{\sigma_n}$ for all $n\geq2$ and $\sigma\notin \bigcup_{l=1}^\infty\prod_{l}$, where $\prod_{l}=\{i_{1}i_{2}\cdots i_{l}j^{\infty}\in\Sigma^{(m)}: i_{l}\neq j, |b_{j}|=p_{j}, |t_{j}|\neq1\}$.

math.CA↗

arXiv2019

The Large High Altitude Air Shower Observatory (LHAASO) Science Book (2021 Edition)

Since the science white paper of the Large High Altitude Air Shower Observatory (LHAASO) published on arXiv in 2019 [e-Print: 1905.02773 (astro-ph.HE)], LHAASO has completed the transition from a project to an operational gamma-ray astronomical observatory LHAASO is a new generation multi-component facility located in Daocheng, Sichuan province of China, at an altitude of 4410 meters. It aims at measuring with unprecedented sensitivity the spectrum, composition, and anisotropy of cosmic rays in the energy range between 10$^{12}$ and 10$^{18}$~eV, and acting simultaneously as a wide aperture (one stereoradiant) continuously operating gamma-ray telescope in the energy range between 10$^{11}$ and $10^{15}$~eV with the designed sensitivity of 1.3\% of the Crab Unit (CU) above 100 TeV. LHAASO's capability of measuring simultaneously different shower components (electrons, muons, and Cherenkov/fluorescence light), will allow it to investigate the origin, acceleration, and propagation of CR through measurement of the energy spectrum, elemental composition, and anisotropy with unprecedented resolution. The remarkable sensitivity of LHAASO will play a key role in CR physics and gamma-ray astronomy for a general and comprehensive exploration of the high energy universe and will allow important studies of fundamental physics (such as indirect dark matter search, Lorentz invariance violation, quantum gravity) and solar and heliospheric physics. The LHAASO Collaboration organized an editorial working group and finished all editorial work of this science book, to summarize the instrumental features and outline the prospects of scientific researches with the LHAASO experiment.

astro-ph.HE↗