Where Are the r-modes? Chandra Observations of Millisecond Pulsars

Abstract

We present the results of {\it Chandra} observations of two non-accreting millisecond pulsars, PSRs J1640$+$2224 (J1640) and J1709$+$2313 (J1709), with low inferred magnetic fields and spin-down rates in order to constrain their surface temperatures, obtain limits on the amplitude of unstable $r$-modes in them, and make comparisons with similar limits obtained for a sample of accreting low-mass X-ray binary (LMXB) neutron stars. We detect both pulsars in the X-ray band for the first time. They are faint, with inferred soft X-ray fluxes ($0.3-3$ keV) of $\approx$ $6\times 10^{-15}$ and $3\times 10^{-15}$ erg cm${}^{-2}$ s${}^{-1}$ for J1640 and J1709, respectively. Spectral analysis assuming hydrogen atmosphere emission gives global effective temperature upper limits ($90\%$ confidence) of $3.3-4.3\times 10^5$ K for J1640 and $3.6-4.7\times 10^5$ K for J1709, where the low end of the range corresponds to canonical neutron stars ($M=1.4M_{\odot }$), and the upper end corresponds to higher-mass stars ($M=2.21M_{\odot }$). Under the assumption that $r$-mode heating provides the thermal support, we obtain dimensionless $r$-mode amplitude upper limits of $3.2-4.8\times 10^{-8}$ and $1.8-2.8\times 10^{-7}$ for J1640 and J1709, respectively, where again the low end of the range corresponds to lower-mass, canonical neutron stars ($M=1.4M_{\odot }$). These limits are about an order of magnitude lower than those we derived previously for a sample of LMXBs, except for the accreting millisecond X-ray pulsar (AMXP) SAX J1808.4$-$3658, which has a comparable amplitude limit to J1640 and J1709.

arXiv comment9 pages, 4 figures, published in ApJ

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• The enigmatic spin evolution of PSR J0537-6910: r-modes, gravitational waves and the case for continued timing
• Chandra studies of the globular cluster 47 Tucanae: A deeper X-ray source catalogue, five new X-ray counterparts to millisecond radio pulsars, and new constraints to r-mode instability window
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