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

Abstract

Abstract We present the results of 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 ≈6 × 10−15 and 3 × 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 × 105 K for J1640 and 3.6–4.7 × 105 K for J1709, where the low end of the range corresponds to canonical neutron stars (M = 1.4 M ⊙), and the upper end corresponds to higher-mass stars (M = 2.21 M ⊙). Under the assumption that r-mode heating provides the thermal support, we obtain dimensionless r-mode amplitude upper limits of 3.2–4.8 × 10−8 and 1.8–2.8 × 10−7 for J1640 and J1709, respectively, where again the low end of the range corresponds to lower-mass, canonical neutron stars (M = 1.4 M ⊙). 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 SAX J1808.4–3658, which has a comparable amplitude limit to J1640 and J1709.