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

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 approx. 6 x 10(exp -15) and 3 x 10( exp -15) erg/sq cm for J1640 and J1709, respectively. Spectral analysis assuming hydrogen atmosphere emission gives global effective temperature upper limits (90% confidence) of 3.3-4.3 x 10(exp 5) K for J1640 and 3.6-4.7 x 10(exp 5) K for J1709, where the low end of the range corresponds to canonical neutron stars (M = 1.4 Stellar Mass), and the upper end corresponds to higher-mass stars (M = 2.21 Stellar Mass). Under the assumption that r-mode heating provides the thermal support, we obtain dimensionless r-mode amplitude upper limits of 3.2-4.8 x 10(exp -8) and 1.8-2.8 x 10(exp -7) for J1640 and J1709, respectively, where again the low end of the range corresponds to lower-mass, canonical neutron stars (M =1.4 Stellar Mass). 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 J1808.43658, which has a comparable amplitude limit to J1640 and J1709.