Chandra study of a complete sample of millisecond pulsars in 47 Tucanae and NGC 6397

We report Chandra observations of the complete sample of millisecond pulsars (MSPs) with precise radio positions in the globular clusters 47 Tuc (NGC 104) and NGC 6397. The X-ray luminosities and colors are derived or constrained and compared to X-ray MSPs previously detected in the field as well as one previously detected in a globular cluster (M28). The 47 Tuc MSPs are predominantly soft sources suggestive of thermal emission from small (r(X) < 0.6 km) polar caps on the neutron star rather than magnetospheric emission and are a relatively homogeneous sample, with most X-ray luminosities in a surprisingly narrow range [L-X similar to (1-4) x 10(30) ergs s(-1)]. We use previously derived intrinsic (P) over dot values and find a new relation between L-X and spin-down luminosity, (E) over dot : L-X proportional to E-beta, with beta similar to 0.5 +/- 0.2 versus similar to 1.0 for both pulsars and MSPs in the field. Adding the single MSP in NGC 6397 constrains beta to 0.5 +/- 0.15. This L-X-(E) over dot relation and also the L-X/(E) over dot versus spin-down age are each similar to that found by Harding & Muslimov for thermal emission from polar cap heating. However, the cluster MSPs are relatively longer lived ( in thermal X-rays) than either the models or field MSPs, which may have additional magnetospheric (nonthermal) components. We suggest that the cluster MSPs may have altered surface magnetic field topology (e.g., multipole), or their neutron stars are more massive from repeated accretion episodes due to encounters and repeated exchange interactions. MSP binary companions on or just off the main sequence (e.g., NGC 6397) are likely to have been reexchanged and might show anomalous (P) over dot and (E) over dot values due to relaxation of misaligned core-crust spins. The radial distribution of similar to 40 soft Chandra sources in 47 Tuc is consistent with a similar to 1.4 M-. component in a multimass King model and with the identified MSP sample. The implied total MSP population in 47 Tuc with L-X greater than or similar to 10(30) ergs s(-1) is similar to 35-90 and can constrain the relative beaming in radio versus soft X-rays. NGC 6397 is relatively deficient in MSPs: its single detected example may have been reexchanged out of the cluster core.