| Abstract
| - Abstract. We report on two Rossi X-ray Timing Explorer (RXTE) observations of the anomalous X-ray pulsars 1E 1048.1-5937 and 1E 2259+586. Both sources have continued their almost constant spin-down during 1995/96. We carried out a search for orbital Doppler shifts, in their observed spin frequencies, deriving stringent limits on the projected semi-axis. Unless these systems have unlikely small inclinations, main-sequence companions can be excluded. If 1E 1048.1-5937 and 1E 2259+586 are indeed binary systems, their companion stars must be either white dwarfs, or helium-burning stars with M≲ 0.8 M☉, possibly underfilling their Roche lobe.
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