New limits on the orbital parameters of 1E 1048.1-5937 and 1E 2259+586 from RXTE observations

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 less than or similar to 0.8 M-., possibly underfilling their Roche lobe.