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The acceleration of particles up to GeV or higher energies in microquasars has been the subject of considerable theoretical and observational efforts in the past few years. Sco X-1 is a microquasar from which evidence of highly energetic particles in the jet has been found when it is in the so-called Horizontal Branch (HB), a state when the radio and hard X-ray fluxes are higher and a powerful relativistic jet is present. Here we present the first very high energy gamma-ray observations of Sco X-1, obtained with the MAGIC telescopes. An analysis of the whole data set does not yield a significant signal, with 95% CL flux upper limits above 300 GeV at the level of 2.4 X 10--12 cm--2 s--1. Simultaneous RXTE observations were conducted to provide the X-ray state of the source. A selection of the gamma-ray data obtained during the HB based on the X-ray colors did not yield a signal either, with an upper limit of 3.4 X 10--12 cm--2 s--1. These upper limits place a constraint on the maximum TeV luminosity to non-thermal X-ray luminosity of L VHE/L ntX 0.02 that can be related to a maximum TeV luminosity to jet power ratio of L VHE/L j 10--3. Our upper limits indicate that the underlying high-energy emission physics in Sco X-1 must be inherently different from that of the hitherto detected gamma-ray binaries.