N414_29c 522..525

The X-ray source known as GRS1915+105 belongs to a group dubbed `microquasars'. These objects are binary systems which sporadically eject matter at speeds that appear superluminal, as is the case for some quasars. GRS1915+105 is also one of only two known binary sources thought to contain a maximally spinning black hole. Determining the basic parameters of GRS195+105, such as the masses of the components, will help us to understand jet formation in this system, as well as providing links to other objects which exhibit jets. Using X-ray data, indirect methods have previously been used to infer a variety of masses for the accreting compact object in the range 10±30 solar masses (M(). Here we report a direct measurement of the orbital period and mass function of GRS1915+105, which allow us to deduce a mass of 14 6 4 M( for the black hole. Black holes with masses .5±7 M( challenge the conventional picture of black-hole formation in binary systems. Based on the mass estimate, we interpret the distinct X-ray variability of GRS1915+105 as arising from instabilities in an accretion disk that is dominated by radiation pressure, and radiating near the Eddington limit (the point where radiation pressure supports matter against gravity). Also, the mass estimate constrains most models which relate observable X-ray properties to the spin of black holes in microquasars. GRS1915+105 is located in the Galactic plane at a distance of ,11±12 kpc (refs 10, 11) and suffers a large extinction of 25± 30 mag in the visual band. Spectroscopic observations in the nearinfrared H and K bands identi®ed absorption features from the atmosphere of the companion (mass-donating star) in the GRS1915+105 binary. The detection of CO and CO band heads plus a few metallic absorption lines suggested a K-M spectral type and luminosity class III (giant). The presence of these band-head features led us to carry out follow-up medium-resolution spectroscopy in the 2.29±2.41 mm wavelength range using the Very Large Telescope (VLT)-Antu equipped with Infrared Spectrometer and Array Camera ISAAC, between April and August 2000 (Fig. 1). Radial velocities were measured for the 16 individual spectra by cross-correlation of the major CO band heads, and a period analysis was carried out (Fig. 2). The periodogram shows a clear peak at a period of 33.5 days (top panel) which we interpret as the orbital period Porb of the binary system. The velocity amplitude is measured to be Kd ˆ 140 6 15 km s 21 (lower panel). Figure 1 shows that the infrared ̄ux is dominated by light from the accretion ̄ow or jet, rather than from the secondary star. There is thus a possibility that phasedependent changes in the continuum near the absorption features may result in an additional source of systematic error in the measured value of Kd. The measured parameters allow us to determine the mass function f(M), that is, the observational lower limit to the mass of the compact object: