Annu. Rev. Astron. Astrophys. 1999. 37: 409-443
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3.1. Superluminal Motions in GRS 1915+105

Figure 2 shows a pair of bright radio condensations emerging in opposite directions from the compact, variable core of GRS 1915+105. Before and after the remarkable ejection event shown in Figure 2, the source ejected other pairs of condensations but with flux densities one to two orders of magnitude weaker. One of these weaker pairs can be seen in the first four maps of Figure 2, as a fainter pair of condensations moving ahead of the bright ones at about the same proper motion and direction.

Figure 2

Figure 2. Pair of radio condensations moving away from the hard X-ray source GRS 1915+105 (Mirabel & Rodríguez 1994). These uniform-weight VLA maps were made at lambda3.5-cm for the 1994 epochs on the right side of each map. The position of the stationary core is indicated with a small cross. The maps have been rotated 60° clockwise for easier display. The cloud to the left appears to move away from the stationary core at 125% the speed of light. Contours are 1, 2, 4, 8, 16, 32, 64, 128, 256 and 512 times 0.2 mJy/beam-1 for all epochs except for March 27 where the contour levels are in units of 0.6 mJy/beam-1. The half power beam width of the observations, 0.2 arc sec, is shown in the top right corner.

In Figure 3 we show the proper motions of the condensations detected from four ejection events in 1994. The angular displacements from the stationary core are consistent with unaccelerated motions. The time separation between ejections suggests a quasi-periodicity at intervals in the range of 20-30 days. Although the clouds in each event appear to move ballistically, always in the same general region of the sky, their position angles suggest changes by ~ 10° in the direction of ejection in one month.

Figure 3

Figure 3. Angular displacements as a function of time for four ejection events observed in 1994 in GRS 1915+105 (Rodríguez & Mirabel 1999a). Top: Angular displacements as a function of time for four approaching condensations corresponding to ejections that took place on (from left to right) 1994 January 29 (triangles), February 19 (squares), March 19 (circles), and April 21 (crosses). Bottom: Angular displacements as a function of time for three receding condensations corresponding to ejections that took place on (from left to right) 1994 February 19 (squares), March 19 (circles), and April 21 (crosses). The clouds of the 1994 January 29 ejection were relatively weak and the receding component could not be detected unambiguously. The dashed lines are the least squares fit to the angular displacements of the 1994 March 19 event, the brighter and better studied. Note that the motions appear to be ballistic (that is, unaccelerated).

Figures 2 and 3 show two asymmetries: one in apparent transverse motions, another in brightness. The cloud that appears to move faster also appears brighter. It has been shown that both asymmetries, in proper motions and in brightness, are consistent with the hypothesis of an anti-parallel ejection of twin clouds moving at relativistic velocities (Mirabel & Rodríguez 1994), as discussed in Section 4. At a distance of 12 kpc the proper motions measured with the VLA in 1994 of the approaching (17.6 ± 0.4 mas d-1) and receding (9.0 ± 0.1 mas d-1) condensations shown in Figure 2 imply apparent velocities on the plane of the sky of 1.25c and 0.65c, respectively. From the analysis of relativistic distorsion effects using the equations in the next section and the VLA data, it is inferred that the ejecta move with a speed of 0.92c at an angle theta = 70° to the line of sight.

Within the errors of the measurements and a precession of leq 10°, relativistic ejections with a stable jet axis at scales of 500-5000 AU and larger were later observed from GRS 1915+105 over a time span of four years (Mirabel et al 1996a, Fender et al 1999, Dhawan et al 1999). The VLBA images of GRS 1915+105 show that the jets are already collimated at milliarcsec scales (Dhawan et al 1999), namely, at about 10 AU from the compact source (Figure 4). The core appears as a synchrotron jet of length ~ 100 AU before and during optically thin flares, and at those scales it already exhibits Doppler boosting. Discrete ejecta have appeared at about 500 AU. Both, the observations with MERLIN (Fender et al 1999) and with the VLBA (Dhawan et al 1999) in the years 1997 and 1998 have shown faster apparent superluminal motions at 1.3c-1.7c at scales of hundreds of AU, and intrinsic expansions of the expelled clouds mostly in the direction of their bulk motions. At present it is not clear if the faster motions measured with the higher resolution observations of MERLIN and VLBA in 1997 relative to the VLA observations in 1994 are due to intrinsic faster ejections, changes in the angle to the line of sight, or to resolution effects between the arrays as suggested by Fender et al (1999).

Figure 4

Figure 4. Contour map of the 2-cm emission from the core of GRS 1915+105, as observed on April 11, 1997 with the Very Long Baseline Array at milliarcsecond angular resolution (Dhawan et al 1999). The angular resolution corresponds to about 10 AU at GRS 1915+105. The half power contour of the beam is shown in the bottom left corner. Contours are -1, 1, 2, 4, 8, 16, 32, 64, and 96 times 0.26 mJy beam-1. The position angle of this ejection at milliarcsec scale is the same as that seen at the arcsec scales three years before.

A secular proper motion of 5.8 ± 1.5 mas yr-1 in the galactic plane, in rough agreement with the HI distance of 12 kpc (Rodríguez et al 1995), has been measured with the VLBA (Dhawan et al 1999).

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