Sonic-Point Movie


Sonic-Point Beat-Frequency Model of Kilohertz QPOs

Variation of Kilohertz QPO Frequency Separation

Numerical computations with radiation forces in full general relativity

Scene1: Summary of Sonic-Point Beat-Frequency Model of Kilohertz QPOs.



A rotating neutron star appears at the center of the screen, colored red. Surrounding the star is an accretion disk--a disk of slowly inspiraling gas, here colored blue. The brightness of the disk indicates the density of the gas; high density is bright blue, low density is dark blue. Notice that the density is much lower inside the sonic radius than outside. When matter reaches the sonic radius, it plunges inward suddenly and hits the star. Hence, matter is sparse this close or closer to the star.



With no localized density fluctuations in the accretion disk, the brightness of the star remains constant. This is represented by flat line on the graph of Flux vs time below the view of the star.



A density fluctuation is introduced onto the accretion disk. This extra clump of matter is moving in a circular orbit at the sonic radius. As the density fluctuation circles the star, matter streams off it and falls to the star's surface. The extra matter falling onto the star causes an increase in x-ray emmission, which is represented by the yellow beam. As shown in the graph os flux vs time, the observed brightness of the star varies as the beam sweeps past us. This effect is sometimes compared to that of a lighthouse. The frequency of this variation is known as 2, or sometimes as the lighthouse frequency.



The magenetic field of the star, represented by a red beam, modulates the flow of material onto the star. When the clump passes through the red beam, more matter streams off than usual. The variation in the stream naturally produces a variation in the yellow beam. This variation in brightness of the yellow beam is charaterised by 1.


Here, the two frequencies, 1 and 2, are plotted on a power spectrum graph.

  • Scene1.mov(9.7 Mb)
    This movie shows the clump orbiting the star, with the graphs of 1 and 2 tracing out below.

    Scene 2, Part 1: Larger Sonic Radius, Negligible Inward Drift

  • Scene2-part1.mov(3.5 Mb)
    Scene 1 is replayed in the co-rotating frame of the density fluctuation. Note that the red beam, rotating with the star, appears to revolve backwards in this frame. The graph of 1 continues to show the modulation in brightness of the yellow beam. Note the material falling off of the density fluctuation every time the red pulsar beam sweeps over the clump. For simplicity, we have removed the graph on 1, the lighthouse frequency.

    Here we see the power spectrum of the received signal from the system. The peak at 1 indicates the frequency of modulation of the yellow beam. The peak at 2, the lighthouse frequency, is plotted as well, even though it is not represented in the time domain. The separation between 1 and (nu)2 is the spin frequency of the star.

    Scene 2, Part 2: Larger Sonic Radius, Significant Inward Drift

  • Scene2-part2.mov(2.4 Mb)
    In this movie, The density fluctuation will no longer be moving in a perfectly circular orbit. Instead, it will fall into the neutron star at a significant rate compared to its orbital speed. In the co-rotating frame of the density fluctuation, the inspiral appears as radial motion toward the star. The radial motion causes a doppler-like effect which increases 1 and a phase shift which decreases 2. The graph of Flux vs. Time from the circular orbit is shown in blue.

    In the power spectrum, note that the peaks of 1 and 2 are closer together when the inward drift is significant as compared to when the density fluctuation orbits circularly.

    Scene 3, Part 1: Smaller Sonic Radius, Negligible Inward Drift

  • Scene3-part1b.mov(2.6 Mb)
    The situation here is much the same as above, except the sonic radius is much closer to the star than in scene 2. The closer sonic radius is caused by a higher overall density of material flowing onto the star. Note in this scene that the density fluctuation orbits much faster around the star. In the corotating frame, shown here, this is apparent in the faster spin of the star and the accompanying red beam.

  • Scene3-part1a.mov(1.4 Mb)
    This movie shows the relative sizes beteen the far and near sonic radii by fading between the two and then zooming in.

    The higher orbital frequency results in the peaks appearing on the right of the power spectrum graph. The separation between the peaks is the spin frequency of the star.

    Scene 3, Part 2: Smaller Sonic Radius, Significant Inward Drift

  • Scene3-part2.mov(2.7 Mb)
    Here, the density fluctuation falls toward the star at a significant rate. Again, note the inward radial motion of the density fluctuation and the resultant phase shift of the yellow beam. The phase shift of the beam will lower 2', while a doppler-like effect of the density fluctuation moving towards the star will increase 1'.

    Note that the inspiral peaks are again bracketed by the circular peaks, just as they were in the far sonic radius case shown in scene 2. The difference, though, is that the separation between the blue inspiral peaks is much smaller here than when the sonic radius is further out.

    Scene 4: Final Graphs

    		 Here are the final graphs of 1 and 2 from scenes three and four, respectively.

    		Sliding the graphs up to make room, we prepare axis for plotting the seperation between 1 and 2 vs 2.

    		Here is the plot of delta vs 2. Note the curve of the blue line representing the significant inward drift model vs the flat line delta vs _s representing the negligible inward drift model.
    		Zoom up on the blue curve and fade up some model parameters.
    		Finally, fade up the data for Sco X-1. Note that the model which assumes negligible inward drift, the flat green line above, does not fit the data.

    Scientific visualization by


    Undergraduate Research Team
    Departments of Physics and Astronomy
    University of Illinois at Urbana-Champaign

    last updated 5.22.01 by dmw
    Center for Theoretical Astrophysics---University of Illinois at Urbana-Champaign
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