X-ray binaries such as GRS-1915 feature a black hole and a regular star. The x-ray luminosity is likely related to the rate of mass flow into the black hole from the star so when there is a lot of mass flow the x-ray luminosity is high but this explanation seems to just beg the question as to why the mass flow would change over time.
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Such objects are surrounded by an accretion disk, that is a disk of gas, the gas being accreted onto the central object. However, at this stage of its life, the accretion disk around the black hole of a binary system like GRS-1915+105 is strongly depleted. Therefore, the accretion rate is not sufficient to support a coutinuous burst. Matter fills the outer disk until a critical density is reached, that triggered an outburst. Mass from the companion star is lost by a Roche lobe overflow mechanism.
References:
- X-ray binaries in general: Remillard & McClintock 2006
- For the outburst X-ray transients in particular: Dubus et al. 2001
