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What would be the typical lifetime of an x-ray binary? I have trouble finding a reference.

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I am not an expert on the topic but probably you have to specify in your search which mass regime are you looking for (low or high mass x-ray binaries). Accretion time must be important and depends on the mass. High-mass stars are young (very short life) < $10^7$ years. This reference is quite old but probably helps a bit:

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The lifetime of an X-ray binary is pretty broad and it depends on the type of X-ray binary you are talking about. There are 3 main types of X-ray binaries:

  1. Low Mass X-ray Binaries
  2. Intermediate Mass X-ray Binaries
  3. High Mass X-ray Binaries

The accretion process is drastically different for each of these types, which means that there is no broad lifetime of an X-ray binary: it depends on the type of X-ray binary you are talking about.

I believe High Mass X-ray Binaries last the longest, give their comparatively lower accretion rate, but again, this is influenced by a wide range of parameters, like the age of the donor star.

In conclusion, the lifetime depends on the type of the X-ray binary, accretion rate, and other parameters.

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