The spin of a number of black holes ( BHs ) in binary systems has been measured .
In the case of BHs found in low-mass X-ray binaries ( LMXBs ) the observed values are in agreement with some theoretical predictions based on binary stellar evolution .
However , using the same evolutionary models , the calculated spins of BHs in high-mass X-ray binaries ( HMXBs ) fall short compared to the observations .
A possible solution to this conundrum is the accretion of high-specific-angular-momentum material after the formation of the BH , although this requires accretion above the Eddington limit .
Another suggestion is that the observed high values of the BHs spin could be the result of an asymmetry during Core Collapse ( CC ) .
The only available energy to spin up the compact object during CC is its binding energy .
A way to convert it to rotational kinetic energy is by using a Standing Accretion Shock Instability ( SASI ) , which can develop during CC and push angular momentum into the central compact object through a spiral mode ( m = 1 ) .
Here we study the CC-SASI scenario and discuss , in the case of LMXBs and HMXBs , the limits for the spin of a stellar-mass BHs .
Our results predict a strong dichotomy in the maximum spin of low-mass compact objects and massive BHs found in HMXBs .
The maximum spin value ( |a _ { \star } | ) for a compact object near the mass boundary between BHs and NSs is found to be somewhere between 0.27 and 0.38 , depending on whether secular or dynamical instabilities limit the efficiency of the spin up process .
For more massive BHs , such as those found in HMXBs , the natal spin is substantially smaller and for \mbox { $M _ { BH } $ } > 8 ~ { } \mbox { $M _ { \odot } $ } spin is limited to values |a _ { \star } | \lesssim 0.05 .
Therefore we conclude that the observed high spins of BHs in HMXBs can not be the result of a CC-SASI spin up .