Present and upcoming time-domain astronomy efforts , in part driven by gravitational-wave followup campaigns , will unveil a variety of rare explosive transients in the sky .
We focus here on pulsational pair-instability evolution , which can result in signatures observable with electromagnetic and gravitational waves .
We simulate grids of bare helium stars to characterize jointly the resulting black hole ( BH ) masses and ejecta composition , velocity , and thermal state .
We find that the stars do not react “ elastically ” to the thermonuclear ignition in the core : there is not a one-to-one correspondence between pair-instability driven ignition and mass ejections , which causes ambiguity in what is an observable pulse .
In agreement with previous studies , we find that for initial helium core masses 37.5 M _ { \odot } \lesssim M _ { \mathrm { He,init } } \lesssim 41 M _ { \odot } ( corresponding to carbon-oxygen core masses 28 M _ { \odot } \lesssim M _ { \mathrm { CO } } \lesssim 30.5 M _ { \odot } ) the explosions are not strong enough to affect the surface .
With increasing initial helium core mass , they become progressively stronger causing first large radial expansion ( 41 M _ { \odot } \lesssim M _ { \mathrm { He,init } } \lesssim 42 M _ { \odot } , corresponding to 30.5 M _ { \odot } \lesssim M _ { \mathrm { CO } } \lesssim 31.4 M _ { \odot } ) , and finally , also mass ejection episodes ( for M _ { \mathrm { He,init } } \gtrsim 42 M _ { \odot } , or M _ { \mathrm { CO } } \gtrsim 31.4 M _ { \odot } ) .
The lowest mass helium core to be fully disrupted in a pair-instability supernova is M _ { \mathrm { He,init } } \simeq 80 M _ { \odot } , corresponding to M _ { \mathrm { CO } } \simeq 57 M _ { \odot } .
Models with M _ { \mathrm { He,init } } \gtrsim 200 M _ { \odot } ( M _ { \mathrm { CO } } \gtrsim 121 M _ { \odot } ) reach the photodisintegration regime , resulting in BHs with masses M _ { \mathrm { BH } } \gtrsim 125 M _ { \odot } .
If the pulsating models produce BHs via ( weak ) explosions , the previously-ejected material might be hit by the blast wave and convert kinetic energy into observable electromagnetic radiation .
We characterize the hydrogen-free circumstellar material from the pulsational pair-instability of helium cores assuming simply that the ejecta maintain a constant velocity after ejection .
We find that our models produce helium-rich ejecta with mass 10 ^ { -3 } M _ { \odot } \lesssim M _ { \mathrm { CSM } } \lesssim 40 M _ { \odot } , the larger values corresponding to the more massive progenitor stars .
These ejecta are typically launched at a few thousand { \mathrm { km s ^ { -1 } } } and reach distances of \sim 10 ^ { 12 } -10 ^ { 15 } \mathrm { cm } before the core-collapse of the star .
The delays between mass ejection events and the final collapse span a wide and mass-dependent range ( from sub-hour to 10 ^ { 4 } years ) , and the shells ejected can also collide with each other , powering supernova impostor events before the final core-collapse .
The range of properties we find suggests a possible connection with ( some ) type Ibn supernovae .