It has been suggested that SNe Ia could be produced in the condition of the violent merger scenario of the double-degenerate model , in which a thermonuclear explosion could be produced when the merging of double carbon-oxygen white dwarfs ( CO WDs ) is still ongoing .
It has been recently found that the nucleus of the bipolar planetary nebula Henize 2-428 consists of double CO WDs that have a total mass of \sim 1.76 M _ { \odot } , a mass ratio of \sim 1 and an orbital period of \sim 4.2 hours , which is the first and only discovered progenitor candidate of SNe Ia predicted by the violent merger scenario .
In this work , we aim to reproduce the evolutionary history of the central double CO WDs of Henize 2-428 .
We find that the planetary nebula Henize 2-428 may originate from a primordial binary that have a \sim 5.4 M _ { \odot } primary and a \sim 2.7 M _ { \odot } secondary with an initial orbital period of \sim 15.9 days .
The double CO WDs are formed after the primordial binary experiencing two Roche-lobe overflows and two common-envelope ejection processes .
According to our calculations , it takes about \sim 840 Myr for the double CO WDs to merge and form an SN Ia driven by the gravitational wave radiation after their birth .
To produce the current status of Henize 2-428 , a large common-envelope parameter is needed .
We also estimate that the rate of SNe Ia from the violent merger scenario is at most 2.9 \times 10 ^ { -4 } yr ^ { -1 } , and that the delay time is in the range of \sim 90 Myr to the Hubble time .