White light indicates the divine consciousness. White is the purity and power of the divine Truth. The white light is a manifestation of pure divine force descending from one of the truth-planes leading to the supramental. The white light is the light of the Mother in which all others are contained and from which they can be manifested.
The white light and the illumining of the heart by the light is a thing of great power in this sadhana.
If the peace once becomes stable, there is no further assimilation needed for that, as that means the whole system is sufficiently prepared to receive and absorb continuously. There may be periods of assimilation necessary for other things, but these periods need not interrupt the inner status. For instance if Force or Ananda or Knowledge begin to descend from above, there might be interruptions and probably would be, the system not being able to absorb in continuous flow, but the peace would remain in the inner being. Or there might even be something like periods of struggle on the surface, but the inner being would remain calm and still watching and undisturbed and, if there is knowledge established within, understanding the action. Only for that the whole being vital, physical, material must have become open and receptive to the peace. Peace would then go on perhaps deepening and becoming wider and wider, but periods of interruption and assimilation would not be needed.