Pulse Core Lexicon
Merger Level Gain
Definition
Merger Level Gain gives the levels a merger adds to the child of the well it makes.
A merger adds the mass it joins, less what it radiates as gravitational waves: about 0.93 levels for equal wells, 0.53 at one to two, 0.29 at one to four, 0.13 at one to ten. Equal mergers climb fastest; a line of lopsided ones needs more generations.
ΔL = log₂((1 + q) · (1 − ε_GW)), where ΔL is the levels added [∅], q the mass ratio, lighter over heavier [∅], and ε_GW the share of the pair's mass radiated [∅].
It connects to Child Level, Level Walk and Gravitational-Wave Power.
Mathematical Expression
From the book · Chapter 3 · Galaxies: the Wells and the Stars Around Them
ΔL = log₂((1 + q) · (1 − ε_GW))
Dimensional analysis:
Where (from the book): ΔL⊛ [∅], q [∅], ε_GW [∅]
[∅]
log₂(([∅] + [∅]) × ([∅] - [∅])) = log₂([∅] × ([∅] - [∅])) = log₂([∅] × [∅]) = log₂([∅]) = [∅]
[∅] = [∅] ✓ Valid PulseCore Verified ✓
How many levels a merger adds to its well's child
Where:
- ΔL [∅] — the levels the merger adds
- q [∅] — the mass ratio, lighter over heavier
- ε_GW [∅] — the share of the pair's mass radiated, by the numerical-relativity fit (Gravitational-Wave Power)
Technical Details
Category Manuscript
Chapter Chapter 3
Importance