Pulse Core Lexicon
Depletion Time Evolution
Definition
Depletion Time Evolution is the Gas Depletion Law's change with the age of a universe: t⇣⊚(a) = t⇣⊚ · a^0.6, the depletion time at the threshold growing with the scale factor, so galaxies used their gas faster when the universe was young. The sky measures it as (1 + z)^(−0.6), about 0.7 billion years at cosmic noon against 2 billion today (Genzel et al. 2015; Tacconi et al. 2018), and with 1 + z = 1/a it reads a^0.6. It is why a universe's star formation rises to a peak near a quarter of its life, cosmic noon, and falls to about an eighth of that rate by the End of its Outward Expansion (Madau & Dickinson 2014). It connects to Gas Depletion Law, End of the Outward Expansion and Eddington Ratio of a Well.
Mathematical Expression
From the book · Chapter 6 · Stellar Formalism: The Gas, the Stellar Mass Unit, and the Stellar Null Well
t⇣⊚(a) = t⇣⊚ · a^(0.6)
Dimensional analysis:
Where (from the book): t⇣⊚(a) [𝕋], t⇣⊚ [𝕋], a [∅]
[𝕋]
[𝕋] × [∅]^([∅]) = [𝕋] × [∅]^([∅]) = [𝕋] × [∅] = [𝕋]
[𝕋] = [𝕋] ✓ Valid PulseCore Verified ✓
Galaxies used their gas faster when the universe was young: the depletion time grows with the scale factor
Where:
- t⇣⊚(a) [𝕋] — the depletion time at the threshold density when the scale factor is a
- t⇣⊚ [𝕋] — its value at full size, a = 1: about 2 × 10⁹ years, 0.145 of the life
- a [∅] — the scale factor, 1 at the End of the Outward Expansion
Technical Details
Category Law
Chapter Chapter 6
Importance
In the book #831 of 1,287 terms · used 1 time