Astrophysics (Index)About

e-folding time

(e-folding)
(time to increase by a factor of e)

A quantity's e-folding time is the time over which it grows or shrinks by a factor of e (2.171828.., Euler's number), quantifying exponential growth or shrinkage. The term is more commonly used for growth; for shrinking quantities, other terms are used, including relaxation time and mean lifetime, and within some areas of science and engineering, it is what is generally meant by lifetime (e.g., the phrase radiative lifetime). The term half-life is analogous to relaxation time but is the time for shrinkage by a factor of 2. The term doubling time is analogous, for growth by a factor of 2. There is a fixed ratio between these based on a factor of 2 versus those based on a factor of e. Equivalences:

half-life (ln 2) × relaxation time 0.69314718056 × relaxation time
relaxation time ( 1/(ln 2) ) × half-life 1.44269504089 × half-life
doubling time (ln 2) × e-folding time 0.69314718056 × e-folding time
e-folding time ( 1/(ln 2) ) × doubling time 1.44269504089 × doubling time

The irrational number, e, is used because it offers some advantageous mathematical relationships. Among these is that relaxation time (based on e) of some type of decaying particles (e.g., free neutrons) does indeed equal the mean of their lifetimes.


(physics,measure)
Further reading:
https://en.wikipedia.org/wiki/E-folding
https://en.wikipedia.org/wiki/Exponential_growth
https://en.wikipedia.org/wiki/Doubling_time
https://en.wikipedia.org/wiki/Relaxation_(physics)
https://en.wikipedia.org/wiki/Exponential_decay
https://en.wikipedia.org/wiki/Half-life
https://dictionary.obspm.fr/index.php?formSearchTextfield=e-folding+time&showAll=1
https://www.physicsforums.com/threads/what-are-e-foldings-and-how-are-they-used-in-various-fields-of-study.674921/
https://e.math.cornell.edu/people/belk/writing/LinearODEs2.pdf

Referenced by pages:
aluminum (Al)
carbon (C)
CNO cycle
deuterium (D)
EXO
helium 1083 nm line
IMB
isotope
metastable
neutron
neutron capture
potassium/thorium ratio (K/Th ratio)
r-process
radioactive decay
radioactivity
relaxation time
Salpeter timescale
technetium star
timescale (t)
titanium (Ti)

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