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✨ feat(dynamics): class-based relaxation time calculators #749

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✨ feat(dynamics): class-based relaxation time calculators #749

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24 changes: 15 additions & 9 deletions src/galax/dynamics/_src/cluster/api.py
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Original file line number Diff line number Diff line change
Expand Up @@ -139,31 +139,37 @@ def relaxation_time(*args: Any, **kwargs: Any) -> u.AbstractQuantity:
>>> M = u.Quantity(1e4, "Msun")
>>> r_hm = u.Quantity(2, "pc")
>>> m_avg = u.Quantity(0.5, "Msun")
>>> G = u.Quantity(4.30091e-3, "pc km2 / (s2 Msun)")

>>> gdc.relaxation_time(M, r_hm, m_avg, G=G).uconvert("Myr")
Quantity(Array(129.50788873, dtype=float64, weak_type=True), unit='Myr')
>>> gdc.relaxation_time(M, r_hm, m_avg=m_avg).uconvert("Myr")
Quantity(Array(129.50777927, dtype=float64), unit='Myr')

There are many different definitions of the relaxation time.
By passing a flag object you can choose the one you want.
Let's work through the built-in options:

>>> flags = gdc.relax_time # (not only flags)

- Baumgardt (1998) (the default):

>>> gdc.relaxation_time(gdc.relax_time.Baumgardt1998, M, r_hm, m_avg, G=G).uconvert("Myr")
Quantity(Array(129.50788873, dtype=float64, ...), unit='Myr')
>>> gdc.relaxation_time(flags.Baumgardt1998, M, r_hm, m_avg=m_avg).uconvert("Myr")
Quantity(Array(129.50777927, dtype=float64), unit='Myr')

- Spitzer and Hart (1971):

>>> gdc.relaxation_time(flags.SpitzerHart1971, M, r_hm, m_avg=m_avg).uconvert("Myr")
Quantity(Array(151.23177551, dtype=float64), unit='Myr')

- Spitzer (1987) half-mass:

>>> lnLambda = 10 # very approximate
>>> gdc.relaxation_time(gdc.relax_time.Spitzer1987HalfMass, M, r_hm, m_avg, lnLambda=lnLambda, G=G).uconvert("Myr")
Quantity(Array(143.38057289, dtype=float64, weak_type=True), unit='Myr')
>>> gdc.relaxation_time(flags.Spitzer1987HalfMass, M, r_hm, m_avg=m_avg, lnLambda=lnLambda).uconvert("Myr")
Quantity(Array(143.38045171, dtype=float64), unit='Myr')

- Spitzer (1987) core:

>>> Mcore, r_c = M / 5, r_hm / 5 # very approximate
>>> gdc.relaxation_time(gdc.relax_time.Spitzer1987Core, Mcore, r_c, m_avg, lnLambda=lnLambda, G=G).uconvert("Myr")
Quantity(Array(11.47044583, dtype=float64, weak_type=True), unit='Myr')
>>> gdc.relaxation_time(flags.Spitzer1987Core, Mcore, r_c, m_avg=m_avg, lnLambda=lnLambda).uconvert("Myr")
Quantity(Array(11.47043614, dtype=float64), unit='Myr')

Using multiple-dispatch, you can register your own relaxation time
definition.
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4 changes: 2 additions & 2 deletions src/galax/dynamics/_src/cluster/dmdt.py
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Expand Up @@ -332,8 +332,8 @@ def __call__(self, t: Time, M: ClusterMass, args: Any, /, **kw: Any) -> Array:
self.relaxation_time_flag,
Mq,
args["r_hm"],
args["m_avg"],
G=pot.constants["G"],
m_avg=args["m_avg"],
constants=pot.constants,
).uconvert("Myr")
r_ratio = u.ustrip("", args["r_hm"] / r_t)

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