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Calculate cluster evolution

Cluster evolution calculation (How-to)

Goal

Compute rotation/activity evolution tracks for a cluster of stars, then (a) inspect per-star tracks, (b) evaluate cluster distributions at a given age, and (c) save/reload the cluster to avoid recomputation.

Prerequisites

Install MORS and download stellar evolution data:

pip install fwl-mors
mors download all

Units: Mstar in M☉, Age in Myr, Prot in days, Omega in Ω☉.

Step 1 — Create a cluster from arrays

Create arrays/lists of masses and rotation rates (same length). If Age is omitted, MORS interprets Omega as the initial (~1 Myr) rotation rate.

import numpy as np
import mors

Mstar = np.array([1.0, 0.5, 0.75])
Omega = np.array([10.0, 10.0, 10.0])

cluster = mors.Cluster(Mstar=Mstar, Omega=Omega)

To show progress while tracks are computed, enable verbose:

cluster = mors.Cluster(Mstar=Mstar, Omega=Omega, verbose=True)

Step 2 — Fit tracks through a specified age (optional)

If you provide Age, MORS fits tracks so that each star passes through the given rotation rate at that age.

One age applied to all stars 

import numpy as np
import mors

Mstar = np.array([1.0, 0.5, 0.75])
Omega = np.array([50.0, 30.0, 40.0])

cluster = mors.Cluster(Mstar=Mstar, Omega=Omega, Age=100.0)  # Myr

Different ages for each star 

import numpy as np
import mors

Mstar = np.array([1.0, 0.5, 0.75])
Omega = np.array([50.0, 30.0, 40.0])
Age   = np.array([80.0, 120.0, 100.0])  # Myr; same length as Mstar/Omega

cluster = mors.Cluster(Mstar=Mstar, Omega=Omega, Age=Age)

Step 3 — Access per-star tracks

Each star is a mors.Star instance stored in cluster.stars.

import matplotlib.pyplot as plt

plt.plot(cluster.stars[0].AgeTrack, cluster.stars[0].LxTrack)
plt.plot(cluster.stars[1].AgeTrack, cluster.stars[1].LxTrack)
plt.plot(cluster.stars[2].AgeTrack, cluster.stars[2].LxTrack)
plt.show()

Some versions also expose stars0, stars1, ... as attributes:

plt.plot(cluster.stars0.AgeTrack, cluster.stars0.LxTrack)

Step 4 — Get cluster values at a fixed age

Use Values(Age=..., Quantity=...) to retrieve an array across the cluster:

Lx = cluster.Values(Age=100.0, Quantity="Lx")

Or use the convenience method named after the quantity:

Lx = cluster.Lx(100.0)

Plot a distribution (e.g., Lx vs mass) at a given age:

import matplotlib.pyplot as plt
plt.scatter(cluster.Mstar, cluster.Lx(100.0))
plt.xlabel("Mstar [Msun]")
plt.ylabel("Lx [erg/s]")
plt.show()

Cluster calculations can be expensive for many stars, so saving is recommended.

cluster.Save(filename="cluster.pickle")
cluster2 = mors.Load("cluster.pickle")

Step 6 — Evolve the built-in “model cluster” (optional)

MORS includes a composite “model cluster” distribution (derived from observed clusters at ~150 Myr evolved back to 1 Myr). You can load it and evolve it like any other cluster:

import mors

Mstar, Omega = mors.ModelCluster()
cluster = mors.Cluster(Mstar=Mstar, Omega=Omega)

Citation note: If you use this model cluster distribution in research, cite the rotation-measurement sources listed in Johnstone et al. (2020), Table 1 (150 Myr bin), in addition to the MORS model paper(s).

Common pitfalls

  • Arrays for Mstar, Omega (and Age if provided) must have matching lengths.
  • Age is in Myr; Omega is in Ω☉.
  • Fitting tracks using Age + Omega can be unreliable at late ages where tracks converge.