Solar Composition

Solar Composition#

Here we show how to work with the LoddersComposition class, which initializes a composition from the present day solar abundances of Lodders [2020]. To access the data tables, follow this link. This class gives the option to set a desired metallicity Z=0.0 and scales the Lodders abundances accordingly. If no metallicity is provided, it will be calculated from the Lodders data as (1 - H - He).

import numpy as np
import matplotlib.pyplot as plt

from ipywidgets import interact, FloatSlider

from pynucastro import networks
from pynucastro.nucdata import Nucleus

Setting solar composition and finding the top 10 most abundant isotopes#

def top_10_isotopes(comp, n=10):
    fracs = sorted(comp.items(), key=lambda frac: frac[1], reverse=True)
    return fracs[:n]

solar = networks.LoddersComposition() ## Default metallicity
top = top_10_isotopes(solar, n=10)

for nuc, X in top:
    print(f"{nuc.short_spec_name:>6} X= {X:.4f}")

    h1 X= 0.7462
   he4 X= 0.2388
   o16 X= 0.0064
   c12 X= 0.0026
  ne20 X= 0.0019
  fe56 X= 0.0011
   n14 X= 0.0007
  si28 X= 0.0006
  mg24 X= 0.0005
   s32 X= 0.0003

Binning Lodders composition to a desired network#

If we wish to use a network that does not contain all isotopes that are in the Lodders composition, then we use Composition.bin_as which will bin the Lodders data to the desired network:

solar = networks.LoddersComposition()

new_comp = [Nucleus("p"),
           Nucleus("he4"),
           Nucleus("o16"),
           Nucleus("c12"),
           Nucleus("ne20"),
           Nucleus("fe56"),
           Nucleus("n14"),
           Nucleus("si28"),
           Nucleus("mg24"),
           Nucleus("s32")] ## Desired network

binned_comp = solar.bin_as(new_comp)
print("Sum of binned comp:", sum(binned_comp.values()))

fig = binned_comp.plot()

Sum of binned comp: 1.000000000000001
_images/2533a710b011841e18b6c8a4d3a387401132efd41d9ef22e8e0201ee4541ee11.png

Scaling H and He with desired metallicty Z#

def xyz_from_comp(comp):
    X = 0.0
    Y = 0.0
    Z = 0.0

    for nuc, X_i in comp.items():
        if nuc.Z == 1: # Total H
            X += X_i
        elif nuc.Z == 2: # Total He
            Y += X_i
        else:
            Z += X_i # Total metals

    return X, Y, Z

solar = networks.LoddersComposition()
X_solar, Y_solar, Z_solar = xyz_from_comp(solar)

print("Default solar metalicity is Z = ", Z_solar)

def plot_lodders(Z):

    comp = networks.LoddersComposition(Z=Z)

    X, Y , Z = xyz_from_comp(comp)

    plt.figure(figsize=(4,4))

    labels = ["H", "He", "Metals"]
    values = [X,Y,Z]

    x = np.arange(len(labels))

    fig, ax = plt.subplots()

    ax.bar(x, values)
    ax.set_xticks(x)
    ax.set_xticklabels(labels)
    ax.set_ylabel("Mass Fractions")
    ax.set_ylim(0, 1.0)
    ax.set_title(f"Lodders Composition at Z = {Z:.3f}")

    plt.show()

interact(
    plot_lodders,
    Z=FloatSlider(
        value=Z_solar,
        min=0.01,
        max=0.04,
        step=0.001,
        description="Z",
        readout_format=".3f"
    )
)

Default solar metalicity is Z =  0.014964158698946859

<function __main__.plot_lodders(Z)>
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