latex_blackbody_radiation

A plot of spectral radiance curves for an ideal radiating blackbody at various temperatures. This example demonstrates the use of mathtext on axes and in Div objects.

Details

Bokeh APIs:

figure.line, bokeh.models.Div

More info:

Mathematical notation

Keywords:

mathtext, latex

import numpy as np

from bokeh.io import curdoc
from bokeh.layouts import column
from bokeh.models import Div
from bokeh.palettes import Spectral
from bokeh.plotting import figure, show

p = figure(
    width=700, height=500, toolbar_location=None,
    title="Black body spectral radiance as a function of frequency")

def spectral_radiance(nu, T):
    h = 6.626e-34   # Planck constant (Js)
    k = 1.3806e-23  # Boltzmann constant (J/K)
    c = 2.9979e8    # Speed of light in vacuum (m/s)
    return (2*h*nu**3/c**2) / (np.exp(h*nu/(k*T)) - 1.0)

Ts = np.arange(2000, 6001, 500)  # Temperature (K)
palette = Spectral[len(Ts)]
nu = np.linspace(0.1, 1e15, 500)  # Frequency (1/s)

for i, T in enumerate(Ts):
    B_nu = spectral_radiance(nu, T)
    p.line(nu/1e15, B_nu/1e-9, line_width=2,
             legend_label=f"T = {T} K", line_color=palette[i])
p.legend.items = list(reversed(p.legend.items))

# Peak radiance line.
Ts = np.linspace(1900, 6101, 50)
peak_freqs = Ts*5.879e10
peak_radiance = spectral_radiance(peak_freqs, Ts)
p.line(peak_freqs/1e15, peak_radiance/1e-9, line_color="silver",
         line_dash="dashed", line_width=2, legend_label="Peak radiance")

curdoc().theme = 'dark_minimal'
p.y_range.start = 0
p.xaxis.axis_label = r"$$\nu \:(10^{15}\ \text{Hz})$$"
p.yaxis.axis_label = r"$$B_\nu(\nu, T) \quad\left(10^{-9}\ \text{W} / (\text{m}^2 \cdot \text{sr} \cdot \text{Hz})\right)$$"

div = Div(text=r"""
A plot of the spectral radiance, defined as a function of the frequency $$\nu$$, is given by the formula
<p \>
$$
\qquad B_\nu(\nu, T) = \frac{2h\nu^3}{c^2} \frac{1}{\exp(h\nu/kT)-1}\ .
$$
""")
show(column(p, div))