latex_blackbody_radiation.py

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

Styling visual attributes > Adding mathematical notations

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  # Boltzman 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"$$\color{white} \nu \:(10^{15} s^{-1})$$"
p.yaxis.axis_label = r"$$\color{white} B_\nu(\nu, T) \quad(10^{-9} J s m^{-3})$$"

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))