BlackBody

class astropy.modeling.physical_models.BlackBody(temperature=<Quantity 5000. K>, scale=1.0, **kwargs)[source]

Bases: astropy.modeling.Fittable1DModel

Blackbody model using the Planck function.

Parameters
temperatureQuantity [:ref: ‘temperature’]

Blackbody temperature.

scalefloat or Quantity [:ref: ‘dimensionless’]

Scale factor

Notes

Model formula:

\[B_{\nu}(T) = A \frac{2 h \nu^{3} / c^{2}}{exp(h \nu / k T) - 1}\]

Examples

>>> from astropy.modeling import models
>>> from astropy import units as u
>>> bb = models.BlackBody(temperature=5000*u.K)
>>> bb(6000 * u.AA)  
<Quantity 1.53254685e-05 erg / (cm2 Hz s sr)>
import numpy as np
import matplotlib.pyplot as plt

from astropy.modeling.models import BlackBody
from astropy import units as u
from astropy.visualization import quantity_support

bb = BlackBody(temperature=5778*u.K)
wav = np.arange(1000, 110000) * u.AA
flux = bb(wav)

with quantity_support():
    plt.figure()
    plt.semilogx(wav, flux)
    plt.axvline(bb.nu_max.to(u.AA, equivalencies=u.spectral()).value, ls='--')
    plt.show()

(png, svg, pdf)

../_images/astropy-modeling-physical_models-BlackBody-1.png

Attributes Summary

bolometric_flux

Bolometric flux.

input_units

This property is used to indicate what units or sets of units the evaluate method expects, and returns a dictionary mapping inputs to units (or None if any units are accepted).

input_units_equivalencies

lambda_max

Peak wavelength when the curve is expressed as power density.

nu_max

Peak frequency when the curve is expressed as power density.

param_names

Names of the parameters that describe models of this type.

scale

temperature

Methods Summary

evaluate(x, temperature, scale)

Evaluate the model.

Attributes Documentation

bolometric_flux

Bolometric flux.

input_units
input_units_equivalencies = {'x': [(Unit("m"), Unit("Hz"), <function spectral.<locals>.<lambda>>), (Unit("m"), Unit("J"), <function spectral.<locals>.<lambda>>), (Unit("Hz"), Unit("J"), <function spectral.<locals>.<lambda>>, <function spectral.<locals>.<lambda>>), (Unit("m"), Unit("1 / m"), <function spectral.<locals>.<lambda>>), (Unit("Hz"), Unit("1 / m"), <function spectral.<locals>.<lambda>>, <function spectral.<locals>.<lambda>>), (Unit("J"), Unit("1 / m"), <function spectral.<locals>.<lambda>>, <function spectral.<locals>.<lambda>>), (Unit("1 / m"), Unit("rad / m"), <function spectral.<locals>.<lambda>>, <function spectral.<locals>.<lambda>>), (Unit("m"), Unit("rad / m"), <function spectral.<locals>.<lambda>>), (Unit("Hz"), Unit("rad / m"), <function spectral.<locals>.<lambda>>, <function spectral.<locals>.<lambda>>), (Unit("J"), Unit("rad / m"), <function spectral.<locals>.<lambda>>, <function spectral.<locals>.<lambda>>)]}
lambda_max

Peak wavelength when the curve is expressed as power density.

nu_max

Peak frequency when the curve is expressed as power density.

param_names = ('temperature', 'scale')

Names of the parameters that describe models of this type.

The parameters in this tuple are in the same order they should be passed in when initializing a model of a specific type. Some types of models, such as polynomial models, have a different number of parameters depending on some other property of the model, such as the degree.

When defining a custom model class the value of this attribute is automatically set by the Parameter attributes defined in the class body.

scale = Parameter('scale', value=1.0, bounds=(0, None))
temperature = Parameter('temperature', value=5000.0, unit=K, bounds=(0, None))

Methods Documentation

evaluate(x, temperature, scale)[source]

Evaluate the model.

Parameters
xfloat, ndarray, or Quantity [:ref: ‘frequency’]

Frequency at which to compute the blackbody. If no units are given, this defaults to Hz.

temperaturefloat, ndarray, or Quantity

Temperature of the blackbody. If no units are given, this defaults to Kelvin.

scalefloat, ndarray, or Quantity [:ref: ‘dimensionless’]

Desired scale for the blackbody.

Returns
ynumber or ndarray

Blackbody spectrum. The units are determined from the units of scale.

Note

Use numpy.errstate to suppress Numpy warnings, if desired.

Warning

Output values might contain nan and inf.

Raises
ValueError

Invalid temperature.

ZeroDivisionError

Wavelength is zero (when converting to frequency).