BlackBody

class astropy.modeling.physical_models.BlackBody(*args, **kwargs)

Bases: Fittable1DModel

Blackbody model using the Planck function.

Parameters:

temperatureQuantity [:ref: ‘temperature’]

Blackbody temperature.

scalefloat or Quantity [:ref: ‘dimensionless’]

Scale factor. If dimensionless, input units will assumed to be in Hz and output units in (erg / (cm ** 2 * s * Hz * sr). If not dimensionless, must be equivalent to either (erg / (cm ** 2 * s * Hz * sr) or erg / (cm ** 2 * s * AA * sr), in which case the result will be returned in the requested units and the scale will be stripped of units (with the float value applied).

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 / (Hz s sr cm2)>

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)

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)

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 (or AA if scale was initialized with units equivalent to erg / (cm ** 2 * s * AA * sr)).

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).