σ šίΘ[c@`srdZddlmZmZmZmZddlZddlmZddl Z ddl m Z ddl mZdd lmZdd lmZdd lmZd d dgZejejdejejZejejdejejZejƒEejde ƒe j!e j"dƒƒp=e j!e j"dƒƒZ#WdQXde fd„ƒYZ$d„Z%d„Z&dS(u– Model and functions related to blackbody radiation. .. _blackbody-planck-law: Blackbody Radiation ------------------- Blackbody flux is calculated with Planck law (:ref:`Rybicki & Lightman 1979 `): .. math:: B_{\lambda}(T) = \frac{2 h c^{2} / \lambda^{5}}{exp(h c / \lambda k T) - 1} B_{\nu}(T) = \frac{2 h \nu^{3} / c^{2}}{exp(h \nu / k T) - 1} where the unit of :math:`B_{\lambda}(T)` is :math:`erg \; s^{-1} cm^{-2} \mathring{A}^{-1} sr^{-1}`, and :math:`B_{\nu}(T)` is :math:`erg \; s^{-1} cm^{-2} Hz^{-1} sr^{-1}`. :func:`~astropy.modeling.blackbody.blackbody_lambda` and :func:`~astropy.modeling.blackbody.blackbody_nu` calculate the blackbody flux for :math:`B_{\lambda}(T)` and :math:`B_{\nu}(T)`, respectively. For blackbody representation as a model, see :class:`BlackBody1D`. .. _blackbody-examples: Examples ^^^^^^^^ >>> import numpy as np >>> from astropy import units as u >>> from astropy.modeling.blackbody import blackbody_lambda, blackbody_nu Calculate blackbody flux for 5000 K at 100 and 10000 Angstrom while suppressing any Numpy warnings: >>> wavelengths = [100, 10000] * u.AA >>> temperature = 5000 * u.K >>> with np.errstate(all='ignore'): ... flux_lam = blackbody_lambda(wavelengths, temperature) ... flux_nu = blackbody_nu(wavelengths, temperature) >>> flux_lam # doctest: +FLOAT_CMP >>> flux_nu # doctest: +FLOAT_CMP Plot a blackbody spectrum for 5000 K: .. plot:: import matplotlib.pyplot as plt import numpy as np from astropy import constants as const from astropy import units as u from astropy.modeling.blackbody import blackbody_lambda temperature = 5000 * u.K wavemax = (const.b_wien / temperature).to(u.AA) # Wien's displacement law waveset = np.logspace( 0, np.log10(wavemax.value + 10 * wavemax.value), num=1000) * u.AA with np.errstate(all='ignore'): flux = blackbody_lambda(waveset, temperature) fig, ax = plt.subplots(figsize=(8, 5)) ax.plot(waveset.value, flux.value) ax.axvline(wavemax.value, ls='--') ax.get_yaxis().get_major_formatter().set_powerlimits((0, 1)) ax.set_xlabel(r'$\lambda$ ({0})'.format(waveset.unit)) ax.set_ylabel(r'$B_{\lambda}(T)$') ax.set_title('Blackbody, T = {0}'.format(temperature)) Note that an array of temperatures can also be given instead of a single temperature. In this case, the Numpy broadcasting rules apply: for instance, if the frequency and temperature have the same shape, the output will have this shape too, while if the frequency is a 2-d array with shape ``(n, m)`` and the temperature is an array with shape ``(m,)``, the output will have a shape ``(n, m)``. See Also ^^^^^^^^ .. _ref-rybicki1979: Rybicki, G. B., & Lightman, A. P. 1979, Radiative Processes in Astrophysics (New York, NY: Wiley) i(tabsolute_importtunicode_literalstdivisiontprint_functionN(t OrderedDicti(tFittable1DModel(t Parameteri(t constants(tunits(tAstropyUserWarningu BlackBody1Du blackbody_nuublackbody_lambdauignoreiθg _ Bt BlackBody1DcB`sŸeZdZedddddejƒZedddejejdej ƒZ e Z iej ƒd6Zd „Zed „ƒZd „Zed „ƒZRS( u( One dimensional blackbody model. Parameters ---------- temperature : :class:`~astropy.units.Quantity` Blackbody temperature. bolometric_flux : :class:`~astropy.units.Quantity` The bolometric flux of the blackbody (i.e., the integral over the spectral axis). Notes ----- Model formula: .. math:: f(x) = \pi B_{\nu} f_{\text{bolometric}} / (\sigma T^{4}) Examples -------- >>> from astropy.modeling import models >>> from astropy import units as u >>> bb = models.BlackBody1D() >>> bb(6000 * u.AA) # doctest: +FLOAT_CMP .. plot:: :include-source: import numpy as np import matplotlib.pyplot as plt from astropy.modeling.models import BlackBody1D from astropy.modeling.blackbody import FLAM from astropy import units as u from astropy.visualization import quantity_support bb = BlackBody1D(temperature=5778*u.K) wav = np.arange(1000, 110000) * u.AA flux = bb(wav).to(FLAM, u.spectral_density(wav)) with quantity_support(): plt.figure() plt.semilogx(wav, flux) plt.axvline(bb.lambda_max.to(u.AA).value, ls='--') plt.show() tdefaultiˆtminitunitiiuxcC`s¦t|tjƒr3|jtjdtjƒƒ}ntj|tjƒ}tjtjt ||ƒt j |djdtj ƒ|}t |dƒr›|S|jSdS(uΥEvaluate the model. Parameters ---------- x : float, `~numpy.ndarray`, or `~astropy.units.Quantity` Frequency at which to compute the blackbody. If no units are given, this defaults to Hz. temperature : float, `~numpy.ndarray`, or `~astropy.units.Quantity` Temperature of the blackbody. If no units are given, this defaults to Kelvin. bolometric_flux : float, `~numpy.ndarray`, or `~astropy.units.Quantity` Desired integral for the blackbody. Returns ------- y : number or ndarray Blackbody spectrum. 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