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Copy file name to clipboardExpand all lines: docs/sbpy/activity/dust.rst
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@@ -10,15 +10,15 @@ The *Afρ* parameter of A'Hearn et al (1984) is based on observations of idealiz
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.. math::
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Afρ = \frac{4 Δ^2 r_h^2}{ρ}\frac{F_c}{F_⊙}
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Afρ = \frac{4 Δ^2 r_h^2}{ρ}\frac{F_c}{F_⊙}
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where *Δ* and *ρ* have the same (linear) units, but :math:`r_h` is in units of au. :math:`F_c` * is the flux density of the comet in the aperture, and :math:`F_⊙` is that of the Sun at 1 au in the same units. See A'Hearn et al. (1984) and Fink & Rubin (2012) for more details.
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The *εfρ* parameter is the thermal emission counterpart to *Afρ*, replacing albedo with IR emissivity, *ε*, and the solar spectrum with the Planck function, *B*:
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.. math::
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εfρ = \frac{F_c Δ^2}{π ρ B(T_c)}
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εfρ = \frac{F_c Δ^2}{π ρ B(T_c)}
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where :math:`T_c` is the spectral temperature of the continuum (Kelley et al. 2013).
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@@ -27,21 +27,21 @@ where :math:`T_c` is the spectral temperature of the continuum (Kelley et al. 20
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`Afrho` and `Efrho` are subclasses of `astropy`'s `~astropy.units.Quantity` and carry units of length.
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>>> import numpy as np
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>>> import astropy.units as u
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>>> from sbpy.activity import Afrho, Efrho
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>>>
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>>> afrho = Afrho(100* u.cm)
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>>> print(afrho) # doctest: +FLOAT_CMP
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100.0 cm
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>>> efrho = Efrho(afrho *3.5)
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>>> print(efrho) # doctest: +FLOAT_CMP
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350.0 cm
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>>> import numpy as np
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>>> import astropy.units as u
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>>> from sbpy.activity import Afrho, Efrho
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>>>
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>>> afrho = Afrho(100* u.cm)
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>>> print(afrho) # doctest: +FLOAT_CMP
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100.0 cm
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>>> efrho = Efrho(afrho *3.5)
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>>> print(efrho) # doctest: +FLOAT_CMP
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350.0 cm
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They may be converted to other units of length just like any `Quantity`:
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>>> afrho.to('m') # doctest: +FLOAT_CMP
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<Afrho 1. m>
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>>> afrho.to('m') # doctest: +FLOAT_CMP
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<Afrho 1. m>
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.. _afrho-to-from-flux-density:
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The solar flux density at 1 au is also needed. We use 1868 W/(m2 μm).
`Afrho` works seamlessly with `sbpy`'s spectral calibration framework (:ref:`sbpy-calib`) when the `astropy` affiliated package `synphot` is installed. The solar flux density (via `~sbpy.calib.solar_fluxd`) is not required, but instead the spectral wavelengths or the system transmission of the instrument and filter:
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@@ -108,15 +108,15 @@ Reproduce the *εfρ* of 246P/NEAT from Kelley et al. (2013).
Phase angle was not used in the previous section. In the *Afρ* formalism, "albedo" includes the scattering phase function, and is more precisely written *A(θ)*, where *θ* is the phase angle. The default behavior for `Afrho` is to compute *A(θ)fρ* as opposed to *A(0°)fρ*. Returning to the A'Hearn et al. data, we scale *Afρ* to 0° from 3.3° phase using the :func:`~sbpy.activity.Afrho.to_phase` method:
The default phase function is the Halley-Marcus composite phase function (:func:`~sbpy.activity.phase_HalleyMarcus`). Any function or callable object that accepts an angle as a `~astropy.units.Quantity` and returns a scalar value may be used:
To correct an observed flux density for the phase function, use the ``phasecor`` option of :func:`~sbpy.activity.Afrho.to_fluxd` and :func:`~sbpy.activity.Afrho.from_fluxd` methods:
Other apertures may be used, as long as they can be converted into an equivalent radius, assuming a coma with a *1/ρ* surface brightness distribution. `~sbpy.activity` has a collection of useful geometries.
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>>> from sbpy.activity import CircularAperture, AnnularAperture, RectangularAperture, GaussianAperture
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