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Make indentation uniform.
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@mkelley
mkelley committed Jun 11, 2023
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160 changes: 80 additions & 80 deletions docs/sbpy/activity/dust.rst
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Expand Up @@ -10,15 +10,15 @@ The *Afρ* parameter of A'Hearn et al (1984) is based on observations of idealiz

.. math::
Afρ = \frac{4 Δ^2 r_h^2}{ρ}\frac{F_c}{F_⊙}
Afρ = \frac{4 Δ^2 r_h^2}{ρ}\frac{F_c}{F_⊙}
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.

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*:

.. math::
εfρ = \frac{F_c Δ^2}{π ρ B(T_c)}
εfρ = \frac{F_c Δ^2}{π ρ B(T_c)}
where :math:`T_c` is the spectral temperature of the continuum (Kelley et al. 2013).

Expand All @@ -27,21 +27,21 @@ where :math:`T_c` is the spectral temperature of the continuum (Kelley et al. 20

`Afrho` and `Efrho` are subclasses of `astropy`'s `~astropy.units.Quantity` and carry units of length.

>>> import numpy as np
>>> import astropy.units as u
>>> from sbpy.activity import Afrho, Efrho
>>>
>>> afrho = Afrho(100 * u.cm)
>>> print(afrho) # doctest: +FLOAT_CMP
100.0 cm
>>> efrho = Efrho(afrho * 3.5)
>>> print(efrho) # doctest: +FLOAT_CMP
350.0 cm
>>> import numpy as np
>>> import astropy.units as u
>>> from sbpy.activity import Afrho, Efrho
>>>
>>> afrho = Afrho(100 * u.cm)
>>> print(afrho) # doctest: +FLOAT_CMP
100.0 cm
>>> efrho = Efrho(afrho * 3.5)
>>> print(efrho) # doctest: +FLOAT_CMP
350.0 cm

They may be converted to other units of length just like any `Quantity`:

>>> afrho.to('m') # doctest: +FLOAT_CMP
<Afrho 1. m>
>>> afrho.to('m') # doctest: +FLOAT_CMP
<Afrho 1. m>

.. _afrho-to-from-flux-density:

Expand All @@ -58,30 +58,30 @@ The quantities may be initialized from flux densities. Here, we reproduce one o

The solar flux density at 1 au is also needed. We use 1868 W/(m2 μm).

>>> from sbpy.data import Ephem
>>> from sbpy.calib import solar_fluxd
>>>
>>> solar_fluxd.set({
... 'λ5240': 1868 * u.W / u.m**2 / u.um,
... 'λ5240(lambda pivot)': 5240 * u.AA
... }) # doctest: +IGNORE_OUTPUT
>>>
>>> flam = 10**-13.99 * u.Unit('erg/(s cm2 AA)')
>>> aper = 27200 * u.km
>>>
>>> eph = Ephem.from_dict({'rh': 4.785 * u.au, 'delta': 3.822 * u.au})
>>>
>>> afrho = Afrho.from_fluxd('λ5240', flam, aper, eph)
>>> print(afrho) # doctest: +FLOAT_CMP
6029.90248952895 cm
>>> from sbpy.data import Ephem
>>> from sbpy.calib import solar_fluxd
>>>
>>> solar_fluxd.set({
... 'λ5240': 1868 * u.W / u.m**2 / u.um,
... 'λ5240(lambda pivot)': 5240 * u.AA
... }) # doctest: +IGNORE_OUTPUT
>>>
>>> flam = 10**-13.99 * u.Unit('erg/(s cm2 AA)')
>>> aper = 27200 * u.km
>>>
>>> eph = Ephem.from_dict({'rh': 4.785 * u.au, 'delta': 3.822 * u.au})
>>>
>>> afrho = Afrho.from_fluxd('λ5240', flam, aper, eph)
>>> print(afrho) # doctest: +FLOAT_CMP
6029.90248952895 cm

Which is within a few percent of 6160 cm computed by A'Hearn et al.. The difference is likely due to the assumed solar flux density in the bandpass.

The `Afrho` class may be converted to a flux density, and the original value is recovered.

>>> f = afrho.to_fluxd('λ5240', aper, eph).to('erg/(s cm2 AA)')
>>> print(np.log10(f.value)) # doctest: +FLOAT_CMP
-13.99
>>> f = afrho.to_fluxd('λ5240', aper, eph).to('erg/(s cm2 AA)')
>>> print(np.log10(f.value)) # doctest: +FLOAT_CMP
-13.99

`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:

Expand All @@ -108,15 +108,15 @@ Reproduce the *εfρ* of 246P/NEAT from Kelley et al. (2013).

.. doctest-requires:: synphot

>>> wave = [15.8, 22.3] * u.um
>>> fluxd = [25.75, 59.2] * u.mJy
>>> aper = 11.1 * u.arcsec
>>> eph = Ephem.from_dict({'rh': 4.28 * u.au, 'delta': 3.71 * u.au})
>>> efrho = Efrho.from_fluxd(wave, fluxd, aper, eph)
>>> for i in range(len(wave)):
... print('{:5.1f} at {:.1f}'.format(efrho[i], wave[i])) # doctest: +FLOAT_CMP
406.2 cm at 15.8 um
427.9 cm at 22.3 um
>>> wave = [15.8, 22.3] * u.um
>>> fluxd = [25.75, 59.2] * u.mJy
>>> aper = 11.1 * u.arcsec
>>> eph = Ephem.from_dict({'rh': 4.28 * u.au, 'delta': 3.71 * u.au})
>>> efrho = Efrho.from_fluxd(wave, fluxd, aper, eph)
>>> for i in range(len(wave)):
... print('{:5.1f} at {:.1f}'.format(efrho[i], wave[i])) # doctest: +FLOAT_CMP
406.2 cm at 15.8 um
427.9 cm at 22.3 um

Compare to 397.0 cm and 424.6 cm listed in Kelley et al. (2013).

Expand All @@ -130,67 +130,67 @@ Estimate the *Afρ* of comet C/2012 S1 (ISON) based on Pan-STARRS 1 photometry i

.. doctest-requires:: synphot

>>> w = 0.617 * u.um
>>> m = 16.02 * u.ABmag
>>> aper = 5 * u.arcsec
>>> eph = {'rh': 5.234 * u.au, 'delta': 4.275 * u.au, 'phase': 2.6 * u.deg}
>>> afrho = Afrho.from_fluxd(w, m, aper, eph)
>>> print(afrho) # doctest: +FLOAT_CMP
1948.496075629444 cm
>>> m2 = afrho.to_fluxd(w, aper, eph, unit=u.ABmag) # doctest: +FLOAT_CMP
>>> print(m2)
16.02 mag(AB)
>>> w = 0.617 * u.um
>>> m = 16.02 * u.ABmag
>>> aper = 5 * u.arcsec
>>> eph = {'rh': 5.234 * u.au, 'delta': 4.275 * u.au, 'phase': 2.6 * u.deg}
>>> afrho = Afrho.from_fluxd(w, m, aper, eph)
>>> print(afrho) # doctest: +FLOAT_CMP
1948.496075629444 cm
>>> m2 = afrho.to_fluxd(w, aper, eph, unit=u.ABmag) # doctest: +FLOAT_CMP
>>> print(m2)
16.02 mag(AB)


Phase angles and functions
^^^^^^^^^^^^^^^^^^^^^^^^^^

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:

>>> afrho = Afrho(6029.9 * u.cm)
>>> print(afrho.to_phase(0 * u.deg, 3.3 * u.deg)) # doctest: +FLOAT_CMP
6886.825981017757 cm
>>> afrho = Afrho(6029.9 * u.cm)
>>> print(afrho.to_phase(0 * u.deg, 3.3 * u.deg)) # doctest: +FLOAT_CMP
6886.825981017757 cm

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:

>>> Phi = lambda phase: 10**(-0.016 / u.deg * phase.to('deg'))
>>> print(afrho.to_phase(0 * u.deg, 3.3 * u.deg, Phi=Phi)) # doctest: +FLOAT_CMP
6809.419810008357 cm
>>> Phi = lambda phase: 10**(-0.016 / u.deg * phase.to('deg'))
>>> print(afrho.to_phase(0 * u.deg, 3.3 * u.deg, Phi=Phi)) # doctest: +FLOAT_CMP
6809.419810008357 cm

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:

>>> flam = 10**-13.99 * u.Unit('erg/(s cm2 AA)')
>>> aper = 27200 * u.km
>>> eph = Ephem.from_dict({
... 'rh': 4.785 * u.au,
... 'delta': 3.822 * u.au,
... 'phase': 3.3 * u.deg
... })
>>>
>>> afrho = Afrho.from_fluxd('λ5240', flam, aper, eph, phasecor=True)
>>> print(afrho) # doctest: +FLOAT_CMP
6886.828824340642 cm
>>> flam = 10**-13.99 * u.Unit('erg/(s cm2 AA)')
>>> aper = 27200 * u.km
>>> eph = Ephem.from_dict({
... 'rh': 4.785 * u.au,
... 'delta': 3.822 * u.au,
... 'phase': 3.3 * u.deg
... })
>>>
>>> afrho = Afrho.from_fluxd('λ5240', flam, aper, eph, phasecor=True)
>>> print(afrho) # doctest: +FLOAT_CMP
6886.828824340642 cm


Apertures
^^^^^^^^^

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.

>>> from sbpy.activity import CircularAperture, AnnularAperture, RectangularAperture, GaussianAperture
>>> apertures = (
... ( '10" radius circle', CircularAperture(10 * u.arcsec)),
... ( '5"–10" annulus', AnnularAperture([5, 10] * u.arcsec)),
... ( '2"x10" slit', RectangularAperture([2, 10] * u.arcsec)),
... ('σ=5" Gaussian beam', GaussianAperture(5 * u.arcsec))
... )
>>> for name, aper in apertures:
... afrho = Afrho.from_fluxd('λ5240', flam, aper, eph)
... print('{:18s} = {:5.0f}'.format(name, afrho)) # doctest: +FLOAT_CMP
>>> from sbpy.activity import CircularAperture, AnnularAperture, RectangularAperture, GaussianAperture
>>> apertures = (
... ( '10" radius circle', CircularAperture(10 * u.arcsec)),
... ( '5"–10" annulus', AnnularAperture([5, 10] * u.arcsec)),
... ( '2"x10" slit', RectangularAperture([2, 10] * u.arcsec)),
... ('σ=5" Gaussian beam', GaussianAperture(5 * u.arcsec))
... )
>>> for name, aper in apertures:
... afrho = Afrho.from_fluxd('λ5240', flam, aper, eph)
... print('{:18s} = {:5.0f}'.format(name, afrho)) # doctest: +FLOAT_CMP
10" radius circle = 5917 cm
5"–10" annulus = 11834 cm
2"x10" slit = 28114 cm
σ=5" Gaussian beam = 9442 cm
σ=5" Gaussian beam = 9442 cm


Reference/API
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