<gh_stars>1-10
# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
dust --- Models for dust
========================

.. autosummary::
   :toctree: generated/

   Activity
   --------
   acrit

   Dust Models
   -----------
   AfrhoRadiation
   AfrhoScattered
   AfrhoThermal

   Phase functions
   ---------------
   phaseK
   phaseH
   phaseHM

"""

import numpy as np
import astropy.units as u
from astropy.units import Quantity

__all__ = [
    'acrit',

    'AfrhoRadiation',
    'AfrhoScattered',
    'AfrhoThermal',

    'phaseK',
    'phaseH',
    'phaseHM'
]

def acrit(Q, vth, R, rho_g=Quantity(1, u.g / u.cm**3),
          rho_n=Quantity(0.3, u.g / u.cm**3), f_active=1.0):
    """Maximum liftable grain radius from a spherical nucleus.

    See Meech and Svoren 2004, Comets II.

    Parameters
    ----------
    Q : Quantity
      Mass production rate of the driving gas.
    vth : Quantity
      Gas expansion speed.
    R : Quantity
      Nucleus radius.
    rho_g : Quantity, optional
      Grain density.
    rho_n : Quantity, optional
      Nucleus mean density.
    f_active : float, optional
      Active fraction of the nucleus.
    
    Returns
    -------
    a : Quantity
      Maximum liftable grain radius.

    """

    from numpy import pi
    import astropy.constants as c

    a = 9 * Q * vth / (64 * pi**2 * rho_g * rho_n * R**3 * c.G)
    return a.to(u.um)

class AfrhoRadiation(object):
    """Light from a comet coma parameterized by Afrho, or similar.

    Methods
    -------
    fluxd : Total flux density from the object.

    Notes
    -----
    Afrho should refer to the value at zero phase angle.

    Inheriting classes should override `fluxd`, and `__init__`
    functions.  `__init__` should take a single argument, `Afrho` (or
    equivalent) as a Quantity.

    As much as possible, keyword arguments must have the same meaning
    in all derived models.

    """

    def __init__(self, Afrho, **kwargs):
        pass

    def __call__(self, *args, **kwargs):
        return self.fluxd(*args, **kwargs)

    def fluxd(self, geom, wave, unit=None):
        pass

class AfrhoScattered(AfrhoRadiation):
    """Scattered light from a comet coma parameterized by Afrho.

    If you use this model, please reference A'Hearn et al. (1984, AJ
    89, 579-591) as the source of the Afrho parameter.

    Parameters
    ----------
    Afrho : Quantity
      The product of albedo at zero phase, A, dust filling factor, f,
      and observer's aperture radius, rho.
    phasef : function, optional
      The phase function of the coma.  Set to `None` to use `phaseK`.

    Methods
    -------
    fluxd : Total flux density from the coma.

    """

    def __init__(self, Afrho, phasef=None, **kwargs):
        self.Afrho = Afrho
        if phasef is None:
            self.phasef = phaseK
        else:
            self.phasef = phasef

    def fluxd(self, geom, wave, rap, unit=u.Unit('W / (m2 um)')):
        """Flux density.

        Parameters
        ----------
        geom : dict of Quantities
          A dictionary-like object with the keys 'rh' (heliocentric
          distance), 'delta' (observer-target distance), and 'phase'
          (phase angle).
        wave : Quantity
          The wavelengths at which to compute the emission.
        rap : Quantity
          The aperture radius, angular or projected distance at the
          comet.
        unit : astropy Units, optional
          The return units.  Must be spectral flux density.

        Returns
        -------
        fluxd : Quantityu
          The flux density from the coma.

        Raises
        ------
        ValueError : If `rap` has incorrect units.

        """

        from ..calib import solar_flux

        if rap.unit.is_equivalent(u.cm):
            rho = rap.to(self.Afrho.unit)
        elif rap.unit.is_equivalent(u.arcsec):
            rho = geom['delta'].to(self.Afrho.unit) * rap.to(u.rad).value
        else:
            raise ValueError("rap must have angular or length units.")

        fsun = solar_flux(wave, unit=unit) / geom['rh'].to(u.au).value**2
        fluxd = (self.Afrho
                 * self.phasef(np.abs(geom['phase'].to(u.deg).value))
                 * rho * fsun / 4.0 / geom['delta'].to(self.Afrho.unit)**2)

        return fluxd

class AfrhoThermal(AfrhoRadiation):
    """Thermal emisson from a coma parameterized by efrho.

    If you use this model, please cite and reference Kelley et
    al. (2013, Icarus 225, 475-494).  They define `epsilon-f-rho` as
    the product of IR emissivity (`epsilon`), dust filling factor
    (`f`), and observer's aperture radius (`rho`).

    The default `ef2af` is 3.5, which assumes `epsilion` is
    approximately 0.9, `A` is approximately 0.25, and the scattering
    and emission filling factors are the same.  This value can roughly
    reproduce the spectral shape of 73P-C/Schwassmann-Wachmann in
    Fig. 16 of Sitko et al. (2011, AJ 142, 80) for `Tscale = 1.12`.

    The default long-wavelength slope, `beta = 0.89+/-0.10`, is from
    an analysis of Hyakutake JCMT data by Jewitt and Matthews (1997,
    AJ 113, 1145).  The break-point, `wave0` = 70 um, is based on my
    own analysis, combining the Jewitt and Matthews fluxes with mid-IR
    fluxes from Mason et al. (1998, ApJ 507, 398).

    Parameters
    ----------
    Afrho : Quantity
      The product of albedo at zero phase, A, dust filling factor, f,
      and observer's aperture radius, rho.
    ef2af : float, optional
      The ratio of epsilon-f_therm to A-f_sca, where f_therm and f_sca
      are the effective thermal and scattered light filling factors,
      (they are not necessarily the same).
    Tscale : float, optional
      The isothermal blackbody sphere temperature scale factor that
      characterizes the spectral shape of the thermal emission.
    beta : float, optional
    wave0 : Quantity, optional
      Scale wavelengths longer than `wave0` by `(wave / wave0)**-beta`.

    Methods
    -------
    fluxd : Total flux density from the coma.

    """

    def __init__(self, Afrho, ef2af=3.5, Tscale=1.1, beta=0.89,
                 wave0=70 * u.um, **kwargs):
        assert isinstance(Afrho, u.Quantity)
        self.Afrho = Afrho
        self.ef2af = ef2af
        self.Tscale = Tscale
        self.beta = beta
        self.wave0 = wave0

    def fluxd(self, geom, wave, rap, unit=u.Unit('W / (m2 um)')):
        """Flux density.

        Parameters
        ----------
        geom : dict of Quantities
          A dictionary-like object with the keys 'rh' (heliocentric
          distance), 'delta' (observer-target distance), and 'phase'
          (phase angle).
        wave : Quantity
          The wavelengths at which to compute the emission.
        rap : Quantity
          The aperture radius, angular or projected distance at the
          comet.
        unit : astropy Units, optional
          The return units.  Must be spectral flux density.

        Returns
        -------
        fluxd : Quantity
          The flux density from the coma.

        Raises
        ------
        ValueError : If `rap` has incorrect units.

        """

        from ..util import planck

        if rap.unit.is_equivalent(u.cm):
            rho = rap.to(self.Afrho.unit)
        elif rap.unit.is_equivalent(u.arcsec):
            rho = geom['delta'].to(self.Afrho.unit) * rap.to(u.rad).value
        else:
            raise ValueError("rap must have angular or length units.")

        T = self.Tscale * 278 / np.sqrt(geom['rh'].to(u.au).value)
        B = planck(wave, T, unit=unit / u.sr).value
        efrho = self.Afrho * self.ef2af
        d = geom['delta'].to(self.Afrho.unit).value
        fluxd = efrho.value * np.pi * B * rho.value / d**2

        if any(wave > self.wave0):
            eps = np.ones(len(wave))
            i = wave > self.wave0
            eps[i] *= (wave[i] / self.wave0)**-self.beta
            fluxd *= eps

        return fluxd * unit

def phaseK(phase):
    """Phase function derived from Kolokolova et al. (2004, Comets II).

    The phase function of K04 is scaled to phasef(0) = 1.0.

    Parameters
    ----------
    phase : float or array
        Phase angle. [degrees]

    Returns
    -------
    phi : float or ndarray
        The phase function.

    Notes
    -----
    To estimate the phase function, I fit a polynomial function to the
    solid line of Kolokolova et al. (2004, Comets II):

      a = array([0.27, 0.21, 0.17, 0.15, 0.14, 0.135, 0.135, 0.135, 0.15,
           0.175, 0.225, 0.3, 0.43, 0.62, 0.775])
      b = array([0.0,  10,   20,   30,   40,   60,    70,   80,   100,
           110,   120,   130, 140,  150,  156])
      fit = poly1d(polyfit(b, a / 0.27, 4))
      plot(b, a, 'o')
      plot(b, fit(b) * min(a), 'r-')

    """

    phasef = np.poly1d([  3.14105489e-08,  -7.84714255e-06,   7.34255521e-04,
                         -3.09608957e-02,   1.00920684e+00])
    return phasef(np.abs(phase))

def phaseH(phase):
    """Halley phase function from Schleicher et al. (1998).

    The Halley phase function is from Schleicher et al. (1998, Icarus
    132, 397-417).  The Comet Halley observations were at phases less
    than 70 degrees.

    Parameters
    ----------
    phase : float or array
        Phase angle. [degrees]

    Returns
    -------
    phi : float or ndarray
        The phase function.

    """

    phasef = np.poly1d([0.000177, -0.01807, 1])
    return phasef(np.abs(phase))

def phaseHM(phase):
    """Halley-Marcus phase function from Schleicher et al. (2011).

    The Halley phase function is first published in Schleicher and
    Bair (2011, AJ 141, 117), but only described in detail by
    Schleicher and Marcus (May 2010) at:

      http://asteroid.lowell.edu/comet/dustphase.html

      "To distinguish this curve from others, we designate this as the
      HM phase function, for the sources of the two components: Halley
      and Marcus, where the Halley curve for smaller phase angles
      comes from our previous work (Schleicher et al. 1998) while Joe
      Marcus has fit a Henyey-Greenstein function to a variety of mid-
      and large-phase angle data sets (Marcus 2007); see here for
      details. Note that we do not consider our composite curve to be
      a definitive result, but rather appropriate for performing
      first-order adjustments to dust measurements for changing phase
      angle."

    Parameters
    ----------
    phase : float or array
        Phase angle. [degrees]

    Returns
    -------
    phi : float or ndarray
        The phase function.

    """

    from scipy.interpolate import splrep, splev

    th = np.arange(181)
    ph = np.array(
        [  1.0000e+00,   9.5960e-01,   9.2170e-01,   8.8590e-01,
           8.5220e-01,   8.2050e-01,   7.9060e-01,   7.6240e-01,
           7.3580e-01,   7.1070e-01,   6.8710e-01,   6.6470e-01,
           6.4360e-01,   6.2370e-01,   6.0490e-01,   5.8720e-01,
           5.7040e-01,   5.5460e-01,   5.3960e-01,   5.2550e-01,
           5.1220e-01,   4.9960e-01,   4.8770e-01,   4.7650e-01,
           4.6590e-01,   4.5590e-01,   4.4650e-01,   4.3770e-01,
           4.2930e-01,   4.2150e-01,   4.1420e-01,   4.0730e-01,
           4.0090e-01,   3.9490e-01,   3.8930e-01,   3.8400e-01,
           3.7920e-01,   3.7470e-01,   3.7060e-01,   3.6680e-01,
           3.6340e-01,   3.6030e-01,   3.5750e-01,   3.5400e-01,
           3.5090e-01,   3.4820e-01,   3.4580e-01,   3.4380e-01,
           3.4210e-01,   3.4070e-01,   3.3970e-01,   3.3890e-01,
           3.3850e-01,   3.3830e-01,   3.3850e-01,   3.3890e-01,
           3.3960e-01,   3.4050e-01,   3.4180e-01,   3.4320e-01,
           3.4500e-01,   3.4700e-01,   3.4930e-01,   3.5180e-01,
           3.5460e-01,   3.5760e-01,   3.6090e-01,   3.6450e-01,
           3.6830e-01,   3.7240e-01,   3.7680e-01,   3.8150e-01,
           3.8650e-01,   3.9170e-01,   3.9730e-01,   4.0320e-01,
           4.0940e-01,   4.1590e-01,   4.2280e-01,   4.3000e-01,
           4.3760e-01,   4.4560e-01,   4.5400e-01,   4.6270e-01,
           4.7200e-01,   4.8160e-01,   4.9180e-01,   5.0240e-01,
           5.1360e-01,   5.2530e-01,   5.3750e-01,   5.5040e-01,
           5.6380e-01,   5.7800e-01,   5.9280e-01,   6.0840e-01,
           6.2470e-01,   6.4190e-01,   6.5990e-01,   6.7880e-01,
           6.9870e-01,   7.1960e-01,   7.4160e-01,   7.6480e-01,
           7.8920e-01,   8.1490e-01,   8.4200e-01,   8.7060e-01,
           9.0080e-01,   9.3270e-01,   9.6640e-01,   1.0021e+00,
           1.0399e+00,   1.0799e+00,   1.1223e+00,   1.1673e+00,
           1.2151e+00,   1.2659e+00,   1.3200e+00,   1.3776e+00,
           1.4389e+00,   1.5045e+00,   1.5744e+00,   1.6493e+00,
           1.7294e+00,   1.8153e+00,   1.9075e+00,   2.0066e+00,
           2.1132e+00,   2.2281e+00,   2.3521e+00,   2.4861e+00,
           2.6312e+00,   2.7884e+00,   2.9592e+00,   3.1450e+00,
           3.3474e+00,   3.5685e+00,   3.8104e+00,   4.0755e+00,
           4.3669e+00,   4.6877e+00,   5.0418e+00,   5.4336e+00,
           5.8682e+00,   6.3518e+00,   6.8912e+00,   7.4948e+00,
           8.1724e+00,   8.9355e+00,   9.7981e+00,   1.0777e+01,
           1.1891e+01,   1.3166e+01,   1.4631e+01,   1.6322e+01,
           1.8283e+01,   2.0570e+01,   2.3252e+01,   2.6418e+01,
           3.0177e+01,   3.4672e+01,   4.0086e+01,   4.6659e+01,
           5.4704e+01,   6.4637e+01,   7.7015e+01,   9.2587e+01,
           1.1237e+02,   1.3775e+02,   1.7060e+02,   2.1348e+02,
           2.6973e+02,   3.4359e+02,   4.3989e+02,   5.6292e+02,
           7.1363e+02,   8.8448e+02,   1.0533e+03,   1.1822e+03,
           1.2312e+03])

    C = splrep(th, ph)
    return splev(np.abs(phase), C)


# update module docstring
from ..util import autodoc
autodoc(globals())
del autodoc


# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
dust --- Models for dust
========================

.. autosummary::
   :toctree: generated/

   Activity
   --------
   acrit

   Dust Models
   -----------
   AfrhoRadiation
   AfrhoScattered
   AfrhoThermal

   Phase functions
   ---------------
   phaseK
   phaseH
   phaseHM

"""

import numpy as np
import astropy.units as u
from astropy.units import Quantity

__all__ = [
    'acrit',

    'AfrhoRadiation',
    'AfrhoScattered',
    'AfrhoThermal',

    'phaseK',
    'phaseH',
    'phaseHM'
]

def acrit(Q, vth, R, rho_g=Quantity(1, u.g / u.cm**3),
          rho_n=Quantity(0.3, u.g / u.cm**3), f_active=1.0):
    """Maximum liftable grain radius from a spherical nucleus.

    See Meech and Svoren 2004, Comets II.

    Parameters
    ----------
    Q : Quantity
      Mass production rate of the driving gas.
    vth : Quantity
      Gas expansion speed.
    R : Quantity
      Nucleus radius.
    rho_g : Quantity, optional
      Grain density.
    rho_n : Quantity, optional
      Nucleus mean density.
    f_active : float, optional
      Active fraction of the nucleus.
    
    Returns
    -------
    a : Quantity
      Maximum liftable grain radius.

    """

    from numpy import pi
    import astropy.constants as c

    a = 9 * Q * vth / (64 * pi**2 * rho_g * rho_n * R**3 * c.G)
    return a.to(u.um)

class AfrhoRadiation(object):
    """Light from a comet coma parameterized by Afrho, or similar.

    Methods
    -------
    fluxd : Total flux density from the object.

    Notes
    -----
    Afrho should refer to the value at zero phase angle.

    Inheriting classes should override `fluxd`, and `__init__`
    functions.  `__init__` should take a single argument, `Afrho` (or
    equivalent) as a Quantity.

    As much as possible, keyword arguments must have the same meaning
    in all derived models.

    """

    def __init__(self, Afrho, **kwargs):
        pass

    def __call__(self, *args, **kwargs):
        return self.fluxd(*args, **kwargs)

    def fluxd(self, geom, wave, unit=None):
        pass

class AfrhoScattered(AfrhoRadiation):
    """Scattered light from a comet coma parameterized by Afrho.

    If you use this model, please reference A'Hearn et al. (1984, AJ
    89, 579-591) as the source of the Afrho parameter.

    Parameters
    ----------
    Afrho : Quantity
      The product of albedo at zero phase, A, dust filling factor, f,
      and observer's aperture radius, rho.
    phasef : function, optional
      The phase function of the coma.  Set to `None` to use `phaseK`.

    Methods
    -------
    fluxd : Total flux density from the coma.

    """

    def __init__(self, Afrho, phasef=None, **kwargs):
        self.Afrho = Afrho
        if phasef is None:
            self.phasef = phaseK
        else:
            self.phasef = phasef

    def fluxd(self, geom, wave, rap, unit=u.Unit('W / (m2 um)')):
        """Flux density.

        Parameters
        ----------
        geom : dict of Quantities
          A dictionary-like object with the keys 'rh' (heliocentric
          distance), 'delta' (observer-target distance), and 'phase'
          (phase angle).
        wave : Quantity
          The wavelengths at which to compute the emission.
        rap : Quantity
          The aperture radius, angular or projected distance at the
          comet.
        unit : astropy Units, optional
          The return units.  Must be spectral flux density.

        Returns
        -------
        fluxd : Quantityu
          The flux density from the coma.

        Raises
        ------
        ValueError : If `rap` has incorrect units.

        """

        from ..calib import solar_flux

        if rap.unit.is_equivalent(u.cm):
            rho = rap.to(self.Afrho.unit)
        elif rap.unit.is_equivalent(u.arcsec):
            rho = geom['delta'].to(self.Afrho.unit) * rap.to(u.rad).value
        else:
            raise ValueError("rap must have angular or length units.")

        fsun = solar_flux(wave, unit=unit) / geom['rh'].to(u.au).value**2
        fluxd = (self.Afrho
                 * self.phasef(np.abs(geom['phase'].to(u.deg).value))
                 * rho * fsun / 4.0 / geom['delta'].to(self.Afrho.unit)**2)

        return fluxd

class AfrhoThermal(AfrhoRadiation):
    """Thermal emisson from a coma parameterized by efrho.

    If you use this model, please cite and reference Kelley et
    al. (2013, Icarus 225, 475-494).  They define `epsilon-f-rho` as
    the product of IR emissivity (`epsilon`), dust filling factor
    (`f`), and observer's aperture radius (`rho`).

    The default `ef2af` is 3.5, which assumes `epsilion` is
    approximately 0.9, `A` is approximately 0.25, and the scattering
    and emission filling factors are the same.  This value can roughly
    reproduce the spectral shape of 73P-C/Schwassmann-Wachmann in
    Fig. 16 of Sitko et al. (2011, AJ 142, 80) for `Tscale = 1.12`.

    The default long-wavelength slope, `beta = 0.89+/-0.10`, is from
    an analysis of Hyakutake JCMT data by Jewitt and Matthews (1997,
    AJ 113, 1145).  The break-point, `wave0` = 70 um, is based on my
    own analysis, combining the Jewitt and Matthews fluxes with mid-IR
    fluxes from Mason et al. (1998, ApJ 507, 398).

    Parameters
    ----------
    Afrho : Quantity
      The product of albedo at zero phase, A, dust filling factor, f,
      and observer's aperture radius, rho.
    ef2af : float, optional
      The ratio of epsilon-f_therm to A-f_sca, where f_therm and f_sca
      are the effective thermal and scattered light filling factors,
      (they are not necessarily the same).
    Tscale : float, optional
      The isothermal blackbody sphere temperature scale factor that
      characterizes the spectral shape of the thermal emission.
    beta : float, optional
    wave0 : Quantity, optional
      Scale wavelengths longer than `wave0` by `(wave / wave0)**-beta`.

    Methods
    -------
    fluxd : Total flux density from the coma.

    """

    def __init__(self, Afrho, ef2af=3.5, Tscale=1.1, beta=0.89,
                 wave0=70 * u.um, **kwargs):
        assert isinstance(Afrho, u.Quantity)
        self.Afrho = Afrho
        self.ef2af = ef2af
        self.Tscale = Tscale
        self.beta = beta
        self.wave0 = wave0

    def fluxd(self, geom, wave, rap, unit=u.Unit('W / (m2 um)')):
        """Flux density.

        Parameters
        ----------
        geom : dict of Quantities
          A dictionary-like object with the keys 'rh' (heliocentric
          distance), 'delta' (observer-target distance), and 'phase'
          (phase angle).
        wave : Quantity
          The wavelengths at which to compute the emission.
        rap : Quantity
          The aperture radius, angular or projected distance at the
          comet.
        unit : astropy Units, optional
          The return units.  Must be spectral flux density.

        Returns
        -------
        fluxd : Quantity
          The flux density from the coma.

        Raises
        ------
        ValueError : If `rap` has incorrect units.

        """

        from ..util import planck

        if rap.unit.is_equivalent(u.cm):
            rho = rap.to(self.Afrho.unit)
        elif rap.unit.is_equivalent(u.arcsec):
            rho = geom['delta'].to(self.Afrho.unit) * rap.to(u.rad).value
        else:
            raise ValueError("rap must have angular or length units.")

        T = self.Tscale * 278 / np.sqrt(geom['rh'].to(u.au).value)
        B = planck(wave, T, unit=unit / u.sr).value
        efrho = self.Afrho * self.ef2af
        d = geom['delta'].to(self.Afrho.unit).value
        fluxd = efrho.value * np.pi * B * rho.value / d**2

        if any(wave > self.wave0):
            eps = np.ones(len(wave))
            i = wave > self.wave0
            eps[i] *= (wave[i] / self.wave0)**-self.beta
            fluxd *= eps

        return fluxd * unit

def phaseK(phase):
    """Phase function derived from Kolokolova et al. (2004, Comets II).

    The phase function of K04 is scaled to phasef(0) = 1.0.

    Parameters
    ----------
    phase : float or array
        Phase angle. [degrees]

    Returns
    -------
    phi : float or ndarray
        The phase function.

    Notes
    -----
    To estimate the phase function, I fit a polynomial function to the
    solid line of Kolokolova et al. (2004, Comets II):

      a = array([0.27, 0.21, 0.17, 0.15, 0.14, 0.135, 0.135, 0.135, 0.15,
           0.175, 0.225, 0.3, 0.43, 0.62, 0.775])
      b = array([0.0,  10,   20,   30,   40,   60,    70,   80,   100,
           110,   120,   130, 140,  150,  156])
      fit = poly1d(polyfit(b, a / 0.27, 4))
      plot(b, a, 'o')
      plot(b, fit(b) * min(a), 'r-')

    """

    phasef = np.poly1d([  3.14105489e-08,  -7.84714255e-06,   7.34255521e-04,
                         -3.09608957e-02,   1.00920684e+00])
    return phasef(np.abs(phase))

def phaseH(phase):
    """Halley phase function from Schleicher et al. (1998).

    The Halley phase function is from Schleicher et al. (1998, Icarus
    132, 397-417).  The Comet Halley observations were at phases less
    than 70 degrees.

    Parameters
    ----------
    phase : float or array
        Phase angle. [degrees]

    Returns
    -------
    phi : float or ndarray
        The phase function.

    """

    phasef = np.poly1d([0.000177, -0.01807, 1])
    return phasef(np.abs(phase))

def phaseHM(phase):
    """Halley-Marcus phase function from Schleicher et al. (2011).

    The Halley phase function is first published in Schleicher and
    Bair (2011, AJ 141, 117), but only described in detail by
    Schleicher and Marcus (May 2010) at:

      http://asteroid.lowell.edu/comet/dustphase.html

      "To distinguish this curve from others, we designate this as the
      HM phase function, for the sources of the two components: Halley
      and Marcus, where the Halley curve for smaller phase angles
      comes from our previous work (Schleicher et al. 1998) while Joe
      Marcus has fit a Henyey-Greenstein function to a variety of mid-
      and large-phase angle data sets (Marcus 2007); see here for
      details. Note that we do not consider our composite curve to be
      a definitive result, but rather appropriate for performing
      first-order adjustments to dust measurements for changing phase
      angle."

    Parameters
    ----------
    phase : float or array
        Phase angle. [degrees]

    Returns
    -------
    phi : float or ndarray
        The phase function.

    """

    from scipy.interpolate import splrep, splev

    th = np.arange(181)
    ph = np.array(
        [  1.0000e+00,   9.5960e-01,   9.2170e-01,   8.8590e-01,
           8.5220e-01,   8.2050e-01,   7.9060e-01,   7.6240e-01,
           7.3580e-01,   7.1070e-01,   6.8710e-01,   6.6470e-01,
           6.4360e-01,   6.2370e-01,   6.0490e-01,   5.8720e-01,
           5.7040e-01,   5.5460e-01,   5.3960e-01,   5.2550e-01,
           5.1220e-01,   4.9960e-01,   4.8770e-01,   4.7650e-01,
           4.6590e-01,   4.5590e-01,   4.4650e-01,   4.3770e-01,
           4.2930e-01,   4.2150e-01,   4.1420e-01,   4.0730e-01,
           4.0090e-01,   3.9490e-01,   3.8930e-01,   3.8400e-01,
           3.7920e-01,   3.7470e-01,   3.7060e-01,   3.6680e-01,
           3.6340e-01,   3.6030e-01,   3.5750e-01,   3.5400e-01,
           3.5090e-01,   3.4820e-01,   3.4580e-01,   3.4380e-01,
           3.4210e-01,   3.4070e-01,   3.3970e-01,   3.3890e-01,
           3.3850e-01,   3.3830e-01,   3.3850e-01,   3.3890e-01,
           3.3960e-01,   3.4050e-01,   3.4180e-01,   3.4320e-01,
           3.4500e-01,   3.4700e-01,   3.4930e-01,   3.5180e-01,
           3.5460e-01,   3.5760e-01,   3.6090e-01,   3.6450e-01,
           3.6830e-01,   3.7240e-01,   3.7680e-01,   3.8150e-01,
           3.8650e-01,   3.9170e-01,   3.9730e-01,   4.0320e-01,
           4.0940e-01,   4.1590e-01,   4.2280e-01,   4.3000e-01,
           4.3760e-01,   4.4560e-01,   4.5400e-01,   4.6270e-01,
           4.7200e-01,   4.8160e-01,   4.9180e-01,   5.0240e-01,
           5.1360e-01,   5.2530e-01,   5.3750e-01,   5.5040e-01,
           5.6380e-01,   5.7800e-01,   5.9280e-01,   6.0840e-01,
           6.2470e-01,   6.4190e-01,   6.5990e-01,   6.7880e-01,
           6.9870e-01,   7.1960e-01,   7.4160e-01,   7.6480e-01,
           7.8920e-01,   8.1490e-01,   8.4200e-01,   8.7060e-01,
           9.0080e-01,   9.3270e-01,   9.6640e-01,   1.0021e+00,
           1.0399e+00,   1.0799e+00,   1.1223e+00,   1.1673e+00,
           1.2151e+00,   1.2659e+00,   1.3200e+00,   1.3776e+00,
           1.4389e+00,   1.5045e+00,   1.5744e+00,   1.6493e+00,
           1.7294e+00,   1.8153e+00,   1.9075e+00,   2.0066e+00,
           2.1132e+00,   2.2281e+00,   2.3521e+00,   2.4861e+00,
           2.6312e+00,   2.7884e+00,   2.9592e+00,   3.1450e+00,
           3.3474e+00,   3.5685e+00,   3.8104e+00,   4.0755e+00,
           4.3669e+00,   4.6877e+00,   5.0418e+00,   5.4336e+00,
           5.8682e+00,   6.3518e+00,   6.8912e+00,   7.4948e+00,
           8.1724e+00,   8.9355e+00,   9.7981e+00,   1.0777e+01,
           1.1891e+01,   1.3166e+01,   1.4631e+01,   1.6322e+01,
           1.8283e+01,   2.0570e+01,   2.3252e+01,   2.6418e+01,
           3.0177e+01,   3.4672e+01,   4.0086e+01,   4.6659e+01,
           5.4704e+01,   6.4637e+01,   7.7015e+01,   9.2587e+01,
           1.1237e+02,   1.3775e+02,   1.7060e+02,   2.1348e+02,
           2.6973e+02,   3.4359e+02,   4.3989e+02,   5.6292e+02,
           7.1363e+02,   8.8448e+02,   1.0533e+03,   1.1822e+03,
           1.2312e+03])

    C = splrep(th, ph)
    return splev(np.abs(phase), C)


# update module docstring
from ..util import autodoc
autodoc(globals())
del autodoc
# Licensed under a 3-clause BSD style license - see LICENSE.rst dust --- Models for dust ========================  .. autosummary::    :toctree: generated/     Activity    --------    acrit     Dust Models    -----------    AfrhoRadiation    AfrhoScattered    AfrhoThermal     Phase functions    ---------------    phaseK    phaseH    phaseHM Maximum liftable grain radius from a spherical nucleus.      See Meech and Svoren 2004, Comets II.      Parameters     ----------     Q : Quantity       Mass production rate of the driving gas.     vth : Quantity       Gas expansion speed.     R : Quantity       Nucleus radius.     rho_g : Quantity, optional       Grain density.     rho_n : Quantity, optional       Nucleus mean density.     f_active : float, optional       Active fraction of the nucleus.          Returns     -------     a : Quantity       Maximum liftable grain radius. Light from a comet coma parameterized by Afrho, or similar.      Methods     -------     fluxd : Total flux density from the object.      Notes     -----     Afrho should refer to the value at zero phase angle.      Inheriting classes should override `fluxd`, and `__init__`     functions.  `__init__` should take a single argument, `Afrho` (or     equivalent) as a Quantity.      As much as possible, keyword arguments must have the same meaning     in all derived models. Scattered light from a comet coma parameterized by Afrho.      If you use this model, please reference A'Hearn et al. (1984, AJ     89, 579-591) as the source of the Afrho parameter.      Parameters     ----------     Afrho : Quantity       The product of albedo at zero phase, A, dust filling factor, f,       and observer's aperture radius, rho.     phasef : function, optional       The phase function of the coma.  Set to `None` to use `phaseK`.      Methods     -------     fluxd : Total flux density from the coma. Flux density.          Parameters         ----------         geom : dict of Quantities           A dictionary-like object with the keys 'rh' (heliocentric           distance), 'delta' (observer-target distance), and 'phase'           (phase angle).         wave : Quantity           The wavelengths at which to compute the emission.         rap : Quantity           The aperture radius, angular or projected distance at the           comet.         unit : astropy Units, optional           The return units.  Must be spectral flux density.          Returns         -------         fluxd : Quantityu           The flux density from the coma.          Raises         ------         ValueError : If `rap` has incorrect units. Thermal emisson from a coma parameterized by efrho.      If you use this model, please cite and reference Kelley et     al. (2013, Icarus 225, 475-494).  They define `epsilon-f-rho` as     the product of IR emissivity (`epsilon`), dust filling factor     (`f`), and observer's aperture radius (`rho`).      The default `ef2af` is 3.5, which assumes `epsilion` is     approximately 0.9, `A` is approximately 0.25, and the scattering     and emission filling factors are the same.  This value can roughly     reproduce the spectral shape of 73P-C/Schwassmann-Wachmann in     Fig. 16 of Sitko et al. (2011, AJ 142, 80) for `Tscale = 1.12`.      The default long-wavelength slope, `beta = 0.89+/-0.10`, is from     an analysis of Hyakutake JCMT data by Jewitt and Matthews (1997,     AJ 113, 1145).  The break-point, `wave0` = 70 um, is based on my     own analysis, combining the Jewitt and Matthews fluxes with mid-IR     fluxes from Mason et al. (1998, ApJ 507, 398).      Parameters     ----------     Afrho : Quantity       The product of albedo at zero phase, A, dust filling factor, f,       and observer's aperture radius, rho.     ef2af : float, optional       The ratio of epsilon-f_therm to A-f_sca, where f_therm and f_sca       are the effective thermal and scattered light filling factors,       (they are not necessarily the same).     Tscale : float, optional       The isothermal blackbody sphere temperature scale factor that       characterizes the spectral shape of the thermal emission.     beta : float, optional     wave0 : Quantity, optional       Scale wavelengths longer than `wave0` by `(wave / wave0)**-beta`.      Methods     -------     fluxd : Total flux density from the coma. Flux density.          Parameters         ----------         geom : dict of Quantities           A dictionary-like object with the keys 'rh' (heliocentric           distance), 'delta' (observer-target distance), and 'phase'           (phase angle).         wave : Quantity           The wavelengths at which to compute the emission.         rap : Quantity           The aperture radius, angular or projected distance at the           comet.         unit : astropy Units, optional           The return units.  Must be spectral flux density.          Returns         -------         fluxd : Quantity           The flux density from the coma.          Raises         ------         ValueError : If `rap` has incorrect units. Phase function derived from Kolokolova et al. (2004, Comets II).      The phase function of K04 is scaled to phasef(0) = 1.0.      Parameters     ----------     phase : float or array         Phase angle. [degrees]      Returns     -------     phi : float or ndarray         The phase function.      Notes     -----     To estimate the phase function, I fit a polynomial function to the     solid line of Kolokolova et al. (2004, Comets II):        a = array([0.27, 0.21, 0.17, 0.15, 0.14, 0.135, 0.135, 0.135, 0.15,            0.175, 0.225, 0.3, 0.43, 0.62, 0.775])       b = array([0.0,  10,   20,   30,   40,   60,    70,   80,   100,            110,   120,   130, 140,  150,  156])       fit = poly1d(polyfit(b, a / 0.27, 4))       plot(b, a, 'o')       plot(b, fit(b) * min(a), 'r-') Halley phase function from Schleicher et al. (1998).      The Halley phase function is from Schleicher et al. (1998, Icarus     132, 397-417).  The Comet Halley observations were at phases less     than 70 degrees.      Parameters     ----------     phase : float or array         Phase angle. [degrees]      Returns     -------     phi : float or ndarray         The phase function. Halley-Marcus phase function from Schleicher et al. (2011).      The Halley phase function is first published in Schleicher and     Bair (2011, AJ 141, 117), but only described in detail by     Schleicher and Marcus (May 2010) at:        http://asteroid.lowell.edu/comet/dustphase.html        "To distinguish this curve from others, we designate this as the       HM phase function, for the sources of the two components: Halley       and Marcus, where the Halley curve for smaller phase angles       comes from our previous work (Schleicher et al. 1998) while Joe       Marcus has fit a Henyey-Greenstein function to a variety of mid-       and large-phase angle data sets (Marcus 2007); see here for       details. Note that we do not consider our composite curve to be       a definitive result, but rather appropriate for performing       first-order adjustments to dust measurements for changing phase       angle."      Parameters     ----------     phase : float or array         Phase angle. [degrees]      Returns     -------     phi : float or ndarray         The phase function. # update module docstring