# Licensed under a 3-clause BSD style license - see LICENSE.rst """A set of standard astronomical equivalencies.""" from __future__ import (absolute_import, division, print_function, unicode_literals) # THIRD-PARTY import numpy as np # LOCAL from ..constants import si as _si from . import si from . import cgs from . import astrophys from . import dimensionless_unscaled __all__ = ['parallax', 'spectral', 'spectral_density', 'doppler_radio', 'doppler_optical', 'doppler_relativistic', 'mass_energy', 'brightness_temperature', 'dimensionless_angles', 'logarithmic', 'temperature', 'temperature_energy'] def dimensionless_angles(): """Allow angles to be equivalent to dimensionless (with 1 rad = 1 m/m = 1). It is special compared to other equivalency pairs in that it allows this independent of the power to which the angle is raised, and indepedent of whether it is part of a more complicated unit. """ return [(si.radian, None)] def logarithmic(): """Allow logarithmic units to be converted to dimensionless fractions""" return [ (dimensionless_unscaled, astrophys.dex, lambda x: np.log10(x), lambda x: 10.**x) ] def parallax(): """ Returns a list of equivalence pairs that handle the conversion between parallax angle and distance. """ return [ (si.arcsecond, astrophys.parsec, lambda x: 1. / x) ] def spectral(): """ Returns a list of equivalence pairs that handle spectral wavelength, wave number, frequency, and energy equivalences. Allows conversions between wavelength units, wave number units, frequency units, and energy units as they relate to light. There are two types of wave number: * spectroscopic - :math:`1 / \\lambda` (per meter) * angular - :math:`2 \\pi / \\lambda` (radian per meter) """ hc = _si.h.value * _si.c.value two_pi = 2.0 * np.pi inv_m_spec = si.m ** -1 inv_m_ang = si.radian / si.m return [ (si.m, si.Hz, lambda x: _si.c.value / x), (si.m, si.J, lambda x: hc / x), (si.Hz, si.J, lambda x: _si.h.value * x, lambda x: x / _si.h.value), (si.m, inv_m_spec, lambda x: 1.0 / x), (si.Hz, inv_m_spec, lambda x: x / _si.c.value, lambda x: _si.c.value * x), (si.J, inv_m_spec, lambda x: x / hc, lambda x: hc * x), (inv_m_spec, inv_m_ang, lambda x: x * two_pi, lambda x: x / two_pi), (si.m, inv_m_ang, lambda x: two_pi / x), (si.Hz, inv_m_ang, lambda x: two_pi * x / _si.c.value, lambda x: _si.c.value * x / two_pi), (si.J, inv_m_ang, lambda x: x * two_pi / hc, lambda x: hc * x / two_pi) ] def spectral_density(wav, factor=None): """ Returns a list of equivalence pairs that handle spectral density with regard to wavelength and frequency. Parameters ---------- wav : `~astropy.units.Quantity` `~astropy.units.Quantity` associated with values being converted (e.g., wavelength or frequency). Notes ----- The ``factor`` argument is left for backward-compatibility with the syntax ``spectral_density(unit, factor)`` but users are encouraged to use ``spectral_density(factor * unit)`` instead. """ from .core import UnitBase if isinstance(wav, UnitBase): if factor is None: raise ValueError( 'If `wav` is specified as a unit, `factor` should be set') wav = factor * wav # Convert to Quantity c_Aps = _si.c.to(si.AA / si.s).value # Angstrom/s h_cgs = _si.h.cgs.value # erg * s hc = c_Aps * h_cgs fla = cgs.erg / si.angstrom / si.cm ** 2 / si.s fnu = cgs.erg / si.Hz / si.cm ** 2 / si.s nufnu = cgs.erg / si.cm ** 2 / si.s lafla = nufnu photlam = astrophys.photon / (si.cm ** 2 * si.s * si.AA) photnu = astrophys.photon / (si.cm ** 2 * si.s * si.Hz) def converter(x): return x * (wav.to(si.AA, spectral()).value ** 2 / c_Aps) def iconverter(x): return x / (wav.to(si.AA, spectral()).value ** 2 / c_Aps) def converter_fnu_nufnu(x): return x * wav.to(si.Hz, spectral()).value def iconverter_fnu_nufnu(x): return x / wav.to(si.Hz, spectral()).value def converter_fla_lafla(x): return x * wav.to(si.AA, spectral()).value def iconverter_fla_lafla(x): return x / wav.to(si.AA, spectral()).value def converter_photlam_fla(x): return hc * x / wav.to(si.AA, spectral()).value def iconverter_photlam_fla(x): return x * wav.to(si.AA, spectral()).value / hc def converter_photlam_fnu(x): return h_cgs * x * wav.to(si.AA, spectral()).value def iconverter_photlam_fnu(x): return x / (wav.to(si.AA, spectral()).value * h_cgs) def converter_photlam_photnu(x): return x * wav.to(si.AA, spectral()).value ** 2 / c_Aps def iconverter_photlam_photnu(x): return c_Aps * x / wav.to(si.AA, spectral()).value ** 2 converter_photnu_fnu = converter_photlam_fla iconverter_photnu_fnu = iconverter_photlam_fla def converter_photnu_fla(x): return x * hc * c_Aps / wav.to(si.AA, spectral()).value ** 3 def iconverter_photnu_fla(x): return x * wav.to(si.AA, spectral()).value ** 3 / (hc * c_Aps) return [ (si.AA, fnu, converter, iconverter), (fla, fnu, converter, iconverter), (si.AA, si.Hz, converter, iconverter), (fla, si.Hz, converter, iconverter), (fnu, nufnu, converter_fnu_nufnu, iconverter_fnu_nufnu), (fla, lafla, converter_fla_lafla, iconverter_fla_lafla), (photlam, fla, converter_photlam_fla, iconverter_photlam_fla), (photlam, fnu, converter_photlam_fnu, iconverter_photlam_fnu), (photlam, photnu, converter_photlam_photnu, iconverter_photlam_photnu), (photnu, fnu, converter_photnu_fnu, iconverter_photnu_fnu), (photnu, fla, converter_photnu_fla, iconverter_photnu_fla) ] def doppler_radio(rest): r""" Return the equivalency pairs for the radio convention for velocity. The radio convention for the relation between velocity and frequency is: :math:`V = c \frac{f_0 - f}{f_0} ; f(V) = f_0 ( 1 - V/c )` Parameters ---------- rest : `~astropy.units.Quantity` Any quantity supported by the standard spectral equivalencies (wavelength, energy, frequency, wave number). References ---------- `NRAO site defining the conventions `_ Examples -------- >>> import astropy.units as u >>> CO_restfreq = 115.27120*u.GHz # rest frequency of 12 CO 1-0 in GHz >>> radio_CO_equiv = u.doppler_radio(CO_restfreq) >>> measured_freq = 115.2832*u.GHz >>> radio_velocity = measured_freq.to(u.km/u.s, equivalencies=radio_CO_equiv) >>> radio_velocity # doctest: +FLOAT_CMP """ ckms = _si.c.to('km/s').value def to_vel_freq(x): restfreq = rest.to(si.Hz, equivalencies=spectral()).value return (restfreq-x) / (restfreq) * ckms def from_vel_freq(x): restfreq = rest.to(si.Hz, equivalencies=spectral()).value voverc = x/ckms return restfreq * (1-voverc) def to_vel_wav(x): restwav = rest.to(si.AA, spectral()).value return (x-restwav) / (x) * ckms def from_vel_wav(x): restwav = rest.to(si.AA, spectral()).value return restwav * ckms / (ckms-x) def to_vel_en(x): resten = rest.to(si.eV, equivalencies=spectral()).value return (resten-x) / (resten) * ckms def from_vel_en(x): resten = rest.to(si.eV, equivalencies=spectral()).value voverc = x/ckms return resten * (1-voverc) return [(si.Hz, si.km/si.s, to_vel_freq, from_vel_freq), (si.AA, si.km/si.s, to_vel_wav, from_vel_wav), (si.eV, si.km/si.s, to_vel_en, from_vel_en), ] def doppler_optical(rest): r""" Return the equivalency pairs for the optical convention for velocity. The optical convention for the relation between velocity and frequency is: :math:`V = c \frac{f_0 - f}{f } ; f(V) = f_0 ( 1 + V/c )^{-1}` Parameters ---------- rest : `~astropy.units.Quantity` Any quantity supported by the standard spectral equivalencies (wavelength, energy, frequency, wave number). References ---------- `NRAO site defining the conventions `_ Examples -------- >>> import astropy.units as u >>> CO_restfreq = 115.27120*u.GHz # rest frequency of 12 CO 1-0 in GHz >>> optical_CO_equiv = u.doppler_optical(CO_restfreq) >>> measured_freq = 115.2832*u.GHz >>> optical_velocity = measured_freq.to(u.km/u.s, equivalencies=optical_CO_equiv) >>> optical_velocity # doctest: +FLOAT_CMP """ ckms = _si.c.to('km/s').value def to_vel_freq(x): restfreq = rest.to(si.Hz, equivalencies=spectral()).value return ckms * (restfreq-x) / x def from_vel_freq(x): restfreq = rest.to(si.Hz, equivalencies=spectral()).value voverc = x/ckms return restfreq / (1+voverc) def to_vel_wav(x): restwav = rest.to(si.AA, spectral()).value return ckms * (x/restwav-1) def from_vel_wav(x): restwav = rest.to(si.AA, spectral()).value voverc = x/ckms return restwav * (1+voverc) def to_vel_en(x): resten = rest.to(si.eV, equivalencies=spectral()).value return ckms * (resten-x) / x def from_vel_en(x): resten = rest.to(si.eV, equivalencies=spectral()).value voverc = x/ckms return resten / (1+voverc) return [(si.Hz, si.km/si.s, to_vel_freq, from_vel_freq), (si.AA, si.km/si.s, to_vel_wav, from_vel_wav), (si.eV, si.km/si.s, to_vel_en, from_vel_en), ] def doppler_relativistic(rest): r""" Return the equivalency pairs for the relativistic convention for velocity. The full relativistic convention for the relation between velocity and frequency is: :math:`V = c \frac{f_0^2 - f^2}{f_0^2 + f^2} ; f(V) = f_0 \frac{\left(1 - (V/c)^2\right)^{1/2}}{(1+V/c)}` Parameters ---------- rest : `~astropy.units.Quantity` Any quantity supported by the standard spectral equivalencies (wavelength, energy, frequency, wave number). References ---------- `NRAO site defining the conventions `_ Examples -------- >>> import astropy.units as u >>> CO_restfreq = 115.27120*u.GHz # rest frequency of 12 CO 1-0 in GHz >>> relativistic_CO_equiv = u.doppler_relativistic(CO_restfreq) >>> measured_freq = 115.2832*u.GHz >>> relativistic_velocity = measured_freq.to(u.km/u.s, equivalencies=relativistic_CO_equiv) >>> relativistic_velocity # doctest: +FLOAT_CMP >>> measured_velocity = 1250 * u.km/u.s >>> relativistic_frequency = measured_velocity.to(u.GHz, equivalencies=relativistic_CO_equiv) >>> relativistic_frequency # doctest: +FLOAT_CMP >>> relativistic_wavelength = measured_velocity.to(u.mm, equivalencies=relativistic_CO_equiv) >>> relativistic_wavelength # doctest: +FLOAT_CMP """ ckms = _si.c.to('km/s').value def to_vel_freq(x): restfreq = rest.to(si.Hz, equivalencies=spectral()).value return (restfreq**2-x**2) / (restfreq**2+x**2) * ckms def from_vel_freq(x): restfreq = rest.to(si.Hz, equivalencies=spectral()).value voverc = x/ckms return restfreq * ((1-voverc) / (1+(voverc)))**0.5 def to_vel_wav(x): restwav = rest.to(si.AA, spectral()).value return (x**2-restwav**2) / (restwav**2+x**2) * ckms def from_vel_wav(x): restwav = rest.to(si.AA, spectral()).value voverc = x/ckms return restwav * ((1+voverc) / (1-voverc))**0.5 def to_vel_en(x): resten = rest.to(si.eV, spectral()).value return (resten**2-x**2) / (resten**2+x**2) * ckms def from_vel_en(x): resten = rest.to(si.eV, spectral()).value voverc = x/ckms return resten * ((1-voverc) / (1+(voverc)))**0.5 return [(si.Hz, si.km/si.s, to_vel_freq, from_vel_freq), (si.AA, si.km/si.s, to_vel_wav, from_vel_wav), (si.eV, si.km/si.s, to_vel_en, from_vel_en), ] def mass_energy(): """ Returns a list of equivalence pairs that handle the conversion between mass and energy. """ return [(si.kg, si.J, lambda x: x * _si.c.value ** 2, lambda x: x / _si.c.value ** 2), (si.kg / si.m ** 2, si.J / si.m ** 2 , lambda x: x * _si.c.value ** 2, lambda x: x / _si.c.value ** 2), (si.kg / si.m ** 3, si.J / si.m ** 3 , lambda x: x * _si.c.value ** 2, lambda x: x / _si.c.value ** 2), (si.kg / si.s, si.J / si.s , lambda x: x * _si.c.value ** 2, lambda x: x / _si.c.value ** 2), ] def brightness_temperature(beam_area, disp): """ Defines the conversion between Jy/beam and "brightness temperature", :math:`T_B`, in Kelvins. The brightness temperature is a unit very commonly used in radio astronomy. See, e.g., "Tools of Radio Astronomy" (Wilson 2009) eqn 8.16 and eqn 8.19 (these pages are available on `google books `__). :math:`T_B \equiv S_\\nu / \left(2 k \\nu^2 / c^2 \\right)` However, the beam area is essential for this computation: the brightness temperature is inversely proportional to the beam area Parameters ---------- beam_area : Beam Area equivalent Beam area in angular units, i.e. steradian equivalent disp : `~astropy.units.Quantity` with spectral units The observed `spectral` equivalent `~astropy.units.Unit` (e.g., frequency or wavelength) Examples -------- Arecibo C-band beam:: >>> import numpy as np >>> from astropy import units as u >>> beam_area = np.pi*(50*u.arcsec)**2 >>> freq = 5*u.GHz >>> equiv = u.brightness_temperature(beam_area, freq) >>> u.Jy.to(u.K, equivalencies=equiv) # doctest: +FLOAT_CMP 7.052588858846446 >>> (1*u.Jy).to(u.K, equivalencies=equiv) # doctest: +FLOAT_CMP VLA synthetic beam:: >>> beam_area = np.pi*(15*u.arcsec)**2 >>> freq = 5*u.GHz >>> equiv = u.brightness_temperature(beam_area, freq) >>> u.Jy.to(u.K, equivalencies=equiv) # doctest: +FLOAT_CMP 78.36209843162719 """ beam = beam_area.to(si.sr).value nu = disp.to(si.GHz, spectral()) def convert_Jy_to_K(x_jybm): factor = (2 * _si.k_B * si.K * nu**2 / _si.c**2).to(astrophys.Jy).value return (x_jybm / beam / factor) def convert_K_to_Jy(x_K): factor = (astrophys.Jy / (2 * _si.k_B * nu**2 / _si.c**2)).to(si.K).value return (x_K * beam / factor) return [(astrophys.Jy, si.K, convert_Jy_to_K, convert_K_to_Jy)] def temperature(): """Convert between Kelvin, Celsius, and Fahrenheit here because Unit and CompositeUnit cannot do addition or subtraction properly. """ from .imperial import deg_F return [ (si.K, si.deg_C, lambda x: x - 273.15, lambda x: x + 273.15), (si.deg_C, deg_F, lambda x: x * 1.8 + 32.0, lambda x: (x - 32.0) / 1.8), (si.K, deg_F, lambda x: (x - 273.15) * 1.8 + 32.0, lambda x: ((x - 32.0) / 1.8) + 273.15)] def temperature_energy(): """Convert between Kelvin and keV(eV) to an equivalent amount.""" return [ (si.K, si.eV, lambda x: x / (_si.e.value / _si.k_B), lambda x: x * (_si.e.value / _si.k_B))]