diff options
Diffstat (limited to 'fg21sim/extragalactic/clusters/emission.py')
| -rw-r--r-- | fg21sim/extragalactic/clusters/emission.py | 201 |
1 files changed, 200 insertions, 1 deletions
diff --git a/fg21sim/extragalactic/clusters/emission.py b/fg21sim/extragalactic/clusters/emission.py index ddecab3..a798470 100644 --- a/fg21sim/extragalactic/clusters/emission.py +++ b/fg21sim/extragalactic/clusters/emission.py @@ -31,7 +31,11 @@ import numpy as np import scipy.special from scipy import integrate, interpolate -from ...utils.units import (Units as AU, Constants as AC) +from ...share import COSMO +from ...utils.convert import Fnu_to_Tb +from ...utils.units import (Units as AU, + UnitConversions as AUC, + Constants as AC) logger = logging.getLogger(__name__) @@ -223,3 +227,198 @@ class SynchrotronEmission: return syncem[0] else: return syncem + + +class HaloEmission: + """ + Calculate the synchrotron emission of a (giant) radio halo. + + Parameters + ---------- + gamma : 1D `~numpy.ndarray` + The Lorentz factors γ of the electron spectrum. + n_e : 1D `~numpy.ndarray` + The electron spectrum (w.r.t. Lorentz factors γ). + Unit: [cm^-3] + B : float + The magnetic field strength. + Unit: [uG] + radius : float, optional + The radio halo radius. + Required to calculate the power. + Unit: [kpc] + redshift : float, optional + The redshift to the radio halo. + Required to calculate the flux, which also requires ``radius``. + """ + def __init__(self, gamma, n_e, B, radius=None, redshift=None): + self.gamma = np.asarray(gamma) + self.n_e = np.asarray(n_e) + self.B = B + self.radius = radius + self.redshift = redshift + + @property + def angular_radius(self): + """ + The angular radius of the radio halo. + Unit: [arcsec] + """ + if self.redshift is None: + raise RuntimeError("parameter 'redshift' is required") + if self.radius is None: + raise RuntimeError("parameter 'radius' is required") + + DA = COSMO.DA(self.redshift) * 1e3 # [Mpc] -> [kpc] + theta = self.radius / DA # [rad] + return theta * AUC.rad2arcsec + + @property + def volume(self): + """ + The halo volume. + Unit: [kpc^3] + """ + if self.radius is None: + raise RuntimeError("parameter 'radius' is required") + + return (4*np.pi/3) * self.radius**3 + + def calc_emissivity(self, frequencies): + """ + Calculate the synchrotron emissivity for the derived electron + spectrum. + + Parameters + ---------- + frequencies : float, or 1D `~numpy.ndarray` + The frequencies where to calculate the synchrotron emissivity. + Unit: [MHz] + + Returns + ------- + emissivity : float, or 1D `~numpy.ndarray` + The calculated synchrotron emissivity at each specified + frequency. + Unit: [erg/s/cm^3/Hz] + """ + syncem = SynchrotronEmission(gamma=self.gamma, n_e=self.n_e, B=self.B) + emissivity = syncem.emissivity(frequencies) + return emissivity + + def calc_power(self, frequencies, emissivity=None): + """ + Calculate the halo synchrotron power (i.e., power *emitted* per + unit frequency) by assuming the emissivity is uniform throughout + the halo volume. + + NOTE + ---- + The calculated power (a.k.a. spectral luminosity) is in units of + [W/Hz] which is common in radio astronomy, instead of [erg/s/Hz]. + 1 [W] = 1e7 [erg/s] + + Parameters + ---------- + frequencies : float, or 1D `~numpy.ndarray` + The frequencies where to calculate the synchrotron power. + Unit: [MHz] + emissivity : float, or 1D `~numpy.ndarray`, optional + The synchrotron emissivity at the input frequencies. + If not provided, then invoke above ``calc_emissivity()`` + method to calculate them. + Unit: [erg/s/cm^3/Hz] + + Returns + ------- + power : float, or 1D `~numpy.ndarray` + The calculated synchrotron power at each input frequency. + Unit: [W/Hz] + """ + frequencies = np.asarray(frequencies) + if emissivity is None: + emissivity = self.calc_emissivity(frequencies=frequencies) + else: + emissivity = np.asarray(emissivity) + power = emissivity * (self.volume * AUC.kpc2cm**3) # [erg/s/Hz] + power *= 1e-7 # [erg/s/Hz] -> [W/Hz] + return power + + def calc_flux(self, frequencies): + """ + Calculate the synchrotron flux density (i.e., power *observed* + per unit frequency) of the halo, with k-correction considered. + + NOTE + ---- + The *k-correction* must be applied to the flux density (Sν) or + specific luminosity (Lν) because the redshifted object is emitting + flux in a different band than that in which you are observing. + And the k-correction depends on the spectrum of the object in + question. For any other spectrum (i.e., vLv != const.), the flux + density Sv is related to the specific luminosity Lv by: + Sv = (1+z) L_v(1+z) / (4π DL^2), + where + * L_v(1+z) is the specific luminosity emitting at frequency v(1+z), + * DL is the luminosity distance to the object at redshift z. + + Reference: Ref.[hogg1999],Eq.(22) + + Returns + ------- + flux : float, or 1D `~numpy.ndarray` + The calculated flux density w.r.t. each input frequency. + Unit: [Jy] = 1e-23 [erg/s/cm^2/Hz] = 1e-26 [W/m^2/Hz] + """ + if self.redshift is None: + raise RuntimeError("parameter 'redshift' is required") + + freqz = np.asarray(frequencies) * (1+self.redshift) + power = self.calc_power(freqz) # [W/Hz] + DL = COSMO.DL(self.redshift) * AUC.Mpc2m # [m] + flux = 1e26 * (1+self.redshift) * power / (4*np.pi * DL*DL) # [Jy] + return flux + + def calc_brightness_mean(self, frequencies, flux=None, pixelsize=None): + """ + Calculate the mean surface brightness (power observed per unit + frequency and per unit solid angle) expressed in *brightness + temperature* at the specified frequencies. + + NOTE + ---- + If the solid angle that the object extends is smaller than the + specified pixel area, then is is assumed to have size of 1 pixel. + + Parameters + ---------- + frequencies : float, or 1D `~numpy.ndarray` + The frequencies where to calculate the mean brightness temperature + Unit: [MHz] + flux : float, or 1D `~numpy.ndarray`, optional + The flux density w.r.t. each input frequency. + Unit: [Jy] + pixelsize : float, optional + The pixel size of the output simulated sky image. + If not provided, then invoke above ``calc_flux()`` method to + calculate them. + Unit: [arcsec] + + Returns + ------- + Tb : float, or 1D `~numpy.ndarray` + The mean brightness temperature at each frequency. + Unit: [K] <-> [Jy/pixel] + """ + frequencies = np.asarray(frequencies) + if flux is None: + flux = self.calc_flux(frequencies=frequencies) # [Jy] + else: + flux = np.asarray(flux) + omega = np.pi * self.angular_radius**2 # [arcsec^2] + if pixelsize and (omega < pixelsize**2): + omega = pixelsize ** 2 # [arcsec^2] + logger.warning("Halo size < 1 pixel; force to be 1 pixel!") + + Tb = Fnu_to_Tb(flux, omega, frequencies) # [K] + return Tb |