Turbulent Scattering¶
The formalism developed by `Macquart&Koay13`_has been ingested into the Turbulence class for calculations of temporal smearing and angular broadening.
Turbulence¶
This class describes the turbulence from a single object with properties listed in the following Table:
| Parameter | Unit | Description | Required? |
|---|---|---|---|
| ne | density; cm**-3 | Fiducial value of electron density | Yes |
| l0 | length; AU | Inner length scale | Yes |
| L0 | length; pc | Outer length scale | Yes |
| zL | unitless | Redshift of scattering medium | Yes |
| beta | unitless | Exponent of turbulence | Yes |
| DL | length; kpc | Thickness of the object | Required for SM |
| lobs | length; cm | Wavelength of interest | Input for tau, theta |
Here is a simple instantiation:
def_l0 = 1*u.AU
def_L0 = 0.001 * u.pc
def_ne = 1e-2 / u.cm**3
def_DL = 1 * u.kpc
def_zL = 1.
turb = Turbulence(def_ne, def_l0, def_L0)
The resultant object can then be used for scattering calculations. Note that in this instantiation, beta has a default value of 11/3 (Kolmogorov) and zL=0.
Temporal Smearing¶
With a Turbulence object defined as above, one can calculate the temporal smearing of a source at a given redshift and for a given observed wavelength (or frequency). Here is an example:
from astropy import constants as const
turb = Turbulence(def_ne, def_l0, def_L0, def_zL)
inu = 1 * u.GHz
lobs = (const.c/inu).to('cm')
# SM, rdiff
turb.set_SM_obj(def_DL)
turb.set_rdiff(lobs)
# tau
zsource = 2.
tau = turb.temporal_smearing(lobs, zsource)
print(tau) # Given in ms
Angular Broadening¶
With a Turbulence object defined as above, one can calculate the angular broadening of a source at a given redshift and for a given observed wavelength (or frequency). Here is an example:
theta = turb.angular_broadening(lobs, zsource) # Returned in arcsec
Intervening Galaxies¶
One may generate a set of random draws for temporal smearing due to the ISM of intervening galaxies towards a source with given redshift using the monte_tau method:
from frb.dlas import monte_tau
zeval = np.array([0.,1.,2.])
taus = monte_tau(np.array(zeval)) # Returned unitless but in ms