DispersionMeasure

class baseband_tasks.dm.DispersionMeasure(value: QuantityLike, unit=None, dtype=<class 'numpy.inexact'>, copy=True, order=None, subok=False, ndmin=0)

Bases: SpecificTypeQuantity

Dispersion measure quantity.

Quantity for electron column density, normally with units of pc / cm**3, with additional methods to help correct for dispersion delays: time_delay, phase_delay, and phase_factor.

Parameters:

dmQuantity or float

Dispersion measure value. If a Quantity is passed, it must have units equivalent to pc/cm**3. If a float is passed, units may be passed to unit, or will otherwise be assumed to be pc/cm**3.

unitUnitBase or None

Units of dm. If None (default), will be set either to the units of dm if dm is an Quantity, or pc/cm**3 otherwise. If dm is a Quantity and unit is also passed, will try to convert dm to unit.

*args, **kwargs

As for Quantity.

Notes

The constant relating dispersion measure to delay is hardcoded to match that of Tempo. See Taylor, Manchester, & Lyne (1993). It is accessible as the dispersion_delay_constant attribute.

Attributes Summary

dispersion_delay_constant

Dispersion delay constant, hardcoded to match that for Tempo.

Methods Summary

phase_delay(freq[, ref_freq])	Phase delay due to dispersion.
phase_factor(freq[, ref_freq])	Complex exponential factor due to dispersion.
time_delay(freq[, ref_freq])	Time delay due to dispersion.

Attributes Documentation

dispersion_delay_constant = <Quantity 4149.37759336 cm3 MHz2 s / pc>

Dispersion delay constant, hardcoded to match that for Tempo.

Methods Documentation

phase_delay(freq, ref_freq=None)

Phase delay due to dispersion.

Parameters:

freqQuantity

Frequency at which to evaluate the dispersion delay.

ref_freqQuantity, optional

Reference frequency relative to which the dispersion delay is evaluated. If not given, infinite frequency is assumed.

Notes

Given the dispersion measure \(\mathrm{DM}\), frequency \(f\) and reference frequency \(f_\mathrm{ref}\), calculates the phase amplitude of the transfer function (Eqn. 5.21, Lorimer & Kramer’s Handbook of Pulsar Astronomy, rewritten to use absolute frequency):

\[\Delta \phi = \frac{e^2\mathrm{DM}}{m_ec} f \left(\frac{1} {f_\mathrm{ref}} - \frac{1}{f}\right)^2\]

phase_factor(freq, ref_freq=None)

Complex exponential factor due to dispersion.

This is just exp(1j * phase_delay).

Parameters:

freqQuantity

Frequency at which to evaluate the dispersion delay.

ref_freqQuantity, optional

Reference frequency relative to which the dispersion delay is evaluated. If not given, infinite frequency is assumed.

time_delay(freq, ref_freq=None)

Time delay due to dispersion.

Parameters:

freqQuantity

Frequency at which to evaluate the dispersion delay.

ref_freqQuantity, optional

Reference frequency relative to which the dispersion delay is evaluated. If not given, infinite frequency is assumed.

Notes

Given the dispersion measure \(\mathrm{DM}\), frequency \(f\) and reference frequency \(f_\mathrm{ref}\), calculates the time delay (Eqn. 4.7, Lorimer & Kramer’s Handbook of Pulsar Astronomy):

\[\Delta t = \frac{e^2}{2\pi m_ec} \mathrm{DM}\left(\frac{1} {f_\mathrm{ref}^2} - \frac{1}{f^2}\right)\]

where the dispersion delay constant is taken to be exactly (inverse of Eqn. 6 of Taylor, Manchester, & Lyne 1993):

\[\frac{e^2}{2\pi m_ec} = \frac{1}{2.410} \times 10^4\, \mathrm{MHz}^2\,\mathrm{pc}^{-1} \,\mathrm{cm}^3\,\mathrm{s}.\]