The ACF for a given delay, tau is determined from S by inverse Fourier transforming over a channel window, acf(tau) = int_nu0^nu1 S(nu) exp(2j pi tau nu) dnu. For a channel near the peak of the transmission spectrum (which is typically a sinc) this multiplies the scale by nu1 - nu0.
The visibility associated with this is then found by attenuating by the square of distance.
Together, for a fiducial units of distance of 1km and channel width of 130kHz this would multiply the spectral power by 0.13 Hz/m^2 which is close enough to unity. Hence it might make sense to choose distances in km and channel widths in kHz
The other spot where gradients might be really large or small could be from using tau in seconds. Delays are < 0.03ms over 10km baselines, hence micro second delays and MHz for channel freqs might be more stable.
Combining the above two points it makes sense to use:
distance in km
delays in microseconds
frequencies in MHz
The spectral power is in units
[S]=Jy m^2 / Hz.The ACF for a given delay,
tauis determined fromSby inverse Fourier transforming over a channel window,acf(tau) = int_nu0^nu1 S(nu) exp(2j pi tau nu) dnu. For a channel near the peak of the transmission spectrum (which is typically a sinc) this multiplies the scale bynu1 - nu0.The visibility associated with this is then found by attenuating by the square of distance.
Together, for a fiducial units of distance of
1kmand channel width of130kHzthis would multiply the spectral power by0.13 Hz/m^2which is close enough to unity. Hence it might make sense to choose distances in km and channel widths in kHzThe other spot where gradients might be really large or small could be from using
tauin seconds. Delays are < 0.03ms over 10km baselines, hence micro second delays and MHz for channel freqs might be more stable.Combining the above two points it makes sense to use: