We analyze the frequency dependence of the dispersion measure ( DM ) , the column density of free electrons to a pulsar , caused by multipath scattering from small scale electron-density fluctuations .
The DM is slightly different along each propagation path and the transverse spread of paths varies greatly with frequency , yielding arrival time perturbations that scale differently than the inverse square of the frequency , the expected dependence for a cold , unmagnetized plasma .
We quantify DM and pulse-arrival-time perturbations analytically for thin phase screens and extended media and verify the results with simulations of thin screens .
The rms difference between DMs across an octave band near 1.5 GHz \sim 4 \times 10 ^ { -5 } { pc cm ^ { -3 } } for pulsars at \sim 1 kpc distance .
Time-of-arrival errors resulting from chromatic DMs are of order a few to hundreds of nanoseconds for pulsars with DM \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } } } 30 pc cm ^ { -3 } observed across an octave band but increase rapidly to microseconds or larger for larger DMs and wider frequency ranges .
Frequency-dependent DMs introduce correlated noise into timing residuals whose power spectrum is ‘ low pass ’ in form .
The correlation time is of order the geometric mean of the refraction times for the highest and lowest radio frequencies used and thus ranges from days to years , depending on the pulsar .
We discuss the implications for methodologies that use large frequency separations or wide bandwidth receivers for timing measurements .
Chromatic DMs are partially mitigable by using an additional chromatic term in arrival time models .
Without mitigation , our results provide an additional term in the noise model for pulsar timing ; they also indicate that in combination with measurement errors from radiometer noise , an arbitrary increase in total frequency range ( or bandwidth ) will yield diminishing benefits and may be detrimental to overall timing precision .