Pulsar Timing Residuals and a Suspected Companion

With 200 observations and 0.5 microsecond precision, the formal uncertainty on a fitted sinusoid amplitude is roughly 0.5 / sqrt(200) = 0.035 microseconds, so a 12-microsecond amplitude is about 340 sigma - highly significant. The 3-year baseline covers about 18 cycles of a 60-day period, so the period is well constrained and not an alias of the sampling. The signal is achromatic after dispersion removal, which rules out a dispersion-measure variation from the interstellar medium. A planet of 2 M_earth in a 60-day orbit around a millisecond pulsar would produce a timing amplitude of order (m_p / M_psr) x (a sin i / c) x P_psr; for a 1.4 M_sun pulsar and a 60-day orbit, the projected semi-major axis is about 1.5 light-seconds, and the amplitude is a few microseconds to tens of microseconds depending on inclination. The 12-microsecond amplitude is therefore plausible for a 2 M_earth planet. The signal is significant and consistent with a planetary companion, but a check for chromatic or spin-down-related systematics is still warranted.

Achromaticity matters because interstellar dispersion is strongly frequency-dependent: a change in dispersion measure along the line of sight would produce residuals that scale as the inverse square of frequency, so the 1.4 and 2.0 GHz residuals would differ by a factor of (2.0/1.4)^2 = 2.04 after dispersion removal. The residuals are consistent across both bands, so a DM variation is excluded. The remaining alternative is a spin-down or timing-model error, such as an unmodeled change in the pulsar's rotation rate or a glitch recovery, which would produce residuals that are achromatic but would not be strictly periodic over 18 cycles. A companion is the simplest explanation, but the team should check for a long-term trend and for a possible second periodicity. If the 60-day signal persists with stable phase over more cycles and shows no chromatic dependence, a planetary companion is the leading interpretation.