The Galactic One-Way Shapiro Delay to PSR B1937+21
  The time delay experienced by a light ray as it passes through a changing
gravitational potential by a non-zero mass distribution along the line of sight
is usually referred to as Shapiro delay. Shapiro delay has been extensively
measured in the Solar system and in binary pulsars, enabling stringent tests of
general relativity as well as measurement of neutron star masses . However,
Shapiro delay is ubiquitous and experienced by all astrophysical messengers on
their way from the source to the Earth. We calculate the "one-way" static
Shapiro delay for the first discovered millisecond pulsar PSR~B1937+21, by
including the contributions from both the dark matter and baryonic matter
between this pulsar and the Earth. We find a value of approximately 5 days (of
which 4.74 days is from the dark matter and 0.22 days from the baryonic
matter). We also calculate the modulation of Shapiro delay from the motion of a
single dark matter halo, and also evaluate the cumulative effects of the motion
of matter distribution on the change in pulsar's period and its derivative. The
time-dependent effects are too small to be detected with the current timing
noise observed for this pulsar. Finally, we would like to emphasize that
although the one-way Shapiro delay is mostly of academic interest for
electromagnetic astronomy, its ubiquity should not be forgotten in the era of
multi-messenger astronomy.
