Will LISA Detect Harmonic Gravitational Waves from Galactic Cosmic
  String Loops?
  Rapid advancement in the observation of cosmic strings has been made in
recent years placing increasingly stringent constraints on their properties,
with $G\mu\lesssim 10^{-11}$ from Pulsar Timing Array (PTA). Cosmic string
loops with low string tension clump in the Galaxy due to slow loop decay and
low gravitational recoil, resulting in great enhancement to loop abundance in
the Galaxy. With an average separation of down to just a fraction of a kpc, and
the total power of gravitational wave (GW) emission dominated by harmonic modes
spanning a wide angular scale, resolved loops located in proximity are
powerful, persistent, and highly monochromatic sources of GW with a harmonic
signature not replicated by any other sources, making them prime targets for
direct detection by the upcoming Laser Interferometer Space Antenna (LISA),
whose frequency range is well-matched. Unlike detection of bursts where the
detection rate scales with loop abundance, the detection rate for harmonic
signal is the result of a complex interplay between the strength of GW
emission, loop abundance, and other sources of noise, and is most suitably
studied through numerical simulations. We develop a robust and flexible
framework for simulating loops in the Galaxy for predicting direct detection of
harmonic signal from resolved loops by LISA. Our simulation reveals that the
most accessible region in the parameter space consists of large loops
$\alpha=0.1$ with low tension $10^{-21}\lesssim G\mu\lesssim 10^{-19}$. Direct
detection of field theory cosmic strings is unlikely, with the detection
probability $p_{\mathrm{det}}\lesssim 2\%$ for a 1-year mission. An extension
suggests that direct detection of cosmic superstrings with a low
intercommutation probability is very promising. Searching for harmonic GW
signal from resolved loops through LISA observations will potentially place
physical constraints on string theory.
