Spiral arm pitch angle and galactic shear rate in N-body simulations of
  disc galaxies
  Spiral galaxies are observed to exhibit a range of morphologies, in
particular in the shape of spiral arms. A key diagnostic parameter is the pitch
angle, which describes how tightly wound the spiral arms are. Observationally
and analytically, a correlation between pitch angle and galactic shear rate has
been detected. For the first time, we examine whether this effect is detected
in N-body simulations by calculating and comparing pitch angles of both
individual density waves and overall spiral structure in a suite of N-body
simulations. We find that higher galactic shear rates produce more tightly
wound spiral arms, both in individual mode patterns (density waves) and in the
overall density enhancement. Although the mode pattern pitch angles by
construction remain constant with time, the overall logarithmic spiral arm
winds over time, which could help to explain the scatter in the relation
between pitch angle versus shear seen from observations. The correlation
between spiral arm pitch angle and galactic shear rate that we find in N-body
simulations may also explain why late Hubble type of spiral galaxies tend to
have more open arms.
