C3 - spirals

• composed by a nucleus and clearly visible spiral arms
• their nuclei have decreasing size down the sequence $a\to c/d$
• common in high density areas
• have red disks and blue spiral arms with more star formation
• richer in gas and dust (hence more star formation)
• produce new stars at a much higher rate

• $i$ is the winding or pitch angle

• if $i\approx 2-5\mathrm{°}$, light, Sa/SBa

• if $i\approx 20-30\mathrm{°}$, loose, Sc/SBc

• can also look at the direction of rotation

image: S Capozziello, A Lattanzi

• trailing arms
  • wrap in the same direction of rotation
  • outer tips point in the opposite direction
  • vast majority are training, due to dynamics
• leading arms
  • wrap in opposite direction
  • outer tips point in the same direction

origin and stability of spiral arms

• if they are material (always formed by the same gas, dust, stars), it is easy to prove that spiral arms would not be stable over a relatively short timescales
• balancing the gravitational and centrifugal forces:

• based on the light distribution, light is localised in the galactic centre
• mass is also localised here
• if far away, assume $M(r)=M=$ constant
• $\omega (r)$ is not constant:

• spiral arms get wrapped up over time

• for many spirals, $v$ is usually constant
• the arc length can be approximated by a straight line, $d\varphi r$

• considering sun's position on the MW at a distance of $r=8$ kpc from the centre, $v==200$ km${}^{-1}$s at $t=1$ Gyr

• $1/\tan i=25.5$, so $\tan i=0.04$ rad, or $i=2.3\mathrm{°}$

• this is quite a tight spiral already, compatible with Sa/SBa

• this is known as the winding problem

• $\omega \propto r^{-3/2}$, or ${\omega }^2\propto r^{-3}M(r)$

• so, how can constant velocity be observed, and what happens to $M(r)$?

• this is evidence for dark matter, however it is not enough to explain the observed constant velocity

• so, galaxies cannot be treated as material (the same stars, gas, dust)

• in the 1960s, Lin and Shu showed that spiral arms arise from density waves

• density waves contain regions with higher gas and stellar densities, and are quasi stationary (evolve slowly compared to the galactic rotation)

• stars have slightly eccentric orbits due to a non-central galactic potential

• the the rotation rate increases with distance

• this causes overlap and intersection of orbits, naturally leading to a kinematic spiral

image: H Cegla, lecture notes

• self gravity reinforces the spiral and makes it stable (quasi stationary)

• over density of gas triggers compression, and hence star formation

• thus young blue stars of the O and B type trace spiral arms

• the lifetimes of the O and B type stars, ${\tau }_{O,B}<{\tau }_{cross}$, time to cross the arm

• so, they die before leaving the arm

• new stars are formed in the mean time

• this, young blue stars always trace spiral arms