4.1 Rotation of the MW Flashcards
What do we assume about the motion of the stars in the MW?
They are flattened onto a disk surrounding a bulge
- Assume Keplerian rotation and equate gravitational and centrifugal acceleration
What is the keplerian rotation assumption?
The relative velocity between stars and gas in the disk is small
What is the encircling radius?
A radius in which most of the galactic mass is contained within it
if r > r_enc, M(r) is constant
What is the expectation relation between velocity and radius of a galaxy
v(r) is prop. to r^-1/2 at large radii
How can we measure v(r) for external galaxies?
Use a spectra of stars (HII regions) and HI regions
- Can also convert any measured Doppler shift into a radial component along the line of sight of the velocity
- Measured radial velocity must be converted to an orbital velocity
What is the equation for the orbital velocity from the tangent method
v(R) = v_r max + v_solar sin(L)
Orbital velocity = maximum radial velocity and the orbital solar velocity where L is the galactic longitude
In what regimes is the tangent method valid?
Between -pi/2 and pi/2 and up to the distance to the sun from the galactic centre
What does the data show for the rotation speed when moving away from the bulge?
It initially decreases as r^-1/2 but then ramps up
- Beyond 8-10kpc, the errorbars are too large
How can we interpret the velocity profile of a galaxy?
The profile is flat at large radii
- Has wiggles which is a sign of spiral arms
- M(r) is proportional to r
How is the velocity profile of a galaxy evidence for dark matter?
There is a large amount of mass at a large radius which isn’t interacting with EM radiation (can’t see it)
- Flat rotational curve of the MW is evidence for DM
What is the Plummer sphere?
A good description for the ddensity profile at large distances from the galactic centre
What does the mass to light ratio depend on?
How many stars were born with mass M
Mass- Luminosity relation (L ~ M^3.5)
SFR
Gas, dust and dark matter
What is the mass to light ratio for galaxies, and what conclusion can be drawn?
It is about 50 M_solar / L_solar
DM drastically increases the mass to light ratio of galaxies
