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# disks - Properties of Spiral Galaxies II Kinematics of...

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Properties of Spiral Galaxies II Kinematics of Disks As in all spiral galaxies, everything in our  Galaxy orbits around the Galactic center Differential rotation - material closer to the  center travels on faster orbits (takes less time  to make one full orbit) Similar to the way the planets orbit the Sun Orbital periods at different distances from GC  tell us the distribution of mass in the Galaxy

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M(R) = 0 R ρ (r) dV Motion at R depends only on M(R) That mass behaves as if centrally concentrated For an object with mass m at R, gravity must balance acceleration of circular motion GM(R)m/R 2 = mv 2 /R M(R) = v(R) 2 R/G Measure v(R) and get M(R) Let (R) = v(R)/R, then M(R) = (R) 2 R 3 /G v(R) or (R) is the rotation curve rotation curve of the galaxy v m M R
Differential galactic rotation produces Doppler shifts in emission lines from gas in the Galactic disk To determine galaxy rotation curve, define Galactic Coordinates b = galactic latitude in degrees above/ below Galactic disk l = galactic longitude in degrees from GC

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Local Standard of Rest (LSR) - reference frame for measuring velocities in the Galaxy. This would be the position of the Sun if its motion were completely governed by orbital motion around the Galaxy The Sun (and most stars) are on slightly perturbed orbits. Sun motion wrt to LSR is determined by looking at average motions of all stars in the Sun’s vicinity. V = V y (velocity in direction of galaxy rotation) U = V x (velocity towards GC) = 10 km/s W = V z (velocity towards NGP) = 7.2 km/s V depends on color – stellar pops •asymmetric drift – mean V rot of stellar pop lags behind LSR more and more with increasing σ of stars. Comparing sun to this reference frame produces V which grows with lag Fit to data gives at S 2 = 0, V = 5.2 km/s
With respect to the LSR, the Sun is moving at about ~14 - 20 km/s towards RA=18h Dec=30 degrees and lies about 10-20 pc above the Galactic plane. Position and Velocity of LSR in Galaxy (adopted in 1985 by IAU; based on globular cluster positions) R o = 8.5 kpc V o = 220 km/s More recently, values of 8 kpc and 200 km/s have been estimated (see SG 2.3 and also Eisenhauer et al. 2003)

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Calculate Doppler shifts for material at P moving with velocity v at a distance d from the Sun (i.e. LSR) and a distance R from the Galactic Center. Radial velocity is: Since cos(90 - x) = sin(x) Convert to l (since we can’t measure θ easily) Putting this into the above equation gives Determining the Rotation Curve V r = R o sin l (V/R – V o /R o )
To map out v throughout Galaxy,

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Back to the board to derive Oort constants – understanding the effects of differential rotation near the sun.
Determination of Rotation Curve of the Milky  Way  Determined from 21-cm line  observations  Assume circular orbits and that there is  at least some Hydrogen all along any  given line-of-sight  Especially important to have measure  of gas at subcentral point

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Find maximum shift of 21-cm line
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disks - Properties of Spiral Galaxies II Kinematics of...

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