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Galactic Astronomy

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Velocity fields of disks Flat disk

- Focus on the central freq. of the received radiation
- Central vel. & dispersion : line profile
- Fig. 8.36 : collection of concentric, circular rings
- r : center to point, n(r) : unit vector normal to the ring of r
Omega(r) : ang. Vel. Of ring

- R : unit vector to observer

- r : center to point, n(r) : unit vector normal to the ring of r

Velocity fields of disks

- Fig. 8.31 : rotation vel.
- Central part : region of solid-body rotation

- Fig. 8.32 : contours of const. v_los spider diagram
- Closed contours in spider diagram : decline in rot.vel.
- Kinematic minor axis : locus of pt.s having same sys. Vel.
- Kinematic major axis : run through nucleus & everywhere perpendicular to local const-vel contours
- Fig. 8.32 : kin. Minor & magor axes – coincide – apparent optical axes

Circular-speed curves

- V_c (r ) : deduce mass interior to rad.
- R_25 usually beyond ½ R_25
- Fig. 8.33 : left panels – in kpc / right ones – func.of R_25
- Kinematic minor axis : locus of pt.s having same sys. Vel.
- At large R/R_25 is correlated with lum.

Circular-speed curves

- Sc at small R/R_25 : max. rot. Speeds (lum. Than faint) at large R/R_25 : flat or falling (lum. Than faint)
- Correl. b/w lum & amp. In cir-sp. Curves Tully-Fisher rel
- Observed cir-sp.curves – mass-to-light ratio Gamma(d) & Gamma(b) (disk, bulge)
- Fig. 8.34 left: disagreement of theory & observation
- Fig. 8.35 : at least 3 times as much mass within 12R_d as within R_25 R_d :disk sacle length
- Cir-sp.curves extend to more than 5R_d generally require significant masses to reside beyond R_25 : DM

Circular-speed curves

- DH emits no light : unknown spatial dist.
- Assume
physically unmotivated

- N-body sim. : NFW law
M_0, a : free parameters

- Gamma increases sharply as the surf. Brightness of gal.s falls below a frac of a percent of the brightness of night sky.

Kinematic warps

- Tilted-ring model : Fig. 8.36 right
- Each ring projects into an ellipse : ellipse vel. contour (fig.8.32)
- Within each ellipse, kin. Axes will be mutually perpendicular

- K : func.of r throug n(r) , kin.maj.axis will twist Fig. 8.37
- Fig. 8.38 : l.o.s pass through disk twice line profile will normally have more than one peak
- Evidence of warps : studies in p.512

Oval distortions

- Observed spidergram : kin. Axes aren’t mutually perpendicular – Fig. 8.39 gas moving on elliptical rather than circular orbits
- Model’s complex : rotation mat. & model-dep. Rel. b/w disk’s shape & vel. Field dep.on nature of driving non-axisym. Grav.potential
- Fig. 8.40 : key points – viewing angle
- Kin.axes are not perpendicular, although photometric axes are for face-on
- Kin. & photo. Minor axes do not coincide
- Kin.maj.axis lies close to line of nodes, esp. at high inclinations