Galactic Astronomy Velocity fields of disks Dong-hyun Lee 2007/08/23

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

Velocity fields of disks Fig : rotation vel. Fig : rotation vel. Central part : region of solid-body rotation Central part : region of solid-body rotation Fig : contours of const. v_los  spider diagram Fig : contours of const. v_los  spider diagram Closed contours in spider diagram : decline in rot.vel. Closed contours in spider diagram : decline in rot.vel. Kinematic minor axis : locus of pt.s having same sys. 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 Kinematic major axis : run through nucleus & everywhere perpendicular to local const-vel contours Fig : kin. Minor & magor axes – coincide – apparent optical axes Fig : kin. Minor & magor axes – coincide – apparent optical axes

Circular-speed curves V_c (r ) : deduce mass interior to rad. V_c (r ) : deduce mass interior to rad. R_25 usually beyond ½ R_25 R_25 usually beyond ½ R_25 Fig : left panels – in kpc / right ones – func.of R_25 Fig : left panels – in kpc / right ones – func.of R_25 Kinematic minor axis : locus of pt.s having same sys. Vel. Kinematic minor axis : locus of pt.s having same sys. Vel. At large R/R_25 is correlated with lum. 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) 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 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) Observed cir-sp.curves – mass-to-light ratio Gamma(d) & Gamma(b) (disk, bulge) Fig left: disagreement of theory & observation Fig left: disagreement of theory & observation Fig : at least 3 times as much mass within 12R_d as within R_25 R_d :disk sacle length Fig : 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 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. DH emits no light : unknown spatial dist. Assume Assume physically unmotivated N-body sim. : NFW law N-body sim. : NFW law M_0, a : free parameters 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. 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 right Tilted-ring model : Fig right Each ring projects into an ellipse : ellipse vel. contour (fig.8.32) Each ring projects into an ellipse : ellipse vel. contour (fig.8.32) Within each ellipse, kin. Axes will be mutually perpendicular Within each ellipse, kin. Axes will be mutually perpendicular K : func.of r throug n(r), kin.maj.axis will twist  Fig K : func.of r throug n(r), kin.maj.axis will twist  Fig Fig : l.o.s pass through disk twice  line profile will normally have more than one peak Fig : l.o.s pass through disk twice  line profile will normally have more than one peak Evidence of warps : studies in p.512 Evidence of warps : studies in p.512

Oval distortions Observed spidergram : kin. Axes aren’t mutually perpendicular – Fig  gas moving on elliptical rather than circular orbits Observed spidergram : kin. Axes aren’t mutually perpendicular – Fig  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 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 : key points – viewing angle Fig : key points – viewing angle Kin.axes are not perpendicular, although photometric axes are for face-on Kin.axes are not perpendicular, although photometric axes are for face-on Kin. & photo. Minor axes do not coincide Kin. & photo. Minor axes do not coincide Kin.maj.axis lies close to line of nodes, esp. at high inclinations Kin.maj.axis lies close to line of nodes, esp. at high inclinations