Table of Content Wavelengths 4 Galaxy Masses Radio Infrared - - PDF document

SLIDE 1

Padova Lecture Series 2007 Lecture 4 2

Table of Content

• 4 – Galaxy Masses
• Structure of our Galaxy
• Rotation and Mass of the Milky Way
• Mass of Spiral Galaxies
• Long-slit vs IFU
• Rotation curves
• HSB vs LSB
• Mass modeling
• Baryonic vs Dark Matter
• Cores vs cusps
• Rotation and velocity dispersion
• Jeans Equation
• Binney diagram: oblate vs prolate rotators
• Non-circular velocities; asymmetric drift
• Mass of Elliptical Galaxies
• Virial estimator
• Lensing studies
• Mass of Galaxy Clusters
• Stellar Masses
• SEDs vs colours

Padova Lecture Series 2007 Lecture 4 4

The Milky Way at Different Wavelengths

Radio Infrared Visible X-rays Gamma Rays

• We now have a wealth
• f data on our own

Galaxy, as these images show.

• It’s clear that the Milky

Way is a far more complex system than

• nce thought.

Padova Lecture Series 2007 Lecture 4 5

The Modern View of the Milky Way

• By the time of Shapley and Plaskett, astronomers had realized

that our home galaxy has the following appearance (imagine that we can view it from outside!)

Padova Lecture Series 2007 Lecture 4 6

Scale heights and velocity dispersions

Padova Lecture Series 2007 Lecture 4 8

Anatomy of the Milky Way

• Our Galaxy is classified a spiral

because of its prominent luminous spiral arms. The high luminosity of the arms is due to the very bright O and B stars which are often located in open clusters and surrounded by very luminous regions of ionized hydrogen (HII regions): the bright objects that delineate the spiral arms are called tracers. NGC 1232 (D=22 Mpc) M39: Open Cluster in Cygnus

Padova Lecture Series 2007 Lecture 4 9

Does the Milky Way Have Spiral Arms?

• Furthermore, dust limits our

view at optical wavelengths to only ~1 to 2 kiloparsecs. This is a small fraction of the Galaxy.

• Is there reason to believe the

Galaxy may have spiral arms?

• Because we are in the plane of the Galaxy, we see all of the

Galaxy’s structure projected onto a thin band across the sky (the Milky Way).

SLIDE 2

Padova Lecture Series 2007 Lecture 4 10

Spiral Arms in the Galaxy M83

• Assume a planet is

located here in M83, a galaxy that is similar to the Milky Way.

• If we can find

the bright OB associations, and measure their distances, we can map the arms.

Padova Lecture Series 2007 Lecture 4 11

Three Spiral Arms Near the Sun

Sun OB Associations Sagittarius Arm Orion Arm Perseus Arm ~ 1 Kpc

To the Galactic Center

• If we want to map out the orbital motions of stars in the Galactic disk,

we need to do three things:

• 1. Find the OB

associations.

• 2. Measure their radial

velocities using spectra and the Doppler Shift.

• 3. Measure the distances

by using their H-R diagrams.

Padova Lecture Series 2007 Lecture 4 12

Radio Maps of Other Galaxies Show That Spiral Arms are Traced by HI

Optical Image 21 cm Radio Image

Padova Lecture Series 2007 Lecture 4 13

HI Map of the Galaxy

• In practice, astronomers

usually use radio

• bservations of neutral

hydrogen (HI) to map out the orbital motions within the disk of the Milky Way.

• Measuring the Doppler

Shift of the neutral hydrogen clouds in the disk, astronomers can:

• 1. map out the rotation

in the disk; and

• 2. measure the mass
• f the Galaxy!

The Milky Way as seen from above, in HI.

Padova Lecture Series 2007 Lecture 4 14

Doppler Shift by Differential Rotation

Padova Lecture Series 2007 Lecture 4 15

Sun Dcenter l The maximum velocity along the line of sight occurs at the tangent point; knowing Dcenter, we can calculate r and l. Position 4 has near zero velocity wrt the sun, and is at a distance 2l from the sun. This method of mapping HI works, provided the HI

• rbits the galaxy with circular velocity.

r

Velocity

4 3 2

HI in the Galaxy: Sizing out the Milky Way

SLIDE 3

Padova Lecture Series 2007 Lecture 4 16

• From the figure, we can see

the distance of the subcentral point to the galactic centre, Rmin

• vmax is the maximum radial

velocity along a given line of sight, we have the angular speed (Rmin )

l sin

min

R R =

max

) sin / ( ) sin (

• +

=

• l

l R v R

Padova Lecture Series 2007 Lecture 4 17

Radial Velocity

• Radial velocity
• Eliminate using the

sine law, and simplify

• Substitute back into

previous equation and factor

l l

• sin

sin ) ( ) 90 cos( ) 90 cos( ) (

• =
• =

R R R v v R v v

r r

• R

R R R / sin / sin / sin / ) 180 sin( l l

• =

=

• vr = (R) 0

[ ]R0 sinl

• Taking material a distance R from the galactic centre, moving in

a circular orbit with speed v(R)

Padova Lecture Series 2007 Lecture 4 18

Rotation Curve of the Galaxy

We measure vr from Doppler shifts and the longitude l

l for any object and we determine the angular speed

) sin / (

• +

=

• l

R vr

Padova Lecture Series 2007 Lecture 4 19

Transverse Velocity

• Relative velocity
• From the figure we can

derive this relationship

• Substituting back into

previous equation

l cos cos ) (

• =

R R R vT

• vT = (R) 0

[ ]R0 cosl (R)d

d R R R d R

• =

+ = l l cos cos cos cos

• Padova Lecture Series 2007

Lecture 4 20

Rotation in the Galactic Disk

• We find that the disk rotates in two

different ways, depending on the distance from the Galactic center:

• 1. Inner Parts: Solid-Body Rotation
• speed rises with radius.
• rbital period is roughly constant.
• 2. Outer Parts: Differential Rotation
• speed is about constant with radius.
• rbital period increases with radius.

Padova Lecture Series 2007 Lecture 4 21

Rotation in the Galactic Disk

Differential Rotation Solid-Body Rotation

Radius from the Center (kpc) Rotation Speed (km/s)

SUN

SLIDE 4

Padova Lecture Series 2007 Lecture 4 22

The Galaxy’s Rotation vs. Radius

vrot

2 = GM(R)/R

M(R) = V2R/G

The rising rotation curve beyond the luminous “edge” of the galaxy shows that the majority of the galaxy’s mass is “dark matter”. Put another way, Mass/Light increases with distance.

Padova Lecture Series 2007 Lecture 4 24

The Galaxy’s Rotation vs. Radius

Rotation Curves and Dark Matter :

V2

circ = V2 bulge + V2 disk + V2 halo

Vcirc is observed; Vdisk is inferred from the light profile, L(R), and assuming a constant mass-to-light ratio, M/L. Vhalo is then deduced by subtracting the different component velocities in

• quadrature. Flat rotation curves Dark matter !

Vcirc = Cste implies that M(R) R and DM(R) R-2

Padova Lecture Series 2007 Lecture 4 25

Halo Density

• We use the rotation curve to give

the mass distribution in the halo

• We take v(r) = vo as constant and

differentiate with respect to r

• We relate M(r) to the density

distribution (r)

• Substitute back into the previous

equation

G r rv r M ) ( ) (

2

= G v dr r dM

2

) ( =

• =

= dr r dM r r r r dr dM ) ( 4 1 ) ( ) ( 4 /

2 2

• 2

2

4 ) ( Gr v r

• =

Isothermal profile

Lecture 4 Padova Lecture Series 2007 26

Vtot = GM R = G(M /L)L R

First evidence for Dark Matter (1933)

Coma cluster: “contains 20x more mass than is visible in the form of galaxies”

Zwicky at Palomar

Padova Lecture Series 2007 Lecture 4 27

The History of Dark Matter

Fritz Zwicky (1898-1974) Pioneer of modern jet engine Predicted neutron stars (1934) and origin of cosmic rays Discovered 120 supernovae Mapped out clusters of galaxies;

• First evidence of dark matter

in galaxies (1933)

• Proposed gravitational lensing

from clusters (1937)

Padova Lecture Series 2007 Lecture 4 28

Virial theorem

• In internal motions, the virial mass is
• In Doppler shifts, the virial mass is

G R v M 3 5

2

= G R v M

r 2

5 =