Our Galaxy
The Milky Way
Chapter 19
Overview & History
 Our Galaxy is a collection of stellar and
interstellar matter – stars, gas, dust, neutron
stars, black holes – held together by gravity.
 Our view of the Galaxy….
History of Galactic (& Extragalactic) Astronomy
1610 - Galileo discovered the Milky Way is comprised of many stars
1755 - Immanuel Kant theorized that the galaxy has a planar
structure, some nebulae might actually be entire other galaxies or
island universes
1774 -1781 - Messier catalog compiled including Andromeda
galaxy as M31
1781-1802 - William and Caroline Herschel conducted first “all-sky
survey” and cataloged 5000 nebulae, resolving some into their
individual stars
1845 - William Parsons (Lord Rosse), using a 72-inch telescope,
classified the nebulae into featureless ellipticals and whirlpool-like
spiral nebulae
History of Galactic (& Extragalactic) Astronomy
1785 - Herschel attempted to determine the shape and size of Galaxy
Assumptions:
All stars have same intrinsic brightness
Star are arranged uniformly throughout the MW
He could see to the edge of the MW
SUN
Herschel could not account well for the effects of dust.
More dust along the disk causes the distribution of stars to drop-off artificially –
objects more than a few kpc from the Sun are obscured by dust.
Weird Units of Distance in Astronomy:
Astronomical Unit (AU) = 93 million miles or 1.5 x 108 km
Distance between Earth and Sun
Light Year = 9.4 x 1012 km
Distance light travels in one year
Parsec = 3 x 1013 km
(or 3.2 light years)
Distance ???
pc (parsecs)
kpc (kiloparsecs)
History of Galactic (& Extragalactic) Astronomy
•Kapteyn (early 1900s) used stellar parallax to estimate the true size of
the Galaxy  Kapteyn Universe
•10kpc diameter and 2kpc thick with the Sun less than a kpc
from the center (rather heliocentric)
•Tried to estimate scattering due to ISM gas but determined it
to be insignificant (most obscuration is due to dust absorption
which has a smaller wavelength dependence)
•Shapley (1919) observed that globular clusters are distributed
asymmetrically in the sky and that if one assumes they are distributed
about the center of the galaxy, this implies the Sun in not near the
center of the Galaxy
•Estimated distances to globular
clusters using variable stars and PM relationship
•Concluded size to be 100kpc
with Sun 15kpc from center
Still wrong…didn’t account for
dust absorption which makes
things look further away
History of Galactic (& Extragalactic) Astronomy
Shapley realized that the globular clusters are all orbiting the center of
our Galaxy and map out the true extent of the Galaxy.
History of Galactic (& Extragalactic) Astronomy
In 1920, the National Academy of Science hosted the Great Debate
concerning the nature of the Spiral Nebulae: were they island universes
outside of the Milky Way?
•Shapley had MW size too big and therefore argued
“NO”, they are part of the Milky Way
•Others at that time believed the Kapteyn model of a
much smaller MW and argued “YES”, they are separate
galaxies.
In 1922-1924 Edwin Hubble resolved the controversy using the superior 100inch telescope at Mount Wilson. He observed Cepheid variables in
Andromeda and, using the P-M relation (distance method), determined its
distance to be 300kpc -- well outside of the MW (still off by a factor of 2 due to poor
Cepheid calibrations)
Morphology of our Galaxy
Also in the early 1900’s, the first kinematic studies of the MW revealed the
velocities of those globular clusters were ~250 km/s, much higher than the mass
of the smaller Kapteyn galaxy model would require. So the galaxy must contain
more stars (and mass) than Kapteyn originally thought in order to keep the star
clusters from flying off.
First detailed kinematic model
(Lindblad 1927) revealed
•A spherical component with random
motions (~250 km/s)  HALO
•A flattened component with rotational
motion measured at 200 to 300 km/s
near the Sun – DISK
•A third component, also spherical,
exists in the center of the galaxy –
BULGE
Stars here also move on mostly
random orbits
Morphology of our Galaxy
The three components of our galaxy (disk, halo and bulge) also
differ in the mix of the types of stars they contain
•Population I: Hot, blue stars and young open clusters accompanied by gas
and dust are primarily found in the disk of the Milky Way
•Population II: red stars and older globular clusters are found in the halo of
the Milky Way
Morphology of our Galaxy
Plotting stars on HR diagrams showed that the populations differed in age and
metallicity (enrichment of elements heavier than Helium):
Pop I young and metal rich
Pop II old and metal poor
Disk – mainly Pop I
Halo – mainly Pop II
Bulge – mix of Pop I and II
Since most stars are
smaller than the sun,
the Milky Way actually
contains far more than
23 billion stars – more
like 200 billion
Differential Rotation
 Everything in the Galaxy orbits around
the Galactic center
 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 the Galactic center can tell us the
distribution of mass in the Galaxy
 Examining motions of stars in the disk
are most helpful for mapping the
distribution of mass
Differential Rotation
M(R) = 0R (r) dV
Motion at distance R from center depends only on M(R)
That mass behaves as if it were centrally concentrated
For an object with mass m at R, gravity must balance acceleration of
M
circular motion
GM(R)m/R2 = mv2/R
M(R) = v(R)2R/G
v
R
Measure v(R) and get M(R)
Let ω(R) = v(R)/R, then
M(R) = ω(R)2R3/G
v(R) or ω(R) gives the rotation curve of the Galaxy.
m
Differential Rotation
Differential galactic rotation produces
Doppler shifts in emission lines from
gas in the Galactic disk
Define Galactic Coordinates
b = galactic latitude in degrees
above/below Galactic disk
l = galactic longitude in degrees from
Galactic Center
Local Standard of Rest
The Sun (and most stars) are on slightly
perturbed orbits that resemble rosettes making it
difficult to measure relative motions of stars
around the Sun.
Establish a reference frame that is a perfect
circular orbit about the Galactic Center.
Local Standard of Rest - reference frame for measuring velocities in the Galaxy.
Position of the Sun if its motion were completely governed by circular motion
around the Galaxy.
Use cylindrical coordinates for the
Galactic plane to define the Sun’s
motion w.r.t the Local Standard of Rest
Local Standard of Rest
To determine the Suns motion wrt to LSR, we observe the average
motions of all stars in the Sun’s vicinity and measure the following:
Π - Πo = U (speed away from GC) = -10.4 km/s [7.5 +/-1 km/s]
Z - Zo = W (speed towards NGP) = 7.3 km/s [6.8 (+/- 0.1) km/s]
Θ - Θo = V (speed in direction of motion) = V = 14.8 km/s [13.5 (+/- 3) km/s]
Bracket values from Francis and Anderson (2009)
The Sun is moving toward the Galactic center, faster
than the LSR, and northward toward the NGP. Net
motion is 19.5 km/s in the direction of constellation
Hercules
Local Standard of Rest
Position and Velocity of the LSR in Galaxy
Ro = 8 kpc (~25,000 light years)
Vo = 220 km/s = 225 kpc/Gyr
Assuming a circular orbit, how long does it take the Sun to travel
around the Galaxy?
223
To = 2πRo/Vo = ___________
Myr
How much mass is there interior to the Sun’s orbit?
GMm/R2 = mv2/R
9 x 1010 M
M = Vo2Ro/G = __________
helpful numbers:
3.1x1013 km/pc G=6.67x10-11 m3/kg/s2 M = 2x1030 kg
The Rotation Curve of the Milky Way
Calculate Doppler shifts for a star moving
with velocity Θ at a distance d from the
Sun (i.e. radial velocity w.r.t. LSR)
Radial velocity is:
vr = Θ cos α – Θo cos (90 – l)
Since cos(90 - x) = sin(x)
vr = Θ cos α – Θo sin l
Convert to l (since we can’t measure α easily) using Law of Sines
sin (90 + α)/Ro = sin l/R = cos α/Ro
Putting this into the above equation gives
First Oort equation:
can now compute ω
in terms of
observables vr and l
and known values
ωo and Ro
The Rotation Curve of the Milky Way
To map out vr throughout Galaxy,
divide the Galaxy into quadrants
based on value of galactic longitude.
Quad I (l<90) - looking to material closest to GC,
[ω - ω0] gets larger and vr increases. At point of
closest approach (subcentral or tangent point) vr
is at maximum for that line-of-site (los) and then
continues to decrease to Sun’s orbit. Beyond
Sun’s orbit, vr becomes negative and increases in
absolute value.
Quad II (180>l>90) - all los pass through orbits
outside of the Sun’s. No maximum vr but
increases with d.
Quad III (270>l>180) - similar to Quad II but
opposite signs.
Quad IV (l>270) - similar to Quad I except reverse
signs.
Measuring the Rotation Curve of the
Milky Way
 Measure Doppler motions of gas rather than
stars. Atomic Hydrogen gas permeates the
Galaxy and emits light in the radio part of EM
spectrum at 21-cm wavelength
 Using LSR to correct for our motion, assume
circular orbits for the gas and that there is at
least some Hydrogen along any given line-ofsight (at all Galactic Longitudes)
 Especially important to have measurable gas at
subcentral/tangent point
Measuring the Rotation Curve of the Milky Way
•Find maximum shift of 21-cm line
along given line-of-sight (los)
•Assign that Doppler shift to material
at the tangent point (closest approach
to GC)
•Rmin = Ro sin l
= Θo
=Θ
•ω(Rmin) = [vmax/(Ro sin l)] + ωo
•By studying los longitude values
from 0 to 90 degrees, Rmin will range
from 0 to Ro
Limitations
•No gas at subcentral point
•Non-circular orbits
•At Rmin = 0 and at Ro, difficult to measure curve due to small Doppler shifts
Measuring the Rotation Curve of the Milky Way
Measuring the Rotation Curve of the Milky Way
Since there is no maximum Doppler shift for los away from GC, rotation
curve beyond Ro is more difficult to determine
Need to measure the velocity and distance of material independently
Use Molecular Clouds :
• get velocity from radial velocities of CO emission in gas clouds
• get distance from spectroscopic parallax of stars forming in clouds
Understanding Rotation Curves
V~
Mass
Radius
For planets in the Solar System, M is dominated by Msun, so M does not
change much with R - Keplarian rotation curve
Inside the Galaxy, M increases with radius, so velocity may stay constant
as mass and radius increase together – Flat rotation curve
Outside the Galaxy, as in the Solar System, M remains constant with
increasing R (if most mass ends at visible edge). Then we would expect
the rotation curve to slope downward in Keplarian-like motion.
Understanding Rotation Curves
Since the Milky Way rotation curve shows no drop in velocities beyond the
visible edge of the disk (around R=15 kpc), this indicates the presence of some
additional, non-luminous material  Dark Matter (matter too dim or weakly
interacting to be detected by current technology)
Even though Dark Matter is detected through measurements of
the Galactic Disk, it is not necessarily confined to the disk and is
likely to be distributed throughout the Galactic Halo. Most galaxies
appear to exist within these Dark Matter Halos.
What mass distribution do you need to get
velocity to be constant with radius?
If v is constant at some value, vo
Equating the two
expressions for dM(r)/dr
What is the Dark Matter?
Neutrinos: low mass particles that interact via gravity or weak nuclear force.
Most neutrinos, produced from nuclear fusion, pass easily through the Sun.
Common particles but low mass prevents them from contributing more than
~few percent of dark matter.
WIMPs - Weakly Interacting Massive Particles – exotic subatomic particles
predicted via supersymmetric extensions of the Standard Model.
Predicted rest mass of 200-500 times that of proton.
Being searched for in particle accelerators and large detector experiments.
MACHOs - Massive Compact Halo Objects
White Dwarf Stars, Red Dwarfs (0.2 Msun), Brown Dwarfs (<0.08 Msun),
Neutron Stars, Black Holes.
Recall that the more massive remnants result from relatively rare high,
mass stellar progenitors.
The Search for Dark Matter (brown or white dwarfs):
MACHOs
•The faint foreground
object (brown or white
dwarf) bends the light of
the background star
because of its
gravitational field
•The light from the
background star is
focused or “lensed” by
this effect and the star
appears brighter.
•MACHO results acount
for only ~20% of dark
matter
Slight Aside on Determining Distances
 We get distances to
nearby planets (e.g. radar
measurements)
 That sets the scale for the
solar system (1 AU).
 Given 1 AU plus stellar
parallax, we find distances to
nearby stars.
Use these nearby stars,
with known distances, fluxes
and luminosities, to calibrate
Luminosity classes in HR
diagram.
Then spectral class + Flux yields Luminosity + Distance for farther stars
(Spectroscopic Parallax).
Cepheids (variable stars) use P-M relation to determined distances to nearby
galaxies
The HR Diagram: Spectroscopic “Parallax”
Example:
1) Determine Temperature from
color or spectral type.
Main Sequence
2) Determine Luminosity based on
Main Sequence position.
3) Compare Luminosity with Flux
(apparent brightness).
4) Use inverse square law to
determine distance.
Flux
=
Luminosity
4d2
Spiral Structure
 Many external galaxies
show spiral structure
 Hard to see the
morphology of the MW
(since we are in it!)
 Use other galaxies’
properties to determine
the nature of the WM
and determine we are
in a spiral galaxy
Spiral Structure
In other galaxies, HII regions and OB associations trace
out spiral arms.
• Using spectroscopic
parallax, we can place the
nearby O and B stars at
their proper distances.
• They appear to
delineate spiral arms.
• Since O and B stars are
young objects, spiral arms
are associated with star
formation.
•Problem: Can’t see very
far in the optical…
Spiral Structure
• Surveys of Giant Molecular Clouds (GMCs) are likely to trace the spiral arms
since these are sites of star formation
• positions interior to Sun’s orbit in Galaxy have some distance ambiguity
•Less distance ambiguity outside of Solar orbit, and better evidence of arm-like
morphology
The Galactic Nucleus
 Inner 500pc of Galaxy
 Extinction makes optical
studies impossible - use radio
or IR
 Observe ionized gas, line
emission, dust, star clusters
 Stellar density is 107 stars
per pc3 (compared to 0.1 in
the solar neighborhood)
 If the Sun were near the GC
 Nearest star would be 1000AU
away
 A million stars brighter than
Sirius in the night sky
 Total starlight more than 200
times brightness of the full Moon
The Galactic Center
Optical vs Radio observations
The Galactic Center
Radio schematic
75pc
150pc
The Galactic Center
Star Formation
•Molecular material in inner 200pc relatively hot and
dense: 104 per cm3 and 70 K
•High velocity dispersion (50 km/s) of molecules
•Mass: 108 Msun
•High density helps star formation but high temps don’t
•SF rate ~ 1Msun/year
•Radio emission shows
bent arc of gas,
filamentary structure
•Also seen in IR
•Thermal and synchrotron
radiation
•X-ray emission (produced
when electrons from
filaments collide with colder
gas cloud) gives gas
temperatures of T=107 to
108 K
•Could result from past SN
explosions
Supermassive Black Hole in the Galactic Center
Radio image (80 pc
across) shows
feature SgrA and
radio filaments
Radio image (10
pc across) shows
feature known as
SgrA West – center
of this is SgrA*
Investigate IR
stellar motions in
region about 1pc
across (a few
lightyears) to
estimate BH mass
•Measure proper motions of stars around
Galactic Center
•Adaptive optics at large telescopes improved
ground-based resolution to 0.5” in IR (stellar
positions measured to 0.002”)
•90 stars identified and proper motions (largest
at 1400 km/s!) centered about SgrA* to within
0.1”
•Velocities consistent with Keplarian motion (all
mass at center)
•M = 2.6 +/- 0.2 x 106 Msun
Curvature of the paths near SgrA* constrain the
volume of the mass to ~ Schwarzchild radius (few x
106 km)  Supermassive Black Hole
Additional evidence - X-ray emission
•Chandra X-ray image of Sgr A* showing
nucleus and several thousand other Xray sources.
•During 2-week observation period,
several X-ray flares occurred.
•Rapidity of flares indicates they
originate near the Schwarzchild radius of
the BH.
•Even during the flares, X-ray emission
from the nucleus is relatively weak.
Suggests that Sgr A* is a starved black
hole, possibly because explosive events
in the past have cleared much of the gas
from around it.