Properties of Spiral Galaxies II Kinematics of Disks

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Properties of Spiral Galaxies IIKinematics 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) ?0R ?(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/R2 mv2/R M(R)
v(R)2R/G Measure v(R) and get M(R) Let ?(R)
v(R)/R, then M(R) ?(R)2R3/G v(R) or ?(R) is
the rotation curve of the galaxy
M
v
R
m
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Differential galactic rotation produces Doppler
shifts in emission lines from gas in the Galactic
disk
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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 Suns vicinity.

• V Vy (velocity in direction of galaxy rotation)
  
• U Vx (velocity towards GC) 10 km/s
• W Vz (velocity towards NGP) 7.2 km/s
• V depends on color stellar pops
• asymmetric drift mean Vrot of stellar pop lags
  behind LSR more and more with increasing s of
  stars.
• Comparing sun to this reference frame produces V
  which grows with lag
• Fit to data gives at S2 0, V 5.2 km/s

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With respect to the LSR, the Sun is moving at
about 14 - 20 km/s towards RA18h Dec30
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) Ro 8.5 kpc Vo
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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Determining the Rotation Curve
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 cant measure ? easily)
Putting this into the above equation gives
Vr Ro sin l (V/R Vo/Ro)
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To map out vr throughout Galaxy, divide the
Galaxy into quadrants based on value of galactic
longitude. Quad I (llt90) - looking to material
closest to GC, ?(R) - ?0 gets larger and vr
increases. At point of closest approach
(subcentral point) vr is at maximum for that los
and then continues to decrease to Suns orbit.
Beyond Suns orbit, vr becomes negative and
increases in absolute value. Quad II (90ltllt180)
- all loss pass through orbits outside of the
Suns. No maximum vr but absolute values
increases with d. Quad III (180ltllt270) - similar
to Quad II but opposite signs. Quad IV (lgt270) -
similar to Quad I except reverse signs.
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Back to the board to derive Oort constants
understanding the effects of differential
rotation near the sun.
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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 along given los
• Assign that Doppler shift to material at the
  subcentral point (closest approach to GC)
• Rmin Ro sin l
• ?(Rmin) vmax/(Ro sin l) ?o
• 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
  (small Doppler velocity hard to determine)

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• Since there is no maximum Doppler shift for los
  away from GC, rotation curve beyond Ro is more
  difficult - measure velocity and distance of
  material independently
• Molecular Clouds
• v from radial velocities of CO emission
• d from stars exciting clouds (spectroscopic
  parallax)

From tangent point method with Vo 200
km/s Compares HI gas slightly above and below
plane
Rotation speed of outer Galaxy Vo 200 km/s and
220 km/s
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• External Spiral Galaxies gas motions in
  galactic disks
• disk dominated by ordered motion rotation
• Vmax 50 400 km/s (most between 150-300 km/s)
• s (gas) 5 10 km/s
• s (stars) 5 50 km/s
• -compare with Ellipticals s 50 500 km/s

Gas measured from Ha ionized gas from disk HII
regions HI (21cm) atomic gas allows us to
see beyond disk stellar edge CO (2.6mm)
molecular gas (CO used to estimate H2) HI in
disks is optically thin little absorption so
mass intensity though in MW HI distribution
hindered by dust in disk emission is optically
thick (mass ? intensity) Deep HI maps detect
1019 H atoms/cm2 or 0.1M?/pc2 Example NGC 7331
contains 1.1 x 1010M? HI gas
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Ratio of galaxy mass in gas increases with later
Hubble type Mgas MHI MH2 Mdyn
dynamical estimate of total mass Spiral galaxies
vary in the amount of molecular to neutral
Hydrogen (50 to 10)
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• Distribution of HI in external galaxies
• centers of disk galaxies are generally gas poor,
  gas is piled in a ring several kpc out (also seen
  in MW and M31)
• more gas than stars in outer regions (little SF)

HI gas in NGC 7331
HI gas in NGC 5033 (Sc)
HI surface density vs radius
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Example Andromeda
H1 - 21cm
FIR (SF dust)
CO - 2.6micron
Optical

• CO displays sharp drop with radius
• Traces spiral arms
• CO more associated with arms than HI which
  permeates galaxy (except in center)
• CO velocity map shows rotation

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• Compare to Distribution of HI and H2 gas in the
  Milky Way
• HI gas - mass does not decrease very quickly
  (mass interior to Ro 109 Msun and outside Ro is
  2x109 Msun)
• H2 gas - falls off rapidly (109 Msun inside Ro
  and 5x108 Msun outside)
• Feature in H2 called molecular ring

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• Correlations with molecular gas content in
  galaxies
• tight correlation between molecular gas content,
  radio continuum emission, and IR luminosity

Molecular gas (CO emission line strength
Radio continuum
Radio continuum
mid-IR luminosity
UV photons from stars converted to IR via
dust Radio continuum from 1) free-free radiation
in hot ionized gas and 2) synchrotron from SNe
remnants ? cool gas, SF, Sne all related to
the formation of massive stars in galactic disks
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Spiral Galaxy Velocity Fields from Gas At radius
R, assume a gas cloud follows near-circular path
with speed V(R) Measure Vr (radial velocity)
doppler shift Velocity at galaxy center is Vsys
systemic velocity Observe a disk in pure
circular motion at inclination i
For a star or gas cloud at radius R and azumuth
f, the radial velocity is
Vr(R,i) Vsys V(R) sini cosf
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Contours of constant Vr connect points with the
same value V(R)cosf ? spider diagram
for disk inclined 30 degrees lines of constant
Vr-Vsys
radius R/Rd

• line AB is the kinematic major axis deviates
  furthest from Vsys
• center line is close to Vsys all motion
  tangential
• Near center, lines are almost parallel to center
  line due since V(R) goes as R (solid body)
• Further out, where rotation speed becomes almost
  constant, lines bend toward radial direction

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• Spiral Galaxy Rotation Curves
• V(R) is of fundamental importance for determining
  M(ltR) since
• V2(R)/R GM(ltR)/R2
• For NGC7331, rotation curve is compared with what
  we expect if the galaxy mass is entirely in stars
  and gas
• assume star (bulge/disk) density R-band light
  and assume M/L
• assume gas surface density (disk) is 1.4 x HI
  intensity
• adjust M/L so that gas and stars in disk account
  for as much of the galaxys rotation as possible
  ? maximum disk model
• Result rotation speed should begin to fall at R
  20 kpc.

75 of mass is in halo
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Spherical halo of dark matter provides the
extra mass to account for rotation velocities
Sa Sb longer scale lengths, more rapid
rotation 50 DM needed V(R) climbs steeply ?
more mass close to center Luminous and dark
matter appears to be very concentrated towards
center of galaxy Sd Sm shorter scale lengths,
slower rotation 80 90 DM needed V(R) climbs
more gradually ? lacks central concentration Dark
halo nearly constant in core
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• What mass distribution is required for a flat
  rotation curve?
• for spherical symmetry
• GM(ltR)m/R2 mV2(R)/R ? M(ltR) V2(R)R/G
• if V is constant, M(R) R
• ?(R) V2/(4pGR2) where VVmax at large R
• Density falls as R-2 for a flat rotation curve
  (slower than an exponential decrease)
• What is the distribution of the Dark Matter Halo?
• N-body simulations of gravitational clustering
  suggest
• ?(r) NFW law
• 
  where Mo and a are
  free parameters (Navarro, Frank White 1997)
• but fits can be made w/very different values of
  free parameters depending on the adopted M/L for
  disk bulge

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To determine Vmax, measure global profile of
21-cm HI emission
Double-horned profile caused by flat rotation
curve W 2 Vmax sin i Measurements like this
for many galaxies revealed... Tully-Fisher
relation L Vmax4 Distance Indicator!
brighter galaxy ? more massive ? faster
rotation Usually use red or IR light for L to
minimize effects of recent SF
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Tully Fisher
In I-band LI/4x1010LI,? (Vmax/200km/s)4 In
H-band LH/3x1010LH,? (Vmax/196km/s)3.8
Galaxies in Ursa Major group based on HI global
profile W/sin i 2Vmax. Open circles are LSB
galaxies.
TF can be dynamically understood without DM.
But, since Vmax comes largely from DM and L from
luminous matter, we see coordination between DM
and LM.
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Determining Vmax for distant galaxies to look for
evolution in TF relation Using optical light to
get rotation curves
ACS
ACS
model
residual
OII
OII
model
residual
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Tully-Fisher Evolution

• Comparing TFR in EGS at 0.9 lt z lt 1.4 to Nearby
  Field Galaxy Survey sample (Kannappan et al.
  2002)
• Offset (assumes no slope change)
• -1.7 mag at z1.1
• rotating disks 1.7 mag brighter at ltzgt1.1 than
  local

(Metevier et al 2006)
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• Kinematic Warps
• most galaxy spider diagrams show deviations from
  pure circular motion
• explained by warps in disk tilted ring model
• HI maps of edge-on disks also reveal warps

M83 model and data for less-inclined disk warp
Edge-on warp
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• Oval Distortions gas moves in oval (elliptical)
  rather than circular motions
• Effects on velocity fields
• kinematic axes not perpendicular
• kinematic and photometric minor axes not aligned
• kinematic major axes close to line-of-nodes (line
  through galaxys center that lies in sky plane
  and galaxys equatorial plane)

line of nodes
Effects of oval distortions on spider
diagrams disks inclined by 1 degree (almost
face-on) left panel major axis at 70 degrees
from LON right panel major axis at 20 degrees
from LON
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• Lop-sidedness
• HI gas appears to be non-axisymmetric in a
  significant number of spiral galaxies
• velocity maps indicate gas moving circularly on
  orbits around nucleus ? gas is non-uniformly
  distributed around each circular orbit
• differential rotation should smear lop-sided
  distribution in few Gyr.
• Not understood why this is so common...

Richter Sancisi (1994) found lop-sidedness in
50 of galaxies!
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Disk Galaxies gas metallicity Measure strength
of emission lines in HII regions O (3727A), O2
(5007), N (6583), S (6724) and correct for
reddening and underlying stellar absorption ?
strength of both O and N fall w/radius N
falls faster
Interstellar abundances of metals in disk
galaxies fall w/galactic radius Since N is a
secondary element, its abundance should be N/H
2O/H Observed - N/H 1.5O/H Central
O/H values increase with galaxy magnitude and
Vmax (due to TF) see Zaritsky et al (1994)
Dors and Copetti (2005) for M101
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• Why the decline of metallicity with radius?
• consider closed-box model of chemical evolution
  (BM 5.3.1)
• Z -p ln fgas
• Z Mheavy elements/Mgas p
  nucleosynthesis yield from stars
• fgas fraction of mass density in
  gas
• gas fraction lower near center of Sa/Sb galaxies
• ? metallicity decreases w/radius
• (trend prediction is correct but no qualitative)
• To match observed trend, p (yield) must vary
  throughout disk larger at small R and high Z
• What else may be happening?
• gas drifts inward carries metals inward
• gas replaced at large radii by accretion of
  metal-poor gas from IGM

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Milky Way disk Stellar ages and
metallicities Edvardsson et al (1993) looked at
200 F and G dwarfs in solar neighborhood to
measure metal abundances and ages. Made an
estimate of each stars characteristic
Galactocentric radius, Rm, based on observed
velocity, Galaxy potential.

• younger stars tend to be more metal rich
  (significant scatter)
• oldest stars have smallest Galactocentric radii
• disk of MW did not extend as far 10 Gyr ago
• we only see old stars near Sun because they pass
  through due to higher random motions
• lowest metallicity stars would appear to have
  smallest Galactocentric radii

Filled Rm lt 7 kpc Open Rm is 7 kpc 9
kpc Cross Rm gt 9 kpc
Since metallicity decreases with age and most old
stars are at low R, not possible to tell how
metallicity changes with R
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• Clues from MW disk star clusters...
• ages and metallicities of clusters can be
  determined from CMDs
• no clear relation between cluster age and
  metallicity
• slight trend with metallicity decreasing with R
  (and also with z-height above plane)

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Disk Galaxies stellar ages and metallicities
Used old, giant branch stars plus CMD and
theoretical models to get stellar metallicity vs
radius Decrease in metallicity with R until 15
kpc, then flat. Is this the halo? Probably not
since halo Fe/H is usually lower (
-1.5). What is the reason for the flattening of
the relation at large R?
Vlajic et al 2008
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Accretion scenario...
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Milky Way disk Stellar and cluster metallicities

• Galactic metallicity decreases with radius (may
  not be smooth)
• gradient disappears beyond RGC values of 10 12
  kpc
• elements produced in Type II SNe are enhanced at
  large R
• consistent with progressive growth of the
  Galactic disk with time and episodic enrichment
  by Type II SNe (e.g. recent enrichment caused by
  enhanced SF from minor mergers)

blue open and green moderate aged (6 Gyr) open
clusters red field stars black plus Cepheid
variables (younger)
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Milky Way Z (as in vertical height) metallicity
trends stellar metallicities from SDSS

• Fe/H for 200,000 F,G stars in sdss
• metallicity distribution of the halo component is
  Gaussian with mean Fe/H -1.46
• disk metallicity distribution is non- Gaussian,
  with small scatter
• median smoothly decreasing with distance from the
  plane from -0.6 at 500 pc to -0.8 beyond several
  kpc