Download Lecture 18, Structure of spiral galaxies

GALAXIES 626
Upcoming Schedule:
Today: Structure of Disk Galaxies
Thursday:Structure of Ellipticals
Tuesday 10th: dark matter
(Emily's paper due)
Thursday 12th :stability of disks/spiral arms
Tuesday 17th: Emily's presentation
(intergalactic metals)
GALAXIES 626
Lecture 17:
The structure of spiral galaxies
NGC 2997 ­ a typical spiral galaxy
NGC 4622
yet another spiral
note how different the
spiral structure can be
from galaxy to galaxy
Elementary properties of spiral galaxies
Milky Way is a “typical” spiral
radius of disk = 15 Kpc
thickness of disk = 300 pc
Regions of a Spiral Galaxy
• Disk
•
•
•
•
younger generation of stars
contains gas and dust
location of the open clusters
Where spiral arms are located
• Bulge
• mixture of both young and old stars
• Halo
• older generation of stars
• contains little gas and dust
• location of the globular clusters
Spiral Galaxies
The disk is the defining stellar component of spiral galaxies. It is the end product of the dissipation of most of the baryons,
and contains almost all of the baryonic angular momentum
Understanding its formation is one of the most important goals of galaxy formation theory. Out of the galaxy formation process come galactic disks with a
high level of regularity in their structure and scaling laws Galaxy formation models need to understand the reasons for this regularity
Spiral galaxy components
1.
Stars
•
•
•
2.
Interstellar Medium
•
•
3.
4.
200 billion stars
Age: from >10 billion years to just formed
Many stars are located in star clusters
Gas between stars
Nebulae, molecular clouds, and diffuse hot and cool gas in between Galactic Center – supermassive Black Hole
Dark Matter
•
•
The total mass of the far exceeds the mass with stars and interstellar medium put together
Hidden, invisible or missing component
The matter in the spiral galaxies emits different kinds of radiation.....
Stars: Halo vs. Disk
• Stars in the disk are relatively young.
• fraction of heavy elements same as or greater than the Sun
• plenty of high­ and low­mass stars, blue and red
• Stars in the halo are old.
• fraction of heavy elements much less than the Sun
• mostly low­mass, red stars
• Stars in the halo must have formed early in the Milky Way Galaxy’s history.
• they formed at a time when few heavy elements existed
• there is little interstellar gas in the halo
• star formation stopped long ago in the halo when all the gas flattened into the disk
The interstellar gas
Disk structure
Empirically, the surface brightness declines with distance
from the center of the galaxy in a characteristic way for
spiral galaxies.
For spiral galaxies, need first to correct for:
• Inclination of the disk
• Dust obscuration
• Average over spiral arms to obtain a mean profile
Corrected disk surface brightness drops off as:
I  R =I  0  e
­R / h
R
where I(0) is the central surface brightness of the disk,
and hR is a characteristic scale length.
surface
brightness
In practice, surface brightness at the center of many spiral
galaxies is dominated by stars in the bulge.
Central surface brightness of disk must be
estimated by extrapolating inward from larger radii.
radius
Typical values for the scale length are:
1 kpc h R 10 kpc
In many, but not all, spiral galaxies the exponential part
of the disk seems to end at some radius Rmax, which is
typically 3 - 5 hR.
Beyond Rmax the surface brightness of the stars decreases
more rapidly - edge of the optically visible galaxy.
The central surface brightness of many spirals is ~ constant,
irrespective of the absolute magnitude of the galaxy!
I B  0  » 21 . 65 mag arcsec ­2
Presumably this arises from physics of galaxy and /
or star formation…
Rotation of spirals
Mostly don’t rotate rigidly ­ wide variety of rotation curves depending on their light distribution. The one on the left is typical for lower luminosity disks, while the one on the right is more typical of the brighter disks like the Milky Way
What keeps the disk in equilibrium ? Most of the kinetic energy is in the rotation
in the radial direction, gravity provides the radial acceleration needed for the ~ circular motion of the stars and gas
in the vertical direction, gravity is balanced by the vertical
pressure gradient associated with the random vertical motions
of the disk stars.
Motion under gravity
Motions of the stars and gas in the disk of a spiral galaxy
are approximately circular (vR and vz << vφ).
Define the circular velocity at radius r in the galaxy as V(r).
Acceleration of the star moving in a circular orbit must be
provided by a net inward gravitational force:
V 2r 
r
=­ F r  r 
To calculate Fr(r), must in principle sum up gravitational
force from bulge, disk and halo.
For spherically symmetric mass distributions:
• Gravitational force at radius r due to matter interior
to that radius is the same as if all the mass were
at the center.
• Gravitational force due to matter outside is zero.
Thus, if the mass enclosed within radius r is M(r), gravitational
force is:
GM  r 
F r =­
r2
(minus sign reflecting that force is directed inward)
Bulge and halo components of the Galaxy are at least
approximately spherically symmetric - assume for now
that those dominate the potential.
Self-gravity due to the disk itself is not spherically
symmetric…
Note: no simple form for the force from disks with realistic
surface density profiles…
Rotation curves of simple systems
1. Point mass M:
V  r =

GM
r
Applications:
• Close to the central black
hole (r < 0.1 pc)
• `Sufficiently far out’ that r
encloses all the Galaxy’s
mass
2. Uniform sphere:
If the density ρ is constant, then:
M  r =
V  r =
4
3

pr 3 ρ
4 pGρ
3
r
Rotation curve rises linearly with radius, period of the
orbit 2πr / V(r) is a constant independent of radius.
Roughly appropriate for central regions of spiral
galaxies.
3. Power law density profile:
If the density falls off as a power law:
ρ r =ρ0

r
−α
r0
…with α < 3 a constant, then:
V  r =

4 pGρ0 r α
0
3−α
r 1−α/ 2
For many galaxies, circular speed curves are
approximately flat (V(r) = constant). Suggests that
mass density in these galaxies may be proportional
to r-2.
4. Simple model for a galaxy with a core:
Spherical density distribution:
4 pGρ  r =
V 2H
r 2 a 2H
• Density tends to constant at small r
• Density tends to r-2 at large r
Corresponding circular velocity curve is:
V  r =V H

1−
aH
r
arctan
 
r
aH
Resulting rotation curve
Navarro, Frenk and White profile
Numerical simulations of the formation of dark matter
halos by Navarro, Frenk and White (1997) suggest that
the dark matter has a single `universal’ profile irrespective
of mass:
d
ρ r 
ρcrit
=
c


r / r s 1r / r s

2
…where ρcrit, δc and rs are all constants which can be
calculated if we know the redshift at which a halo forms.
Slope of NFW profile is -1 in center, -3 at large radius.
Circular velocity rotation curves for NFW profile
Measuring galaxy rotation curves
Consider a galaxy in pure circular rotation, with rotation
velocity V(R). Axis of rotation of the galaxy makes an
angle i to our line of sight.
If we measure the apparent velocity in the disk at an angle φ,
measured in the disk, then line of sight (radial) velocity is:
V r  R , i =V sys V  R  sin i cos f
where Vsys is the systemic velocity of the galaxy.
If we measure Vr across the galaxy, and can infer the
inclination i, then obtain the full rotation curve V(R).
Even if the galaxy is not resolved, measuring the amount
of emission as a function of the line of sight velocity gives
a measure of the peak rotation speed in the galaxy Vmax:
W » 2 V max sin i
Can use the Doppler shift of any convenient spectral
line to measure the line of sight velocity:
λ obs
λemit
=1
Vr
c
Optical: for nearby galaxies use Hα spectral line to measure
rotation curves. Distant galaxies use spectral line of
oxygen. Measures rotation of the stars.
Radio: traditional measure of rotation curves. Use 21cm line
of hydrogen. Measures rotation of the neutral hydrogen
gas disk.
Major advantage: detectable gas disk extends further out
than detectable stellar disk.
Examples of spiral galaxy rotation curves
Typically flat or even rising out to many scale lengths of
the exponential disk.
If all the mass in these galaxies was provided by stars and
gas, expect that V(R) would drop as R-1/2 at R > few x hR.
Existence of flat (or even rising) rotation curves at these
radii imply additional unseen mass - dark matter.
Rotation curve measurements on their own only indicate that
the dark matter must be:
• Dynamically dominant at large radii (required proportion
of dark matter ~50% in Sa / Sb galaxies, 80-90% in
Sd galaxies).
• Have a more extended distribution than either the stars
or the gas.
Note: no evidence for dark matter on the scale of the Solar
System, or in the nearby Galactic disk.
The evidence for dark matter is clear for
galaxies with 21 cm HI rotation curves that extend far
out, to R >> 3 h.
maximum disk decomposition for NGC 3198: M/LB = 3.8 for disk
observed
Why are spiral disks so uniform?
Why do the observed galaxies occupy such a a small fraction of possible structural configurations: size, surface brightness, shapes, etc..
•Stability?
•Initial Conditions?
•Feed­back during the formation?
Present Structural Parameter Relations for Disk Galaxies
Disk Size vs Mass/Luminosity
• Galaxy size scales with luminosity/stellar mass
• At given luminosity/size: fairly broad (log normal) distribution
• Rd~M*1/3 •
Constant central surface brightness
Disks
Disks
Spheroids
Spheroids
Shen et al 2003 SDSS
Another way of seeing the uniformity: Tully-Fisher relation
Plot the maximum circular velocity of spiral galaxies
against their luminosity in a given band:
Find that L and Vmax are
closely correlated
Smallest scatter when L is
measured in the red or the
near-infrared wavebands
e.g. in the H band centered at 1.65 µm:
L H » 3 ´ 10 10
Roughly,

V max
196 km/s

3.8
L H , solar
LµV 4max
Important use as extragalactic distance indicator:
• Measure Vmax, eg from radio observations of HI
• Infer L in a given band from the Tully-Fisher relation,
and convert to absolute magnitude
• Measure the apparent magnitude
• Use:
d
m−M =5 log
 
10 pc
…to estimate distance
Origin of the Tully-Fisher relation
In part, Tully-Fisher relation reflects simple gravitational
dynamics of a disk galaxy...
Estimate the luminosity and maximum circular velocity of
an exponential disk of stars.
Luminosity
Empirically, disk galaxies have an exponential surface
brightness profile:
−R / h
I  R = I  0  e
R
…with central surface brightness I(0) a constant. Integrate
this across annuli to get the total luminosity:
¥
−R / h
Lµ ∫ 2 p RI  0  e
0
R
dR
Can integrate this expression by parts, finding:
LµI  0  h 2R
i.e. for constant central surface brightness, luminosity
scales with the square of the scale length.
Circular velocity
If the mass in the stars of the exponential disk dominates
the rotation curve, then the enclosed mass within radius
R will be proportional to the enclosed luminosity:
R
−R ' / h
M  R  µL  R  µ ∫ 2 p R' I  0  e
R
d R'
0
Approximately, use formula for spherical mass distribution
to get V(R):
V 2  R  GM  R 
R
=
R2
This gives,
2
V  R µ
[
hR
R
−
hR
R
−R / h
e
R
−R / h
−e
R
]
´ hR
Dependence on R always occurs via the combination R / hR
Function in square brackets
peaks at R ~ 1.8 hR
Conclude that:
V max µ
h
R
Eliminate hR using previous
result: LµV 4
max
…the Tully-Fisher relation!
Problems with this `explanation’
This argument shows that it is plausible that a relation akin
to the Tully-Fisher law should exist.
Does not really explain the exact form:
• Flat rotation curves imply that enclosed mass is
not mostly stars (except very near the center).
For the same argument to work for dark matter,
need to additionally assume that M/L = constant.
• Derivation makes use of I(0) = constant, which is
not an obvious fact.
What determines sizes of stellar disks?
Angular momentum
Arising from halo size and spin parameter λ
Dark halo and its adiabatic contraction do matter
Conversion of gas to stars
Internal re­distribution of angular momentum
Bar instabilities?
Still too hard a problem for the simulations as we discussed previously
Look­back observations and disk formation
Disk evolution with redshift: What might we expect?
• Sizes from Initial Angular Momentum
Rexp(M*) ~ M*
x λ
1/3 ­
md­4/3jd x H(z) 2/3 • When did the presently existing disks form?
– 1/3 of all stars at z~0 are in disks
– 40% of all stars (now) have formed since z~1 (mostly in disks)
– Majority of the Milky Way disk stars have formed in the last 7Gyrs z~1  z~0 is the most important epoch for building today’s stellar disks – Note: higher SFRs at z>0  higher surface brightness(?)
Disk Evolution to z~1
=
µv
st
n
co
How did the surface brightness of disk galaxies evolve since z~1?
brighter
For luminous galaxies, the mean surface brightness has dropped by 1mag over the last 7Gyrs
Freeman “law”
1 mag
MV<­20
Evolution of the mean surface mass density of disks since z~1
M*>1010Mo
Redshift Evolution of the Tully­Fisher Relation
Expected change in surface brightness from the observed stellar population changes
Size­evolution from z~2.5 to z~0
At a given (V­band) luminosity,
galaxies were about 2.5x smaller at z~2.5 than now.
At a given stellar mass, they were only 1.4x smaller than now.
Galaxies at high­z were bigger than the naïve halo­scalings lead
us to expect!
H2/3(z)
Summary
• Disks at high­z (0.5­2.5) seem to live on the same locus in the M*,R,(σ) plane
• Evolution of this locus in the LV,R plane, reflects changes in stellar mass­to­light ratio
This argues for galaxies evolving along those relations.
(?) disks grow “inside out”, along R(M)
~M1/3
End