Download The Initial Mass Function (IMF) Continued

The Initial Mass Function (IMF) Continued
• IMF ψ(m, t) = number of stars formed per unit
volume per unit time
• Critical measurement for interpreting observations of
distant (and nearby!) galaxies
• Probably varies with environment and/or time, but:
– usually assumed constant in space and time
– only meaningful when averaged over significant volume
• Nomenclature
– often approximated as power law
ψ(m) dm = ψ0 m-α
α ~ 2.35 historical value,
still considered a good
value for high mass end
or
log ψ(m) d(log m) = ψ0 m-γ
γ = α-1
1
Field Star IMF: Results
• Salpeter 1955, ApJ, 121, 161
̶
IMF
a = 2.35
M = 1-40 M~
• Scalo 1986, Fund Cos Phys, 11, 1
– rough power law IMF for M > 1 M~
– strong flattening below 1 M~ (see
next page)
• recent studies suggest high-mass
slope closer to Salpeter
PDMF
• infrared surveys confirm flattening of
IMF at low masses
– no vast reservoir of free-floating
brown dwarfs, planets
– consistent with microlensing results
Kroupa, Tout, Gilmore 1990, MNRAS, 244, 76
2
Scalo IMFs
Miller & Scalo (1979)
Scalo (1986)
The Scalo IMF has
been used often in
galaxy modeling but in
under predicts the
mass in low mass stars
and may also be
somewhat deficient in
10-40 solar mass stars.
Be careful when
choosing ingredients
for galaxy modeling!
3
4
IMF in Clusters
• stars are at same distance
and age, simplifying analysis
• provides consistency check on
field IMF
• constrains universality of IMF
• limited by statistics, limited
mass range (esp. for old
clusters)
• results:
– most cluster IMFs consistent
with field, within small
number statistics
– globular cluster IMFs also
consistent
– some evidence for local
variations in young clusters
5
Orion Nebula Cluster and the Low-Mass IMF
Hillenbrand 1997, AJ, 113, 1733 (see also Luhman et al.2000 who observed a
number of clusters and demonstrated that the cluster and field IMFs are very
similar)
6
Combining Cluster IMFs
• The combination of different
limiting magnitudes and turnoff
masses for the clusters may
lead to distortions!
• Another problem: If upper
stellar mass limit in cluster is
limited by available cluster
mass, combined IMF will be too
steep -- cluster mass spectrum
gives smaller probability for
obtaining more massive stars
(Reddish 1978). Discrete
sampling effects need to be
explicitly considered.
7
Theoretical Conceptions of Processes Controlling the IMF
(after a talk by John Scalo)
some process gives scalefree hierarchical structure
“turbulence”
transient, unbound
quasi-equilibrium
cores
condensations form
in molecular clouds
spiral shearing
gradual loss of support
ambipolar
diffusion
disk MRI
SN, SB
bound by external shocks
instabilities in
instabilities in
expanding
turbulent
shells
compressions
ambipolar
filamentation
turbulent
dissipation
magnetic
reconnection
lull in external
energy input
quiescent
gravitational
instablity
cooling
instabilities bending mode
instability
gravitationally
unstable cores
collisional coalescence
and fragmentation
growth, termination by
accretion
disk disruption
disruption by turbulent
shearing or shocks
]
collapsing
protostars
accretion,
mass loss,
dynamical
interactions
feedback on
entire process
UV radiation
SNe, SBs
winds,
jets
IMF
8
Is the IMF Invariant?
• Need you ask after the
previous chart???
• This question has been
debated for a long time
– Limited statistics, selection
effects may cause apparent
differences
– Substantial evidence for bimodal star formation which
is a form of varying IMF
– No clear cut evidence for
slope variations within given
mass ranges
From Weidener and Kroupa 2005 ApJ 625 754
9
Dispersal of Open Clusters
Open clusters eventually
disappear as easily recognized
entities
- Most clusters not massive
enough to be gravitationally
bound
- Differential rotation
exacerbates the dispersal
10
Globular Clusters
• Have been a key element of many stellar population studies
• Used to be a bone of contention as GC ages appeared to be at
variance with the age of the Universe
• Have ~100,000s of members and usually can survive passage through
the plane of the Milky Way (but beware of mass segregation effects)
M80
11
Globular Cluster Properties
• MW has ~150 globular clusters – last ones to be found
were discovered at 2microns by the 2MASS survey [big
ellipticals have many more GCs; M87 has over a 1000]
• Masses range from ~1000M~ to ~1x106M~
• Metallicity ranges from 0.004 of solar to about solar
• Some are very strongly centrally concentrated while
others are not
• Integrated light has a spectral type ranging from F3 to
G5: most of the variation is due to the variation in
metallicity {redder = more metal-rich}
• Milky Way clusters have a relatively small age range (all
old) but other galaxies show big spreads in ages
12
Are Globular Clusters Small Galaxies?
It is very tempting to think of
globular clusters as an extension of
the mass sequence of elliptical
galaxies….
But
Some GCs clearly form as part of
the initial sequence in the formation
of larger galaxies so they may be
remnants of cloud collapse.
It is also not at all certain how many
GCs have black holes in their
centers.
GCs interact with their parent
galaxies so their properties may be
strongly modified relative to an
isolated dwarf elliptical.
GCs are virtually all quite spherical
with little flattening unlike dwarf
ellipticals (most oblate are the
equivalent of E3; flattening is due to
rotation).
Frogel, Persson, & Cohen 1980
13
More HR Diagrams
Open Cluster
Metallicity
Lower
Higher
Sharpness of the turn-off from the MS onto the subgiant branch
indicates that the stars in a cluster have a very small age spread (~2%).
Horizontal branch is bluer for lower metallicities but HBs show a range
of properties at a given metallicity (related to “2nd parameter” issue)
14
WD Cooling Curve
• HST photometry has
revealed the white
dwarf population in GCs
(about 10% of the total
mass of a GC).
• The WD sequence is not
a mass sequence but
rather a cooling
sequence.
• Might be possible to use
the WD sequence as a
check on cluster ages.
15
Distribution in the Milky Way
16
Metallicities
⎛ N Fe ⎞
⎛ N Fe ⎞
⎡ Fe ⎤
One definition of metallicity:
= log ⎜
⎟ − log ⎜
⎟
⎢
⎥
H
N
N
Another scheme:
⎣ ⎦
⎝ H⎠
⎝ H ⎠~
(X,Y,Z) = fractional abundances by
Detailed studies reveal that α-process
mass of H, He, everything else
elements from core collapse SN are
Solar = (0.70,0.28.0.02)
more enriched than Fe => GCs
enriched preferentially by massive stars
14 Gyr
isochrones
Line width indicates Z: .0001,.001,.006
Horizontal Branch
Spread
on HB
implies
a
spread
in
mass
loss.
Solid have Y=0.2, dotted have Y=0.3
17
Ages
• As recently as 1996 entire
Annual Reviews articles were
dedicated to discussions of GC
ages which ranged from 10 to
20 Gyr.
• Ages are now important as
markers of halo collapse
• Accurate ages require good
metallicity data, distances,
and careful fitting of
isochrones.
• Age spread greatest among
more metal-rich clusters
(~4Gyr?) which are ~2 Gyr
younger than metal-poor
clusters
• MS turn-off best age indicator
– note similarity of shapes
(and hence colors) of the
giant branch.
MV(TO) = 2.70 log(t/Gyr) + 0.30[Fe/H] + 1.41
18
GC Luminosity Functions
•
Metalpoor
•
•
Metalrich
Source confusion has plagued attempts to
produce reliable LFs
Converting LFs to mass functions reveals slope
variations from cluster to cluster with
shallower slopes for more metal-rich clusters
Slopes most strongly correlated with cluster
location in the galaxy => low mass stars may
be stripped away by interactions with the disk
so a universal IMF may hold.
GC
Field
Deficit in GCs as
these luminosities
are on the giant
branch
19
GC Luminosity Profiles
• Multi-mass King model fits the data but
has a number of parameters
• Can test the multi-mass King model by
looking for other evidence of energy
equipartition
If equipartition prevails, more massive
stars will be moving more slowly and
found preferentially near the centers of
clusters. The LFs in the figure to the
right were measured at three different
radii and the larger radii clearly have
more low mass stars. Note that mass
segregation enhances the loss of low
mass stars due to tidal stripping.
20
Central Cusps
Globular clusters have
sufficiently high core stellar
densities and are old
enough that it is surprising
that only about 20% of
GCs show central cusps.
Naively one would expect
that all would have
experienced core collapse.
What “re-inflates” the
cores?
Could black holes cause
the central cusps?
21
Internal Kinematics
• Because of the spherical shapes and modest number of
stars, globular clusters were a target for some of the first
N-body simulations
• Star densities in the core are sufficiently high a number of
interesting dynamical effects may be seen:
–
–
–
–
Energy transfer between binaries and the cluster system
Core collapse
Mass segregation
Merging of stars:
• Blue stragglers have masses of ~1.3M: so they should not be present
given the current ages of clusters.
• Blue stragglers are concentrated towards the centers of clusters
• Models of stellar collisions resulting in remnants match the properties
of blue stragglers
22
Correlation of Properties w/
Location
• Initial supposition was the GCs formed
during the initial collapse of the protoMilky Way (ELS model)
• More metal-rich clusters are
concentrated towards the plane and
have a significant component of
rotation in their motions.
• More metal-rich clusters also appear to
be slightly younger than more metalpoor clusters
• Cluster formation no doubt traced some
of the early collapse of the galaxy, but
the picture is more complicated and
evidence from GC systems around other
galaxies suggests that clusters can form
in major star formation events (eg.,
starbursts, mergers)
• Also need to consider possibility that a
cluster might be the remnant of
accretion of a satellite galaxy
Zinn 1985 ApJ 293 424
23
Do GCs Harbor Black Holes?
• GCs could anchor the
low mass end of the
M-σ relation
• In principle, 3-D
velocity distributions
could be observed for
GCs
• So far best data come
from HST proper
motion measurements
(McLaughlin et al. 2006)
• Upper limit on MBH for
47 Tuc is ~1000M~
24
X
M15 result has been retracted.
25
Globular Clusters in other Galaxies
• GCs form when galaxies have starbursts, not in more passive star
formation as seen in disks so they should reflect major episodes of
star formation in the past and the formation of the most massive
parts of galaxies, the spheroids.
• Many extragalactic globular cluster systems have been observed
(see Brodie and Strader ARAA 2006)
M104’s cluster
system from
Spitler et al.
2006. Blue
crosses denote
metal-poor
clusters and red
circles denote
metal-rich
clusters.
26
Bimodal Distributions Common
• Just as the MW globular population shows blue and red (metalpoor and metal-rich) groups, so do many populations around
other galaxies.
Intermediate age &
metallicity
Old & metal-rich
Old & metal-poor
GCs around M87
Examples from M31’s GC population
27
Bigger Galaxies = More Globular Clusters
• T is the number of clusters
per 109 M~ so the relative
numbers of clusters increase
with galaxy mass, not just
the absolute number.
• Why there are more GCs
per unit mass in more
massive galaxies is unclear:
Does this rule out formation
of giant ellipticals from
mergers of disk galaxies? Is
this the result of more early
cluster formation in the
deeper DM haloes that
produce giant ellipticals?
Does environment play a
role?
Squares = cluster galaxies, circles =
field
28
Relationship to Galaxy Mass/Luminosity
• Metallicity of
globular clusters is
correlated with the
mass of the parent
galaxy.
• This correlation
provides a
significant
constraint on
galaxy formation
models.
Peak GC metallicity vs galaxy MB for red
and blue clusters.
29
Radial Distribution of GCs
NGC 1399
Filled = metal-rich globulars
Open = metal-poor
• Just as in the MW,
more metal rich
clusters tend to be
more centrally
concentrated around
the parent galaxy
• Metal-rich clusters
follow the light
distribution closely
suggesting that these
clusters formed at
about the same time as
the bulk of the stars.
30
Formation of GCs
• Low metallicity clusters must have formed very early,
around z~10-15 and their formation must have been
truncated by reionization. The minimum masses that
could cool and collapse, ~108 M~ => ~106 M~ in stars,
are strongly suggestive of present day GCs.
• DM simulations can reproduce many of the properties of
low metallicity cluster populations
• High metallicity clusters are much more complicated –
formation of clusters in mergers and starbursts suggests
that these clusters have a varied formation history
31
Antennae Clusters
32
DM Simulation
• Green in this simulation at z=12 represents regions with sufficiently
high density that they can cool and form stars
• Boxes show such peaks and where they end up at z=0
Z=0
Z=12
33
DM Simulation of MW Clusters
Radial distribution of
metal-poor clusters in the
MW can be reproduced if
GCs form in >2.5σ peaks
Have a mass > 2x108 M~
Formed stars by z~10
Interesting note: JWST
may have sufficient
sensitivity to detect newly
formed GCs
From Moore et al. 2006
34