Transcript The Formation of Stars and Planets

The Astonishing Slowness of Star
Formation
Mordecai-Mark Mac Low
Dept. of Astrophysics
American Museum of Natural History
Collaborators
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Miguel A. de Avillez (U. Evora, Portugal)
Javier Ballesteros-Paredes (UNAM Morelia, Mexico)
Dinshaw Balsara (Notre Dame)
Andreas Burkert (MPI für Astronomie, Germany)
Fabian Heitsch (U. Colorado/Boulder)
Jongsoo Kim (Korea Astronomy Observatory)
Ralf Klessen (Astrophys. Inst. Potsdam, Germany)
Volker Ossenkopf (ESTEC, Netherlands)
Michael D. Smith (Armagh Observatory, N. Ireland)
The Oddness of Solid Rock
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Rock is dense: 2500 kg m-3
Even water is dense: 1000 kg m-3:
Stars are denser: 105 kg m-3 at center
The average density of the Universe is 10-27 kg m-3
Even within galaxies, interstellar gas has a density
of 10-21 kg m-3, or 1 atom cm-3.
• How did galaxies, stars and planets ever form?
Gravitational Stability
• Criterion for stability of
gas against gravitational
collapse found by Jeans
(1902).
• Pressure opposes
collapse: sound waves
with speed cs must cross
region to communicate
pressure changes before
collapse
cs
J

;
t ff
λJ
density ρ
J
cs
;
MJ
J3
Galaxy Formation
• Gas and dark matter
uniform to 20 ppm when
cosmic microwave
background emitted.
• Denser regions collapse
until pressure supports
• Further collapse depends
on cooling (atomic
collisions excite radiation,
which escapes).
Virgo Consortium
What is a star?
• Gas collapses under its own gravity
• Densities build up until
fusion starts in the center.
pressure
•Resulting thermal pressure
opposes gravity
•Star is in hydrostatic
equilibrium, with pressure
balancing gravity
gravity
fusion
Star Formation Rate
• What determines the rate of star formation
in galaxies?
1/ 2
n


6
t

10
yr
  3 -3 
• Free-fall time ff 
 10 cm 
• Galaxy lifetimes greater than 109 yr.
• Yet star formation continues today.
• How are starbursts, low surface brightness
galaxies different?
Observations
• Young stars can be identified by
surrounding infalling material, models of
stellar evolution.
• Youngest stars only observed in dense
clouds of interstellar gas and dust.
• Densities are high enough to shield interior
from hard UV radiation from stars, allowing
molecules (primarily H2, but also CO, NH3,
H2O) to form.
Molecular Cloud Lifetimes
• Cloud lifetimes estimated by Blitz & Shu
(1980) to be around 30 Myr in Milky Way
– Locations downstream from spiral arms
– Stellar ages associated with clouds
• Much shorter lifetimes of 5-10 Myr
proposed by Ballesteros-Paredes et al. (1999),
Fukui et al. (1998).
– stars >10 Myr old not tied with clouds
– Cluster ages vs. associated molecular gas
• Individual cloud lifetimes vs. ensemble
lifetimes
Molecular Cloud Kinematics
• Molecular spectral line ratioes show cloud
temperatures to be of order 10 K, with
sound speeds ~0.2 km/s
• Line widths are much broader than thermal,
corresponding to random motions of order
1-10 km/s, or Mach numbers 5-50.
• Strong shocks should be produced, quickly
dissipating the kinetic energy.
Magnetic Fields
• In standard scenario, magnetic fields:
– Convert shocks into Alfvén waves (transverse
MHD waves), which acts as a lossless spring
that stores and returns kinetic energy, allowing
observed supersonic motions to persist
– Provide magnetohydrostatic support against
collapse—ambipolar diffusion (neutral drift
through ions) determines time scale for star
formation (Mouschovias, Shu, Nakano)
• We find magnetic fields either insufficient
or unnecessary for these purposes.
Decaying Turbulence
• Computations with two methods
– ZEUS hydro and MHD (Stone & Norman 1992, ApJ
Suppl.). Available from the URL
zeus.ncsa.uiuc.edu:lca_home_page.html
– Smoothed particle hydrodynamics (SPH), using
sink particles (Bate et al.) when G0, on a
GRAPE 3 special-purpose computer (ancestor of
our GRAPE 6 machines)
• Periodic, uniform-density, isothermal cube
• Gaussian initial velocity perturbations
ML 1999
2563
time
time
1283
Kinetic Energy Decay
2563
323
ZEUS
hydro
weak
MHD
193
strong
MHD
SPH
hydro
703
Decay Rate
• Quantify loss of energy from turbulent,
supersonic flow
• Measure kinetic energy of boxes driven
with constant energy input
• Use constant Gaussian driving pattern with
narrow range of wavelengths
• Vary energy input rate, wavelength,
magnetic field strength
E 1
E  10
k=2
k=4
k=8
ML 1999
ML 1999
Ekin  
0.21

3
rms
mkv
m = mass
v = rms velocity
k = wavenumber = 2/d
How fast does turbulence decay?
compare decay time
Ek
td 
(dEk dt )
• Mrms >>  in molec. clouds
• d/J < 1 needed for support
Jeans length
to free-fall time
t ff   J cs
driving length = 2/k
to find:
td

 1.2
t ff

d

J
M rms
• Turbulence decays in
less than a free-fall time
in molecular clouds
•Observed motions cannot
 1 come from initial
conditions.
Mach number
Can Turbulence Support Against
Gravitational Collapse?
• Analytic work (Bonazzola et al., Léorat et al.)
suggests that d < J needed for support
• Test by adding self-gravity to ZEUS and SPH
turbulence models
• Zero or decaying turbulence models both
collapse efficiently (Klessen & Burkert)
• Resolution of cores difficult as collapse
continues, so bracket reality with grid, SPH
computations
Numerical Considerations
• Cannot capture core behavior correctly
• Bracket with different techniques
– Sink particles in SPH: indestructible once formed
– Uniform grid: cores can’t collapse, destroyed
easily by passing shocks
• Magnetic fields diffuse through grid
– Minimum number of zones in a Jeans wavelength
required to prevent spurious collapse (Heitsch, Mac
Low & Klessen 2001)
Klessen, Heitsch, ML (2000)
Heitsch, ML, Klessen (2000)
Rose Center for Earth & Space
Images showing star formation and the
formation of an HII region from the new
Space Show
“Are we Alone: The Search For Life”
M
= 1
Mbox
box = 1
Klessen, Heitsch, ML (2000)
 d   J / M rms
Magnetic fields
reduce the
fraction of mass
in collapsed
objects, but do
not prevent local
collapse.
Heitsch, ML, Klessen (2001)
Local collapse
• Collapse occurs if
m  mJ ,T  v3 / 
D  J  cs / 
• When  increases, smaller regions collapse
• Isothermal shocks give      M 2
• Unless compressed regions are turbulently
supported, they collapse locally despite
global support
Driven vs. Decaying
Projected
positions of sink
particles from
SPH models
Klessen, Heitsch, Mac Low (2000)
Modes of Star Formation
• Slow, scattered star formation occurs in
regions supported by turbulence due to low
densities or high turbulent velocities.
Observed in regions like Taurus.
• Fast, clustered star formation occurs in
regions that are not supported by
turbulence, either due to density
enhancements or decay of turbulence.
Resembles regions like Orion, or starburst
knots.
What’s driving the turbulence?
• Gravitational collapse fails due to fast decay
• Protostellar jets and outflows
– Most energy deposited outside clouds
• Rotational shear of galaxies via magnetic
coupling to gas (Sellwood & Balbus 1999)
– Probably gives background value (~6 km/s)
– Dominant for low surface brightness galaxies,
outer regions of normal galaxies?
Supernova Driving
• In active star-forming galaxies, SN driving
dominates other mechanisms
• Strength of driving depends on star-formation
rate, allowing self-regulation
• 3D models (ML, Balsara, Avillez, Kim, 2001, on astro-ph):
– Hydro adaptive grid (Avillez 2000) on 3000 x 3000 x
60,000 light year box with galactic disk, clustered,
random SNe, and SN rates 1, 6, 10x Galactic value
– RIEMANN MHD framework (Balsara 2000) on 600
light year periodic box with SN rate 12x Galactic
value
Explosions as Bright as Galaxies,
• (Type II) supernovae
occur when massive star
fuses all available
elements and
gravitationally collapses.
• Core forms a neutron star
or black hole, while outer
layers bounce
explosively, releasing
1051 ergs of energy
Cassiopeia A supernova remnant
3 light years
Chandra X-ray Observatory
Simulations of SN-Driving
• Avillez (2000) AMR parallel code
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–
–
–
vertical stratification,
equilibrium ionization radiative cooling
isolated and clustered SNe (twice galactic rate)
No self-gravity, molecule formation
• Show cut through plane of 3D simulation
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–
–
–
0.625 pc resolution in plane (800 x 800 equiv. resol.)
Log of density
70 Myr
1 x 1 kpc shown
• RIEMANN MHD framework (Balsara 2000) on 200
pc periodic box (1283) with SN rate 12x Galactic
value
Show disk movie from Avillez
Magnetic Pressure
Thermal Pressue
ML, Balsara, Avillez, Kim
Temperature
Density
Next Steps
• Understanding molecular cloud formation
– Turbulent compression vs gravitational
contraction, including chemistry
– Multi-scale computations including both cloud
and core formation to capture entire star
formation sequence
• Modeling the driving of turbulence
– Supernova driving vs. shear flows
– Are large-scale star formation rates predictable?
(empirical answer is yes: Schmidt laws)
Overcooling in Galaxy Formation
• Far too many dwarf galaxies cool and collapse around
galaxies the size of the Milky Way in numerical
simulations neglecting star formation, compared to
observations (White & Rees 1978, Klypin et al. 1999, Moore
et al. 1999).
• Ionization by hard UV radiation (λ < 91.2 nm) alone
may (Chiu, Gnedin, & Ostriker 2001), or may not (Navarro
& Steinmetz 1997) provide enough heating.
• Dwarf galaxy wind disruption could be solution (or
contribute to it, Scannapieco et al. 2000, 2001ab).
Starburst galaxies
• When regulation mechanisms fail, star
formation rates can be 100x Milky Way’s
• The most massive of the newly formed
young stars explode as supernovae in only a
few Myr.
• In starburst galaxies, these supernovae can
drive a wind completely out of the galaxy
into the surrounding intergalactic gas.
Parameter Space
Dwarf galaxies
• Typical haloes in LCDM with values form first.
h  0.7, 0  0.37,   0.63, b  0.05,  8  0.8
photoevaporation
(Barkana & Loeb)
H2 cooling
(Ciardi & Ferrara
00, Tegmark 97)
Log Mhalo
Lyacooling
redshift
Blowouts From Isolated Dwarfs
•2D, axisymmetric
models
•Log density shown
in color scale
•Box sizes of
90,000 x 45,000
light years
ML & Ferrara 1999
Goals for Study of Cosmological
Blowouts
• Better understand feedback from early
galaxies
– Kinetic and thermal energy ejection into
intergalactic medium (IGM)
– Stop further infall of gas in own halo
– Pollution of IGM by ejected heavy elements
– Escape of ionizing radiation through bubbles
• Calibrate sub-gridscale models for
cosmological feedback in large-scale codes
t=initial
t=50 Myr
t=collapse
t=90 Myr
t=initial
t=collapse
t=50 Myr
t=90 Myr
Mechanical Feedback Results
• Accreting gas haloes can suppress ejection
• With large enough starburst they can
themselves be swept away.
• Kinetic energy feedback primarily in form
of ejected accreting material, not hot gas
Star Formation in the Universe
• Efficiency and speed of star formation in
galaxies determined by the supersonic
turbulent motions in the interstellar gas
• Turbulence likely driven by combination of
supernova explosions and galactic shear
• Efficient star formation in young galaxies
drives winds that can retard further growth
of that galaxy and probably also nearby
galaxies.
Local Dwarf Models
• Mac Low & Ferrara (1999) models:
– dwarf disks with constant surface density in
hydrostatic equilibrium
– Radii from Ferrara & Tolstoy (2000)
– potential of DM dominates (softened isotherm. sph.)
– Persic, Salucci, Stel (1996) scaling of DM to visible mass
• Starburst energy injected at galaxy centers
– Excess cooling of hot gas prevented with tracer field
– Conduction approximated with mass injection at center
– 50 Myr of SN energy input (instantaneous burst)
• Low-density IGM for low-z, isolated dwarfs
Numerical Methods
• ZEUS-3D (Stone & Norman 1992), second-order,
Eulerian, artificial viscosity
• Ionization equilibrium cooling of ambient gas,
with strength dependent on metallicity Z (semiimplicit energy equation)
• Density-dependent heating for thermodynamical
balance
• Tracer field using Yabe & Xiao (1993) transform
• Turn off cooling in hot regions to avoid poisoning
Isolated Dwarfs
• Metals in SN ejecta escape easily
– Hot, shocked ejecta have sound speed greater
than escape velocity in galaxies up to LMC size
• Mass much harder to strip.
– In most galaxies, shock “blows out” to IGM
before reaching most of ISM
– Mass ejected efficiently only from galaxies
with baryonic mass < 106 M (“blowaway”)
More Realistic Blowouts
• Higher pressures and galactic haloes
confine blowouts (Silich & Tenorio-Tagle 1998,
2001)
• Blowouts in galactic clusters with highpressure IGM (Murakami & Babul 1999)
– Pressure confines blowout
– But ram pressure from orbital motion important
• Inclusion of Type I SNe (Recchi et al. 2001)
• Cosmological blowouts: infall also can limit
mass ejection
Changes for cosmological case
• Infalling halo
• Dark matter solution taken from spherical
collapse model of Gaussian perturbation
(Meiksin 1994)
• Gas cooling and collapse solved for directly
• Starburst size determined from cooled mass
and star formation efficiency (SFE).
• Galaxy sizes as function of redshift (Mo,
Mao & White)
• Disk potentials included
• Metalfree
curve from
Sutherland &
Dopita, with
log  (erg cm3 s-1)
Cooling
cutoff at
103.5 K (no
molecules)
• Compton
cooling at
low, high T
4
log T (K)
for ionized
36
3 -1
4


(5.4

10
erg
cm
s
)(1

z
)
T / ne
gas.
comp
8
t=initial
t=50 Myr
t=collapse
t=90 Myr
t=initial
t=50 Myr
t=collapse
t=90 Myr
Future work
•What drives the turbulence?
•Supernovae?
•Young stellar jets?
•Rotation of the galaxy?
•How do star-forming molecular clouds form?
•What quantitatively determines the star formation
rate?
Conclusions
• Galactic winds couple inefficiently to the ISM, so
ISM ejection (‘blowaway’) is hard.
• Metal ejection much easier.
• Accretion can substantially alter behavior of
starburst blowouts
• Observations only show the tip of the iceberg
• Reasonable assumptions about star formation
efficiency can still result in metal and mass
ejection
• Quantitative benchmarks being defined for use in
large-scale simulations
• Ionization can escape efficiently if shell fragments
early (when most photons come out)
Conclusions
• Accretion can substantially alter behavior of
starburst blowouts
• Reasonable assumptions about SFE can still
result in metal and mass ejection
• Quantitative boundaries being defined for
use in large-scale simulations
• Ionization escapes efficiently, but only at
early times (when most photons come out)
Conclusions
• Supernova feedback can drive winds, allow
ionizing radiation to escape.
• Metals escape efficiently, mass less so.
• Effects of winds
The IGM
• Metal-enriched to Z  103 Z at z ~ 3
• Ly a forest linewidths 10 km s-1 broader
than predicted by ionization alone (Theuns et
al. 1998, Bryan et al. 1999)
• Universe reionized at z < 5 (Becker et al 2001,
Djorgovski et al. 2001)
• Dwarf galaxies with masses 106.5-109 M
condense early, producing ionizing radiation
and SN-driven winds
Galaxy Formation Delay
• Dwarf galaxy winds
also will affect
nearby objects.
• Mechanical energy
input sufficient to
sweep away gas in
still linear overdense regions
(Scannapieco et al.
2000, 2001)
Scannapieco, Ferrara, & Broadhurst 2000
Numerical Feedback
SF only
outflows
SF only
outflows
Scannapieco, Thacker, & Davis 2001
Supernova Rate
Pressure
Galactic
6x
ML, Balsara, Avillez, Kim
10 x
Log-Normal Fits
•Hydro model at
Galactic SN rate
cool gas
•Theory of Passot &
Vazquez-Semadeni (PRD,
1998) from vrms
log normal
tilted log normal
Distribution of gas pressures
By volume
By mass
Large mass of cold gas at high pressures: pressureconfined atomic and molecular clouds?
Summary
• Driven turbulence can account for:
– supersonic motions in molecular clouds
– Very different rates of star formation in
starbursts, normal galaxies, LSB
• Driving most likely from SNe and MRI
• SN driving can explain normal ISM.
Regions of intense star formation probably
unsupported and collapsing.
• Pressure distribution in ISM not power-law
due to shocks alone but log-normal due to
shocks and rarefactions together.
Length and Time Scales
1 atom cm-3, but a whole lot of cm3!
The volume of the Galaxy is roughly
4 R 2 z 12  (45,000 l.y.) 2 (200 l.y.)
 10  25  (104 )2  2 102  102108102
 1012 l.y.3
1 light year = 9.5 1017 cm, so
1 l.y.3  (1018 )3  1054 cm3
volume=1012 1054  1066 cm3 !
90 000 light years
M100, by WFPC2 team, with Hubble Space Telescope
Gravitational Collapse
• Gravity acts everywhere. If nothing resists
it, indefinite collapse occurs.
• From primordial gas to interstellar densities
takes a 100 million years
• From interstellar densities to stellar
densities takes another 30 million years
Oh, the Pressure!
• What stops gravitational collapse?
• Angular momentum: forms disk
•Conservation of angular momentum
•Gas dissipation
pressure
gravity
angular
momentum
gravity
• Thermal pressure: forms star
•Optical thickness
•Fusion (first D, then H)
The First Stars, and their Gifts
• Cooling only due to molecular hydrogen
• Stars likely very massive -- hundreds of
solar masses.
• Massive stars are short-lived (1-10 million
years), exploding as supernovae, and
producing all elements heavier than
hydrogen, helium and lithium.
Our Ingredients
• Sun and other modern stars
– Hydrogen & helium: from the big bang
– Trace elements (everything else): from earlier
stars and supernovae
• Earth and other rocky planets
– Carbon, nitrogen, oxygen: from dying lowmass stars
– Everything heavier (Si, Fe, Al, Mg, …, U):
from supernova explosions
– Traces of hydrogen and helium in much
reduced quantities
But why are stars still forming?
• Gravity should cause gas to collapse to
stellar densities in tens of millions of years
• Yet galaxies have been around for a
thousand times as long—10 billion years
• How can star formation still be occurring?
• Two major explanations proposed
Delay of Star Formation
• “Standard model”
• Magnetic fields thread
ionized interstellar gas
• Once and future theory
• Supersonic turbulence
maintains support
Magnetic fields
• Star formation occurs
when neutral gas is
dragged by gravity
through ions tied to
magnetic field.
Turbulence
• Supersonic motions prevent collapse in bulk of gas.
• But, shock waves compress
some of gas, causing local
collapse despite global
support
Observations (a polemical summary)
Magnetic Support
• Strong magnetic fields
observed, but not quite
strong enough
• Too many young stars
in dense molecular
cloud cores
• Too little age spread
between nearby stars
Turbulence
• Supersonic motions
observed
• Cloud shapes appear
correct
• Both isolated and
clustered star
formation occurs
The Oddness of Liquid Water
• Terrestrial life in all its many forms depends
on liquid water. Other life could be
different, but we don’t know how.
• Liquid water on surface seen only on Earth
• Subsurface water maybe on Mars, probably
on Jovian moons (Europa, Ganymede,
Callisto)
• Extrasolar planets all gas giants, but moons
and terrestrial planets of unknown
properties could accompany them.