Transcript Polarimetry & Star

A Recipe
for Star
Formation
Alyssa A. Goodman
Department of Astronomy
Harvard University
A(G’s) Recipe for (z=0) Star
Formation
Ingredients:
Molecular Gas (well-chilled, lightly-ionized)
Magnetic Field
Gravity
Optional: Pressure Cooker (e.g. nearby
supernova)
A(G’s) Recipe for (z=0) Star
Formation
Steps:
1. Allow gravity to form “molecular clouds” (watch
out for turbulence, clouds might take a while to form…or use
pressure-cooker to speed up the process)
2. Allow turbulent cascade to form in molecular
cloud (be careful with the B-field)
3. Let magnetic turbulence & support decay
enough for “dense cores” to form in molecular
clouds (be careful to watch for core-core interactions &
outflows)
4. Watch dense cores slowly collapse, until one (or
several?) Kelvin-Helmholtz-radiating protostar(s)
form(s) near the center
A(G’s) Recipe for (z=0) Star
Formation
Steps:
1. Allow gravity to form “molecular clouds” (watch
out for turbulence, clouds might take a while to form…or use
pressure-cooker to speed up the process)
2. Allow turbulent cascade to form in molecular
cloud (be careful with the B-field)
3. Let magnetic turbulence & support decay
enough for “dense cores” to form in molecular
clouds (be careful to watch for core-core interactions &
outflows)
4. Watch dense cores slowly collapse, until one (or
several?) Kelvin-Helmholtz-radiating protostar(s)
form(s) near the center
A(G’s) Recipe for (z=0) Star
Formation
This Recipe Makes:
At least one, and sometimes many, stars.
(Notes: Industrial-strength recipe, available from R. Kennicutt et
al. makes the IMF.)
“Residual” dusty disks around stars, which
often form planets.
A big mess--much of which is recyclable,
given enough time.
Steps in the
Recipe
Today:
“Step #3”
(a.k.a. GMC or Cloud Complex)
Radio Spectral-line Observations of Molecular Clouds
Spectral Line Observations
“Integrated Intensity Map”
Region of Radio Spectral-Line Survey
Alves, Lada & Lada 199
Velocity as a "Fourth" Dimension
Spectral Line Observations
Loss of
1 dimension
Mountain Range
No loss of
information
Tools in this 4D (x-y-v-Intensity)
Space






Speedometers: v(z) gives gas velocity
Tachometers: v(z)[(x,y)] measures angular
momentum
Thermometers: line strength inter-comparisons give
Tkinetic, Tex (and t)
Pseudo-thermometers: line widths give velocity
dispersion (usually >> sound speed)
Magnetometers: Zeeman Effect & polarized
spectral-lines give B
Combinations give density, mass
Tools in this 4D (x-y-v-Intensity)
Space






Speedometers: v(z) gives gas velocity
Tachometers: v(z)[(x,y)] measures angular
momentum
Thermometers: chemical analyses & line strength
inter-comparison give Tex, Tkinetic
Pseudo-thermometers: line widths give velocity
dispersion (usually >> sound speed)
Magnetometers: Zeeman Effect & polarized
spectral-lines give B
Combinations give density, mass
Step 3: “Forming
the Blobs that
will form the
Stars”
“Step #3”
(a.k.a. GMC or Cloud Complex)
Coherent Cores:
“Islands of Calm in a Turbulent
Sea”
"Rolling Waves" by KanO
Tsunenobu © The Idemitsu
Museum of Arts.
“Larson’s Law” Scaling Relations
(1981)
(line width)~(size)1/2
(density)~(size)-1
Curves assume M=K=G
(Myers & Goodman 1988)
“Line width-Size Relations”
Ensemble of Clouds
Non-thermal Line Width
Type 1: “Larson’s Law”
Tracer
Tracer
Tracer
Tracer
Tracer
Dv~R0.5
1
2
3
4
5
More?
FWHM of Various Tracers Shown
Observed Size
Gives overall state of ISM~magnetic virial equilibrium.
See Larson 1981; Myers & Goodman 1988 for examples.
Figure: Goodman et al. 1998
(Some of) the Original Evidence for
Coherence
TMC-1C, OH 1667 MHz
TMC-1C, NH3 ( 1, 1)
Dv intrinsic =(0.25±0.02)T
1
-0.10±0.05
A
1
9
8
8
7
7
D v intrinsic [km s
-1
D v [km s ]
-1
]
9
6
5
4
6
5
4
3
3
-0.6±0.1
Dv=(0.67±0.02)T A
2
3
4
5
6
7
8
9
2
1
TA [ K]
Goodman, Barranco, Wilner & Heyer 1998
2
6
7
8
9
2
3
0.1
4
5
6
7
8
9
1
TA [ K]
1
9
8
7
6
5
4
r3
Why Line
Strength
is a Proxy for
Size near a
Core
B1 (OH)
3
1
9
8
7
6
5
Goodman, Barranco, Wilner & Heyer 1998
r2
Antenna Temperature [K]
r1
4
3
TMC-1C (OH)
1
9
8
7
6
5
4
3
Peak (r 1)
Half-Power (r 2)
10% (r3)
L1251A (C
2
3
4 5 6
18
2
O)
3
4 5 6
0.1
Size of Contour [pc]
2
1
Line width-Size Relations
Non-thermal Line Width
“Type 4:” Single Cloud Observed in a Single Tracer
Type 4
Type 4
Observed Size
Gives information on power spectrum of velocity fluctuations.
See Barranco & Goodman 1998; Goodman, Barranco, Heyer & Wilner 1998.
Better Evidence for Coherence
1
1
9
1
9
IRAM 30-m C
8
17
O (1-0)
9
IRAM 30-m C
8
18
O (2-1)
6
6
-1
5
-1
5
Dv [km s
4
Dv [km s
-1
Dv [km s
4
4
3
3
2
2
3
4
5
6
7
8
9
4x10
1
TA [ K]
5
2
7
7
6
6
-1
5
-1
5
4
Dv [km s
Dv [km s
4
4
3
3
2
-1
3
4
5
6
6
8 9
2
3
4
5
6
7
8 9
2
1
TA [ K]
0.1
TA [ K]
"Radius" f rom Peak [ pc]
1
0.1
0.01
3
2
9
8
8
7
6
5
4
A
]
Dv NT [km s
-1
]
-1
4
3
TMC-1C, OH 1667 M Hz
-0.7±0.2
Dv NT=(0.64±0.05)T
A
2
2
2
5
Dv NT [km s
]
-1
Dv NT [km s
3
"Radius" f rom Peak [ pc]
3
6
6
4
-1
-0.11±0.07
Dv NT=(0.20±0.02)T
7
7
8
2x10
TMC-1C, NH3 ( 1, 1)
9
9
3
4
5
6
7
8
9
2
1
TA [ K]
3
6
7
8
9
FCRAO
C34C34SS(2-1)
(2-1)
FCRAO
TA [ K]
"Radius" f rom Peak [ pc]
0.1
1
1
8
2
7
0.1
10
7
3
2
2x10
5
8
7
Dv [km s
-1
5
]
6
6
9
FCRAO C O (1-0)
8
5
1
]
8
4
1
18
FCRAOC
C17
OO
(1-0)(1-0)
FCRAO
3
TA [ K]
9
17
S (2-1)
2
6
1
9
]
0
TA [ K]
1
34
3
Type 4 slope
appears to
decrease with
density, as predicted.
2
C
]
6
]
7
]
7
5
IRAM 30-m
8
7
9
2
3
0.1
Goodman, Barranco, Heyer & Wilner 1998
4
5
6
7
8
9
1
TA [ K]
TA [ K]
3
4
The Latest Evidence for Coherence
N2H+: Coherence in the Ionized Gas
TMC-1C
0.7
N2H+ FCRAO
200
0.6
0.4
0.5
0.35
0.35
0.5
0.45
0.4
-1
0.3
Dv [km s ]
100
0.45
0.5
0
0.4
0.3
0.5
0.4
0.35
0.3
0.2
-100
+
N2H Thermal Width
0.1
0.1
100
0
-100
-200
-300
0.2
0.3
0.4
0.5
TA [K]
Goodman, Arce, Caselli, Heyer, Williams & Wilner 1999
0.6
0.7
Types of Line width-Size Relations
Non-thermal Line Width
“Type 3:” Single Cloud Observed in Multiple Tracers
Density
Observed Size
Types of Line width-Size Relations
Non-thermal Line Width
“Type 3:” Single Cloud Observed in Multiple Tracers
0
Observed Size
Gives pressure structure of an individual cloud.
See Fuller & Myers 1992.
“Coherence” in Spatial Distribution of Stars
10
-4
10
Size-2[pc]
-3
10
10
-1
Ro
10
0
1
8
9
8
6
5
4
3
4
sNT [km s-1]
Coherent
6
Turbulent
log Sc(q) [stars/sq. deg]
7
2
2
Parameterized Line Width-Size Relation
0.1
-5
-4
-3
-2
-1
0
log q [deg]
Goodman et al. 1998
Larson 1995; see also Gomez et al. 1993; Simon 1997
Coherent Dense Core
~0.1 pc
(in Taurus)
Coherent Core; N~R0.9
“Chaff”; N~R0.1
Timescales
8
7
6
5
4
10,000 yr
100,000 yr
GMC’s
1 Myr
3
Velocity [km/s]
2
1
9
8
7
6
5
4
3
2
0.1
0.01
100 Myr
10 Myr
Cores
0.1
1
Size Scale [pc]
10
100
Ingredients for a Coherent
Core
RECALL...
“Ingredients:

Molecular Gas (well-

Magnetic Field
Gravity
Optional: Pressure
Cooker (e.g. nearby

chilled, lightly-ionized)


supernova)”

What combination of
molecules?
How well chilled?
How lightly ionized?
How strong a field?
How much gravity
(mass)?
Effects of external
pressure?
Strong vs. Weak B-Field
b=0.01
Stone, Gammie & Ostriker 1999
[T / 10 K]
b=[
2
-3
nH / 100 cm ][ B / 1.4 mG]
2
b=1
•Driven Turbulence; M K; no gravity
•Colors: log density
•Computational volume: 2563
•Dark blue lines: B-field
•Red : isosurface of passive contaminant after saturation
The Superstore
Learning More from “Too Much” Data
1950
10
pixels
10
10
10
10
1980
1990
2000
8
Product
10
7
4
6
10
5
3
N channels
4
S/N
10
N pixels
10
3
2
1
2
10
1950
1960
1970
1980
Year
1990
2000
0
Npixels
(S/N)*N
10
1970
Nchannels, S/N in 1 hour,
*N channels
10
1960
The Spectral Correlation Function
Figure from Falgarone et al. 1994 Simulation
How the SCF Works

Measures
similarity of
neighboring
spectra within a
specified “beam”
size


lag & scaling
adjustable
signal-to-noise
accounted for
See: Rosolowsky, Goodman,
Wilner & Williams 1999; Padoan,
Rosolowsky & Goodman 1999.
Goals of “SCF” Project






Develop “sharp tool” for statistical analysis of ISM,
using as much data of a data cube as possible
Compare information from this tool with other tools (e.g
CLUMPFIND, GAUSSCLUMPS, ACF, Wavelets),
applied to same cubes
Incorporate continuum information
Use best suite of tools to compare “real” & “simulated”
ISM
Adjust simulations to match, understanding physical
inputs
Develop a prescription for finding star-forming gas
Antenna Temperature Map
greyscale: TA=0.04 to 0. 3 K
“Raw” SCF Map
Application
of the
“Raw” SCF
Data shown: C18O map of Rosette,
courtesy M. Heyer et al.
greyscale: while=low correlation; black=high
Results: Rosolowsky, Padoan
& Goodman 1999
Antenna Temperature Map
greyscale: TA=0.04 to 0. 3 K
“Normalized” SCF Map
Application
of the SCF
Data shown: C18O map of Rosette,
courtesy M. Heyer et al.
greyscale: while=low correlation; black=high
Results: Rosolowsky, Padoan
& Goodman 1999
SCF Distributions
Original Data
Randomized Positions
Normalized C18O Data for
Rosette Molecular Cloud
Unbound High-Latitude Cloud
Self-Gravitating, Star-Forming
Region
Preliminary
Insights from
the SCF
Rosolowsky,
Goodman, Williams
& Wilner 1999
No gravity, No B field
No gravity, Yes B field
Yes gravity, Yes B field
Can the SCF describe gas
physically?
Increasing Similarity of Spectra to Neighbors
0.8
Rosette C 18O
0.6
Rosette
13CO
Rosette
13CO
Peaks
HCl2 C 18O
0.4
Rosette C 18O Peaks
G,O,S
0.2
MacLow et al.
HCl2 C 18O Peaks
Increasing Similarity of ALL Spectra in Map
Change in Mean SCF with Randomization
1.0
Falgarone et al.
0.0
0.0
0.2
0.4
0.6
Mean SCF Value
see Padoan, Rosolowsky & Goodman 1999
0.8
1.0
1.2
Q. Can the SCF find Star-Forming
Gas?
A. Empirically, but that’s not good enough.
Helping the SCF
 Physical
training? Incorporate “coherence”
ideas
 Add CONTINUUM information
"Continuum" Information
Motte, André & Neri 1998
A very busy
kitchen.
MHD Waves
Infall
Outflows
MHD Turbulence
SNe/GRB
H II Regions
Thermal
Motions
A very busy
kitchen.
Next Time: The Effects of pc-Scale Outflows
Héctor Arce
A(G’s) Recipe for (z=0) Star
Formation
Ingredients:
Molecular Gas (well-chilled, lightly-ionized)
Magnetic Field
Gravity
Optional: Pressure Cooker (e.g. nearby
supernova)
A(G’s) Recipe for (z=0) Star
Formation
Steps:
1. Allow gravity to form “molecular clouds” (watch
out for turbulence, clouds might take a while to form…or use
pressure-cooker to speed up the process)
2. Allow turbulent cascade to form in molecular
cloud (be careful with the B-field)
3. Let magnetic turbulence & support decay
enough for “dense cores” to form in molecular
clouds (be careful to watch for core-core interactions &
outflows)
4. Watch dense cores slowly collapse, until one (or
several?) Kelvin-Helmholtz-radiating protostar(s)
form(s) near the center
A(G’s) Recipe for (z=0) Star
Formation
Steps:
1. Allow gravity to form “molecular clouds” (watch
out for turbulence, clouds might take a while to form…or use
pressure-cooker to speed up the process)
2. Allow turbulent cascade to form in molecular
cloud (be careful with the B-field)
3. Let magnetic turbulence & support decay
enough for “dense cores” to form in molecular
clouds (be careful to watch for core-core interactions &
outflows)
4. Watch dense cores slowly collapse, until one (or
several?) Kelvin-Helmholtz-radiating protostar(s)
form(s) near the center
A(G’s) Recipe for (z=0) Star
Formation
This Recipe Makes:
At least one, and sometimes many, stars.
(Notes: Industrial-strength recipe, available from R. Kennicutt et
al. makes the IMF.)
“Residual” dusty disks around stars, which
often form planets.
A big mess--much of which is recyclable,
given enough time.
A Recipe
for Star
Formation
Alyssa A. Goodman
Department of Astronomy
Harvard University