dusty dark nebulae and the origin of stellar masses colloquium: stsci april 08

Dusty Dark Nebulae and the Origin of Stellar Masses

Colloquium: STScI April 08

The Unsolved Problem of Star Formation

Boundary Conditions & Initial Conditions

Dusty Dark Nebulae and the Origin of Stellar Masses


BOUNDARY CONDITIONS


Compositions, Luminosities, Temperatures, Sizes, & Masses

BOUNDARY CONDITIONS


Compositions, Luminosities, Temperatures, Sizes, & Masses

Once formed, the entire life history of a star is essentially predetermined by a single parameter: the star’s initial mass.

The IMF (the frequency distribution of stellar masses at birth) plays a pivotal role in the evolution of all stellar systems from clusters to galaxies.

BOUNDARY CONDITIONS

The Initial Mass Function (IMF) = first fundamental boundary condition


HBL DBL

Com

ple

teness

lim

itBrown Dwarfs

Sun

The IMF exhibits a broad peak between 0.6 and 0.1 M suggesting a characteristic mass associated with the star formation process.

Brown Dwarfs account for only 1 in 5 objects in IMF!

Fundamental Boundary Conditions

Muench et al. 20021- The Initial Mass Function (IMF)

2- Stellar Multiplicity

Most (~70%) stars are single!

Beichman & Tanner

Multiplicity is a function of stellar mass

Lada 2006

Fundamental Boundary Conditions

INITIAL CONDITIONS

Stars form in Dense, Dark Cloud Cores

Initial Conditions = Basic physical properties of starless cores:

mass, size, temperature density, pressure, kinematics

The Team Members:

Harvard-Smithsonian CfA:

Charles Lada Gus MuenchJill Rathborne

Calar Alto Observatory:

Joao Alves Carlos Roman-Zuniga

European Southern Observatory:

Marco Lombardi

Basic Properties of the Pipe Cloud:

Distance: 130 pc

Mass: 104 M

SIze: ~3 x 14 pc

Star Formation Activity: Insignificant

The Pipe Nebula Project

Alex Mellinger

Extinction and the Identification and basic properties of dense cores.

INITIAL CONDITIONS:

Seeing the Light Through the Dark

Core Maps after wavelet decompositionRAW Wavelet Decomposed

Distribution of core masses (159 cores)

Alves, Lombardi, Lada 2007

Alves, Lombardi, Lada 2007

Stars

Distribution of core masses

Probability Density Function for the Pipe Core Mass Function

Pipe CMF

IMFs x 3.3

Alves, Lombardi & Lada 2007

Star Formation Efficiency is the Key

The IMF derives directly from the CMF after modification by a constant SFE

Mean Core Densities

Median Core Density = 7000 cm-3

Lada et al. 2007

Mass – Radius Relation

Constant Column Density:M ~ R2 (Larson’s Laws)

Radio Molecular Lines and the Nature of the Cores

stem = 0.26 km/s

Core to Core Velocity Dispersion (C18O)

bowl = 0.28 km/s

Muench et al. 2007

Rathborne et al. 2007

NH3 Line Survey

NH3 detections indicate n(H2) > 104 cm-3

Rathborne et al. 2007

NH3 Line Survey

NH3 detections indicate n(H2) > 104 cm-3

Radially Stratified Cores

Subsonic

Supersonic

NT (

km/s

)

Dense cores are thermally supported!

Such cores must evolve on ACOUSTIC timescales!!

B 68: Radial Density Profile

max = 6.9 0.2

Critical Bonnor-Ebert Sphere

e

d

d

d

d 22

1

0.18 km/s

Pthermal / PNT ~ 10-14!!

Barnard 68 is a thermally supported Cloud!

Broderick, Keto, Lada & Narayan, 2007

B68 Surface Velocity FIeld

100 50 0 -50

RA OFFSET (arc sec)

-100

-50

0

DE

C O

FF

SET

(arc

sec

)

V(CS - C18O)

B68

Core Pulsation

2 GP

Ptotal = Pthermal + PNT

ISM

Core structure is set by the requirement of pressureequilibrium with external medium!

Core structure is set by the requirement of pressureequilibrium with external medium!

Lada et al. 2007

Pressure and the Origin of CoreMasses: From CMF to IMF

The BE Critical Mass corresponds approximately to the characteristic mass of the core mass function!

Origin of Cores:Thermal Fragmentation in a Pressurized Medium

Non-equilibrium

Equilibrium

MBE = 1.15 (ns)-0.5 T1.5 (solar masses)

IC 348

TaurusLuhman 2004

Luhman et al. 2003

P/k ~ 105

P/k ~ 106

From CMF to IMF: Setting the Mass Scale of the IMF

The effect of increasing External Pressure

mBE = C x a4 (Psurface) -0.5

IC 348

TaurusLuhman 2004

Luhman et al. 2003

P/k ~ 105

Pinternal = Pthermal + PNT + B2/8π

The effect of decreasing internal Pressure

x 2

mBE = C x a4 (Psurface) -0.5

From CMF to IMF: Setting the Mass Scale of the IMF

(aeffective)2 = Pinternal

High Pressure Regions: Embedded Cluster Cores

P/k ~ 106 –107 K cm-3

Multiplicity increases with stellar mass

Mul

tiple

Sta

rs

Single Stars

Fundamental Boundary Condition #2: Stellar Multiplicity

ORIGIN OF THE IMF:

**mBE = Constant x a4 (Psurface) -0.5 Bonnor-Ebert Mass Scale

- CMF{logm} = c1 (log{m/m0}, si); m0= mBE

**

IMF{logm} = c2 (log{m/m0}, sk); m0=SFE mBE

ORIGIN OF THE IMF:

**mBE = Constant x a4 (Psurface) -0.5 Bonnor-Ebert Mass Scale


**


Yield = Mdg x SFE = b(t) x Δt

Mdg = mass of dense gas (n>104)

b(t) = stellar birthrate

What determines the Star Formation Rate?

(E. Lada 1991)

Most stars form in clusters

Stars form exclusively in dense (n > 104 cm-3) gas


Lombardi, Lada & Alves 2008


On GMC scales, the amount of gas (MDG) at high density (>104 cm-3) and high extinction (AV > 6-10 mag; gas > 100 M pc-2)

SFR = SF MDG /SF

Conjecture:

SFR ~ MDG

SF = ff ~ (G )-1/2

for n = 104 cm-3:

ff = 3 x 105 yrs = constant



SFR = SF MDG /SF if SF ~ (G )-1/2 then SFR ~ 3/2

Conjecture:

Gao & Solomon 2004

SFR ~ MDG


if SF ~ (G )-1/2 then SFR ~ 3/2

Conjecture:

SFR = A (gas )1.6

Kennicutt 1998

Schmidt-Kennicutt Law


DG ~ (gas)1.6On the other hand:


Conjecture:

SFR = A (gas )1.6

Kennicutt 1998


Pgas~ <> (aeff)2



Conjecture:

SFR = A (gas )1.6

Kennicutt 1998


Pgas~ G (gas)2

SFR ~ (Pgas )n ; n = ¾ (?)


Conclusions:

1- Distribution of core masses similar to stellar IMF but shifted to higher masses by factor of 3-4.

2- SFE ≈ 25-30%

3- Cores are DENSE CORES

4- Cores are THERMALLY supported

5- Cores are PRESSURE CONFINED: Psurface = Pexternal

6- BE mass CMF characteristic mass:

thermal fragmentation under PRESSURE

ORIGIN OF THE IMF:

**mBE = Constant x a4 (Pexternal) -0.5 Bonnor-Ebert Mass Scale

The IMF produced in a star forming event may be determined by only a fewvery basic physical parameters, e.g., Temperature and External Pressure.

The IMF produced in a star forming event may be determined by only a fewvery basic physical parameters, e.g., Temperature and External Pressure.


**


The End !

Pressure

Pressure !

Pressure

Three things to remember from this talk:

dusty dark nebulae and the origin of stellar masses colloquium: stsci april 08

Documents

stars initial mass

pipe core mass functionalves

kms core

core pulsationptotal

lombardi lada

characteristic mass

function of stellar

stellar systems