interstellar gas & star formationkdouglass/classes/ast142/lectures/14_lecture.pdfinterstellar...

Interstellar Gas &Star Formation

Interstellar Atoms and MoleculesMolecular Clouds

Gravitational CollapseFree-Fall Timescale

Pre-MS stars and the Hayashi Track

March 5, 2020

University of Rochester

Interstellar gas & Star formation

Topics:I Interstellar atoms and moleculesI Molecular clouds and gravitational

stabilityI Collapse of a spherical cloud: free-fall

timeI Synopsis of star formationI The initial mass functionI Formation of protostellar disks and jetsI Pre-MS stars and the Hayashi track

Reading: Kutner Ch. 15, Ryden Sec. 17.1

March 5, 2020 (UR) Astronomy 142 | Spring 2020 2 / 34

Ionizing gas in the interstellar medium

When an atom absorbs a photon with energy greater than the ionization potential for itselectron(s), the electron will be stripped from the atom. Photoionization results in thenow free electron having a kinetic energy equal to the energy difference of the incomingphoton and the ionization potential.

Collisional ionization can also occur, when a free electron with total kinetic energy greaterthan the ionization potential collides with the atom. The final speeds of the two freeelectrons is based on conservation of energy and momentum.

Free electrons can be captured by the ions, with a photon carrying away the excessenergy. Recombination can result in the electron being located in any of the availableenergy states (ground or excited).


Kirchoff’s Laws of Spectroscopy


Evidence for interstellar gas

Apparent through spectral lines seen in absorption against stars or in emission elsewhere.

“Nebulae:” hydrogen emission lines, plus a variety of other bright lines not readilyidentifiable in the laboratory.I Bowen 1928: extra lines are mostly forbidden lines in the spectrum of the ions,

mostly neutral, singly or doubly ionized, of the more abundant elements:I Oxygen (O/H ≈ 7× 10−4)I Nitrogen (N/H ≈ 1× 10−4)I Carbon (C/H ≈ 3× 10−4)

It was obvious right away that the lines must originate in very low density diffusematerial, which is difficult to reproduce in labs on Earth. Best vacuum on Earth is now∼ 103 cm−3; in space ∼ 0.1− 1 cm−3.


http://adsabs.harvard.edu/abs/1928ApJ....67....1B

Forbidden lines

What are forbidden lines? And how can we see them if they are forbidden? In short, theterm is a bit of a misnomer.I Atomic and molecular transitions are governed by selection rules that tell us what

changes in quantum states are allowed during the transition. The selection rules aredetermined by the physical process governing the transition.

I But we approximate these interactions to varying degrees of accuracy, with thelowest-accuracy (“first-order”) effects dominating and then sub-dominant“higher-order” effects added as corrections.

I Selection rules that apply to first-order effects may forbid certain transitions, but thehigher-order interactions may allow the transitions (albeit at low rates). These are the“forbidden transitions” which produce forbidden lines.


https://en.wikipedia.org/wiki/Selection_rule

Planetary Nebula NGC 7662 & its visible spectrumNGC 7662: the Snowball Nebula (or “Blue Snowball Nebula”)

Almost all of the emission is in the form of spectral lines: H and He recombination linesand forbidden lines of heavier elements.

Color image taken at Mees Observatory in AST 111. Visible spectrum from Pic du Midi Observatory.


http://www.astrosurf.com/buil/us/mission2/mission2.htm

Role of interstellar gas in the galaxy

Interstellar gas is the reservoir of material for star formation and star death.I Stars form by gravitational collapse of interstellar clouds.

I Dying stars return fusion-processed material to the ISM, enriching it in heavierelements and providing material for new stars.

Many properties of interstellar gas clouds are measurable with high precision: densitytemperature, pressure, elemental/molecular abundance, etc.I For the purpose of studying galactic structure, dynamics, and evolution, the gas in

the ISM is a useful complement to the information available from stars.


Milky Way stars, dust, and interstellar gasStarlight, extinction

Starlight

Dust (emission)

Molecular gas

Neutral atomic gas


The components of the ISM

Diffuse ISM neutral atomic clouds embedded inionized medium

Dense ISM neutral molecular clouds

Ionized nebulae HII regions, planetary nebulae,SN remnants

H II region NGC 604 in Triangulum (NASA/HST).


The components of the ISMDiffuse ISM

Diffuse ISM: clouds of mass 103 − 106M�, 10− 100 pc in size, 10− 104 K in temperature.I Mostly neutral atomic material embedded in a much less dense and very hot

(> 105 K) ionized medium.

I Mostly in the form of dark clouds with nH = 0.1− 10 cm−3 and T = 10− 100 K.

I Dark because the extinction by dust they contain can be as high as AV ∼ 3.

I The neutral diffuse ISM fills 40%–80% of the volume of the Milky Way.

I There is about 109 − 1010M� of neutral diffuse ISM in the Galaxy!

I Spectral line tracers: HI 21 cm line; C+ line at 157.7 µm.


The components of the ISMDense ISM

Dense ISM: H neutral and mostly molecular instead of atomic, in the form of clouds withdensities nH2 = 10− 106 cm−3. Temperature is 10− 100 K, mass is 103 − 106M�.I As much mass (total in Galaxy) as the diffuse ISM, 109 − 1010M� but volume is small

in comparison.

I Molecular cloud complexes are usually physically connected to complexes of diffuseatomic clouds.

I The visual extinction through a molecular cloud is� 1.

I Best spectra line tracers are rotational lines of CO. H2 radiates too poorly and isexcited too inefficiently to be an effective tracer.

I 180 molecular species have been detected so far in interstellar clouds. Smallestmolecule: H2; largest: C70 fullerene.

I See Al Wootten’s list of reported ISM molecules at NRAO


http://www.cv.nrao.edu/~awootten/allmols.html

The components of the ISMIonized nebulae

Ionized Nebulae include HII regions, planetary nebulae, and supernova remnants.

I Hydrogen is fully ionized in ionized nebulae; other elements may be multiplyionized.

I These objects have negligible mass on the galactic scale but they are very bright atvisible and radio wavelengths.

I They are the most easily noticed components of the ISM.

I Spectral line tracers: hydrogen recombination lines, “forbidden” lines of relativelyabundant ions and atoms (C, N, O, etc.).

I Electron densities are usually around ne = 10− 104 cm−3. Temperatures are about104 K in HII regions and planetary nebulae.


The components of the ISMIonized nebulae

Planetary nebulae consist of gas ejected and ionized by stars with core masses below theSAC mass that are becoming white dwarfs.

HII regions are associated with young, massive O-type stars in star forming regions.I They always seem to occur on the edges of giant molecular cloud

complexes. The Orion clouds are the nearest and best example.

Supernova remnants are what their name implies. Their ionization traces the advance ofthe blast wave into the ISM rather than photoionization by UV starlight.I The matter in SNRs tends to be in lower ionization states than in HII

regions and planetary nebulae.


Heating and cooling of the ISMHII regions and planetary nebulae

Heating Photoionization by starlight; UV light with E > 13.6 eV ionizes hydrogen,imparting kinetic energy to the electrons produced.

Cooling Collisional excitation followed by emission of forbidden lines by ions of C,N, and O (mostly). The more metals, the more efficiently the cooling.

EAtomicenergylevels

e -atominelasticcollision

hn


Heating and cooling of the ISMNeutral, Diffuse ISM

Heating UV light (hν = 5− 13 eV) in background starlight, known as the interstellarradiation field (ISRF).I Heating occurs via the photoelectric effect on dust grains.I Carbon can be ionized by E = hν = 11 eV photons and thus is usually

singly ionized (C II) in the diffuse ISM even when hydrogen is neutraland atomic.

Cooling Excitation of excited carbon (CII) by collisions with H atoms and electrons,followed by radiation in the forbidden 157.7 µm line.


Heating and cooling of the ISMMolecular Clouds

Heating Not well understood, but we know it cannot be starlight directly. Bestcandidates:Turbulence driven by stellar winds and outflows.Cosmic rays ions accelerated to 1015 eV in supernova remnants.

Cooling Collisional excitation followed by radiation in the rotational lines of themore abundant molecules like CO, OH, H2O.

I Molecular clouds are frequently dense and cold enough to be unstable and collapseunder their own weight.

I As we will see, the gravitational instability of molecular clouds is the principalmeans by which stars are formed in the galaxy.


Molecular clouds: Internal structure

I Molecular clouds are clumpy; they tend to consist of denser clumps in a range ofsizes and masses, blending into a less-dense background.

I Molecular clouds are cold; they tend to have T < 20 K.

I Molecular clouds are turbulent: the random internal velocities are typically∼ 1 km/s, much larger than the average molecular speeds in a quiescent gas inequilibrium at the same temperature.

I Molecular clouds (and clumps) generally rotate slowly.

I Molecular clouds are magnetized: they are threaded by the same magnetic fluxpresent when the material was diffuse and atomic. Now it has been compressed to amuch smaller size, and the fields are correspondingly larger.


Molecular clouds & star formation

As a result:I Clumps get massive enough and cold enough that the gas pressure cannot hold up

their weight, and they collapse.I As clumps collapse they heat in their cores.I If they are sufficiently massive and collapse to a small enough scale, temperatures can

reach the fusion ignition point and a star is formed.

I The clumps are constantly being rearranged, compressed, or distended byturbulence.

I Collapse does not happen with spherical symmetry; often collapse is easier along theaxis of rotation because of centrifugal forces.


Collapse of a clump: the Jeans massConsider a constant-density clump and its central pressure:

Pc ≈GM2

R4 from weight

=ρkTµ

from ideal gas law

Balancing the pressure gives

GM2

R4 = ρGMR

=ρkTµ

=⇒ MR

=kTµG

and assuming the mass is uniformly distributed gives

ρ =3M

4πR3 =⇒ R =

(3M4πρ

)1/3

∴ M =kTµG

(3

4πρ

)1/3

M1/3 =⇒ M =

(kTµG

)3/2 ( 34πρ

)1/2


Collapse of a clump: the Jeans massDefine the Jeans mass MJ as the critical mass for collapse:

M =

(kTµG

)3/2 ( 34πρ

)1/2

If a clump’s mass exceeds the Jeans mass for its density, temperature, and composition, itwill collapse under its weight.

Example: A pure molecular Hydrogen cloudFor a cloud of H2:

µ = 3.3× 10−24 gT = 20 K

n = 1.4× 105 cm−3

∴ MJ = 1M�


Time scale of spherical gravitational collapse

For spherically symmetric collapse, in free fall, we will see that

tff =

√3π

32Gρ0ρ0 = µn = initial mass density

= 1012 s = 30 kyr

for ρ0 = 4.7× 10−19 g/cm3.I This is very fast by astrophysical standards. We should therefore have to get very

lucky to catch a star in the act of formation.

I The result applies to a spherically symmetric collapse, and we know the collapsecannot really be very spherical (as angular momentum is conserved) so this is offeredonly as a crude estimate.


Spherical free-fall time: Derivation

Follow a test particle that starts from rest at distance r0 from the center of the cloud attime t = 0. How long until it reaches the center, i.e., until the clump collapses to a point?

F = ma

−GMmr2 = m

d2rdt2

This is a 1D, nonlinear 2nd-order differential equation. M is the mass interior to r and isconstant. Multiplying both sides by dr

dt and integrate over t:

∫ t

0dt′

drdt′

d2rdt′2

= −GM∫ t

0

1r2

drdt′

dt′

Note that v = drdt and dv = d2r

dt2 dt and start solving.


Spherical free-fall time: Derivation∫ t

0

drdt′

d2rdt′2

dt′ = −GM∫ t

0

1r2

drdt′

dt′∫ v

0v′ dv′ = −GM

∫ r

r0

dr′

r′2

12

v2 =GM

r− GM

r0

Substitute back v = drdt :

12

(drdt

)2

=GM

r− GM

r0

drdt

= −

√2GM

r− 2GM

r0

choosing the negative root so that the particle moves to smaller r.March 5, 2020 (UR) Astronomy 142 | Spring 2020 24 / 34

Spherical free-fall time: DerivationNow insert M = 4π

3 r30ρ0:

drdt

= −r0

√8πGρ0

3

( r0

r− 1)

Make a geometric u substitution r = r0 cos2 u:

drdt

= r0ddt

cos2 u = −2r0 cos u sin ududt

=⇒ dudt

=1

2 cos u sin u

√8πGρ0

3

(1

cos2 u− 1)

=1

2 cos2 u sin u

√8πGρ0

3(1− cos2 u)

=1

2 cos2 u

√8πGρ0

3


Spherical free-fall time: DerivationSeparate variables and integrate:∫ u

u0

cos2 u′du′ =12

√8πGρ0

3

∫ tff

0dt where

t = 0 : r = r0 r0 = r0 cos2 u0 =⇒ u0 = 0

t = tff : r = 0 0 = r0 cos2 u0 =⇒ u0 =π

2

=⇒∫ π/2

0cos2 u′du′ =

12

∫ π/2

0

[1 + cos 2u′

]du′ =

12

√8πGρ0

3

∫ tff

0dt[

u2+

sin 2u4

]π/2

0=

π

4=

tff

2

√8πGρ0

3

tff =

√3π

32Gρ0


Typical timescales

The number densities in the cores of molecular clouds can be quite large, of ordernmc = 106 cm−3.

If the gas is pure molecular hydrogen, then the typical density in the ISM is

ρ0 = µn = 2mpnmc ≈ 3× 10−18g/cm3

Plugging into the expression for the free-fall time gives a convenient expression in termsof these units:

tff =

√3π

32Gρ0= 40 kyr

(ρ0

3× 10−18 g/cm3

)−1/2

Question: If the Galaxy is ∼10 Gyr old and molecular clouds can collapse on such shorttimescales, why are any molecular clouds left?


Star formation synopsis

Molecular clump collapses gravitationally:I To a disk shape at first

I Collapse along the other two dimensions happens more slowly because of a rotation(angular momentum) and, possibly and to a lesser extent, magnetic forces

I Smaller scales — higher density regions — collapse faster (“inside-out collapse”)

I Central “core” gradually accretes some of the rest of the disk

I A bipolar outflow helps to get rid of the last of the accreted material’s angularmomentum.

The core becomes a star, and the remnants of the disk become a planetary system.


The initial mass function

The initial mass distribution is an empiricalfunction describing the distribution of stellarmasses that will form from a singlemolecular cloud.

Observations of numerous young stellarclusters reveal that their stellar massdistributions are nearly identical (theprimary difference due to the cluster’s age).


Bipolar jets and disks associated with young stars


Star formationThe outflows are supersonic (w.r.t. the molecular surroundings) and thus shocks aredriven into the ambient medium. The energy and momentum injected contributes to thesupport of the molecular cloud and can induce or hinder further star formation in theneighborhood.

L1641 VLA1/HH1-2 (Bally et al. 2002):


http://adsabs.harvard.edu/abs/2002AJ....123.2627B

Pre-Main Sequence stars

The young stars themselves are relativelyunextinguished at visible wavelengths unless thedisk is viewed edge-on; they have twodistinctive features:I The spectra show emission lines, notably

hydrogen recombination lines, and UVexcess emission, both produced in accretionshocks in material falling onto the star fromthe disk.

I Spectral type G/K/M: T Tauri stars. Earliertypes: Herbig Ae/Be stars.



I It takes lower-mass young stars millions of years to settle down to their final sizesand get fusion running.

I During this slow gravitational collapse, the conversion of gravitational potentialenergy dominates the luminosity of young stars. Recall that gravitationally-drivenluminosity is

L = −35

GM2

R2dRdt

I The gravitational collapse luminosity decreases with time and the star’s effectivetemperature changes little while this is going on. So the young star descends almostvertically at first through the H-R diagram. This path is called the Hayashi track.


https://en.wikipedia.org/wiki/Hayashi_track


I The Hayashi track happens to be the reverse ofthe path each star would take at the end of its lifeas it becomes a red giant.

I For a given age, the redder (lower mass, laterspectral type) stars lie further above the mainsequence than the bluer ones.

Right: T Tauri tracks (Stahler 1988). The Main Sequence is shown bythe diagonal line.


http://adsabs.harvard.edu/abs/1988PASP..100.1474S

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