Interstellar Medium (ISM)

Hiroyuki Hirashita (平下 博之) ASIAA

1. ISM Composition/Phases 2. Interaction with Radiation 3. Multi-Phase ISM 4. Dynamical Processes 5. Summary

Topics

An ISM lecture needs one semester. We only briefly touch main topics and show some examples of numerical research (to motivate your further studies).

1. ISM Composition/Phases

Elemental Composition (Solar)Lodders (2010)

Metals/heavy elements

Metallicity

Hydrogenatomic hydrogen H I ionized hydrogen H II

ionization potential: E = 13.6 eV E = h(c/λ) → λ = 912 Å

H+e-H+

H+ H+e-

e-

molecular hydrogen H2

e-

Atomic Hydrogen (21 cm)

Ionized Gas (Hα; recombination lines)

H II regions ← mainly ionized by UV photons from OB stars ~ Recent star forming regions (star-formation tracer)

Finkbeiner (2003)

Hot Gas (X-Ray)

Diffuse hot gas (> 106 K) heated by supernovae, etc.

Molecular Gas (CO)

Dame et al. (2001)

Useful tracer of cold H2 gas: CO-to-H2 conversion factor XCO = NH2/WCO = 1.8 × 1020 cm-2 K-1 km-1 s (in the MW)

Dust

Lund Observatory

Optical (λ ~ 0.5 µm) Image of the Milky Way

Dark clouds in the Milky Way ← Dust extinction (= absorption + scattering)

Dust: Small particles most likely silicate and graphite, or something similar

Dust Emission in the Far InfraredAKARI 140 µm

Dust emission

2. Interaction with Radiation

Radiation Transfer

Definition of Intensity (energy flow on a line) 　　dE = Iν dA dt dΩ dν Iν [erg/cm2/s/sr/Hz]

dA

dΩ

n

dI⌫ds

= �⌫⇢I⌫ + j⌫

Radiation Transfer Equation

s

absorbing and emitting medium

Iν(s): intensity

Emission jν [erg/cm3/s/Hz]Absorption

κν [cm2/g]: mass absorption coefficient ρ [g/cm3]: density

Optical Depth

Optical depth: dτν = ρκνds ∝ “number of absorptions” τν >> 1: optically thick τν << 1: optically thin

dI⌫ds

= �⌫⇢I⌫ + j⌫

Sν = jν/(ρκν): source function Sν = Bν(T) (Planck function) for LTE

dI⌫d⌧⌫

= �I⌫ + S⌫

A Simple Solution

For a constant source function:

τν

absorbing and emitting medium

Iν(τν): intensityIν(0)

dI⌫d⌧⌫

= �I⌫ + S⌫

I⌫(⌧⌫) = I⌫(0)e�⌧⌫ + S⌫(1� e�⌧⌫ )

Extinction of bkg light Emission

Dust Extinction

Magnitude: mλ = –2.5 log Iλ + const. Extinction (= absorption + scattering): Aλ = mλ(s) – mλ(0) = 2.5[log Iλ(0)e –τλ –log Iλ(0)] = (2.5 log e) τλ

Iλ(0) Iλ(0)e –τλ

Extinction Curves

Pei (1992)

Grain size distribution n(a) ∝ a – 3.5

(Mathis et al. 1977)

amin = 0.005 µmamax = 0.25 µm

A λ/A

0.44

µm

shorter wavelength ↓ larger extinction

“Reddening”

Scicluna & Siebenmorgen (2015)

The “effective” extinction curve (attenuation curve) depends on the clumpiness.

Effects of Complicated Dust Distribution

Infrared Emission of Dust

Li & Draine (2001)

Large grains (LGs) Silicate + carbonaceous material

Excess by very small grains (VSGs)

Wavelength (µm)

Inte

nsity

Effects of UV Radiation

Orion Nebula (HST)

H II Region

NLyc =4⇡

3R3

Sn2�B

Number of Lyman continuum (> 13.6 eV) photons emitted per time.

Case B: Lyman series/continuum (transitions down to n = 1) are optically thick. Recombination rate to n >= 2 levels contributes to the loss of ionizing photons.RS: Strömgren radiusRS ' 1.2

⇣ n

103 cm�3

⌘�2/3

NLyc

5⇥ 1049 s�1

!1/3

pc

Photodissociation Region (PDR)

Tielens & Hollenbach (1985)

Field et al. (1966)

Lyman-Werner bandsDissociation

Abundant Line Emissions from PDRs

Bisbas et al. (2021)

3. Multi-Phase ISMMcKee & Ostriker (1977)

HeatingFormation of free electrons by radiation causes heating (energy transfer from radiation to gas).

Major heating mechanisms: Photoionization (H + γ → H+ + e-) Photoelectric emission (dust + γ → dust+ + e-)

e-

CoolingThermal energy is converted into radiation: ex.

nk

nj

nγjk nγkj Aul

n: number density of colliding species

Ejk

e- A A

A

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⇤ = nX

j<k

Ejk(nj�jk � nk�kj)

excited

Two-Phase Model of Neutral MediumWolfire et al. (1995)

Thermal equilibrium: Λ = Γ (cooling) = (heating)

Lyα line cooling ~ Photoelectric heating at low density (T ~ 104 K)

C II line cooling ~ Photoelectric heating at high density (T ~ 100 K)

Field et al. (1969)

ISM Structures in SimulationAoyama, Hirashita, et al. (2017)

Realistic structures are more dynamic, but we still see some characteristic features in the phase diagram.

Molecular Clouds

See Yueh-Ning’s talk for the processes leading to star formation.

Image courtesy of Nigel Sharp (NOAO), NSF

ESO

Various Tracers and Critical Densitynu

nl

nγlu nγul Aul

Statistical equilibrium: nlnγlu = nunγul + nuAul γlu = (gu/gl)γul exp(-Eul/kBT)

nu

nl=

gu/gl exp(�Eul/kBT )

1 + ncr/nncr ⌘

Aul

�ulCritical density

Critical density ~ Typical density which the line is suitable for tracing. Critical densities at 10 K: CO(1-0): 4×103 cm-3, CO(3-2): 7×104 cm-3 HCO+(1-0): 2×105 cm-3, HCO+(3-2) : 3×106 cm-3 HCN(1-0): 2×106 cm-3, HCN(3-2): 6×107 cm-3

n: number density of colliding species

4. Dynamical Processes

See Hung-Yi’s talk for hydrodynamic equations.

Characteristic ScalesFree-fall time: gravitational contraction tff ~ 1/(Gρ)1/2 Crossing time: hydrodynamic effects tcr ~ L/v v = cs = (γP/ρ)1/2 ∝ T1/2 (for sound wave) v = vA = (B2/4πρ)1/2 (for Alfvén wave) Cooling time: gas cooling tcool ~ kBT/nΛ Jeans length/mass (typical size/mass for gravitationally bound structures) λJ ~ cs tff ∝ (T/ρ)1/2 MJ ~ ρλJ3 ∝ T 3/2/ρ1/2 Estimate these quantities for the objects you like.

ShocksConservation laws in hydrodynamic equations:

ρ1 u1 → p1 T1

ρ2 u2 → p2 T2

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p1 + ⇢1u21 = p2 + ⇢2u

22

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u2

✓1

2⇢2u

22 + U2

◆� u1

✓1

2⇢1u

21 + U1

◆= u1p1 � u2p2

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U =1

1� �p

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p2p1

=2�

� + 1M2 � � � 1

� + 1

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u2

u1=

⇢1⇢2

=2

� + 1

1

M2+

� � 1

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M2 ⌘ ⇢1u21

�p1=

u21

C21

Mach number

Expansion of H II Region

ri

ionization frontShock

Conservation laws at the ionization front and shock front Constant ionization photon luminosity (ρII ∝ ri -3/2; see Strömgren radius)

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riri0

=

✓1 +

7

4

CIIt

ri0

◆4/7CII : Sound speed in the H II region ri0: initial radius of H II region (under ρII =ρI)

External Ionizing RadiationIliev, Hirashita, Ferrara (2006)

Ionizing radiation

Ionizing photons incident on a cloud could cause compression, inducing star formation, or evaporation, suppressing star formation.

Supernova Blast Wave

rs ~ (E/ρ1)1/5t2/5

Sedov solution

rs

ρ1Based on the pressure inside the SN remnant (described by E and rs), and assuming a strong shock, we obtain the relation Vs and rs (under a given ρ1.

See Yen-Chen’s talk for SN explosion.

Supernovae and Dust DestructionHu et al. (2019)

5. SummaryOverviewed the following processes in the ISM: (1) Radiation transfer. (2) Ionization and dissociation. (3) Heating and cooling. (4) Multi-phase ISM. (5) Dynamical processes (hydrodynamic treatment of the ISM).

Further Reading

• Spitzer, L. 1978, “Physical Processes in the Interstellar Medium” • Tielens, A. G. G. M. 2005, “The Physics and Chemistry of the Interstellar Medium”