Whittle : EXTRAGALACTIC ASTRONOMY

 
     
 

1 : Preliminaries	6 :   Dynamics I	11 : Star Formation	16 : Cosmology
2 : Morphology	7 :   Ellipticals	12 : Interactions	17 : Structure Growth
3 : Surveys	8 :   Dynamics II	13 : Groups & Clusters	18 : Galaxy Formation
4 : Lum. Functions	9 :   Gas & Dust	14 : Nuclei & BHs	19 : Reionization & IGM
5 : Spirals	10 : Populations	15 : AGNs & Quasars	20 : Dark Matter

(1) Galaxy ISMs : An Overview

• Like the Earth, galaxies have an atmosphere     a gaseous component held "down" by gravity
  this atmosphere fills the space between stars, hence:   interstellar medium (ISM)
  by mass, the ISM is usually not very important: M_ISM 1% M_stars
  The average midplane density is ~1 cm^-3     columns ~3×10²¹cm^-2/kpc (~0.005 gm cm^-2/kpc)
    galaxy disks have "thickness" 5 cm of Earth's atmosphere (~1 meter of air to the GC).

• The ISM contains: starlight; gas; dust; cosmic rays; magnetic fields
  Near the sun they all have similar energy density pressure   1 eV cm^-3

• The element mix is the usual: H/He/others:   74/24/2   (% by mass);   90/10/0.01   (% by number)
  Of the "others", ~10-50% have condensed out as solid particles: "dust".

• Despite its low mass, the ISM is ultimately very important, for several reasons:

  1. It plays a crucial role in the star gas cycle
     
     • in spirals and irregulars, it facilitates ongoing (& current) star formation
     • it is a repository for element buildup and is therefore integral to chemical evolution

  2. Because it can cool, its collapse is dissipational
     • stars can form !!     hot gas   cold gas   stars
       
     • new generations of stars "cool" spiral disks, allowing arm formation
       
     • globally, gas can migrate inwards to smaller radii:
         galaxies are smaller than dark matter halos !
         galaxies have steep density gradients
         galaxy nuclei can have very high densities, including an SMBH

  3. Being atomic/molecular, its emission & absorption provides enormous diagnostic information
     Some examples :
     
     • Doppler motions reveal galaxy dynamics
       
     • abundance measurements allow study of chemical evolution
       
     • physical conditions: density; temp; pressure; turbulence; columns; mass, can all be derived
       
     • some emission lines can be seen (relatively) easily at cosmological distances.
       
     • high redshift QSO absorption lines reveal halo & disk evolution.

  4. The ISM can dominate a galaxy's integrated SED (spectral energy distribution):
     starlight dominates the UV-NIR; but the ISM dominates outside this range.
     • Mid-IR to Sub-mm is dominated by emission from dust
       
     • Soft X-rays come from the hot ISM phase (though X ray binares can be important)
       
     • cm-radio comes either from HII regions or a relativistic magnetoionic plasma
       
     • certain emission lines (eg Ly; [CII]158µ) can be major coolants

• The ISM is energized primarily by stars (starlight, winds, supernovae)
    UV starlight photoionizes atoms & dissociates molecules; photo-ejected electrons heat gas
    SN shocks heat/ionize/accelerate gas & are largely responsible for the ISM's complexity.

• The ISM can be highly inhomogeneous, with several phases
  These phases are (roughly): hot/warm/cold, with low/medium/high density
  In a wide range of conditions these phases have similar pressures   P/k nT 10⁴ 1 eV cm^-3.
  However, in dynamic situations, pressure balance is no longer applicable.

  The ISM contains cloud and intercloud components with density contrast ~ 10²-10⁵
    these clouds are not like terrestrial clouds; more like blocks of wood or lead hanging in the air.

• The ISM is a dynamic environment, with mass exchange between phases
  
  • cooling facilitates: hot     warm     cold     stars.
    
  • supernovae inject energy which accelerates the gas and continuously rearranges the geometry
      e.g. a disk ISM will "boil" & "bubble" with gas cycling out & back above the disk.
  • sporadically, tidal encounters & their resulting starbursts can:
    • add fresh (low metallicity) gas
      
    • energize and evacuate large regions
      
    • cycle gas into the halo, some of which may return later.
      
    • radically alter the ISM, e.g. spiral + spiral     elliptical.

  As always, our current view is just one frame of a long and intricate movie.

• What about the distribution of ISM (particularly in spiral disks)?

  1. Globally the scale height depends on the phase's temperature/velocity dispersion and
       colder phases are confined closer to the plane
       hotter &/or more turbulent phases are thicker
       in disks, the ISM flares at large radii and is thinner at small radii).
     However, high local energy density can affect this distribution by driving vertical blow-out.

  2. Locally: the ISM is highly complex & "foamy"
     SN evacuate complex interconnected "superbubbles"
     between are sheets & clouds of denser colder gas.

• The Milky Way can act as a template for studying other galaxy ISMs
  As usual, the proximity of the MW's ISM offers important insights
  Hence, MW ISM studies are now extensive & comprise a major area within astronomy
  Here, we consider only the bare essentials, providing a framework for discussing ISM in other galaxies.

(2) ISM Components & Their Observational Signatures

While ultimately ISM gas spans all conditions, in practice much resides in one of several components
These components are distinguished by their phase (n,T,X_e) and their location
This figure and the following table summarize the major components:

Component	Temp K	Density midplane cm-3	Pressure nT K cm-3	Xe ionization	FF filling %	<h> thickness pc
Intercloud
Hot HII (HIM)	106	0.002	2000	1	50:	3000:
Warm HII (WIM)	8000	0.15	1200	1	20	1000
Warm HI (WNM)	8000	0.3:	2400	0.5	30:	500
Clouds
Cold HI (CNM)	120	25	3000	0.1	2	100
Cold H2 (CNM)	15	200	3000	10-4	0.1	75

Note that overall, the intercloud/cloud fraction by mass is ~50 : 50 but by volume it is ~98 : 2


• Three other important components add to the mix :
  1. Dust:   1nm - 1µm solid particles are found in essentially all phases
     ~50% heavy elements are in dust (~100% of the refractories)
     Dust is discussed more in section 8 (link)

  2. Magnetic fields:   generally a few µGauss in both ordered and random components
     energy density: B²/8 10^-12 erg cm^-3 1 eV cm^-3
     field compression in superbubble expansion effects on ISM structure (see below).

  3. Cosmic Rays:   relativistic electrons & protons, created in SN shocks
     these diffuse throughout the galaxy and permeate all phases (some even hit the earth)
     they are a primary heating source in DMC cores (which are otherwise shielded).
     the most energetic electrons + magnetic fields     radio synchrotron
     proton collisions with nuclei     diffuse gamma emission
     equipartition with B field likely, so suspect ~1 eV cm^-3

All observations involve either emission or absorption
these, in turn, depend on Emission Measure (EM) and column density (N)
• Emission processes are usually collisional, so are   n²
  surface brightness is therefore     <n²> dl   pc cm^-6     Emission Measure (EM).

• Absorption processes, in contrast, are     <n> dl   cm^-2     Column Density (N).

• For ionized gas, the relevant density is usually n_e
  The table shows EM & N_e for various systems:

  Medium	ne cm-3	Size pc	EM pc cm-6	Emission Visibility	Ne cm-2	Absorption Visibility
  Young Nova	107	10-3	1011	v. bright!	3 ×1022	thick
  PN	104	10-1	107	bright	3 ×1021	good
  HII Region	10	102	104	fine	3 ×1021	good
  Diffuse ISM	10-1	103	10	difficult	3 ×1020	good
  Halo	10-3	104	10-2	invisible	3 ×1019	fine

  Note, for a typical crossection ~ a_Bohr ~ 10^-16 cm^-2,   N ~ 10¹⁴ cm^-2 gives ~ 1%
  This is easily measurable with suitable background source
    low density gas invisible in emission can often be studied in absorption.

• Photoioniztion thresholds render the ISM highly opaque in the EUV:
  ionization potentials for H, He, He⁺ are 13.6, 24.6, 54.4 eV (= 91, 50, 25 nm)
  since _photo     (E-E_i)^-3, then:
  • the ISM is highly opaque in EUV (13.6 - 100 eV)
    
  • it is becoming transparent in soft X-ray (~0.6 keV)
    
  • it is completely transparent by 2 keV.

• A wide range of E transitions yield features at many wavelengths:

  Transition E eV	wavelength range	Cause
  10-6	21 cm	electron spin flip in atomic H
  10-2 - 10-3	FIR - mm	molecular rotation
  0.1 - 0.01	NIR - FIR	gas molecular vibration;   bond bending in dust
  0.03 - 0.003	MIR - sub-mm	phonons in dust @ T ~ 1000-10 K
  1 - 10	UV - NIR	outer shell electron transitions   in atoms and molecules
  10 - 103	EUV - X-ray	inner shell electron transition;   50 - 500 km s-1 post shock gas

  Note some useful conversions: E_eV 1240/_nm     T_K / 7740   per particle.
  so @ T 10⁵K,   H & He are fully ionized, and kT ~ EUV - soft X-ray

• This gas has T ~ 8000K and resides in:
  • star forming HII regions   (n_e ~ 1 - 100+ cm^-3)
  • diffuse ionized gas   (n_e ~ 0.01 - 1 cm^-3)

• In both cases, equilibrium occurs when:
  1. ionization rate = recombination rate   (ionization balance)
  2. heating = cooling   (thermal balance)
  ionization is from stellar UV photons;   recombination occurs naturally
  heating is from photo-ejected electrons;   cooling is via emission lines

• Note that in these circumstances the ionization degree does not reflect the temperature
  e.g. at 8000K,   O  O⁺  O²⁺ cannot occur by collisions (it is too cold)
  but a weak radiation field of 50 eV (250A) photons can ionize up to O²⁺.

  (i) Hydrogen Recombination Radiation

• electrons are captured by protons and the resulting cascade emits photons.
  the rate is n_en_p cm^-3 s^-1,   where is a recombination coefficient (units are cm³ s^-1).

• Usually, the gas is optically thick to Ly-, which is trapped (termed: case B)
  the total recombination rate is then _B = 4.52 & 2.58 × 10^-13 cm³s^-1 (for 5000 & 10,000 K)
  While for just H it is _H = 5.38 & 3.01 × 10^-14 cm³s^-1 (for 5000 & 10,000 K)
  

• The table gives some useful Hydrogen line wavelengths and relative strengths (Case B; T = 10⁴ K):

  Series (lower level)	wav ratio/H	wav ratio/H	wav ratio/H	wav ratio/H	Series Limit wav
  1:   Lyman	1216 Avac 23	1026 Avac ??	973 Avac ??	950 Avac ??	912 Avac
  2:   Balmer	6563 A 2.86	4861 A 1.00	4340 A 0.47	4101 A 0.26	3646 A
  3:   Paschen	1.87 µ 0.339	1.28 µ 0.163	1.09 µ 0.090	1.00 µ 0.055	0.82 µ
  4:   Brackett	4.05 µ 0.080	2.63 µ 0.045	2.16 µ 0.028	1.94 µ 0.018	1.45 µ

  Note that the Ly- flux is often difficult to predict:
  it is resonantly scattered and either:

  it is absorbed by dust, or
  the 2 1 transition goes via 2-photon decay

• Cascades between very high n (~100) give radio recombination lines
  e.g. H109 at 5.8cm comes from transitions n=109 108
  These lines are useful since they are unaffected by dust; though they are quite weak.

  (ii) Collisionally Excited Fine Structure Lines

(3) Theories of the Multi-Phase ISM

(4) Gas in Disk Galaxies

(5) Gas in Elliptical Galaxies

(6) Gas in Galactic Nuclei

(7) Gas in Galaxy Halos

(8) Dust: Particles in the ISM

• All ISM gas phases are optically transparent (or very nearly)
  However, the Milky Way shows patchy obscuration of background starlight (image)
  What causes this optical absorption?     solid particles with size a _light (nm - µm)
  Astronomers call these particles "dust", though a better word might be "smoke".

• By human standards, the ISM is exceedingly filthy.
  Imagine bringing the ISM to atmospheric number density (3 × 10¹⁹ cm^-3)
    it would be a thick smog with ~1 mag/meter   [~1 mag/inch at _air]   !!
    You could not see across a room   [your hand in front of your face]   !!
    Walking just a few paces, you'd be covered in an extremely fine black soot.
    This is a chain-smoker's heaven/nightmare: the smoke is rich in carcinogenic PAHs.

• Why is the ISM so dirty ?   Because stars are dirty furnaces.
  For 10 Gyr they've been "polluting" the ISM by making & blowing off heavy elements
  Typically, 10-50% of these elements condense as tiny solid particles: graphite/silicates/ices
    Our atmosphere is clear by comparison because it doesn't contain ~1% particulates.

• Dust has a huge impact on EM radiation, spanning 3 decades (~1000A - 100µm).
  It absorbs UV & optical but is transparent in the IR (grains have size ~_UV).
    important contributions have come from Copernicus, IUE, HST.
  It emits in the IR (since its equilibrium temperature is ~10-100K)
    important contributions have come from IRAS, COBE, ISO, Spitzer.
  

Let's gain some insights from a simplified, yet useful, treatment.
Assume an ISM metallicity of Z~2% (by mass) of which f_d ~ 0.1 is condensed as grains.
Assume all grains have dimension a (~0.1µm) and density (~1 gm cm^-3).
The grains absorb and emit as black bodies modified by efficiencies Q_abs() and Q_em()
In reality, Q_abs ~ 1 in the UV, and Q_em << 1 in the IR (see below)
However, for now let's take Q_abs = Q_em = 1 (perfect black bodies)


(i) H column for significant dust opacity

What hydrogen column has geometrical covering factor 1 in dust particles?
• In terms of the hydrogen column, N_H cm^-2, the projected mass density in dust is simply:
  N_d a³ = N_H m_p Z f_d   gm cm^-2   where N_d cm^-2 is the column in dust.

  Substituting for N_d, the total geometrical cross section in dust particles is :
  N_d a² = (N_Hm_p Z f_d)/( a³) × a² 3 × 10^-22 × N_Hf_d (Z/Z) × ( a_µ)^-1 cm^-2
  where is in gm cm^-3, a is in µm, and Z = 0.02 is solar metallicity.
  (using a² is OK here, since the absorption efficiency Q_abs ~ 1 in the UV/opt).

• For our fiducials, unit covering factor (N_da² ~ 1 cm²) occurs for N_H ~ 3 × 10²¹ cm^-2
  Thus, hydrogen columns ~10^21.5 cm^-2 mark when dust absorption will be important.
  In fact, this simple estimate is very close to the observed value: A_V N_H / (2 x 10²¹) mags.

• Using the observed value, paths through the ISM suffer an absorption A_V ~ 1.6 × n_H d_kpc mags
    Spiral disks are optically thick in the plane, for which <n_H> ~ 1 cm^-3
    However, with N_H~10²¹ cm^-2 perpendicular to spiral disks, they are borderline transparent.
    DMCs are extremely opaque, since n_H~10⁵ gives A_V~100 mag across 1 pc.
    The hot phase (n_H ~ 10^-3 cm^-3) is tansparent (even without likely dust destruction).

  (ii) Dust number density

  Continuing briefly, the dust particle number density is:
• n_d/n_H = (m_pZf_d) / ( a³) = 3.3×10^-14 (Z/Z f_d) / ( a_µ³) = 3.3×10^-12 for a ~0.1µm and f_d~0.1
  For n_H ~ 1 cm^-3 (the ISM average) this gives n_d ~ 1 per (100m)³;
  For n_H ~ 10⁶ cm^-3 (a DMC core) it is ~1 m^-3
    dust particles are few and far between !!

  (iii) Dust Temperature

• In the ISM, ambient starlight usually has a much greater energy flux than local particles.
    dust is heated mainly by starlight
  At equilibrium, therefore, starlight heating balances radiative cooling
  There are two common geometries:
  1. For isotropic starlight flux J_s erg/s/cm²/sr we have:
     4J_s a² Q_abs     4a² T_d⁴ Q_em     T_d     (J_s / )^1/4 (Q_abs/Q_em)^1/4

  2. For a distance d from a point source of luminosity L we have:
     L/(4d²) a² Q_abs     4a² T_d⁴ Q_em     T_d     (L/16d²)^1/4 (Q_abs/Q_em)^1/4

  Both are independent of a, and T_d applies equally for interstellar asteroids, planets, or people.
  [This is not quite true, since both Qs do in fact depend on a].

• Consider dust in the general interstellar radiation field. What is J_s?
  It is roughly what we witness on a clear moonless night, ~0.002 erg/s/cm²/sr.
  For Q_abs = Q_em = 1     T_d     3.2K     interstellar space feels very cold!
  This result was first obtained by Eddington in 1926.
  

• This value is, in fact, too low by about ×5.
  The reason is that dust does not behave like a black body
  It absorbs UV better than it radiates IR     a "green-house" effect.
  The correction factor, [Q_abs(UV)/Q_em(IR)]^1/4 is discussed below (link).

• Dust embedded in HII regions is exposed to a more intense radiation field.
  From 2 we have:   T_d     0.62 × [ (L/L) / d_pc² ]^1/4 (Q_abs/Q_em)^1/4   K
  giving T_d ~ 10K for L ~ 10⁵L and d ~ 1pc   (with Q_abs = Q_em = 1)

  Again, this is a factor of a few too low, but still illustrates just how cold dust usually is.

• Dust never achieves high enough temperature to emit outside the IR because:
  
  it has no internal energy source
  it's only energy input is starlight
  it can emit with fairly high efficiency, because it is a solid
  it behaves as a macroscopic, not quantum, system (with one exception, see below)
  above ~1500K it evaporates     it never contributes below the Near-IR
  

  (iv) Dust Emission Efficiency

• In a typical spiral, M_ISM 0.05 M_stars and M_dust 0.01 M_ISM giving M_dust 0.0005 M_stars
  However, within factors of a few, L_IR L_opt and we discover that L_dust L_stars
  How can such a tiny mass of very cold dust compete with nuclear furnaces 10⁴× more massive?
    dust has a huge surface area to mass ratio
  

• Consider the sun: it has 1 M, and a surface with area A = 1.3 × 10¹¹ cm², at T ~ 6000K
  Now consider 1 M of ISM with 2% heavy elements in dust with a ~ 0.1µm and ~ 1 gm cm^-3
  That makes 4 × 10⁴⁶ grains with total surface area 5 × 10³⁷ cm² ~ 10¹⁵ A   !!
  Per unit area, the dust has vastly lower radiative efficiency:
  
  (T_d/T)⁴ ~ (10/6000)⁴ ~ 10^-11
  Q_em(IR) ~ 10^-4 relative to black body efficiency (see below)
  
  After integrating over populations of both dust and stars:
    dust is a more efficient radiator than stars, per unit mass
  

For our purposes, dust is important for least two reasons
1. it can significantly affect our view of galaxies :
   - it blocks UV and optical, which may need correcting
   - its emission may enhance or even dominate a galaxy's IR emission

2. it can significantly affect crucial ISM processes:
   - it facilitates ISM chemistry (surface catalysis)
   - it can alter HII region structure (e.g. via Ly destruction)
   - it dominates DMC cooling, helping star formation
   - it can effectively short circuit the deposition of UV/optical input to the ISM
       (absorbing and then reradiating in the FIR; e.g. starbursts & AGN).

• The simple estimates in (b) above hide a multitude of details
  Specifically, we want to explore:
  • the composition of grains and their size distribution
  • the life cycle of grains: origin, growth and destruction
  • dust's affect on light: its emission and absorption properties
  • whether dust properties depend on environment (e.g. different ISM phases)
  • dust's contriubution to galaxy SEDs (spectral energy distributions)

(9) Dust: Physical Properties

Ascertaining the properties of dust grains has been remarkably difficult, and is still incomplete.
There are two main reasons for this difficulty:
• They are solids; most astrophysical material is ionic/atomic, with simpler associated physics
• Because they are solids, they have more complex/unclear spectral signatures
  
Nevertheless, progress has been steady, and the subject is now quite sophisticated.
Here we cover just the basic results.

• If heavy elements reside in dust, they must be missing from the ISM gas.
  One can study dust composition by studying gas depletion
  Gas phase abundances are measured from interstellar absorption lines in stellar spectra.

• The depletion index is defined logarithmically:
  D(X) = log₁₀[N(X)/N(H)]_obs   -   log₁₀[N(X)/N(H)]_ISM
  
  where [N(X)/N(H)]_ISM is the normal relative abundance of element X (usually taken to be solar).
  For example, D(C) = -0.7 means C/H is only 20% of its expected value     80% must be in dust.

• Measurements of diffuse clouds (n_H~10-100 cm^-3) shows significant total depletion ~50%.
  Expressed as a total "metallicity", Z_d ~ 0.008 (where Z=0.016)
    ~1% of the ISM is in dust, or equivalently ~50% of ISM metals reside in dust.

• However, the depletion varies greatly from element to element.
  Specifically, depletions increase with condensation temperature, T_c (see figure).
  [T_c(X) is the temperature when 50% of element X is solid, for equilibrium conditions]
  e.g. Al, Ca, Ti, Fe, Ni are ~100% depleted, while C, N, O, S, Zn show modest or no depletion.
    dust formation involves condensation/adsorption, & not all elements bind efficiently to dust.

• Depletions also vary with environment: (see figures)
  depletion is less for hotter/turbulent ISM & higher velocity clouds
    harsh environments (eg shocks) destroy dust &/or prevent it growing
  depletion increases with ISM gas density, at least for some elements
    higher densities facilitate grain growth via adsoption

• In terms of total mass, depletions give the following overall content for dust:
  
  O: 50%   C: 20%   Fe: 13%   Si: 7%   Mg: 6%   others: 5%
  
  How they are combined is less clear, though IR spectral features help:
    Silicon is in silicates (XSiO₃ pyroxines; XSiO₄ olivines), where X is mainly Mg, with some Fe.
    Carbon is in graphite, Polycyclic Aromatic Hydrocarbons (PAH), and amorphous carbon
    Fe in metallic iron inclusions
  (these results do not include the various ices which probably condense onto dust in DMCs)
  

• The depletion patterns support a dust model with resilient refractory core + transient mantle
  The elements Fe, Ti, Ni, Ca are primarily core while Mg and Si can be gained and lost.

• Here's a table which summarizes the various dust populations and their properties: figure

• There are several sites of dust formation (images)
  1. winds from evolved RG and AGB stars
  2. winds from young massive stars (e.g. Carina).
  3. nova ejecta
  4. supernova ejecta
  5. directly from gas phase condensation

• These all involve outflowing winds with decreasing density and temperature
  Refractory seeds form and grow by adsorption
  The growth rate depends on the wind density, temperature, velocity, and time in the flow.
  The growth is non-equilibrium -- simple condensation tracks wont work
  The growth also involves feedback:
  As dust forms radiation pressure increases wind speed increases stops dust growth.

• There are two types of winds (figures)
  1. O-rich winds make silicate grains
     metal oxide seeds (e.g. Al₂O₃ ; CaTiO₃)
     silicate mantles added (e.g. MgSiO₄ fosterite; MgSiO₄ enstatite)
     Fe may also be included (e.g. FeSiO₃ pyroxene).
  2. C-rich winds make graphite & Polycyclic Aromatic Hydrocarbon (PAH) grains
     C₂H₂ (acetylene) nucleation 1-few benzene rings PAHs
     grow to ~10-50A (~500 atoms), so these are small grains.

• In some environments, grains can grow by adsorption
  most efficient when kT_{gas phonon}   so collisions lose energy to lattice and adhere
    results in depletion of metals from the gas phase
  Examples:
  
  • in cold DMCs, grains can grow ice mantles (e.g. H₂, CO, CO₂, CH₄)
  • in proto-stellar disks it is sufficiently dense for grain + grain coagulation
    large "fluffy" grains ( 1 µm 75% filling factor).

• Many environments are hostile to grains
  • Near stars, photon heating can sublimate icy mantles
  • More extreme radiation environments can sublimate the entire grain
    (e.g. near AGNs, T_dust 1000K).
  • Shocks from SNRs and stellar winds high kT particles "sputtering"
    
    > 400 km s^-1   ion-grain sputtering
    < 400 km s^-1   grain-grain shattering
    both tend to break up grains power law size distribution (see below).
    ultimately, shocks and high T ISM phases can destroy grains completely.

• Grain sizes span three decades:   0.001µm (1nm)     1 µm   (~100 10¹¹ atoms)
  Thats equivalent to salt grains     basket balls !
  Clearly, within this huge range one might expect quite distinct grain populations,
  perhaps with different compositions, origins and histories (images).

• The final grain size distribution depends on :
  
  • the injected size distribution from stellar winds
    
  • subsequent modification by growth and destruction processes.
  Both these can vary from location to location

• The final mix usually contains varying amounts of the following components:
  
  1. A "classical" population of relatively large, dielectric (silicate?) grains
     There is evidence for a power law size distribution: dn/da a^-3.5 with a_max ~ 0.3µm
     This population explains:
     the basic ^-1 form of the UV/optical extinction curve;
     large scattering efficiency (~60%) and scattering angle (~45^o) in the optical
     a_max comes from dust's IR transparency
     
  2. Very small grains (nano-grains) are required in several contexts:
     almost isotropic scattering in the FUV
     the 2175A broad near-UV absorption feature suggests ~20 nm graphite grains
     2-20µ emission T_d ~1000K single photon heating of 100 atom grains (see below)
     
  3. Large grains ~1-10µm can form in DMC cores
     Only in these sheltered environments can ices condense and grains coagulate
     these grains are found in solar system materials (a relic of formation)
     they are very cold, and should emit in the extreme FIR and sub-mm (invisible to IRAS).
     other evidence & statements ? (TBD)
     

• Different extinction laws can be explained by different proportions of these components [10biv]

(e) Interaction with Light: Mie Theory

• First, recall a general refractive index is complex, m = n - ik, where k tracks absorption.
  Ices are good dielectrics, so k is small and n is roughly independent of wavelength.
  Metals have k ~ n and both may vary significantly with wavelength.

• Absorption and scattering efficiences, Q_abs Q_sca, are expressed relative to geometrical :
  e.g. for a particular grain/wavelength/index, Mie theory evaluates (see figure, for m = 1.5 - 0.05i)
  
  Q_abs(X,m) = (absorption cross-section) / a²
  Q_sca(X,m) = (scattering cross-section) / a²
  which define
  extinction efficiency :   Q_ext = Q_abs + Q_sca
  and albedo :   Alb = Q_sca / Q_ext

• Scattering can be studied by observing reflection nebulae and the diffuse galactic light.
  In the optical and UV, scattering is significant with Alb ~ 0.6   (figure)
    grains have significant dielectric character, consistent with silicates.

• The mean scattering angle can reveal grain size:
  forward for << a     isotropic for >> a
  Observations suggest :
    significant (~45^o) angle in optical,   increasing (more isotropic) in UV
    optical scattering grains have a~0.1-0.3µm,
    UV scattering grains are much smaller
  

• In the limit of << a,   Mie theory gives: (figures)
  Q_abs = 1   (ie a² as expected, independent of wavelength)
  Q_sca = 1   (also a², from diffraction)
  Q_ext = Q_abs + Q_sca = 2, which is double the simple geometrical cross section.
  

• In the limit of >> a   (i.e. X = 2a/ << 1),   Mie theory gives:
  Q_abs     -4 X Im[M]     ^-1 Im[M]    where M = (m² - 1)/(m² + 2)
  Q_sca     8/3 X⁴ |M|^{2     -4}
  
    For pure dielectrics (m real, k = 0) then Q_sca = Q_ext   ^-4 and we recover Rayleigh scattering.
    For some absorption (m complex, k 0) then Q_ext Q_abs     ^-1
  which is the correct form for the extinction law in the near, mid and far-IR
    confirming that there are no very large grains (a << 1 - few µm).

• Mie theory calculates Q_abs() for absorption, but what about emission: Q_em() ?
  By great good fortune, they are the same !!
    Recall Kirchoff's law: "good (bad) absorbers are good (bad) emitters".
  more specifically, for thermal emission:
  F_em() = Q_em() × B(T)   per unit area, where B(T) is the Planck function; and
  Q_em() = Q_abs()   whose functional form is given above
  (this has its roots in the reversibility of all interactions; a principle called "detailed balance")

• It is now clear that since dust grains don't absorb much in the IR, they will be poor IR emitters
  Of course, being good emitters in the UV doesn't help, since B_UV(T) is tiny when T ~ few K !
  We now have the "green-house" factor:
    Q_abs(UV) / Q_em(IR)     Q_abs(UV) / Q_abs(IR)

(f) Dust Temperatures

(i) Inferred from IR emission

• First, recall the basic Wein relations for the peak of the Planck function (there are two of them!)
  
  The peak of B d is at 2900µm/T(K)
  The peak of B d is 2.82kT/h or 5000µm/T(K)
    Often, the difference won't matter.
    Sometimes it does: so check if spectra are in f vs or f vs (e.g. Jy vs ^-1).

• In fact, since dust's radiative efficiency Q_em     a/   (see below)
    even a single T_d & single size population doesn't yield a Planck function!
  In reality, a range of T_d and grain sizes undermines a straightforward inference of T_d
  Nevertheless, emission in NIR (1-5µm) MIR (5-25µm) and FIR (25-300µm) sub-mm (300-1000µm) does indicate clearly different mean values of T_d.

• Overall, dust emission can span a broad range, NIR to FIR (sub-mm at higher redshift):
    T_d spans a wide range: 1000 - 10K,   however ...
  
  In most galaxies, the bulk is in the FIR, ~60 - 200µm
  
    the majority of dust has T_d ~ 10 - 50K
  

  (ii) Equilibrium T_d Estimates

• The zeroth order calculation was done in 8-b-iv above: (link)
    dust heating balances black body cooling, with both modified by efficiency (Q) factors
  For pure black bodies, this yields the Eddington values, which are too low by factors ~few.

• To improve on this we need :
  
  the absorption and emission efficiencies, Q_abs(a,,m) and Q_em(a,,m)
  which need integrating over grain size distribution, and incident and outgoing spectra
  if the region is ionized, one should include the important isotropic trapped Ly field
  any collisional heating terms should also be included

• Let's consider the most important factors: Q_abs and Q_em
  Treating grains as black bodies:   Q_abs = Q_em = 1 at all is:
  
  OK in the UV - they are good absorbers
  BAD in the IR - they are poor emitters (since a << ).
    the correction factor [Q_abs(UV)/Q_em(IR)]^1/4 > 1
    the resulting "green-house effect" pushes T_d above the Eddington value.
  Fortunately, uncertainties in the correction term are muted by the 1/4 power.

• Let's use the Mie theory from above to estimate the correction term
  First, consider the absorption efficiency for optical/UV starlight:
  For grain sizes ~0.1µm, X = 2a/ 1 - 5 for 5000A - 1000A
    Q_abs ~ 1 even for poorly absorbing grains (m = 1.5 -0.05i)   (see figure).
  But, at longer wavelengths and smaller grains Q_abs drops well below 1
    in practice, then, L should be replaced by L_,UV and Q_abs can be set to 1

• For Q_em(IR) we use Kirchoff's law and ask instead: what is Q_abs(IR) ?
  Again, relying on Mie theory; for >> a, we have Q_abs     -4 X Im[M]
  for a~0.1µm, X = 2a/ ~ 0.005 in the FIR
  Im[M] ~ -0.5 -0.025 for 1.5-1.0i (eg metal oxide) m = 1.5-0.05i (eg an ice)
    Q_em(FIR) = Q_abs(FIR) ~ 0.01 - 0.0005.

• Thus, our correction factor to T_d is (Q_abs/Q_em)^1/4   ~   3 - 7
  We expect ~3 for poor dielectrics/shorter wavelengths/warmer temps/larger grains
  We expect ~7 for good dielectrics/longer wavelengths/colder temps/smaller grains
  

• Using the modified equilibrium relation, we find:
  1. Interstellar dust, warmed by a weak isotropic radiation field: J_s ~ 0.002 erg/s/cm²/sr yields
     T_d ~ (J_s/)^1/4 × (Q_abs/Q_em)^1/4 3.2 × 5 ~ 15K
     This cold component is called interstellar "cirrus", and emits in the FIR ~ 100-300µm
     It is seen in other galaxies when not dominated by warmer (eg star formation) components
     It is slightly warmer in Ellipticals, with their higher interstellar radiation field.
     It probably shows a temperature gradient decreasing outwards, as J_s declines.

  2. Because they are complex environments, HII regions have a range of T_d
     Close to O stars T_d ~ 50K; In shrouded regions T_d ~ 10K
     Heating by trapped Ly is often important: T_d ~ 100K

  3. Deep inside DMCs, shielded from all external radiation, T_d ~ few K
     Here, the source of heating is X-rays from the surrounding hot phase, and cosmic rays.

  4. In AGN the dust can be appreciably warmer, for example:
     using L_AGN ~ 10¹⁰ L   and grain green-house factor ~5, we get
       Narrow Line Region (~100pc) temperatures: T_d ~ 100K
       Broad Line Region (~0.1 pc) temperatures: T_d ~ 3000K
     AGN's typically have "warm" IRAS colors from NLR dust:   F₂₅ / F₆₀     3 × F₆₀ / F₁₀₀
     Note that dust may not survive in the BLR:   T_d     T_sublimate ~ 2000 K (check)

  (iii) Thermal Spikes from Single Photons

• There are some puzzling observations:
  sometimes, where we expect T_d ~ 30K, we find 2 - 25µm emission   T_d 1000K !!
  there are galactic sources where T_d is independent of distance from the central star
  How do we understand these results?

• A population of very small grains: 100 atoms; possibly PAH
  For these grains a single UV photon carries enough energy to heat the entire grain to ~ 1000K.
  e.g. 1000A photon has 10eV, and a grain of N atoms has thermal capacity ~3Nk per Kelvin
    10eV = 3NkT giving T ~ 500K for an N=100 atom grain.
    well above the equilibrium temperature from a classical (non-photon) radiation field.
  Such hot grains radiate in the NIR

• However, they don't stay hot long !!
  At a few 100K they quickly radiate their thermal energy: t_cool 1 second
  These grains have a "spikey" thermal history: mostly cold, with brief spikes of a few 100K (image)

(10) Dust: Emission & Absorption

• As expected, there are two types of emission/absorption associated with dust:
  Continuum: thermal emission; and roughly ^-1 absorption and scattering
  Lines and Bands: both emission and absorption features.

• We have already encountered dust's thermal continuum emission;
  it is thought to be roughly Planckian, modified by an emissivity   ^-1

  Now let's look at the other emission and absorption signatures of dust.

• Lines & band features derive from specific bond stretching or bending modes
  However, they are shifted and/or broadened due to the lattice environment.
  Most, though not all, of these features are now identified.

• Examples:
  1. There is a very broad near-UV absorption feature centered at 2175A
     it is thought to arise from a surface charge resonance on small (20nm) graphite grains.
  2. The 3-12µm region has several PAH features (image)
     e.g. 3.3,   6.2,   7.7,   8.6,   11.3,   12.7µm
     these arise from various C-H and C-C bending and stretching modes.
  3. Broad silicate absorption (and emission) features (see fig)
     3.1µm : O-H stretch
     6µm : H-O-H bend
     9.7µm : Si-O stretch
     18µm : Si-O-Si bend
  4. The so-called Diffuse Infrared Bands (DIB) are emission/absorption features near ??-??µm
     their total and relative strengths vary, though are relatively low
     their origin is still unknown. uncertain.

(i) Basic Scenario

• Interstellar dust both absorbs and scatters light, blue more than red
  Stars therefore appear both fainter (extinction) and redder (reddening)
  The absorbed light is reradiated in the FIR & escapes the galaxy
  The scattered light contributes to the diffuse background light
      (and in certain circumstances can appear as a reflection nebula).

• Adopting a standard radiation transfer scenario (see fig)
  If I_0, enters a region and I emerges, with I(abs) absorbed and I(sca) scattered, then
  I = I_0, - I(abs) - I(sca)     and   I / I_0, = exp(-)
  where is the extinction optical depth

• In terms of magnitudes of extinction, A,
  A = -2.5 log₁₀(I / I_0,) = -2.5 log₁₀[ exp(-) ] = 1.086 ×
    extinction in magnitudes is, roughly, the optical depth.
  Observationally, of course, A gives an increase in apparent magnitude:
  e.g. for the V band: A_V = m_V - m_V,0 V - V₀     (A is always +ve)

  (ii) Standard Extinction Law

• Extinction depends on wavelength, and many studies have tried to measure this dependence
  e.g. divide spectra of two stars of the same spectral type, only one of which is reddened. (figure)
  The results are surprisingly consistent, and one speaks of a standard extinction law
  (variations do exist (see below), and should be kept in mind as a source of uncertainty)

• One way to describe extinction is using the normalized function A / A_V  where A_V = A_=5500A
  Here is a plot of A / A_V : (figure)
  It rises from zero in the IR, roughly as ^-1, and peaks in the UV at 700A
  There are features superposed at 2175A; 9.7µm; and 18µm (see above)
  (Note: because A ^-1 over a wide range, extinction laws are usually plotted vs ^-1)

• A number of algebraic fits to this "reddening law" exist.
  A commonly used one is given by Cardelli , Clayton, & Mathis (1989, ApJ 345 245)   e-link

• A more physically based approach models the extinction curve using different dust populations
  Two such models are shown here: figures

• The innocuous looking extinction curve hides an enormous variation in transparency:
  For example: at 4400A A_B/A_V 1.33 and at 5µm A_M/A_V 0.023
  So, comparing extinction in the blue and mid-IR, we have A_B / A_M 57
  A good example is the Galactic center, for which:
    A_M ~ 0.6 mag   (57% transparent),
    A_B ~ 34.5 mag   (1.6 × 10^-12%   transparent -- utterly invisible) !!

• Note that since A ^-1 at long wavelengths, we can obtain A in the mid and far IR
  e.g. A_60µ = 1/60 A_1µ = 1/60 A_J, and hence A_60µ = 1/60 × A_J/A_V × A_V = A_V / 212.

  (iii) Some Other Parameters

• So far, we have encountered A and A_V, or in general A_X for band X (e.g. UBVRIJHKLMN)
  

• Often, reddening is easier to measure than extinction
  so another useful parameter is :
  E_B-V = (B - V) - (B - V)₀ = A_B - A_V   or its generic relative E _{- V} = A - A_V
  E values are differences in color and are therefore easier to measure
  (you may know the color of an unreddened F5 star, but you don't know its apparent magnitude).

• Since all optical depths are additive, E_B-V and A_V are proportional
  specifically, we define
  R_V = A_V / E_B-V 3.1   for the standard extinction law.
  Note that 1/R_V = (A_B - A_V) / A_V   =   A_B / A_V   -   1
  which measures the slope of the extinction curve in the 4500A - 5500A region
  Note that bigger values of R_V mean shallower slope and less UV extinction for a given A_V.

• Since E's are more easily measured than A's, the extinction law is often given in the form:
  E_-V / E_B-V     (see figure)
  If R_V is known, one may obtain A / A_V from the relation:
  E_-V / E_B-V = R_V (A / A_V   -   1)
  Since extinction goes to zero as , we have :
  E_-V / E_B-V   (A - A_B) / (A_B - A_B)     (-A_V) / (A_B - A_B)     -R_V
  which is the usual way that R_V is measured.
  Hence, if the full range of E_-V / E_B-V is known, one may obtain A / A_V

  (iv) Variations in the Extinction Law

• Above ~ 7000A (R), the extinction law seems quite universal
    one can correct with confidence using the standard law.
  this is because for >> a, standard scattering theory works (see below), and A ^-1

• Below ~ 5500A (V), the form of A can vary with both environment and metallicity
  (this is why B&M advocate A_J as normalization rather than A_V)
  There has been considerable effort to characterize these variations.

• Generally, lower density and lower metallicity gives
    weaker 2175A feature and steeper UV slope (lower R_V)
  Here's a comparison of three curves of decreasing metallicity: (figures)
  MW LMC SMC : relative metallicities 1 1/2.5 1/7

• Similarly, there is some evidence for higher R_V (4-5) in DMCs
    lower UV absorption, consistent with larger grains growing in the cold dense gas

• One version of the UV part of the extinction law makes these variations more explicit:
  
  E_-V / E_B-V = [c1 + c2.x] + [c3.D(x)] + [c4.F(x)]     for x=^-1 > 3.3µm^-1 ( < 3000A)
  The three terms are roughly independent, and correspond to three grain populations:
  1. [c1 + c2.x] : large "classical" grains. Slope (c2) depends on size distribution:
     slope decreases as <a> increases (higher R_V).
  2. [c3.D(x)] : small (20nm) graphite grains.
     D(x) sets the location & width of the 2175A feature.
  3. [c4.F(x)] : v. small (dielectric?) grains which affect the FUV (1100-1700A) part
     F(x) is cubic polynomial fit to FUV rise after linear and 2175A features removed.

• Finally: knowledge of the extinction law in other galaxies (besides LMC,SMC) is still rudimentary.
  Hopefully, the various grain populations identified locally are neverthelss present.

  (v) Correcting for Reddening and Extinction

• Often, dust is simply a nuisance, and we need to correct for the effects of extinction:
  This involves three steps:
  1. choose an extinction law (usually, the standard one)
  2. estimate A_V using something of known color
  3. apply the corrections, both to color and, if needed, flux.

• Here's an approach suited to an emission line spectrum:
  consider two emission lines at ₁ and ₂ with true fluxes F₁ and F₂
  Their observed fluxes are:
  f₁ = F₁ dex(-0.4 A₁) and
  f₂ = F₂ dex(-0.4 A₂)
  writing observed and true flux ratios as f₁/f₂ = r_1,2 and F₁/F₂ = R_1,2,
  and noting that A₁ = A_V × (A₁/A_V), and A₂ = A_V × (A₂/A_V), we have
  r_1,2 = R_1,2 dex[-0.4 ( A₁ - A₂) ]
  giving
  -2.5 log₁₀ (r_1,2/R_1,2) = A_V [ (A₁/A_V) - (A₂/A_V)   ]
  Hence, from measured r_1,2, and knowing R_1,2 and the extinction law A/A_V, we can derive A_V

• Once A_V is known, it is straightforward to correct any other flux or flux ratio.
  for example :
  F₃ = f₃ dex[ +0.4 A_V × (A₃/A_V) ], and
  R_3,4 = r_3,4 dex [ +0.4 A_V × [ (A₃/A_V) - (A₄/A_V) ] ]

• We need some initial line ratios where we know their unreddened values.
  There are several to choose from, but usually the Balmer series is used.
  For a wide range of conditions, the Balmer series have case B ratios:

  H (6563A)	H (4861A)	H (4340A)	H (4101A)
  2.86	1.00	0.47	0.26

  So, for example, for a measured H/H ratio, we derive A_V from :
  A_V = -2.5 / [A_H - A_H]   × log₁₀ [ (H/H) / 2.86 ]
  where A_H is A_6563A/A_V is given by the extinction law (similary for A_H)
  For the standard extinction law, we get
  A_V = ?? × log₁₀ [ (H/H) / 2.86 ]

• Be careful in your choice of Hydrogen recombination lines.
  The Lyman and Balmer/Lyman ratios often suffer optical depth effects and deviate from case B.
  This is especially true at high densities, e.g. in AGN BLRs and even AGN NLRs.
  Usually, however, Balmer, Paschen, and Brackett series are OK
  The exception is H/H which in AGN NLRs is closer to 3.1 than 2.86.

• This whole analysis assumes the source lies behind a uniform screen of dust
  Be careful: if the emission region is itself pervaded by dust things are more complicated
  
  each color samples a different volume (more in the red)
  the dust may itself alter the ionization/emission structure of the region.
  the gas phase abundances may also be altered by depletion onto dust.
  Usually, there is insufficient information to improve on the foreground screen analysis.

  (vi) Dust to Gas Ratios

• To first order, extinction & reddening are proportional to total hydrogen column (figure)
  E_B-V 1.72 × 10^-22 N_H mag
  A_V     5.34 × 10^-22 N_H mag
  where N_H (in cm^-2) is summed over H⁺, HI, and H₂
  the quantity E_B-V/N_H is called the dust to gas ratio

• A physical measure of dust to gas ratio is
  
  Z_d = (mass in dust)/(mass in H + He)
  for solar metallicity, complete depletion yields Z_d, = 0.016

• there is some evidence that the D-to-G ratio is lower (less dust) in
  
  hotter ISM phases
  higher velocity clouds
  consistent with dust destruction in shocks.

• Not surprisingly, a lower metallicity also seems to lower the total gas/dust ratio
  
  A_V = 17 × 10^-23 R_V N_H     (MW)
  A_V =   4 × 10^-23 R_V N_H     (LMC)
  A_V = ~3 × 10^-23 R_V N_H     (SMC)

  (vii) X-ray Absorption

  (viii) Polarization

(11) Dust Emission from Galaxies

• The appearance of dust in galaxies has a long History: (see Topic 1.2c)
  In 1920 Curtis used dust lanes to argue (correctly) for the external nature of Spiral Nebulae,
  
  edge on nebulae have dark lanes which resemble the Milky Way's "zone of avoidance"
    Spiral Nebulae are external versions of MW.

• Dust is ubiquitous: it is found in ~all galaxies; and throughout each galaxy (e.g. Sombrero)
  however, its role can vary greatly from one galaxy to the next.

• The subject has developed slowly: recent progress has been due mainly to advances in IR detection.

(a) Absorption of Galaxy Light

• since dust size a 0.5µm it absorbes UV & optical efficiently
  This can have two important impacts on our measurement of galaxies:
  it affects the optical/UV appearance, hiding important regions
  it can significantly reduce their apparent luminosity,
    undermines studies of, e.g., M/L ratios; Tully-Fisher relation; Dark Matter.
  
  Need to understand and correct for this absorption.
  One approach: study how galaxy photometry depends on galaxy inclination.

  (i) Inclination Effects

• This also has a long history; Holmberg (1950s) plots <µ_B>   vs   a/b   (mean surface brightness vs inclination)
  On average, as galaxies change from face on to edge on, one expects:
  if optically thin, one expects inclined galaxies to be brighter (same light, less projected area)
  if optically thick, one expects inclined galaxies to be same or dimmer (only see to A_V ~ 1).
    he finds dust dimming is modest-to-important

• Since then, there have been many "correction formulae" published: m_i = f(a/b, Hubble Type) [Topic 3.7e]
  Applying these corrections reduces scatter in astrophysically meaningful plots (figure)

• Be alert: some formulae correct to "face on"; others to "dust free", e.g.
  
  RC3 corrects to face on
  RSA corrects to dust free
  these can differ in B by ~1 mag for the same galaxy !

  (ii) Perpendicular Opacity of Disks

  A critical question is whether disks are optically thick or thin.... Much debate in the 1990s.
  Without rehashing that debate, it now seems that disks are:
  
  optically thick towards the center, but transparent at the edges
  thick in patches, particularly near spiral arms
  there can be significant variations between galaxies.
  In response to the overall uncertainties,
    most work on M/L ratios (e.g. TF relation) is now done in the near IR (I or H band)

  (iii) Hidden Star Formation

  Near-IR & Mid-IR imaging can reveal optically invisible star formation regions
  
  • in normal spiral disks, obscured SF knots can be seen in spiral arms (e.g. M51)
    
  • in starbursts, much dust is made which obscures the optical light.
      burried super star clusters emerge in the IR (e.g. the antennae)
      from SB to LIG to ULIG; L_FIR up by 10³ while L_opt up by only ×3 (see Topic 11.7d and SED image)
  • At the highest luminosity, there is a population of optically invisible z~2 ULIGs
      probably young, buried SB/QSO before blow-out.

(b) Emission: Broad Band SEDs

• FIR emission from dust is a ubiquitous feature of galaxy spectra
  since stars emit ~no radiation beyond 25µ, dust dominates the Mid- Far-IR
  Since starbursts & AGN are powerful UV emitters, & dust is a good UV absorber:
    sometimes, Mid-Far-IR from dust dominates entire galaxy SED
  

• As an example, here is the MW's ISM SED, and the SED of two AGN: figures

  (i) Four Contributions to the FIR

  Mid- and Far-IR emission can have varying contributions from :
  1. Cold dust in the general ISM heated by the blue/UV ISRF ("cirrus")
     
     10 - 30K     60 - 500µ
  2. Warmer dust in molecular clouds heated by nearby star formation
     
     50 - 100K     25 - 100µ
  3. Yet warmer dust heated by an AGN
     
     150 - 200K     adds a 25µ component
  4. Hotter dust in winds from evolved red giants
     
     100 - 1000K     12 - 25µ

  (ii) Other Factors Affecting the IR output

  1. Current & past star formation rates
     
     UV output is a strong function of age (highest for current massive star formation).
  2. Metallicity & dust composition/size distribution
     composition & particle size affects absorption & radiation (e.g. single photon heating)
  3. Relative location of dust & sources of radiation
     UV flux defines eqlm dust temperature (dust close to SF; galaxy nuclei; is warmer)

  (iii) Variation Along the Hubble Sequence

• A number of properties vary systematically along the Hubble sequence,   E     Sc (see Topic 2.9)
  e.g. star formation rates increase & HI content increases
    one might expect systematic variation of FIR/dust emission with Hubble sequence.

• Often color-color plots are useful
  e.g. for IRAS with 4 bands: 12µ 25µ 60µ 100µ, one can define colors in two common ways:
  1. Log of flux ratio [12]/[25]     log(F₁₂/F₂₅), with F₁₂ = f at 12 µ in Jansky's (i.e. per Hz)
     
  2. An effective two-point spectral index, e.g. ₁₂²⁵, where is defined by f

  Here are two such plots for various galaxy types: (image)

• Understanding these FIR color-color plots was slow to develop
  One must consider two dust types:
  1. large grains at eqlm temp, which increases with SFR
     these affect the 25-60-100µ fluxes
  2. small stochastically (quantum) heated grains with ~fixed (high) temperature
     these affect the 12-25µ fluxes
  And three radiation fields:
  1. high flux UV field from young stars
  2. UV from older population, whose flux depends on stellar density
  3. an AGN, if present.

• The FIR colors arise in the following way:
  • Low SFR disks (e.g. Sa) have cirrus so cold that its 25µ flux is very low:
      the large grains have low (cold) [60]/[100]
      the small grains have ~ equal F₁₂ & F₂₅

  • high SFR in irregulars (Sdm - Im) have warmer large grain emission,
      [60]/[100] is higher, and begins to dominate the F₂₅ band
      with F₂₅ rising fast, the [12]/[25] now appears low

  • In ellipticals & SOs, there is little/no star formation, however:
    Es & SOs have high stellar densities in the bulge with correspondingly high ISRF
    dust, if it is present, is usually in the nuclear regions, where the ISRF is high.
      cirrus has intermediate temperature, with intermediate [12]/[25] & [60]/[100]
      FIR luminosities consistent with heating by UV from post AGB stars (r 1 kpc)
    (there is still some disagreememt over whether red giant winds contribute in E/SOs).

  • Dust composition is also relevent:
    It seems: from Im (low Z)     E (high Z),   small/large grain ratio increases.

  (iv) Starbursts

  The IR SEDs of starbursts is discussed in Topic 11.7d
  Briefly, as the luminosity of the starburst increases (see image)
  
    L_IR increases correspondingly; ~×10³ @ ULIGS
    however, absorption suppresses optical increase to ~×3-4
    dust temperature gets warmer, mainly at 60µ (30-60K)

  (v) AGN

• Accretion power in AGN generates an intense "hard" spectrum
  This can heat dust in the near-nuclear regions.
    in the kpc-scale NLR, T_d ~ 150-200K giving a 25µ component.
    in the sub-pc sclae BLR, T_d ~ 500-1000K
  can give a Near-IR component 1-5µ (though may not survive)

• At higher luminosity, the dust signature may depend on age:
  early: post-merger, SB+AGN, shrouded
  late: ISM blown away, SB declines   bare AGN dominated SED.

(c) Emission: Spectral Features

While the IR has many spectral features, there are two major features attributable to dust: