Measurements Tools of Interstellar Matterhosting.astro.cornell.edu/academics/courses/astro... ·...

Measurements Tools of Interstellar MatterMeasurements Tools of Interstellar Matter

1. Absorption, Reddening and Polarization of Starlight2. Hot Gas Emission (UV and X-rays)3. Optical Emission Lines4. Dust (thermal and PAH) emission5. 21cm HI 6. Radio Recombination Lines7. Molecular Lines8.

Rays9. Radio Continuum (thermal Bremsstrahlung and

Synchrotron)10.Faraday Rotation11.Pulsar Dispersion Measure12.Zeeman Effect (Magnetic fields)

Historical Background

-Hartmann (1904) “stationary lines” in spectrum of spectroscopic binaries stellar lines “move”, due to orbital Doppler shifts

interstellar clouds do not partake of orbital motion: “stationary”

-Angular sizes of Open Clusters (Trumpler 1930s)A star cluster of diameter d at distance D has angular size = (d/D)Hence the average solid angle subtended by a star cluster, 2 , shoulddecrease with D like the flux f=L/4D2

Log f

Log

Obscuration dims the moredistant clusters

-Adams (1940s) measured CaII lineabsorption in hundreds of stars: cloudy nature of IS gas


1939 StromgrenStromgren proposes that emission-line nebulae are regions of photoionized gas surrounding hot stars. There are 3 basic types of such nebulae:

* HII RegionsHII Regions regions surrounding O, B stars

* Planetary NebulaePlanetary Nebulae regions surrounding hot remnants of old stars

on their way to the white dwarf phase

* SNR SNR (a) Young (“plerionsplerions”=“Crab-like”), regions photoionized

by UV synchrotron radiation from relativistic electrons

originating in the SN stellar remnant (a neutron star)

(b) Old, regions photoionized by X-rays produced in the

shock wave which heats the ISM gas to 105 – 106 K


•1945 In a remarkable paper, van de Hulst reviews a number of mechanisms for the production of radio radiation and postulates the detectability of the 21cm HI line, to be later detected by Ewen & Purcell (1951 Nature 168,356), Muller & Oort (1951 ibidem p 357) and Christiansen & Hindman (ibidem)•1963 While spectral lines of a few diatomic molecules (CH, CN) were detected optically in the 1930s, the detection of OH at 18 cm (Townes et al) opens the era of radio molecular astronomy. CO is first detected by Wilson et al.•1973 Molecular Hydrogen is first detected by Carruthers in absorption in the UV (note that most of the (cold) H2 is still undetectable).•Space and stratospheric telescopes reveal the IR, UV and high energy ISM, from the 1970s on:• Copernicus (early 70s, UV), IUE (1980-1996, UV), EUVE (1994-9, far UV)

HST (1990-), FUSE (1999-) • IRAS (1983; 12, 25,60, 100 m), COBE (1989-93), WMAP (2001-),

Spitzer (2003-), KAO (1972-1995)• Uhuru, Einstein, ROSAT, ASCA, Chandra, XMM

Halpha Emission in the Milky Way (credit: Finkbeiner et al)

Galactic HI (credit: Dickey & Lockman)

Haslam et al 1982 408 MHz map of MW

CO in the MWCredit: Dame et al.

COBE FIR (60-240 m)

Dust (from IRAS and COBE; credit: Schlegel et al.

ROSAT medium-soft X-ray (0.5-0.9 keV)

ROSAT soft (0.25 keV) X-ray MW map

Compton GRO/Egret

Gamma-ray (>100MeV) MW map

Emission processes:

Electron Bremsstrahlung:

CR electrons + ISM nuclei

rays

Neutral

decay : CR protons + ISM nuclei 0

rays

Inverse Compton : CR electrons + ISRF photons

rays

Some Basic DefinitionsSome Basic Definitions

*Thermal or Kinetic EquilibriumThermal or Kinetic Equilibrium of a gas: when particles, through elastic collisions, quickly establish a Maxwellian distribution of velocities

*Local Thermodynamic Equilibrium (LTE) : Local Thermodynamic Equilibrium (LTE) : gas parameters (e.g. density, temperature, etc.) vary in space and time, but they do so slowly, so they can be considered to be constant over some local neighborhood.

kTh

j

iLTEj

LTEi e

gg

nn /

*Excitation Equilibrium :Excitation Equilibrium : in LTE, the relative populations of energy levels i and j of an atom or molecule are regulated by Boltzmann’s eqn. with g are the statistical weights and T the kinetic temperature of the gas. If the gas is not in LTE, the populations are parametrized by the excitation temperature excitation temperature TTexcexc (e.g. the “spin temperature” of the 21cm line).Departures from LTE in the populations are usually identified by cofficients

exckTh

j

i

j

i egg

nn /

LTEiii nnb /

RadiativeRadiative Transfer FundamentalsTransfer Fundamentals

d

dA

n

k

Specific IntensitySpecific Intensity

The radiant energy crossing a surface element dA (normal n), contained in direction within the solid angle d, in the time interval dt and frequency range () is

ddtdnkdAIdE

where I

is operationally defined as the specific intensity or brightnessIts cgs units are: erg/(sec sterad Hz cm2 )The net flux crossing the element dA is (in vicinity of a source, F

is non-zero; in the general field, which may be isotropic, it is =0)

dIF cos

As radiation propagates trough a medium, energy is removed from the radiation field by absorption and contributed by emission. The equation of equation of radiativeradiative transfer transfer regulates the radiant energy budget:

dI

/ds = (sources) – (sinks)Where ds is a path length element along the ray propagation direction.

In free space (no sources or sinks), the specific intensity is constant.

Rybicki & Lightman ch. 1


dtddVdjdE

If the medium is emitting, its emission emission coefficientcoefficient j

represents the energy emitted by the medium, per unit time, per unit volume, per unit frequency interval, per unit solid angle.

In a region of isotropic emission, the emissivityemissivity

is usually defined as the energy emitted per unit mass, directionally averaged, so that

)4/( ddVdtddE

4/j

As the ray bundle travels a distance ds through a region of emission coefficient j

, its specific intensity is increased by:dsjdI


The absorption coefficientabsorption coefficient

is defined in such a way that, in the absence of emission

ds represents the fractional loss of intensity as the ray bundle travels a distance ds:

dsIdI

The mass absorption coefficient mass absorption coefficient , sometimes called opacityopacity is defined as /

The equation of equation of radiativeradiative transfer transfer : dI

/ds = (sources) – (sinks)then becomes:

jIdsdI /


jIdsdI /

Defining the source function source function as we can rewrite

and the “formal” solution of the equation of radiative transfer is

/jS

''

0

)( )()0()('

dSeeII

Where is the optical depthoptical depthdsd

SIddI /


jIdsdI /Consider 2 simple cases:

1. Emission only which has solution:

)()(]')(exp[)()( so

s

so esIdsssIsIo

jdsdI /')'()()( dssjsII

s

soo

The increase in intensity is the integral of the emission coeff along path.

2. Absorption only which has solution: IdsdI /

Intensity decreases exponentially along the path.

Medium said to be optically thin when 1


''

0

)( )()0()('

dSeeII

SIddI /

Consider the case of a constant source function. Then

eSISeSeII ])0([)1()0()(

Note: - if I>S, dI/dS<0 I decreases along the path

- if I<S, dI/dS>0 I increases along the path

- as opacity increases, I

S


1)/exp(/2)(

23

kThchTB

Given the Planck functionPlanck function

For any value of the specific intensity I, define brightness temperaturebrightness temperature TTbb by the relation

)( bTBI

In the limit where h/kT<<1, usually valid in the Radio Astronomy regime, the Rayleigh-Jeans approximation is valid and

bTckI )/2( 22

For a thermal emitter, KirchhoffKirchhoff’’s relations relation holds: [i.e. the source function is equal to B

(T) ] Bj

Einstein CoefficientsEinstein Coefficients

1

2Probability, per unit time, that an atom in state 2 makes a spontaneous transition to level 1

Probability, per unit time, that an atom in state 1 absorbs a photon and transitions to state 2

Probability, per unit time, that atom in state 2 makes a stimulated transition to state 1

JBJB

A

21

12

21

dIJ

dJJ

)4/1(

)(0

Where

is the mean intensity

and the line profile function1)(0

d

g1

g2

E=ho

212

3

21

212121

2 BchA

BgBg

The Einstein coeffs are related as follows:

))((4

)(4

212121

212

BnBnh

Anhj

o

o

In terms of the Einstein coefficients, the emission and absorption coefficients are:

Where n1 and n2 are the populations of the two energy levels

Einstein CoefficientsEinstein Coefficients

If populations are in equilibrium at temperature T:kThe

gg

nn /

2

1

2

1

)()1)(()4/( /

121

TBSeBnh kTh

In that case:

If the energy levels are not degenerate:

And if they are degenerate, the sumis over all substates of the 2 levels

Where d21 is a transition matrix moment with units of an electric dipole, which represents the transition strength.

hcdA 3

221

321

4

21 3||64

221

23

321

4

21 ||13

|64 dghc

A

T=T_ex=excitation temperature

(See R&L 10.3) for derivation

Optical DepthOptical Depth

dsnngngcAds 2

21

122

221 1)(

8

))((4

)(4

212121

212

BnBnh

Anhj

o

o

212

3

21

212121

2 BchA

BgBg

kThegg

nn /

2

1

2

1

Combining:

W/1~)(Very roughly:

Equivalent Width of line

2/

321

2

18

NeW

AcexkTh

Which is

2123

21 || dA

Note that

And N2 is the column density of particles in the upper energy level 2

+

+

2/

321

2

18

NeW

AcexkTh


exi

ex

kTE

ii

totkTE

egTQ

NTQ

egN

/

/22

)()(

12

Ntot is the column density of particles at any energy stateQ(T) is the partition function

221 || d

•For IR transitions,

•For radio totNNN

kTh

12

1/ )](/[|| 212 TWQNd totIR

1/ exkTh )](/)[/(|| 212 TWQNkThd totexradioradio

radio

ex

radio

IR

radio

IR

hkT

dd

2

21

21

||||

•In equality of |d21 |, IR lines of a given species can be >> optically thick than radio lines•Abundant molecules such as CO, HCN, NH3, H2O have roto-vibrational transitions with |d21 | ~0.01 x those of pure rotational transitions hence the two sets of lines have similar optical depths•HI is very abundant, yet |d21 | for the spin flip transition is very small, the 21cm line is generally optically thin

10010~ radio

ex

hkT

Profiles of Spectral LinesProfiles of Spectral Lines

Profiles of Spectral Lines: 1 Natural WidthProfiles of Spectral Lines: 1 Natural Width

Energy levels are not infinitely sharp: the energy width of a level is related to the lifetime of the level via Heisenberg’s Uncertainty Principle. The energy width of the transition between two levels is quantifed by the Einstein A coefficient. Semiclassically, the process can be described as the product of an oscillation of frequency

, exponentially damped at a rate .

1|)(|

)(

2

2

dttf

eAetf tti o

0

)(22/1)()( dteeF tti o

iiF

o

)(2

)()()( 2/1

222 )4/()(1

4)(

o

I

The FT of f(t) is

which can be rewritten as

And the power spectrum |F(power spectrum |F()|)|22 is:

'

'n

nnn AFor an energy state n, the damp rate is related to the sum of the Einstein coeffs. of all states n’ lower than n

Profiles of Spectral Lines: 1 Natural WidthProfiles of Spectral Lines: 1 Natural Width

222 )4/()(1

4)(

o

This math form is referred to as a “Lorentz profile” – and sometimes as the “Cauchy distribution” and as the “Witch of Agnesi”.

Maria Maria GaetanaGaetana AgnesiAgnesi

(1718-1799)

The curve is discussed in “Instituzioni analitiche ad uso della gioventu italiana” (1748), the first book discussing both differential and integral calculus

Italian mathematician. She lectured at Bologna. A polyglot, when she was 9 years old she composed and delivered an hour-long speech in Latin to an academic gathering. The subject was women's right to be educated.

In Italian, the curve is called la versiera di Agnesi which means "the curve of Agnesi". Early on the word “versiera” was mistranslated by Cambridge professor John Colson as "witch", and the mistranslation into English stuck.

The Witch of The Witch of AgnesiAgnesi

Curve construction scheme

Profiles of Spectral Lines: 2 Profiles of Spectral Lines: 2 CollisionalCollisional BroadeningBroadening

As an atom collides with another particle, the collision may not result in a change of energy state; however the collision can be thought of producing a break in the phase of the f(t) associated with its energy levels, thus “resetting to zero” the lifetime of coherence. The resulting energy broadening is similar to the natural broadening, i.e. a Lorentz profile with width

The line profile function due to natural + natural + collisionalcollisional broadening then is

collt/2'

collnatural

o

t/2)4/()(

4/)( 22

2

where the line profile function is defined to be such that

0

1)( d

Note that

=

for

Hence we can refer to

as the Lorentzian half linewidth

Profiles of Spectral Lines: 3 Doppler BroadeningProfiles of Spectral Lines: 3 Doppler Broadening

]cos)/(1[])/(1[

cos)/(12/12 cV

cVcV

ooobs

The Doppler shift for a source moving at speed V and angle theta is

For V<<c

kTmVeVkTmVP 2/2

2/32

24)(

kTmVzekTmNdN 2/

2/12/1 2

2/

mkTcvv

e

oD

vvv

D

Do

/2

1)(22 )/()(

2/1

oooo vvv /)(/)( Note that the Doppler shiftDoppler shift (often a source of confusion between optical and (some) radio astronomers

A gas of particles of mass m in LTE at temperature T has a vel distribution:

The distribution of one component of V is

The resulting line profile function is

where the Doppler Width Doppler Width is

Profiles of Spectral Lines: 3 Doppler BroadeningProfiles of Spectral Lines: 3 Doppler Broadening

2

)/()(2/1

2

1)(22

turbo

D

vvv

D

mkT

cvv

e Do

Often, small-scale turbulenceturbulence in the gas, which produces Doppler broadening, is included in the Doppler width

Example: what is the thermal width of the WNM (T~6000K) HI 21cm Example: what is the thermal width of the WNM (T~6000K) HI 21cm line?line?

skmTVV

kHzTkHzT

TmkT

cvv

DHPFW

D

oD

/72.683.02

2.19606.01067.11037.12

1031042.12

2/13

2/13

2/1

24

16

10

9

5.16)6000(/ KTHPFW skm

KTT )10/( 33

Profiles of Spectral Lines: putting it all Profiles of Spectral Lines: putting it all together together Voigt ProfileVoigt Profile

Do

D

y

D

zzoo

vVDo

vvvu

va

dyyua

eauaH

uaHvv

dVcVvvvevcvv

Dz

/)(

4/)(

),(

),()()(

)4/()/()/(

4)(

22

2/11

22

)/(

2

2

2

The Doppler profile is Gaussian; the Lorentz profile has extended wings. The combined line profile results from averaging the latter over the range of l.o.s. velocities:

Voigt profileVoigt profile(HjertingFunction)

No analytical solution, it is integrated numerically.

Small a Lorentz wings unimportant

Pure Doppler (Gaussian)

Pure Lorentzian

Profiles of Spectral Lines: Voigt ProfileProfiles of Spectral Lines: Voigt Profile

Do

D

y

vvvu

va

dyyua

eauaH

/)(

4/)(

),( 22

2

The H function has no analytical solution, it is integrated numerically.

Note: Note: for small a Lorentz wings unimportant; a is an indication of the relative importance of Lorentz to Doppler width.

A series expansion of H(a,u) in powers of a yields

where the first 2 terms are

)()(),( 1 uaHuHuaH o

2

)( uo euH 22/1

1 )( uuH

Describes the Doppler core Describes the Lorentz wings

Phase Structure of the ISMPhase Structure of the ISM

Forms of Pressure in the ISMForms of Pressure in the ISM

The prevailing picture of the ISM is one where, at least in part, pressure equilibrium between different phases prevails. It is common to express the gas thermal pressurethermal pressure as the product nTnT, in units of cm-3 K.

Other forms of pressure are also important, namely:

* Magnetic pressure, Magnetic pressure, BB22/8/8

* Hydrodynamic (ram) pressure, * Hydrodynamic (ram) pressure, from moving clouds & shock waves

* Radiation pressure, * Radiation pressure, particularly in vicinity of stars

* Cosmic Ray pressure* Cosmic Ray pressure

E.g. in a cloud of n~10 cm-3 , T=100

P ~ 1000 cm-3 K ,

in the ionized warm medium of n~0.1 cm-3, T=10 K P ~ 1000 cm-3 K

an ordered B=2 G P~1200 cm-3 K (but note that a tangled B yields

a reduced pressure)

Forms of Energy Density in the ISMForms of Energy Density in the ISM

3

3

3

32

32

322

33

/26.0

/5.0

/8.0

//

13.021

/024.08

/)(1000

13.0

cmeVu

cmeVu

cmeVu

cmeVskm

Vcmn

Vu

cmeVBBu

cmeVcmK

nTnkTu

CMB

starlight

cr

gasgasgashydro

GB

th

After R. Pogge web notes

Note that all densities are of comparable value.

Phase Structure of the ISMPhase Structure of the ISM

Two basic papers:

••Field, Goldsmith & Field, Goldsmith & HabingHabing (1969 (1969 ApJ 155, L149: FGH)) introduced the idea of an ISM in equilibrium between 2 thermally stable phases, following the seminal paper on the theory of Thermal Instability by Field Field (1965, ApJ 142, 531).

••McKee & McKee & OstrikerOstriker (1977(1977 ApJApJ 218, 148: MO) 218, 148: MO) introduced the time variable impact of SN and proposed a 3-phase scenario.

• see the review by Cox Cox 2005, ARAA 43, 337

•Let’s go through them one at a time – first the 2-phase medium of FGH

Phase Structure of the ISM: FGHPhase Structure of the ISM: FGH

nGTnTnL )(),( 2

Suppose the IS gas is in stationary conditions, with density n and temperature T (both variable in space). Its thermal balance is characterized by the “generalized loss function”:

where the first term on right is the cooling rate per unit volume and the second is the heating rate per unit volume. For L>0 net cooling

L<0 net heatingL=0 thermal balance

Heating Sources:Heating Sources: 1. Photoelectrons from dust grains1. Photoelectrons from dust grainsHigh energy photons in the ISRF can knock off e from dust grains. Those ejected from small grains and PAHs are effective in heating the IS gas. Estimated yield erg s-1 cm-3

Heating Sources:Heating Sources: 2. Photoelectrons from atoms & molecules via ISRF2. Photoelectrons from atoms & molecules via ISRFEstimated yield erg s-1 cm-3

Heating Sources:Heating Sources: 3. Cosmic Rays 3. Cosmic Rays (source considered by FGH)Estimated yield erg s-1 cm-3

nnG 261 106

22/1272 106 nTnG

nnG 283 108


Interstellar cooling function (after Dalgarno & McCray 1972 ARAA 10,375)

At T>107 Km cooling is dominated by thermal bremsstrahlung (free- free), and it is proportional to T1/2

C+,Si+,O

Ly

O++

CIV

OVI

He Fe


Cooling Mechanisms:Cooling Mechanisms:

At low T<100K, the main cooling agent is the 157.7 157.7 m transition of Cm transition of C++, which has an excitation temperature of 92 K92 K. The upper state of the transition is populated mainly by collisions with electrons. Other important coolants at low T are the 35 35 m line of Sim line of Si++ ((TTexcexc =412 K) =412 K) and the two O O lines at 147 lines at 147 m (m (TTexcexc =228 K) and 63=228 K) and 63 m (m (TTexcexc =335 K).=335 K).

At 8000 K < T< 20000 K, collisional excitation and ionization of H produces the steep increase in the cooling curve

Excitation and ionization of higher order ions dominate the cooling between 20000 K and 106 K

Thermal bremsstrahlung (~ T1/2 ) dominates above 106 K.


A B C D

L<0L<0

L>0L>0

L=0L=0

Log TLog T

Log PLog P

Consider a region of the ISM for which L(n,T)=0; apply a perturbation to one of the thermodynamical variables: is the region restored to equilibrium? The Field thermal instability criterion says the equilibrium is unstableunstable if

0

XSL

S= entropyX=variable kept const. (e.g. pressure)

0

PTL

Condition of instability for an isobaric perturb.

Consider a perturbation on n at point A:

n up at constant P, T must go down; that drives the gas to region with L<0 restoring the gas to equilibrium gas at point A (and C) is stablestable

Similarly, gas at points B and D is in unstable equilibrium

stablestableunstable

unstable

Cold Phase (A):Cold Phase (A):

n>10, T~300K

Warm Warm IntercloudIntercloud (C ):(C ):

n<0.1 T>8000 K

Phase Structure of the ISM: a hot phasePhase Structure of the ISM: a hot phase

•1956 SpitzerSpitzer proposes the idea of a hot gaseous “galactic corona”, in pressure equilibrium with disk IS gas.•1974 Cox & Smith Cox & Smith propose that such a phase could be maintained by SNe•1977 McKee & McKee & OstrikerOstriker elaborate the scenario

It is clear from previous slide that a hot (T>105 K) phase is not thermally stable – and yet we live inside such a hot “local bubble”, with n~0.005 cm-3.In a low density medium, collisions are rarer and cooling times are long - ~106 yr >> than the galactic SN rate ~50-100 yr SNe can continuously reheat the gas before it can cool much

MO estimate that the resulting hot phase would have

T ~ 10T ~ 1066 K n ~ 0.002 cmK n ~ 0.002 cm--33 volume filling factor ~ 0.75volume filling factor ~ 0.75

in rough pressure equilibrium with the cold and warm phases.

Neither the 2-phase nor the 3-phase picture is correct: observations show an even wider variety of “phases”, and thermal pressure equilibrium is not the norm, suggesting that if pressure balance is roughly held, thermal pressure may not always be the main player magnetic, c.r. P?

From McKee & Ostriker

From McKee & Ostriker

The idea of a hot phase heated by SNe was first proposed by Cox & Smith in 1974, who introduced the porosity factor porosity factor as an indicator of the volume filling and connectiveness of SN bubbles q>1 means most bubbles connect into a pervasive hot medium. They estimated a relatively low porosity of q ~ 1. McKee & Ostriker refined the definition of q: 3.1

0414.028.1

51135.0 nTnESq

Hot ISM Phase

S-13 = SN rate p u volume in 10-13 pc-3 yr-1

E-51 = avg SN energy in 1051 erg/sn = ambient nr density cm-3

<nT> = ISM pressure in 10-4 cm-3 K

and derived q>3 most bubbles overlap. Current view is for a much smaller value of q.

Three common misconceived scenarios (according to Cox 2005 ARAA review)

Extract from Cox ARAA 2005

ROSAT soft X-ray (0.5-0.9 keV)

Phase Structure of the ISM: ObservationsPhase Structure of the ISM: Observations

1.1. Molecular CloudsMolecular Clouds. .

n > 1000 cmn > 1000 cm--33 T ~ 10T ~ 10--20 K 20% 20 K 20% of ISM by mass volume filling f<1%f<1%

Molec. Clouds are gravi-bound, sites of SF Main tracer: CO

2.2. Cold Neutral Medium (CNM)Cold Neutral Medium (CNM)

n ~10n ~10--50 cm50 cm--33 T ~ 100 K 5T ~ 100 K 5--20% 20% of ISM by mass f ~1f ~1--4%4%

HI clouds, filaments Main tracers: HI 21cm absorption, UV, opt absorption

3. Warm Neutral Medium (WNM)3. Warm Neutral Medium (WNM)

n ~ 0.1n ~ 0.1--0.5 cm0.5 cm--33 T ~6000 K 30T ~6000 K 30--60% 60% of ISM by mass f ~ 40f ~ 40--70%70%

Envelopes of mol. Clouds, HII (photodissociation) regions Tracer: HI 21cm

4. Warm Ionized Medium (WIM)4. Warm Ionized Medium (WIM)

n ~ 0.1 cmn ~ 0.1 cm--33 T~6000T~6000--12000 K <10% by mass f ~ 20%12000 K <10% by mass f ~ 20%

Contains 90% of HII in ISM (rest in HII regns) Traced by diffuse, low SB H

5. Hot Ionized Medium (HIM)5. Hot Ionized Medium (HIM)

n < 0.01 cmn < 0.01 cm--33 T ~ 10T ~ 1055--66K K mass fraction? Volume filling factor?

Hot disk gas buoyant, escapes to halo: bubbles? fountain:? hot corona?hot corona? main tracers: OIV, NV, CIV absorption at T~105 K, then OVI and X-rays

The Curve of Growth MethodThe Curve of Growth Method

Observations of Optical/UV Interstellar LinesObservations of Optical/UV Interstellar Lines

The strongest optical interstellar lines seen in absorption in stellar spectra are

Na I D lines 589.0, 589.6 nmCa II H & K lines 393.3, 396.8 nm

And in the UVH I Lyman seriesMg II 280.0 nmO and C ionsH2 Lyman bands

Lines typically exhibit multiple components (early indications of a “cloudy” ISM).

What information do we infer from this type of study? cloud kinematics, column densities, gas phase chemical abundances

Main tool for analysis

Curve of GrowthCurve of Growth

Observations of Optical/UV Interstellar Lines: the Curve of GrowObservations of Optical/UV Interstellar Lines: the Curve of Growth Methodth Method

o

o

III

,

,

1

0

EW

dI

IIEW

o

o

,

, The equivalent width EWequivalent width EW of a spectral line is

where I

is the continuum level near the line

Independently on the brightness of the stellar continuum, EW is a measure of the the fraction of the light fraction of the light absorbed by the absorbed by the intervening cloud.intervening cloud. EW should not be confused with velocity width.velocity width.


dsnngngcAds 2

21

122

221 1)(

8

))((4

)(4

212121

212

BnBnh

Anhj

o

o

212

3

21

212121

2 BchA

BgBg

kThegg

nn /

2

1

2

1

Combining:

W/1~)(Very roughly:

Equivalent Width of line

2/

321

2

18

NeW

AcexkTh

Which is

2123

21 || dA

Note that

And N2 is the column density of particles in the upper energy level 2

+

+

RECALL:


In the case of optical/UV interstellar absorption lines h

>>kT and stimulated emission can be neglected. Thenwe are in the so-called “pure absorption” case:

In the absence of a Source term, the solution of the equation of transfer is simply

121)(4

Bnh o

eII )0()(

Do

D

y

D

vvvu

va

dyyua

eauaH

uaHvv

/)(

4/)(

),(

),()()(

22

2/11

2

duededI

IIEW uaH

Do

o o )1()1( ),(

,

,

Recall

and recompute optical depth,converting from frequencies to wavelengths (optical astronomers prefer it that way),

Enter in the equation of transfer and obtain:

2/2)/( turboD mkTc

with

)()(),( 1 uaHuHuaH o

2

)( uo euH 22/1

1 )( uuH


The tool used to convert EW into a column density is known as Curve of Curve of GrowthGrowth. Consider the following cases:

1. Small a 1. Small a (Lorentz wings unimportant), small (< 1) optical depth, small (< 1) optical depth

dueEW uaHD

o )1( ),(

oD

uoD

uaHD

EW

duedueEW o

/

)1(2),(

EW grows linearly with : linear part of curve of growth linear part of curve of growth

2. Small a 2. Small a (Lorentz wings unimportant), large (>> 1) optical depth, large (>> 1) optical depth

duedueEW

uoo e

DuaH

D )1()1(2

),( 2

1u

oee

1 for small u (line saturates)0 for large u

In between (“turnover”):

2ln12

oou

o ue oDoD uEW ln2)2(

Integral is from –infty to +infnty, hence 2uo

EW grows very slowly even for very large changes in : flat part of the curve of growth flat part of the curve of growth (see graph 2 slide down)(see graph 2 slide down)


3. Large a 3. Large a (Lorentz wings important), large (>>1) optical depth, large (>>1) optical depth

)/(),( 22

uaeuaH uoo

Recall the series expansion of H(a,u)

For large a, the second term becomes dominant: as the line core becomes saturated, “growth” of the line can take place in the unsaturated Lorentz wings. Then:

dueEW uaD

o )1(2/

22 / uat oWith the change of variables, the integral has an analytical solution:

oD aEW 2/12 ““squaresquare--root law root law ““part of the curve of growthpart of the curve of growth(see graph next slide)

Clearly, the linear and square-root law parts of the CoG are more useful in deriving optical depths and column densities.


Linear

Flat

Square-root law

Difference in shapes of optically thick lines:

Gaussian

Lorentzian

Pilfered from A440 course at RIT

21212

12

2

12 ||)(8 dEEmchvmf

X-axis of CoG usually expressed as the product Nf, of the number of particles in the lower level, the wavelength and the oscillator strength of the transition: tau

Curve of Growth Method: Lyman Curve of Growth Method: Lyman

The HI Lyman series, arising from the n=1 ground state of Hydrogen, have typically very high optical depths in the ISM. Column densities are usually derived from the square-root law part of the CoG, i.e. the lines present substantial Lorentz wings.

For Lyman (121.567 nm), ISM EWs (generally in the square-root regime) can be converted to column densities via

218,

)(10867.12 AngstromcmHIEWN

At high z, however, most of the Lyman absorption lines pertain to a category of low column density, optically thin clouds,with Doppler broadened line profiles, the so-called Lyman Lyman forestforest. While saturated Lyman clouds with high column densities are also detected (Damped Damped Lyman Lyman cloudsclouds), ), these are much rarer. In the following slides, text from the lucid introduction by Rauch, 1998 ARAA 36, 267. We’ll revisit the topic in more detail later in the course.

Note the difference in the Ly forest in the spectrum of a low z QSO (3C273) and that of a high z QSO.(from W. Keel’s website)

dN/dz ~ (1+z)p what’s p?

E. Wright’s cartoon showing the geometry of Ly forest absorbers.

Note difficulty in determining continuum levels, and hence in obtaining EWs

The Lyman

forest is an absorption phenomenon in the spectra of background quasistellar objects (QSOs). It can be observed in the ultraviolet (UV) and optical wavelength range, from the local universe up to the highest redshifts where QSOs are found (currently z ~ 5). Neutral hydrogen intersected by the line of sight (LOS) to a QSO will cause absorption of the QSO continuum by the redshifted Ly

(1215.67 Å) UV resonance line. In an expanding universe homogeneously filled with gas, the continuously redshifted Ly

line will produce an absorption trough blueward of the QSO's Ly

emission line (independent predictions by Gunn & Peterson 1965; Scheuer 1965; Shklovski 1965). Gunn & Peterson found such a spectral region of reduced flux, and used this measurement to put upper limits on the amount of intergalactic neutral hydrogen. The large cross-section for the Ly

transition makes this technique by far the most sensitive method for detecting baryons at any redshift.

Introduction of Rauch’s review: 1998 ARAA 36, 267 (1)

Figure 1. High resolution (FWHM 6.6 km s-1) spectrum of the zem

= 3.62 QSO 1422+23 (V = 16.5), taken with the Keck HIRES (signal-to-noise ratio ~ 150 per resolution element, exposure time 25000 s). Data from Womble

et al (1996).

Bahcall

& Salpeter

(1965)

suggested that there should also be a population of discrete absorption lines from a more clumpy gas distribution, specifically from intervening groups of galaxies. Discrete lines were observed shortly thereafter (Lynds

& Stockton 1966, Burbidge et al 1966, Stockton & Lynds

1966, Kinman

1966), but the quest for their precise origin has given rise to a long and, at times, controversial debate; only in recent years does the issue appear to have been resolved (see

below). Soon thereafter, the simultaneous detection of higher order lines of the Lyman series

(e.g. Baldwin et al 1974) had confirmed the suggestion (Lynds

1970) that most of the absorption is indeed from H I Lyα. At higher spectral resolution, the Lyα

forest can be resolved into hundreds (in z > 2 QSO spectra) of distinct absorption lines, the appearance of which gave rise to the label Lyα

forest (Weymann

et al 1981; see Figure 1). A small fraction of the lines hidden in the forest are not caused by H I

but belong to UV transitions from several common metal or heavy element ions (various ionization stages of

C, O, Mg, Si, Fe, and Al are most frequently seen). These metal lines are invariably associated with strong Lyα

lines. At column densities N(H I) exceeding 1017

cm

2, the gas becomes optically thick to ionizing radiation, and a discontinuity at the Lyman limit (912 Å) is detectable. In systems with N(H)>1019

cm

2, self-shielding renders the gas predominantly neutral. The damping wings of the Lorentzian

component of the absorption profile begin to be detected from about the same column density, reaching their maximum in the “damped Lyα

systems.”

The question of whether the majority of the absorption systems are truly intervening at cosmological distances from the quasar, or ejected by it, which had received considerable interest in the earlier days, is now settled in favor of the intervening hypothesis. The huge momentum requirements for ejection (Goldreich

& Sargent

1976), the outcome of the Bahcall

& Peebles test (Bahcall

& Peebles 1969, Young et al 1982a) for a random redshift

distribution of absorbers to different QSOs, the discovery of galaxies at the same redshifts

as metal absorption systems (Bergeron 1986), and the detection of high metallicity

gas in systems close to the QSO and low metallicities

more than 30,000 km 1 away from it (Petitjean

et al 1994) leave no doubt that most of the systems are not physically related to the QSO against which they are observed.



…The basic observational properties of the Lyα

forest were established in the late 1970s and early 1980s, when the combination of 4-m telescopes (e.g. the AAT, KPNO, MMT, Palomar) and sensitive photon counting electronic detectors (e.g. the University College London's IPCS) first permitted quantitative spectroscopy on high redshift

QSOs

to be performed. Making use of the new technology, the work by Sargent

et al (1980) set the stage for what for many years has been the

standard picture of the Lyα

forest: Lyα

absorbers were found to be consistent with a new class of astronomical objects, intergalactic gas clouds, which are distinct from galaxies (and metal absorption systems) by their large rate of incidence (dN

/dz) and their weak clustering. Upper limits on the gas temperature

and estimates for the ambient UV flux and for the cloud sizes were found to be

consistent with a highly ionized (nHI/nH

≤

10-4) optically thin gas kept at a temperature T ~ 3 ×

104

K by photoionization

heating. Sargent

et al (1980)

suggested that denser clouds in pressure equilibrium with a hotter (i.e. more tenuous) confining intercloud

medium (ICM) could explain the apparent lack of change of these

objects with time. It was argued that this picture matches the inferred cloud properties better than clouds held together by gravity, and there were a number of other appealing features. In the wake of the dark matter–based structure formation scenarios, the pressure-confined clouds have given way to models where Lyα

clouds arise as a natural immediate consequence of gravitational collapse.

In an earlier review, Weymann

et al (1981)

introduced a classification of absorption systems that is still

useful, although some of the distinction has been blurred by the

most recent research (Cowie

et al 1995, Tytler

et al 1995). In particular, the earlier review distinguished two classes of absorption systems, physically separated from the QSO environment, according to whether they do, or do not, show metal absorption lines in addition to the ubiquituous

Lyα. For most of the Lyα, clouds detectable with current technology [i.e. N(H I) >1012 cm 2], metal lines with metallicities

common at high redshifts

(Z

<10-2

Zsun

) are simply below the detection threshold. Therefore, this classification is simply an observational one. Rather than explore the nature of the division, if appropriate, between metal absorbers and Lyα

systems, here we concentrate on the low column density absorbers. The study of metal absorption systems, possibly of great relevance to galaxy formation, is left for future review.

Student’s brief presentations:

1. What’s the Gunn-Peterson Effect? 15min

2. What’s the dependence of Ly forest cloud count on HI column density?What’s the dependence on (1+z)? 15min

(What’s the conversion from EW to N(HI) for optically thin clouds?)

Mon Sep 27

Presenters: have a .ppt or .pdf file of your presentation delivered to RG or MH by noon of Sep 27

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