giant hii regions lecture07 handouts

8/17/2019 Giant HII Regions Lecture07 Handouts

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University of Heidelberg, Center for Astronomy

Giant Star-Forming Regions

Dimitrios A. Gouliermis & Ralf S. Klessen

Lecture #7Physical Processes in

Ionized Hydrogen Regions

Part II

Giant Star-Forming RegionsGouliermis & Klessen

(tentative) Schedule of the Course

WS 2012 - 2013 Lecture 7 2

Lect. 1

19-Oct-2012 Course Overview

Motivation for the Course/Schedule; Overview of Physical Processes in HII Regions; Classification of HII regions

Lect. 2

26-Oct-2012 Introduction to the Physics of the ISM I

Phases of the ISM; Transitions; Introduction to cooling mechanisms

Lect. 3

2-Nov-2012 Introduction to the Physics of the ISM II

Atomic Transitions; Gas Cooling; Collisional Excitat ion

Lect. 4

9-Nov-2012 Introduction to the Physics of the ISM III

Gas Heating; Photo-ionization; Photo-electric heating; PAHs

Lect. 5

16-Nov-2012

Interstellar DustComposition, Spectral Features, Grain Size Distributions, Extinction

Lect. 6

23-Nov-2012 Physical Processes in HII Regions I

Radiative Processes; Photo-ionization & Recombination of hydrogen; Photoionization Equilibrium

Lect. 7

30-Nov-2012 Physical Processes in HII Regions II

Heating and Cooling of HII Regions; Strömgren Theory; Forbidden lines and Line Diagnostics

Lect. 8

7-Dec-2012 Photodissociation regions (PDR)

Ionization & Energy Balance; Dissociation of Molecular Hydrogen; Structure; Observations

Lect. 9

14-Dec-2012 Stellar Feedback Processes

Dynamics of the ISM; Ionization fronts; Expansion of HII regions; Stellar Winds and Supernovas

Lect. 10

11-Jan-2012

Stellar Content of HII Regions I

Massive Stellar Evolution; Mass-Loss; Rotation; Binary interaction; Spectral features of OB stars; Runaway stars - StellarCluster dynamics

Lect. 11

18-Jan-2012

Stellar Content of HII Regions IIPre--Main-Sequence (PMS) Stars; Young Stellar Systems; Stellar Initial Mass Function; Age determination &History

Lect. 12

25-Jan-2012

Star Formation (SF)Isothermal shperes and Jeans mass; Molecular Cores collapse; Protostars

Lect. 13

1-Feb-2012 Star Formation

PMS Stellar Evolution/Contraction; Characteristics of T Tauri stars; Herbig Ae/Be Stars; Multiple SF


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Physical Processes in HII RegionsPart II

In this Lecture

• Strömgren Theory (for Hydrogen)

• Heating & Cooling of HII Regions

• The Role of Helium

• Forbidden Lines (CELs)

• Line Diagnostics for HII Regions

WS 2012 - 2013 3Lecture 7

–

Literature• Osterbrock & Ferland , 2006, Ch. 2

• Spitzer , 1978, Sec. 6.1

• Tielens, 2005, Ch. 7


The Strömgren Theory •

Real HII regions are inhomogeneous. Their properties aredetermined by the local ionization parameter.

• Modeling HII regions requires a good calculation of thestellar FUV radiation field (usually through Monte Carlo).

• A simple (avoiding the above complications) but veryuseful theory to describe an HII region as a uniformspherical region, is this by Bengt Strömgren (1939).

•

It examines the effects of the electromagnetic radiation ofa single star (or a tight cluster of similar stars) of a givensurface temperature and luminosity on the surroundinginterstellar medium of a given density.

WS 2012 - 2013 Lecture 7 4

Classical Article: Strömgren, Bengt The Physical State of Interstellar Hydrogen,The Astrophysical Journal, 89, 526-547 (1939)


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The Strömgren Theory• The interstellar medium is taken to be homogeneous and

consisting entirely of hydrogen.

•

Strömgren theory describes the relationship between theluminosity and temperature of the exciting star, i.e., theintensity of the ionizing sources, on the one hand, and thedensity of the surrounding hydrogen gas on the other.

•

The size of the idealized ionized region is calculated asthe Strömgren radius.

• Strömgren’s model also shows that there is a very sharp

cut-off of the degree of ionization at the edge of theStrömgren sphere, because the transition region betweenthe highly ionized and the surrounding neutral gas is verynarrow, compared to the overall size of the sphere.

WS 2012 - 2013 Lecture 7 5


The Strömgren Theory

Basic Realationships

• The hotter and more luminous the exciting star, the largerthe Strömgren sphere.

•

The denser the surrounding hydrogen gas, the smaller theStrömgren sphere.

WS 2012 - 2013 Lecture 7 6


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The Strömgren Sphere

WS 2012 - 2013 Lecture 7 7

The Strömgren sphere radius R S is determined by balancing the

total rates of ionization and recombination inside it.

The total ionization rate as a function of distance from the star ina spherical volume around it is:

" HnH J (r) =

3S H

4# r3

In the stationary situation, which is typical for an HII region, the

number of ionizations equals the number of recombinations, andtherefore:

" HnH J (r) = ne

2# 2(T )


The Strömgren Sphere

WS 2012 - 2013 Lecture 7 8

From equating the ionization and recombinations rates we get:

Where S H (in S 491049 photons s –1) is the rate at which the central

star produces photons that ionize H, and x = ne/n the ionizationdegree. Since the gas is considered fully ionized ( x ~ 1):

S H

=

4"

3 R

S

3ne

2# 2

=

4"

3 R

S

3(nx)

2# 2

RS=

3

4"

S H

n2

# 2

$

%

& '

(

)

1

3


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Strömgren Spheres Characteristics

WS 2012 - 2013 Lecture 7 9

Numerical value for T = 7,000 K. In reality n is determined by thedynamics of the HII region, i.e., its expansion into the non-uniform surrounding ISM.

RS =3

4"

S H

n

2

# 2

$

% &

'

( )

1

3

* 61.7 S 49

n

2

$

% &

'

( )

1

3

pc



WS 2012 - 2013 Lecture 7 10

Ionization Parameter U S and radial column density nR S.

U S =n"

n=

S

4" RS2cn

=(4" /3) RS

3

n2

# 2

4" RS2cn

=# 2

3cnRS

nRS =

n 3

4"

S

n2#

2

$

% &

'

( )

1/ 3

=

3

4"

nS

# 2

$

% &

'

( )

1/ 3

=

3

4"# 2

$

% &

'

( )

1/ 3

nS ( )1/ 3

We consider a location just inside R S where x = 1, we ignoreattenuation of the spectrum, and apply ionization equilibrium:

and thus, U S=

" 2

3c

3

4#" 2

$

% &

'

( )

1/ 3

nS ( )1/ 3

Both U S and nR S are proportional to (nS )1/3.


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WS 2012 - 2013 Lecture 7 11

Ionization Parameter U S and radial column density nR S.

U S " 3.3 #10

$3n

2S 49( )

1/ 3

RS= 8.6 #10

20(n

2S 49 )

1/3 cm

2

By substituting with typical numerical values, !2 = 3.65!10 –13

cm3 s –1, n = n2100 cm –3 and S = S4910

49 photons s –1 we get:

The radial column density nR S is related to the “average”column density:

N =(4" /3)nRS

3

" RS2

=

4

3

nRS #1.15 $10

21n

2S 49( )

1/ 3

cm%2

As n increases for fixed S, the column increases as n1/3.Therefore, small dense HII regions can have large columns.

This is the case of ultra-compact HII (UCHII) regions.



WS 2012 - 2013 Lecture 7 12

The H+ /H ratio. From results so far for the ionization parameterwe have (Lecture 6):

Substituting we have:

which expresses the H+/H ratio in terms of the optical depth at theLyman edge. Recalling (Lect. 6) that "1 = 6.33!10

–18 cm2, we get:

nH+

nH

0

=

U

U H

U H=

" 2 xe

# 1c( I 4 / I 1) U

S=

" 2

3cnR

S

nH

+

nH

0

=

1

3" 1nRS( I 4 / I 1) =

1

4" 1 N ( I 4 / I 1)

" # 1

=$ 1 N = (6.33%10

&18)(1.15 %10

21)(S

49n

2)1/ 3

= 7280(S 49n2)1/ 3

The H+ /H is about 1/8 of this value, and thus ~900(S49n2)1/3.


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WS 2012 - 2013 Lecture 7 13

Thickness of H+ /H transition region !R S.

" # 1

= $ RSnH0% 1

=1

This is the region in which x(H) goes from 0 to 1. Its thickness isroughly the distance for an ionizing photon to be absorbed:

If we neglect hardening of the spectrum and define the transitionwhere n(H) = 0.5n, we have:

" RS

RS

=

1

1

2 nH0# 1 RS

=

1

3

8# 1 N

=

2

3

U H

U S

I 4

I 1

$ 3.5 %10&4(S 49n2)

&1/ 3

!R S, as well as, H+ /H ratio, U S, and nR S, all depend on the

Strömgren parameter (Sn)1/3.


“Real” Strömgren Spheres

WS 2012 - 2013 Lecture 7 14

• Real HII Regions are rarely circular

•

Nonetheless, Strömgren’s theory Illustrates the basic roles of photo-ionization and recombination.

The Ring Nebula (M 57)

All images: Hubble Space Telescope (AURA/ STScI/ NASA/ ESA)

The Helix Nebula (NGC 7293) The Spirograph nebula (IC 418)


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Ionization Balance Summary• The excess energy over the ionization potential is

carried away by the photo-electron as kinetic energy.

• Recombination is slow (~100 yr for #$103 cm%3),while e-e collisions occur on ~30 sec timescales.

• Electrons collisions exchange energy leading toMaxwell velocity distribution (Thermal emission).

• Thermal electrons excite low-lying levels of tracespecies.

• Downward radiative transitions cool the nebula.

• This energy balance sets the temperature of the gas.

WS 2012 - 2013 15Lecture 7


Thermal Balance

WS 2012 - 2013 Lecture 7 16

Temperature of Photoionized Gas. The one important heatingmechanism (photo-electric heating) involves the dissipation of theexcess energy of the photoelectrons (generated by the absorption ofstellar UV photons) in Coulomb collisions with ambient electrons:

The mean energy of the photoelectrons is

E 2 =

h(" #" 1)$ " 4% J

"

h" d "

" 1

&

'

$ "

4% J "

h" d "

" 1

&

'

where J " is the mean intensity of the radiation field.

A detailed treatment of heating and cooling in HII regions is given inSpitzer Sec. 6.1

E e

= h" # h" 1

~ kT


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Photoelectric Heating

WS 2012 - 2013 Lecture 7 17

Spitzer expresses the mean photoelectron energy in terms of the stellareffective temperature:

With # $ nH the photoionization rate per unit volume, the volumetric heatingrate is

" = # $ nH% kT *

! 0 is the value near the star, ‹! › is averaged over an HII region. Thefirst decreases and the second increases with T *, as does also theirratio ‹! ›/! 0.

" = E 2 /kT *


Recombination Cooling

WS 2012 - 2013 Lecture 7 18

Radiation is the main cooling mechanism of the ISM. In HII regions, radiation from recombination provides aminimum amount of cooling : each recombination drainsthermal energy & me"

2 from the gas. The total cooling rateper ion is

The recombination cross section % j varies as " 2

(Lecture #6).Therefore the rate of cooling by recombination is determinedby the thermal average of " 3 & " 2 = " , i.e., T &. (This is

confirmed by the exact calculations of Spitzer.)

1

2m "

3# j

j =k

$

%


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Recombination Cooling Rate

WS 2012 - 2013 Lecture 7 19

The volumetric cooling, neglecting recombinations to the

ground state (on-the-spot rate approximation) is

!2: Recombination function (Spitzer Table 5-2, p. 107) "2: Energy gain function (Spitzer Eq. 6-8, p. 135 & Table 6.2).Roughly 3/2kT of electron thermal energy is lost in

each recombination in an HII region.

"rec= #

2n

en(H

+

)kT $

2

% 2


Preliminary Thermal Balance for Pure H

WS 2012 - 2013 Lecture 7 20

Net energy gain associated to recombinations (Spitzer Eq. 6-9)

For recombination cooling to balance with photoelectricheating requires

So, the predicted temperature is much greater than what isobserved: There must be other coolants at work!

"ep =2.07 #10

$11nenp

T1/2

E 2% 1(h& 1 /kT ) $ kT ' 1(h& 1 /kT ){ } erg

cm3 s

(energy gain resulting from captures of electrons by protons)

In HII regions, where the “on-the-spot” approximation applies, allrecaptures to the ground level can be ignored, and !1 and "1 can bereplaced by !2 and "2.

"ep = 0#T

T *

=

$

% & >1


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The Role of He in HII Regions

• He has high IP: He 24.6 eV (504Å); He+ 54.4 eV (228Å)(see also Lecture #4)

• Very hot stars are needed to ionize He+ (T* > 50,000 K).O-type stars are not enough, so their HII regions haveno He++. Planetary nebula stars or AGN.

• The radiation that ionizes He also ionizes H.

• He recombination radiation photoionizes H.

•

The He threshold photoionization cross section is largerthan that for H, largely compensating for its smallerabundance.

WS 2012 - 2013 Lecture 7 21


Ionization of He by O- & B-type stars

• B0 star, T eff $ 30,000K – Spectrum peaks at ~13.6 eV

• Many photons in 13.6 - 24.6 eV range

•

Few photons with hv > 24.6 eV –

Two Strömgren spheres• Small central He+ zone surrounded by large H+ region

• O6 star, T eff $ 40,000 K – Spectrum peaks beyond 24.6 eV

• Lots of photons with hv > 24.6 eV

–

Single Strömgren sphere• H+ and He+ zones coincide

WS 2012 - 2013 Lecture 7 22


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Ionization Structure in Model HII Regions

WS 2012 - 2013 Lecture 7 23

For an O6 star, the abundant supply of He-ionizing photons keeps both H and He

ionized, whereas the smaller number generated by a B star are absorbed close

to the star.

Osterbrock & Ferland, Astrophysics of Gaseous Nebulae

and Active Galactic Nuclei , University Science Books, 2006


Nebular Lines: Historical Overview• Helium

–

Discovered by Pierre Janssen in1868 in Solar emissionlines (at 5816 Å), and also identified on Earth in 1895.

• Nebulium –

Discovered by William Huggins in 1864 in emissionnebulae at 500.7, 495.9, and 372 nm.

– Identified in 1927 by Ira Sprague Bowen as [OIII] and[OII].

– Significance: highlighted the possibility of long-lived

quantum states and focused attention on understandingselection rules in quantum mechanics.

WS 2012 - 2013 Lecture 7 24


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Cooling of HII Regions

• Photoelectric heating balanced by recombinationcooling in a pure hydrogen model predicted too hightemperatures for HII regions.

•

This suggests that another cooling agent is in action.

•

Collisional excitation of elements heavier than H is avery efficient cooling process (Lecture #3).

• Common ions of O, N, C, Ne, Ar all have levels that are~1eV above ground state, i.e., easily collisionally excited.

•

Forbidden transitions due to collisional cooling frommetal ions are important around T = 104K.

WS 2012 - 2013 Lecture 7 25


Cooling of HII Regions

WS 2012 - 2013 Lecture 7 26

Long slit optical spectrum of the Orion Bar.

• The optical line emission of HII regions is dominated by therecombination lines of H & He and by the forbidden lines of heavyelements (even more so for SNRs and AGN), important for cooling.

Thus, collisional excitation of heavy elements must be included inphotoionization calculations.


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Optical Spectrum of an HII region

WS 2012 - 2013 Lecture 7 27

Planetary Nebula NGC 3242(ESO 1.5-m in Chile) Blue: recombination lines of H and He

Red: forbidden lines of ‘metals’


Atomic hydrogen recombination lines

WS 2012 - 2013 Lecture 7 28

1

"

= R# 1

nl2 $

1

nu2

%

& '

(

) *

nl : Lower level

nu : Upper level

R : Rydberg's constant (1.097"107 m#1)


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Collisional De-excitation

WS 2012 - 2013 Lecture 7 29

The de-excitation rate coefficient, #ul, is related to the excitation ratecoefficient, #lu, by detailed balance:

" lu=gu

gl

e# E ul / kT "

ul

" ul =

# ul($ )$ =

4

%

µ

2kT

&

' (

)

* + 3 / 2

# ul($ )

0

,

- $ 3e.

µ $ 2

2kT d $

A rate coefficient is a thermal average of a cross section, e.g.,

with $ the reduced mass of the system and % ul(" ) the collisional de-

excitation cross section at the relative velocity, " , of the collisionpartners. The cross section and thus the rate coefficient will depend onthe interaction potential of the collision partners. For, e.g., neutralpartners #ulT

1/2, while for electron–ion collisions #ulT –1/2.


Critical Density for collisions

WS 2012 - 2013 Lecture 7 30

The two-level model (Lecture #3, Slide 16) illustrates how the coolingdepends on the density of the collision partner relative to the criticaldensity:

ncrit =" (# ul) Aul

$ ul

For HII regions, electrons are the excitation sources, and #ul is given instandard form (Osterbrock & Ferland Eq. 3.20):

" ul=

8.629 #10$6

T 1/ 2

%ul

gu

&(' ul): escape probability of a photon formed at optical depth ' . Aul: Einstein coefficient for spontaneous emission.#ul: Collisional (de-excitation) rate coefficient.

Where "ul is the collision strength and gu the statistical weight of level u.


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Forbidden Transitions through collisions

WS 2012 - 2013 Lecture 7 31

Typical values of #ul are 10 –7 cm3 s –1. Osterbrock & Ferland provide

tables of atomic properties of heavy elements. Table 3-15 gives asampling of critical densities at 10,000K. For the 2p2 ions OIII & NII:

•

ncrit (NII: 1D"3P; 6500 Å) = 6.6 ! 104 cm –3 •

ncrit (OIII: 1D"3P; 5000 Å) = 6.8 ! 105 cm –3

These transitions will be sub-thermally excited in many HII regions.

Forbidden lines or collisionally excited lines (CELs) arise when anelectron is excited by a collision into a ‘metastable state’.

In high densities (~108 cm –3) the electron would almost immediatelybe knocked out of a metastable state by collision and not be given timeto emit a photon. In low densities, the time between collisions is longenough to allow to the ion to radiate spontaneously.


[OIII]

WS 2012 - 2013 Lecture 7 32

Schematic illustration for one level of O III showing the energy level splittingfor a configuration-averaged model, an L-S term split model, and a fine-

structure splitting model. From S. Bashkin & J. O. Stoner 1975: Atomicenergy levels and Grotrian Diagrams Vols.1 & 2

OIII (1s22s22p2) has two 2p electrons (isoelectronic with NII and CI).The electron spins couple to a total spin S = 0,1. The two orbital angularmomenta couple to total L = 0,1,2. Of the 6 LS-coupling states, & satisfy thePauli Exclusion Principle: 1S0

1D2 3PJ (J =0 ,1,2), with different spatial wave

functions and Coulomb energies.


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Grotrian Diagram for the OIII triplet

WS 2012 - 2013 Lecture 7 33

From S. Bashkin & J. O. Stoner 1975: Atomic energy levels and Grotrian Diagrams Vols. 1 & 2.(Labels on the solid lines refer to the transition wavelengths.)


Forbidden Lines Cooling

•

Transition rates for producing CELs are very low

(~10 –3 – 100 s –1)

• H recombination rates are much higher (~109 s –1)

•

Photons are very likely to escape the nebula beforebeing absorbed and so absorption can be ignored.

•

They can remove a lot of heat from the nebula, resolvingthe high temperature issue if recombination only isconsidered.

• The higher the metallicity (i.e. heavy-element content) of a

nebula, the faster it cools to thermal equilibrium, and the

stronger the forbidden lines are.

WS 2012 - 2013 Lecture 7 34


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Typical Forbidden Lines

WS 2012 - 2013 Lecture 7 35

(N+)

(O2+)

Common forbidden lines:

Optical: [OIII] 4959,5007 Å, [NII] 6548,6584 Å, [SII] 6717,6731 ÅInfrared: [OIII] 52,88 µm, [NIII] 57 µm


Line Ratios as “Thermometers”

•

Relative Intensities of CELs

provide a measure of electron

temperatures in HII regions.

•

Widely used are the intensityratio of the [OIII] lines !4363/

!5007, or !4363/!4959, or(!4959+!5007)/!4363.

WS 2012 - 2013 Lecture 7 36

[OIII] (!4959+!5007)/!4363 intensity

ratio as a function of temperature.

From Osterbrock (1989).

Explanation: More energetic (hotter) free

photoelectrons are needed to push electronsin the upper state than to populate the lower

energy levels. So the line strength ratio

immediately measures how hot the electron

plasma in a nebula is (see previous slide).


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Line Ratios as density measures

WS 2012 - 2013 Lecture 7 37

Variation of [OII] (solid line) and [SII](dashed line) intensity ratios as a function

of ne at Te = 10000 K.

From Osterbrock (1989).

•

Relative Intensities of CELs

provide also a measure ofelectron densities in HIIregions.

• The most commonly used

density measure is the

intensity ratio of the [SII] lines

!6717/!6731 or the [OII] lines

!3726/!3729.

Explanation: The de-excitation

rate is only a function of electron

density.


Line Ratios as abundance measures

WS 2012 - 2013 Lecture 7 38

•

The strengths of certain forbidden lines of heavy ions in HIIregions and PNe, combined with knowledge of the electrontemperature and density in the nebula, allow us todetermine the abundance of these ions (and collectively oftheir respective element) relative to Hydrogen. For example:

Where ne is the electron density; f (T e) is the fraction of O2+ ions able to

emit at 4959 Å (with a strong dependence on nebular) and I ('4959)/I (H !)is the flux of the [OII] 4959 Å line relative to H !.

N (O2+)

N (H+

)~

ne

f (T e)

I (" 4959)

I (H# )

•

We measure the strength of the forbidden lines from all the

ionic stages of an element (e.g. O, O+, O2+) and add up all theabundances to find the total abundance relative to H.


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Summary• Photoionization (photoelectric effect) heats a

gaseous nebula.

• The simple Stroemgren theory describes thecharacteristics of a pure hydrogen nebula.

• Helium plays important role in real emissionnebulae.

• Recombination & Collisional excitation cool HIIregions.

• These cooling processes produce emission lines.

• These lines are used as diagnostics forcharacterizing HII regions.

WS 2012 - 2013 Lecture 7 39

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