Interstellar medium

Roberto Decarli

Extragalactic Astronomy

A.Y. 2004-2005

- What is the ISM?- Emission and absorption

- Electromagnetic wave propagation- Structure and other astronomical hints

- Computational models

What is the ISM?- Gas, dust, cosmic rays which all affect wave propagation in the whole electromagnetic spectrum

- Both atomic and molecular components

- Both neutral and ionized regions

- Density varies between 0,01 and 100 atoms/cm3

- Temperature may change between few and several million K

- Equilibrium approximation is only a good starting point, but nature is more complex

Neutral and ionized regionsWe can consider two kind of regions in the ISM, according to the amount of hydrogen ionization.

Neutral regions can be divided in three classes:1- Warm component (T ~ 100 to 1000 K);

2- Cool component (T ~ 100 K), also known as HI regions, traced by 21 cm emission line;

3- Cold component (T ~ 10 K), also known as H2 regions, traced by molecular emission.

Ionized regions can be divided in two classes:1- Warm component (T ~ 1000 to 10000 K), also known as HII region;

2- Hot component (T >> 10000 K), near SNR.

Why gas is ionized?

Gas ionization occurs for three reasons:

-The temperature is high enough to cause ionization of atoms during thermal collisions;

- Ultraviolet radiation from stars produces photoelectric effect (hydrogen ionization energy is 13,6 eV);

- Cosmic rays and high-energy stellar material ejected as stellar winds or during violent phenomena (e.g. SN) ionize the medium during particle collisions.

Wave absorptionFree charges q, when accelerated, emit radiation whose power is:

I = emission intensity; E = electric wave field; T= Thomson

If we consider bounded electrons, oscillating with pulsation 0 around the nucleus, and a monocromatic radiation with frequency , the cross-section acquire a frequency dependence:

432 2

3

22 cEI

caq

P TT

RTTem

eErr

4

0222

00

..

)(1

For << 0. This approximation rules the blue colour of sky during day and the reddish colour of the sky at sunrise and sunset.

DustDust reddens observed spectra. This effect makes colour index appear higher, notwithstanding spectral classes. We may define:

RR

drndrn00

Column density

Optical depth:

086,1

)0()(

5,2 f

RfLogAMagnitude

extintion:

12),( 12 AAE Colour excess:

We can measure A by measuring m-M at different wavelengths for stars near the Sun and stars far from it. If stars belong to the same spectral class, apparent magnitude difference can be plotted in function of frequency. For ∞ absorption vanishes and we can measure Log(d1/d2). With this information we can find A.

Dust may also scatter and diffuse

incident radiation.

V838 Monocerotis

explosion lighted

surrounding dust

(probably stellar

material from previous

explosions), as seen from

HST.

Thermal emission (simplified) – 1

Consider the interaction between a free electron and an ion (free-free interaction). Ion dynamic is negligible, according to mass difference. Electron speed may be assumed as:

If b ≈ n-1/3, deflection (see Rutherford’s scattering) results:

So electron trajectory may be considered a straight line. We can pass in frequency domain simply applying Fourier transform:

Whole emission may be assumed to happen in t = b/v. If t >> 1, the exponential rapidly oscillates, and the integral vanishes; if t << 1, eit ~ 1 and integral is v. Emission spectrum results:

scmTm

Tkvv K

e

b /1003,68

][5

000055,0arctan2arctan2][

2

2

KeT

Zbvm

Ze

dtevava ti ˆ2

2223

622

3

2

38

32

bvmceZ

vce

ddW

e for t << 1

Thermal emission (simplified) – 2

This equation concerns the interaction between an electron and an ion. Integrating over the whole number of ions and electron:

vdtbdbnddW

ndVd

dWi

b

be

2

max

mintotal

Number of ions in the ring between b and b+db from

the electron

Distance covered by the electron in dt

bmax ~ v/, while there are two considerations to do for bmin: a) electron potential energy cannot exceed its kinetic energy, so: bmin ≈ 2Ze2/mev2; b) according to Heisenberg, bmin ≈ h/mev. One must refer the maximum of these two, in order to follow both conditions. Total emission spectrum is: min

max223

6

total

ln316

bb

Znnvmc

edVdtd

dWie

e

We considered only ion-electron interactions. Ion-ion and electron-electron interactions contribute only in quadrupole terms, since dipole variations vanish if interacting particle masses are equal.

Thermal emission (simplified) – 3

Now we need assumption about electron speed distribution. If Maxwell distribution is considered, that is we assume electron to be in thermal equilibrium, we have:

where the ln term was absorbed in g = Gaunt factor and weighted over the speed distribution. j is the emission coefficient. For thermal cases, we recall Kirchhoff’s law: j = B(T) where is the absorption coefficient and B(T) is blackbody brilliance. Inverting, in Wien approximation ∝-3; in Rayleight-Jeans cases, ∝ -2 (omitting logarithmic dependence).

Optical depth in RJ cases results:

jgeZnn

Tmkcme

dVdtddW Tkh

ieebe

b 43

2316 2

21

3

6

total

RnTdxnTdx ee22232

depthISM

22232 1010 in cgs units

Emission Measure (EM)where we assumed ne ≈ ni (hydrogen plasma).

Thermal emission (more accurate)Analogous results may be obtained considering Fourier transform of other physical quantities, such as electron speed or ion potential.

A deeper study of bremsstrahlung interaction should consider quantum effects on energy exchange [Oster (1961)]. The most important difference is that quantum treatment consider electron energy loss due to radiation. Another difference is that impact parameter doesn’t explicitly appear in quantum treatment. At T < 500000 K, quantum equations are the same as those obtained by classical methods. At greater temperatures, quantum correction leads to:

Tk

Tkm

Znncm

ej b

b

eie

e

4ln

23

324 2

32

6

where = 0,577216 is Euler number. Main dependences are the same as in classical equation.

Thermal and black body emissionWe have thermal emission when radiation is produced only (or mainly) by thermal processes such as bremsstrahlung. If all radiation which enlightens a source is absorbed and reprocessed, we speak of black body emission. Analytically, we speak of black body emission when tends to infinity. In this case, gas is opaque and we can only see the surface of the source.Vantages:

- effective temperature univocally determinates whole emission spectrum.

Against: - radiation gives information only of surface structure: nothing of internal processes can be observed. Sun photosphere is an example of gas

with high optical depth. Photosphere emission spectrum follows Planck

equation.

Discrete spectrum – 1

Discrete spectra are produced by excitation and disexcitation of electrons in atoms and by level exchanges in molecular structure. According to quantum mechanics, transitions between states m and n due to electromagnetic perturbations for a bounded electron are of this type:

2)0()0(

22

202

)()(01

2

10

|||||)(|

)(

)(2

nxki

me

nm

tititxkitxki

e

ee

uepiucm

AT

eTeTeepcm

eAtH

pAcm

exV

mp

HHH

Introducing radiation energy density, U = (E2+B2)/8 = 22A0

2/c2 : 2)0()0(222 ||||

)(2

1

nxki

mnm

nm

emn uepiut

Um

P

or:

2)0()0(222 ||||

)(2

1

nxki

mnm

nm

e

mnmn uepiu

Umdt

dP

nm = (En-Em)/h

Discrete spectrum – 2

We can explicate the physical meaning of the terms in brackets introducing Einstein coefficients: let gn, gm be the statistical weights of the two states. Let En > Em. We define:

where: and is the line shape (normalized).We can use radiation energy density U() instead of j by relation: U=jc/4.

In thermodynamic equilibrium:

and: so, using Planck brilliance:

Anm : transition probability per unit time for spontaneous emission.

Bmn J: transition probability per unit time for absorption.

Bnm J: transition probability per unit time for stimulated emission.

0

)( djJ

)( JBAnJBn nmnmnmnm

Tkh

n

m

n

m bnmegg

nn

nmnm

nmnmnm

Bch

A

BgBg

2

32

TemperatureEquation: let us know equilibrium temperature of the ISM studying the intensity of emissions and absorption. According to medium temperature, a line may be observed as an emission or absorption line. Studying line intensities in gas spectrum, and energy levels associated with those transitions, we can understand which is gas temperature.

Tkh

n

m

n

m bnmegg

nn

VCC0307 in RGB VCC0307 in Hnet + R filter

Lines, lines…Atomic lines:- Balmer, Lyman and other series: H, H, H, K, K, … (l=±1, m=0,±1; S=0, L=0,±1, J=0,±1 except J=0 to J=0);- Prohibited transitions: [OIII];- Hyperfine structure transition: 21 cm line (100 K).

Molecular lines: - Rotational spectra;- Roto-vibration spectra (no pure vibration spectra are observed).

Maser lines: -H2O emission.

Ions and isotopes have different energetic values => different lines

ISM Chemistry: abundances of atomic and molecular hydrogen; He, C, O, Na and many other elements (from star metallicity); OH ion; NH3, H2O, H2CO, CO and many other molecules.

Line shifts and shapesEmission and absorption lines may appear shifted from the rest frequency because of several factors: if radiation source is moving towards us, the line shows a blue shift. If the source is moving away from us, the line shows a red shift. If the source moves because of thermal agitation, the line shape appears flattened. If the source is sunk in an important gravitational field, the line presents redshift. Another reason of redshift is cosmic expansion.Rotational curve of CGCG 522106

5500

5600

5700

5800

5900

6000

6100

-25 -20 -15 -10 -5 0 5 10 15 20

Distance from galactic centre [kpc]

Helio

centr

ic s

peed [km

/s]

Rotational curve for CGCG 522106 galaxy. Data from our Loiano observations during February, 2005. We used H shift in order to measure heliocentric speed as Doppler shift. Galaxy distance can be obtained measuring central redshift and by Hubble law. In this case: D = 83 Mpc, but literature puts D = 65,2 Mpc => heliocentric speed isn’t only cosmological.

Photoelectric effectUV and x radiation is absorbed by ISM thanks to photoelectric effect. This is a bound-free interaction between radiation and matter. In order to let an electron out of nucleus potential well, radiation must pass it a certain amount of energy (ionization energy: it’s 13,6 eV for H, which correspond to UV radiation). Star UV emission is strongly responsible of all-around medium ionization.

Pleiades

Peeters et Al. (2005) proved that important fractions of UV emission by massive stars is absorbed and reemitted as IR.

This emission can be observed both in continuum and in lines from ions (N+, N++, O++, S++ and others). In these regions, Tgas~10 Tdust.

Synchrotron emission – 1Galactic and stellar magnetic fields force charges to follow spiral path along field lines. This accelerated motion causes energy emission by radiation. This process is called cyclotron or synchrotron emission, according with (non) relativistic particle speed. Consider relativistic case:

0

exteext

e

Bvcm

eB

cv

me

dtvd

We assume that kinetic energy loss during a revolution is small, so |v| is constant. Acceleration is: a⊥ = sv⊥, where s = eBext/mec. Radiated power results:

Normal components

Parallel component

834 222

extT BcP

for a single electron emission. Averaging over an isotropic speed distribution leads to:

52

2224

3

242

32

32

cmvBe

cae

Pe

ext

Emission is beamed: an observer detects waves only during a small time interval, that means frequency spectrum is spread.

Synchrotron emission – 2

Assuming a power law distribution for electrons, N(E)dE = CE-pdE, and using E = mec2:

An observer sees emission during time:

21

)()( 2/)1(2/)3(2/)1(

psdfdfP pppp

tot

sin1

1sin12

3ss

obs cv

t

Period

Beam width

= angle between observer

and rotation planeDoppler term ~

1/(22)Its inverse represents -times the cut-off frequency of spectrum. Observed power dependence can be approximated to a power law spectrum such as P() ∝ -s.

using = /cut-off ∝ -

2

if the domain is large enough the integral is almost

constantAs synchrotron emission is ordered along line fields, it’s partially polarized. For power law electron distributions, = (p+1)/(p+7/3).

Synchrotron effectsRazin effect:

Since synchrotron emission takes place in clouds with =[1-(p/)2]1/2, electrons speed must be rescaled: ’=. Power is spread on larger angles 2/’. At low frequencies emission spectrum tends to 3/2 dependence.Self-absorption effect:

Synchrotron photon energy distribution is proportional to -(p-1)/2, while energy distribution for electrons goes with -p/2: at low frequencies photon energy distribution may overcome electrons one. This is physically impossible, according to energy conservation law. In this case, self-absorption takes place: some irradiated photons are absorbed by electrons. This effect leads to a correction in the emission power dependence on frequency (5/2).

Synchrotron spectrum

0,01

0,1

1

10

100

1000

1 10 100 1000 10000 100000 1000000

Frequency [MHz]

I

Pure Synchrotron Synchrotron + Razin effect Synchrotron + Self-Absorption

∝ -0,8

∝

+2,

5∝ +

1,5

SuperNova RemnantsSuperNova Remnants

are probably

the strongest

synchrotron sources.

Radio synchrotron emission is sometimes associated

with optical emission

which lights on ejected materials.

Compton effect

In this case we speak of “inverse Compton” effect. Photon is energized by electron of a factor ~2.

Interaction between an energetic photon and a free, rest electron may be treated as Compton interaction. From energy and momentum conservations, photon energy loss follows the law:

2

2

2

sin16

3

in

out

out

in

in

outTd

d

Interaction cross-section is given by Klein-Nishina formula:

A)cos1(02426,0)cos1(

cmh

e

)cos1('

1''

)'cos1('

)cos1('

2cme

ininout

outoutout

ininin

Where in and out represent photon energy before and after the collision. If we do not stand in electron rest frame, corrections must be made:

Wave propagation in plasma Consider a ionized ISM region, in which external magnetic field is present. Electromagnetic waves are affected by charges and field presence. Charges are accelerated by Lorentz force (let Bext = (Bext)z):

z

zextxy

zextyx

ext

Eme

BvcEme

BvcEme

Bcv

Eme

dtvd 1

1

zz

g

xgyy

g

xygx

Eme

v

EEi

me

v

EiE

me

v

00

2200

0

2200

0

Using vi = v0i ei(t + kx)

where g = eBext/mec. Inserting these equations in Maxwell system, we obtain a new dielectric tensor (p

2 = 4nee2/me):

2

2

22

2

22

2

22

2

22

2

0

100

01)(

0)(

1

p

g

p

g

gp

g

gp

g

p

which is diagonal only for Bext 0; this means that in presence of external magnetic field the medium is anisotropic. Applying this to wave equation we obtain four values for wave number k: waves go in two directions and in both senses of each direction.

Faraday rotation

Due to two propagation modes, two polarized components of radiation propagate in different ways: this leads to rotation of optical axis for polarized radiation (Faraday rotation) and to polarization of unpolarized radiation.

Since d = k dr, total rotation angle is:

Wave number, normalized to k+(/2),

for Bext = 1 microGauss

-3,E-14

-2,E-14

-1,E-14

0,E+00

1,E-14

2,E-14

3,E-14

0 30 60 90 120 150 180

j [degrees]

k/(k t

rasv

+)

Faraday rotation (Bext = 1 Gauss)

0,000000

0,000002

0,000004

0,000006

0,000008

0,000010

0,000012

0,000014

0,000016

0,000018

0,000020

0 30 60 90 120 150 180

j [degrees]

d/d

r [r

ad/k

m]

R

exte

R

exte RBndrBnkdr0

//0

//

Rotation Measure (RM)

Dispersion

that is, wave speed in the medium is a function of frequency. An impulsed signal (such as pulsars) will cross gas cloud in different time according to the frequency:

phase

2

1v

ck

c p

In the hypothesis of small magnetic field, refraction index is:

R Rp

R

dxdxcv

dxt

0 0

2

0phase 21

1211

)(

Measuring at different frequencies 1, 2, we have:

Rnme

dxnme

ttt ee

R

ee

2

221

2

022

21

2

12

112112)()(

Dispersion Measure (DM)

Crab Pulsar, at the centre of radio source Taurus A (SNR).

Summing up

Combining these measures we can obtain:- (EM/DM) = <ne

2>/<ne> = <ne> if ISM is homogeneous;

- (R2 EM/DM2 ) – 1 = Var[ne] (if R can be otherwise estimated);

- (RM/DM) = < Bext //> = magnetic field intensity.

We defined:- <ne

2> R = EM =Emission measure;- <ne> < Bext //> R = RM = Rotation measure;- <ne> R = DM = Dispersion measure.

We found a way to measure ISM homogeneity and galactic field intensity. From line intensities we get info about gas temperature. For thermodynamic equilibrium, bubbles with major n have minor temperature => we can estimate ne/n. Analogously, with good hypothesis on ne/n we can estimate gas temperature, and confront it with values obtained from line emission (see Bridle, 1969).

ISM structureISM inhomogeneous structure has been studied for years. Bridle (1969) used combinations of emission, rotation and dispersion measures. He obtained a model based on cold bubbles with ne≈0,035 cm-3 r ≈ 5 pc sunk in a continuum with ne≈0,004 cm-3 (one every 60 pc); ne/nH≈0,002 (in bubbles) to 0,02 (in continuum).

A recent work of Inoue (2005) is based on UV absorption. Two stable phases are found (cold and warm) for neutral gas with T<10000 K. Cold clumps are assumed to be gravitationally stable (with Jeans radius of 10,4 pc) and in thermal equilibrium. Dusty clumps are treated as mega-grains; this approximation let him reduce the problem to mono-dimensional geometry. An example of absorption law is discussed in its dependences on dust density, gas temperature and other parameters. A survey of more UV spectra from other galaxies is needed, with the help of Galex.

ISM and galaxy structureISM emission is largely used to study Milky Way structure and dynamic. Gòmez and Cox (2004) consider the interaction among matter and magnetic field lines in a 3D computational model. Both 2 and 4 arms spiral galaxies are considered. As gas hurts the spiral structure, magnetic field seems to deflect it, so that the gas looks like “jumping” the spiral arms. Tidal effects due to matter fluxes are considered both along spiral arms and in radial direction. Synchrotron expected emission is also studied.

Nakanishi (2004) use angular momentum conservation, close orbits model and cylindrical symmetry to develop a computational technique to calculate gas orbits from redshift measures in a bidimensional model. Applying this model to NGC 4569, he finds deviations from the observed values of the order of experimental errors. From this model Nakanishi determinates galaxy mass distribution.

Bibliography- Bridle, A.H., Nature, Vol. 221, No. 5181, pp 648-649 (1969)- Burke, B.F. and Graham-Schmidt, T., An introduction to Radio Astronomy, Cambridge, Cambridge University Press (1997) - Gòmez, G.C. and Cox, D.P, Astro-ph, 0407412 v1 (2004)- Gòmez, G.C. and Cox, D.P, Astro-ph, 0407413 v1 (2004)- Inoue, A.K., Astro-ph, 0502067 v1 (2005)- Jackson, J.D., Elettrodinamica classica, Zanichelli, 1974- Nakanishi, H, ApJ, 617, 315 (2004)- Oster, L., Rev. Modern Phys., 33,525 (1961)- Peeters, E., Martìn-Hernàndez, N.L., Rodrìguez-Fernàndez, N.J., Tielens, A.G.G.M., Astro-ph, 0503711 v1 (2005)- Rybicki, G.B. and Lightman, A.P., Radiative processes in Astrophysics, Cambridge (1979)- Vàrosi, F., Dwek, E., ApJ, 523, 265 (1999)

On the web:- http://babbage.sissa.it/- http://goldmine.mib.infn/- http://hubble.nasa.gov/

Thanks to prof. Giuseppe Gavazzi for images and data about H emission.