Diapositiva 1

1
Roberto Decarli
Interstellar medium
- What is the ISM?- Emission and absorption-
Electromagnetic wave propagation- Structure and
other astronomical hints- Computational models
Extragalactic Astronomy A.Y. 2004-2005
2
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

3
Neutral and ionized regions
We can consider two kind of regions in the ISM,
according to the amount of hydrogen ionization.
Neutral regions can be divided in three
classes1- 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 classes1-
Warm component (T 1000 to 10000 K), also known
as HII region 2- Hot component (T gtgt 10000 K),
near SNR.
4
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.

5
Wave absorption
Free charges q, when accelerated, emit radiation
whose power is I emission intensity E
electric wave field sT sThomson If we consider
bounded electrons, oscillating with pulsation w0
around the nucleus, and a monocromatic radiation
with frequency w, the cross-section acquire a
frequency dependence
For w ltlt w0. This approximation rules the blue
colour of sky during day and the reddish colour
of the sky at sunrise and sunset.
6
Dust
Dust reddens observed spectra. This effect makes
colour index appear higher, notwithstanding
spectral classes. We may define
Optical depth
Column density
Magnitude extintion
Colour excess
We can measure Al 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 l ? 8
absorption vanishes and we can measure
Log(d1/d2). With this information we can find Al.
7
Dust may also scatter and diffuse incident
radiation. V838 Monocerotis explosion lighted
surrounding dust (probably stellar material from
previous explosions), as seen from HST.
8
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 Rutherfords 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 Dt b/v. If wDt gtgt 1, the exponential
rapidly oscillates, and the integral vanishes if
wDt ltlt 1, eiwt 1 and integral is Dv. Emission
spectrum results
for wDt ltlt 1
9
Thermal emission (simplified) 2
This equation concerns the interaction between an
electron and an ion. Integrating over the whole
number of ions and electron
Number of ions in the ring between b and bdb
from the electron
Distance covered by the electron in dt
bmax v/w, while there are two considerations to
do for bmin a) electron potential energy cannot
exceed its kinetic energy, so bmin 2Ze2/emev2
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
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.
10
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.
jw is the emission coefficient. For thermal
cases, we recall Kirchhoffs law jw awBn(T)
where aw is the absorption coefficient and
Bn(T) is blackbody brilliance. Inverting, in Wien
approximation aw?n-3 in Rayleight-Jeans cases,
aw ? n-2 (omitting logarithmic dependence). Optica
l depth in RJ cases results
in cgs units
Emission Measure (EM)
where we assumed ne ni (hydrogen plasma).
11
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 doesnt explicitly appear in
quantum treatment. At T lt 500000 K, quantum
equations are the same as those obtained by
classical methods. At greater temperatures,
quantum correction leads to
where g 0,577216 is Euler number. Main
dependences are the same as in classical equation.
12
Thermal and black body emission
We 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 t 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.
13
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
Introducing radiation energy density, Un
(E2B2)/8p 2pn2A02/c2
or
nnm (En-Em)/h
14
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 gt Em. We define
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.
where and f(n) is the line shape (normalized).
We can use radiation energy density U(n) instead
of jn by relation Ujnc/4p. In thermodynamic
equilibrium and so, using Planck
brilliance
15
Temperature
Equation 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.
VCC0307 in RGB
VCC0307 in Hanet R filter
16
Lines, lines

• Atomic lines
• - Balmer, Lyman and other series Ha, Hb, Hg, Ka,
  Kb, (Dl1, Dm0,1 DS0, DL0,1, DJ0,1
  except J0 to J0)
• 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
  gt 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.
17
Line shifts and shapes
Emission 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 for CGCG 522106 galaxy. Data
from our Loiano observations during February,
2005. We used Ha 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 gt
heliocentric speed isnt only cosmological.
18
Photoelectric effect
UV 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 its 13,6 eV for H,
which correspond to UV radiation). Star UV
emission is strongly responsible of all-around
medium ionization.
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, Tgas10 Tdust.
Pleiades
19
Synchrotron emission 1
Galactic 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
Normal components Parallel component
We assume that kinetic energy loss during a
revolution is small, so v is constant.
Acceleration is a? wsv?, where ws
eBext/gmec. Radiated power results
for a single electron emission. Averaging over an
isotropic speed distribution leads to
Emission is beamed an observer detects waves
only during a small time interval, that means
frequency spectrum is spread.
20
Synchrotron emission 2
An observer sees emission during time
a angle between observer and rotation plane
Beam width
Period
Doppler term 1/(2g2)
Its inverse represents g-times the cut-off
frequency of spectrum. Observed power dependence
can be approximated to a power law spectrum such
as P(w) ? w-s.
Assuming a power law distribution for electrons,
N(E)dE CE-pdE, and using E g mec2
using x w/wcut-off ? g-2
if the domain is large enough the integral is
almost constant
As synchrotron emission is ordered along line
fields, its partially polarized. For power law
electron distributions, P (p1)/(p7/3).
21
Synchrotron effects
Razin effect
Since synchrotron emission takes place in clouds
with m1-(wp/w)21/2, electrons speed must be
rescaled bbm lt b. Power is spread on larger
angles 2/g. At low frequencies emission spectrum
tends to w3/2 dependence.
Self-absorption effect
Synchrotron photon energy distribution is
proportional to w-(p-1)/2, while energy
distribution for electrons goes with w-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 (w5/2).
22
Synchrotron spectrum
? n -0,8
? n 2,5
? n 1,5
23
SuperNova Remnants
SuperNova Remnants are probably the strongest
synchrotron sources. Radio synchrotron emission
is sometimes associated with optical emission
which lights on ejected materials.
24
Compton effect
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
Interaction cross-section is given by
Klein-Nishina formula
Where ein and eout represent photon energy before
and after the collision. If we do not stand in
electron rest frame, corrections must be made
In this case we speak of inverse Compton
effect. Photon is energized by electron of a
factor g2.
25
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)
Using vi v0i ei(wt kx)
where wg eBext/mec. Inserting these equations
in Maxwell system, we obtain a new dielectric
tensor (wp2 4pnee2/me)
which is diagonal only for Bext ? 0 this means
that in presence of external magnetic field the
medium is anisotropic. Applying this e to wave
equation we obtain four values for wave number k
waves go in two directions and in both senses of
each direction.
26
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 dJ
Dk dr, total rotation angle is
Rotation Measure (RM)
27
Dispersion
In the hypothesis of small magnetic field,
refraction index is
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
Measuring at different frequencies w1, w2, we
have
Dispersion Measure (DM)
Crab Pulsar, at the centre of radio source Taurus
A (SNR).
28
Summing up
We defined - ltne2gt R EM Emission measure -
ltnegt lt Bext //gt R RM Rotation measure -
ltnegt R DM Dispersion measure.
Combining these measures we can obtain -
(EM/DM) ltne2gt/ltnegt ltnegt if ISM is
homogeneous - (R2 EM/DM2 ) 1 Varne (if R
can be otherwise estimated) - (RM/DM) lt Bext
//gt magnetic field intensity.
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 gt 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).
29
ISM structure
ISM 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
ne0,035 cm-3 r 5 pc sunk in a continuum with
ne0,004 cm-3 (one every 60 pc) ne/nH0,002 (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 Tlt10000 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.
30
ISM and galaxy structure
ISM 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.
31
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 Ha emission.