Transcript Diapositiva 1 - INAF - OA

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
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 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 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 absorption
Free charges q, when accelerated, emit radiation whose power is:
2q 2a 2
cE 2
P 
sT I  sT
3
3c
4
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:
4
w 
eE
1
  s R
r  w0r 
 s  sT
 sT 
2
2 2
me
(w 0  w )
 w0 

..

For w << w0. This approximation rules the blue
colour of sky during day and the reddish colour
of the sky at sunrise and sunset.
Dust
Dust reddens observed spectra. This effect makes colour index
appear higher, notwithstanding spectral classes. We may define:
Optical depth:
R
R
0
0
    ns d r  s   n d r
Column density
Magnitude extintion:
Colour excess:
A  2,5Log
f  (R )
 1,086 
f  (0)
E (2 , 1)  A  A
2
1
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:
8k bT
v v 
 6,03 105 T [ K ]cm / s
me
If b ≈ n-1/3, deflection (see Rutherford’s scattering) results:
Ze 2


Z
  2 a r ct a n

2
a
r
ct
a
n
0
,
00055

0
T
[
K
]
me b v 2


So electron trajectory may be considered a straight line. We can pass in
frequency domain simply applying Fourier transform:
a  v   w 2aˆ   ve iwt dt
Whole emission may be assumed to happen in Dt = b/v. If wDt >> 1, the
exponential rapidly oscillates, and the integral vanishes; if wDt << 1, eiwt ~ 1
and integral is Dv. Emission spectrum results:
dW
2e 2
8Z 2e 6
2
for wDt << 1

Dv 
3
3
2 2 2
dw 3c
3c mev b
Thermal emission (simplified) – 2
This equation concerns the interaction between an electron and an ion.
Integrating over the whole number of ions and electron:
b ma x
dW
dW
 ne 
n i 2bdb vdt
dwdV t o t a l
b mi n dw
Number of ions in the ring between b Distance covered by the
and b+db from the electron
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:
bmax
dW
16e 6
2

n
n
Z
ln
dwd Vd t t o t al 3c 3me2v e i
bmin
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:
12
6


dW
16e
2
2  hn k bT



n
n
Z
e
g  4j w
dwd Vd t t o t a l 3m e c 3  3k bT me  e i
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 Kirchhoff’s 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).
Optical depth in RJ cases results:

2
a
d
x

10
T
 w
I S Md e p t h
n 2  ne2d x  102T
3 2
where we assumed ne ≈ ni (hydrogen plasma).
n 2 ne2 R
3 2
in cgs units
Emission Measure (EM)
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:
me 4k bT
32e 6
2
4j 
ne n i Z
ln
2 3
k bT
 w
3me c 2
where  = 0,577216 is Euler number. Main dependences are the same as in
classical equation.
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  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

p
e  
H H 0  H1 
V ( x ) 
Ap
2m e
mec

e A0   i (kx wt )
 i (k x  wt )
H1(t )  
p e e
e
 T e iwt  T e iwt
mec


   ikx
A02
(0 )
| (T  )n m |  2 2 | u m | ip  e e
| u n(0 ) |2
me c
Introducing radiation energy density, Un = (E2+B2)/8 = 2n2A02/c2 :
  ikx
1
U (n n m )
(0 )
(0 )
2
Pn m 
t
|

u
|

i
p

e
e
|
u

|
m
n
22me2 n n2 m
or:
  ikx
d Pn m
1
U (n n m )
(0 )
(0 )
2
 n m 

|

u
|

i
p

e
e
|
u

|
m
n
dt
22me2 n n2 m
2
nnm = (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:
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: J   j n f (n )dn and f(n) is the line shape (normalized).
0
We can use radiation energy density U(n) instead of jn by relation: U=jnc/4.
In thermodynamic equilibrium:
and:
n m g m hn nm

e
nn
gn
k bT
n m B mn J n n (An m  B n m J )
so, using Planck brilliance:
g m B mn  g n B n m
An m 
2hn 3
c
2
Bn m
n m g m hn nm

e
nn
gn
Temperature
k bT
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
Lines, lines…
Atomic lines:
- Balmer, Lyman and other series: Ha, Hb, H, Ka, Kb, …
DL=0,±1, DJ=0,±1 except J=0 to J=0);
(Dl=±1, Dm=0,±1; DS=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 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 of CGCG 522106
6100
Heliocentric speed [km/s]
6000
5900
5800
5700
5600
5500
-25
-20
-15
-10
-5
0
5
Distance from galactic centre [kpc]
10
15
20
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 =>
heliocentric speed isn’t only
cosmological.
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: it’s 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, Tgas~10 Tdust.
Pleiades
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: 



e
dv
e

d t me 
(
  
v  Be x t

v
  B e x t    m e c 
c
 
0

)
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/mec.
Radiated power results: 2 4 2
4 2 2
2
P 
2e  a
2e  B ex tv 

3
3 c
3 me 2c 5
for a single electron emission. Averaging over an isotropic speed
distribution leads to:
4
P 
3
sT cb 2 2 (B e2x t 8 )
Emission is beamed: an observer detects waves only during a small
time interval, that means frequency spectrum is spread.
Synchrotron emission – 2
An observer sees emission during time:
a = angle
between
observer and
rotation plane
1
1
 v 
Dt o b s 
1    3
 ws sina  c   ws sina
2
Beam width
Period
Doppler term ~ 1/(22)
Its inverse represents -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 =  mec2:
Pt o t   f (w )  p d  w ( p 1) / 2  f ( ) ( p  3) / 2d  w ( p 1) / 2
using  = w/wcut-off ∝ -2

s 
p 1
2
if the domain is large
enough the integral is
almost constant
As synchrotron emission is ordered along line fields, it’s partially
polarized. For power law electron distributions,  = (p+1)/(p+7/3).
Synchrotron effects
Razin effect:
Since synchrotron emission takes place in clouds with m=[1-(wp/w)2]1/2,
electrons speed must be rescaled: b’=bm  b. Power is spread on larger
angles 2/’. 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).
Synchrotron spectrum
1000
100
I
10
1
0,1
0,01
1
10
100
1000
10000
100000
1000000
Frequency [MHz]
Pure Synchrotron
Synchrotron + Razin effect
Synchrotron + Self-Absorption
SuperNova Remnants
SuperNova
Remnants are
probably the
strongest
synchrotron
sources. Radio
synchrotron
emission is
sometimes
associated with
optical emission
which lights on
ejected
materials.
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:
D 

h
(1  cos )  0 ,02426(1  cos ) A
me c
Interaction cross-section is given by Klein-Nishina formula:

e o2u t  e in e o u t
ds
3

sT 2 

 sin2  
d 16
e in  e o u t e in

Where ein and eout represent photon energy before and after the
collision. If we do not stand in electron rest frame, corrections must
e 'in  e in (1  b cosin )
be made:
e o u t  e 'o u t  (1  b cos 'o u t )

e 'o u t  e 'in 1 


e 'in
(1  cos)
2
mec

In this case we speak of “inverse Compton” effect. Photon is
energized by electron of a factor ~2.
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):
(
(
e
1
 m E x  c v y (B e x t )z

 
dv
e   v
  e

E y  1c v x (B e x t )z
 E   Bex t   
dt m 
c
 m
e

E

m z
)
)
Using
vi = v0i ei(wt + kx)

e w g E 0 y  iwE 0 x
v

 0x m
2
2
w

w
g


e iwE 0 y  w g E 0 x
v 0 y 
m
w g2  w 2

e E 0z

v


0
z

m w

where wg = eBext/mec. Inserting these equations in Maxwell system,
we obtain a new dielectric tensor (wp2 = 4nee2/me):


w p2 w g
w p2
1


0


2
2
w (w g2  w 2 )
 wg  w

2
2
 w p wg

wp
e  e0 
1

0

2
2
2
2
w
(
w

w
)
w

w


g
g
2 

wp

0
0
1 2 
w 

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.
Wave number, normalized to k + (/2),
Faraday rotation
for B ext = 1 microGauss
3,E-14
Since d = Dk dr, total rotation angle
R
R
is:
  Dkd r   ne Bex t //d r ne Bex t //R
0
0
Rotation Measure (RM)
1,E-14
0,E+00
-1,E-14
-2,E-14
-3,E-14
0
30
60
90
120
150
180
j [degrees]
Faraday rotation (B ext = 1 Gauss)
0,000020
0,000018
d/dr [rad/km]
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.
Dk/(k trasv+)
2,E-14
0,000016
0,000014
0,000012
0,000010
0,000008
0,000006
0,000004
0,000002
0,000000
0
30
60
90
120
j [degrees]
150
180
Dispersion
In the hypothesis of small magnetic field, refraction index is:
2
w 
c
c
m  k  1   p  
w
v p h a se
 w 
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:
R
1  1  wp
t (w ) 
  m d x   1  
v
c 0
2 0  2  w
0 p h ase
R
dx
1
R



2

d x

Measuring at different frequencies w1, w2, we have:
R
2e 2  1
1 
2e 2  1
1 
 2  2   ne d x 
 2  2  ne R
Dt  t (w2 )  t (w1) 
me  w1 w2  0
me  w1 w2 
Dispersion Measure (DM)
Crab Pulsar, at the centre
of radio source Taurus A
(SNR).
Summing up
We defined:
- <ne2> R = EM =Emission measure;
- <ne> < Bext //> R = RM = Rotation measure;
- <ne> R = DM = Dispersion measure.
Combining these measures we can obtain:
- (EM/DM) = <ne2>/<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 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 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
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 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.
Bibliography
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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 a emission.