Transcript feb18_rg

Overview of HI Astrophysics
Riccardo Giovanelli
A620 - Feb 2004
The Bohr Atom
Given a hydrogenic atom of nuclear
charge Ze, if the Hamiltonian depends
only on r, i.e. 
The wave function is
2
2
p
Ze
H o  (

)  E o 
2me
r
nlm  (1 / r ) Rnl (r )Ylm ( ,  )
Where the Rnl(r) is an expansion in Laguerre polynomials and the spherical harmonics
Ylm(,f) are expansions of associated Legendre functions
n, l and m are integer quantum numbers
The bound energy levels depend only on n :
Eno  (hcR)( Z / n) 2  ( 2 me c 2 / 2)( Z / n) 2
Where R is Rydberg’s constant and

is the fine structure constant.
Spin-Orbit Interaction - 1
An orbiting electron is equivalent to a small current loop  it produces
 
a magnetic field
H  (e / cr 3 )( r  v )
of dipole moment:
m =(1/c) (current in the loop) x (orbit area) = (1/c)(charge/period) x (orbit area
=(1/c) (orbit area/period) x charge
In an elliptical orbit, (orbit area/period) = const. = Pf/2m
so that:
(Kepler’s II)


m  (e / 2me c) p
If we express the orbital angular momentum in units of h/2p 
then

m   L

where
  e / 2mec
 
L  p / 
is the Bohr magneton.

An electron is also endowed with intrinsic SPIN, of angular momentum S

associated to which there is a spin magnetic moment

  S
Spin-Orbit Interaction - 2
In the presence of a magnetic field, a dipole tends to align itself with the field.
If dipole and field are misaligned, a torque is produced:

torque  m  H  mH sin 

In order to change the angle
, work must be done against the field:
 
work   (torque)d  mH cos   m  H
So we can ascribe a “potential energy of orientation” to a magnetic dipole in a field,
i.e. different energy levels will correspond to different orientations b/w field & dipole.
In a hydrogenic atom, by SPIN-ORBIT INTERACTION, we refer to that between
the spin magnetic dipole of the orbiting electron and the magnetic field arising from
its orbital motion.
One of the consequences of the spin-orbit interaction is the
Appearance of FINE STRUCTURE in the atomic energy levels.
Atomic Vector model
F
Total atomic angular momentum
Electron orbital angular momentum
Nuclear spin angular momentum
J
L
Total electronic
angular momentum
I
S
Electronic spin
angular momentum
Fine Structure
The effects of relativistic corrections and the spin-orbit interaction can be treated
2
2
4
2  
p
Ze
cp
2
Z

o
( H o  P)  [(

)

S

L
]


(
E
 E fs )
3
3
2me
r
(2me c)
r
as a perturbation term in the Hamiltonian.
The resulting fine structure correction to the atomic energy levels is (Sommerfeld 1916):
E fs 
 2 RhcZ 4  J ( J  1)  L( L  1)  S ( S  1)
n
3


L( L  1)( 2 L  1)
which for the H atom reduces to:
Since
Eno  (hcR )( Z / n) 2
E fs 

 2 Rhc  3
n3
3
1 



4n L  1 / 2 
1 
 

 4n j  1 / 2 
E fs / Eno   2 / n  105
i.e. considering FS a perturbation is justified
Hyperfine Structure
The L-S coupling scheme leading to the fine structure correction can be applied
to the interaction between the nuclear spin and the total electronic momentum.
This interaction leads to the so-called “hyperfine structure” correction.

m g  I
As in the case of the electronic spin, the magnetic moment associated with the
nuclear spin is proportional to the nuclear spin angular momentum:
n
I n
where the nuclear magneton

 n  e / 2m p c   (me / m p )
is 3 orders of magnitude smaller than the Bohr magneton.
While the spin-orbit (L-S) perturbation term in the Hamiltonian is
The nuclear spin – electronic (I-J) perturbation term is
 2
 n
The energy level hyperfine structure correction is (Fermi & Bethe 1933):
Ehs  ( Rhcg I )( me / m p )n
2
So that:
Eno : E fs : Ehs  1 :
3
F ( F  1)  I ( I  1)  J ( J  1)
J ( J  1)( 2 L  1)
 2  2 me
n
:
nm p
The HI Line
For the Hydrogen atom,
I=1/2, so
F=J+1/2 and J-1/2
For the ground state 1S1/2 (l=0, j=1/2) , the energy difference between the
F=1 and f=0 energy levels is:
E  h 
 2 g I hcRm e
Which corresponds to
n3m p
2 j 1
8 2
  g I cR(me / m p )
j ( j  1)( 2l  1) 3
 = 1420.4058 MHz
The upper level (F=1) is a triplet (2F+1=3)  e and p have parallel spins
The lower level (F=0) is a singlet (2F+1=1)  e and p have antiparallel spins
The astrophysical importance of the transition was first realized by
Van de Hulst in 1944. The transition was ~ simultaneously detected in 1951
In the US, the Netehrlads and Australia (1951: Nature 168, 356).
HI Line: transition probability
E
1
The transition probability for
spontaneous emission 1  0 is
0
For the 21 cm line,
64p 4 3
A10 
S10
3
3hc g1
g1  2F  1  3
S10  3 2
Hence:
A10  2.85 10
15
1

s  1110 yr
The smallness of the spontaneous transition probability is due to
- the fact that the transition is “forbidden” (l = 0)
- the dependence of A10 on
3
The “natural” halfwidth of the transition is
5 x 10-16 Hz
7

1
The transition is
mainly excited by
other mechanisms,
which make it
orders of magnitude
more frequent
Spin Temperature
If n1 and no are the population densities of atoms in levels f=1 and f=0,
characterized by statistical weights g1 and go , we define Spin Temperature Ts
via
n1 g1

exp( h / kTs )
no g o
For the HI line, the ratio of statistical weights is 3, and
h/k=0.068 K
The main excitation mechanisms for the 21 cm line are:
- Collisions
- Excitation by radio frequency radiation
- Excitation by Lyman alpha photons
Field (1958) expressed the spin temperature as a weighted average of the three:
Ts 
TR  ycollTk  y Ly TLy
1  ycoll  y Ly
Where TR is the temperature of the radiation field at 21 cm, Tk is the kinetic
temperature of the gas and TLy measures the “color” of the Ly- radiation field
Spin Temperature- Examples
1. Consider a “standard” ISM cold cloud:
Tk = 100K, nH = 10 cm-3 , ne = 10-3 cm-3
where TR = TCMB = 3 K and far from HII regions:
ycoll : yLy = 350:10-5
and
T s = Tk
levels are fully regulated by collisions.
2. Consider a warm, mainly neutral IS cloud:
no nearby continuum sources, no Lyman 
Ycoll~1.5
and
:
Tk = 5000K, nH = 0.5 cm-3, ne = 0.01 cm-3
Ts ~ 3100 K
levels still regulated by collisions but out of TE
3. Consider the vicinity of an HII region, with high Lyman
 flux:
Ts = T k
the spin temperature is thermal, but fully regulated by the Lyman
 flux.
HI Absorption coefficient
Einstein Coefficients: given a two-level atom, we define three coefficients that
mediate transitions between levels:
- A10 probability per unit time for a spontaneous transition from 1 to 0 [s-1]
- B01 multiplied by the mean intensity of the radiation field at the frequency
10 , yields the prob per u. time of absorption: 0  1
- B10 multiplied by the mean intensity of the radiation field at the frequency
10 , yields the prob per u. time of that a transition 1  0 be stimulated
by an incoming photon
The following relations hold:
g0 B01 = g1 B10
and
A10 /B10 = 2h3 /c2
Using these, it can be shown that the absorption coefficient , defined as the
fractional loss of intensity of a ray bundle travelling through unit distance within
the absorbing medium, i.e.
can be written as:
dI = -  I ds
3 A10c 2 h
14
1
1


(

)
n

1
.
03

10
n
T

(

)
cm
o
o s
8p  2 kTs
HI 21 cm Line transfer
Consider the equation of radiative transfer:
where j is the emission coefficient and I
is the specific intensity of the radiation field;
dI / ds   I  j
2kT 2
j   B(T ) 
c2
by Kirchhoff’s relation:
d  ds
Integrating (*) and introducing the optical depth

=0
I=I(0)
 ‘
I  I (0)e    e (  ') (2pTs 2 / c 2 )d '

0
Introducing “brightness temperature”

Tb 
Tb  Tb (0)e    e (  ')Ts d '
c2
2 k
2
I
… and if
0

Tb  Tb (0)  Ts (1  e )
Ts is constant throughout:
(*)
HI 21 cm Line transfer-2

Tb  Tb (0)  Ts (1  e )
1. Suppose we observe a cloud of very high optical depth 
2. Suppose the background radiation field is negligible (
and the cloud is optically thin (
Recall that
and
Then:
< 1). Then
Tb  Ts
Tb(0)~0 )

Tb  Ts  Ts  ds
3 A10c 2 h
0
14
1
1


(

)
n

1
.
03

10
n
T

(

)
cm
o
o s
8p  2 kTs
n1 g1

exp( h / kTs )
no g o
to show that
g1  h / kTs
nH  n1  no  no (1  e
)  4no
g0

3 A10c 2 h
Tb 
( )  nH ds
2
32p 
k
0
21cm line, optically thin case: Column density
Converting frequency to velocity:
( )d  P(V )dV
P(V )  ( / c) ( )
where
And integrating over the line profile, we obtain the cloud column density:
N H  1.83 1018  Tb (V )dV
Atoms cm-2
Where V is in km/s
Caveat: We assumed the background radiation to be negligible, i.e.
If Ts is comparable with
Tb (0)  Ts
TCMB, for example, then the correct expression for NH is
1
 Ts  TCMB 
 dV
N H  1.83 10  Tb (V )
 Ts

18
21cm line, optically thin case: Column density observational limits
Consider a receiving system with system temperature of ~ 30 K,
Integration time of 60 sec and spectral resolution of 4 km/s ~ 20 kHz;
The radiometer equation yields
Trms  0.03K
Thus a 5-sigma detection limit will yield a minimum detectable brightness
Temperature of ~ 0.14 K
If we assume that the cloud “fills the beam”, and that the velocity
Width of the cloud is 20 km/s, then
N H ,min  5 1018 cm2
No detections of HI in emission are known below
NH~1018
21cm line, optically thin case: Column density
Inverting
N H  1.83 1018  Tb (V )dV
we can write, for the
optical depth at line center:
  5.2 1019 N H [cm2 ]Ts 1V 1[km / s]
Note that, for spin temperatures on order of 100K and cloud velocity widths on
order of 10 km/s, for  > 1 column densities > than 1021 are required
Since the galactic plane is thin, face-on galaxies seldom exhibit evidence for
significant optical thickness: the vast majority of the atomic gas is in optically
thin clouds. As disks approach the edge-on aspect, velocity spread to a large
extent prevents optical depth to increase significantly.
As a result, HI masses of disk galaxies can, to first order, be inferred from
The optically thin assumption.
Total HI Mass: Disk Galaxies
The HI column density towards the direction (,f is
y
N H ( ,  )  1.823 1018  Tb ( ,  , V )dV
In c.g.s. units (freq in Hz):
N H ( ,  )  3.848 1014  Tb ( ,  , )d
x
If the galaxy is at distance D, then
  x/D
  y/D
So the total nr of HI atoms in the galaxy is
2
N
dxdy

D
 H
 N H ( ,  )d
s
Where the second integral is over the solid angle subtended by the source.
Converting Tb to specific intensity I, and using the definition of flux density
S   I ( ,  )d
s
(over)
Total HI Mass: Disk Galaxies-2
We can express:
So that
2
 T ( , , )dd  2k  S d
b
M HI  3.848 1014 D 2
2
S ( )d

2k
Converting from atomic masses to solar masses, expressing D in Mpc
flux density in Jy [ 10-26 W m-2 Hz-1] and V in km/s:
M HI / M sun  2.36 10 D
5
Note that this measure of HI mass will always
Underestimate the true mass, since it is computed
Assuming
  1 and
T  T
s
cmb
2
Mpc
S
Jy
dV
This is usually
referred as the
Flux Integral
and is expressed
in [ Jy km/s ]
1940
Van de Hulst & Oort make good use of wartime
1950
1951: HI line first detected
1953: Hindman & Kerr detect HI in Magellanic Clouds
1960
Green Bank
Nancay
Effelsberg
Parkes, J.Bank
1970
1980
1990
First 100 galaxies
1975: Roberts review
1977: Tully-Fisher
VLA and WSRT come on line
Arecibo upgraded to L band;
broad-band correlators, LNRs
Cluster deficiency, Synthesis maps,
DLA systems, interacting systems
Rotation Curves, DM,
Redshift Surveys
Peculiar velocity surveys, deep mapping
2000
Multifeed systems : large-scale surveys
HI Mass Function
in the local Universe
HI Mass Density
Parkes HIPASS survey: Zwaan et al. 2003
(more from Brian on this)
Visibility of
even most
massive
galaxies is
lost at
moderately low
cosmic
distances
Low mass systems are only visible in the
very local Universe. Even if abundant, we
only detect a few.
Parkes
HIPASS
Survey
Very near extragalactic space…
(more later from Erik)
High Velocity Clouds
?
Credit: B. Wakker
The Magellanic Stream
Discovered in 1974 by
Mathewson, Cleary & Murray
Putman et al. 2003
ATCA map
Putman et al. 1998 @ Parkes
Sensing Dark Matter
M31
Effelsberg data
Roberts, Whitehurst
& Cram 1978
[Van Albada, Bahcall, Begeman & Sancisi 1985]
WSRT Map
[Swaters, Sancisi & van der Hulst 1997]
[Cote’, Carignan & Sancisi 1991]
A page from Dr. Bosma’s Galactic Pathology Manual
[Bosma 1981]
HI Deficiency in groups and clusters
Virgo Cluster
HI Deficiency
Arecibo data
HI Disk Diameter
[Giovanelli & Haynes 1983]
Virgo
Cluster
VLA data
[Cayatte, van Gorkom,
Balkowski & Kotanyi
1990]
VIRGO
Cluster
Dots: galaxies w/
measured HI
Contours: HI deficiency
Grey map: ROSAT
0.4-2.4 keV
Solanes et al. 2002
Way beyond the stars
DDO 154
Carignan & Beaulieu 1989
VLA D-array
DDO 154
Arecibo map outer extent [Hoffman et al. 1993]
Extent of
optical
image
Carignan & Beaulieu 1989
VLA D-array HI column density contours
M(total)/M(stars)
M(total)/M(HI)
Carignan &
Beaulieu 1989
From L. van Zee’s gallery of Pathetic Galaxies (BCDs)
VLA maps
Van Zee & Haynes
Van Zee, Skillman & Salzer
Van Zee, Westphal & Haynes
NGC 3628
Leo Triplet
Haynes, Giovanelli & Roberts 1979
Arecibo data
NGC 3627
NGC 3623
See
John Hibbard’s
Gallery of Rogues
at
www.nrao.edu/
astrores/
HIrogues
… and where there aren’t any stars
M96 Ring
Schneider et al 1989 VLA map
Schneider, Helou, Salpeter &
Terzian 1983
Arecibo map
Schneider, Salpeter & Terzian 19
HI 1225+01
Optical galaxy
Chengalur, Giovanelli & Haynes 1991 VLA data
[first detected by Giovanelli, Williams & Haynes 1989 at Arecibo]
HIPASS J1712-64
M(HI)=1.7x10 7 solarm
at D=3.2 Mpc
V(GSR)=332 km/s …. a Magellanic ejecta HVC?
Kilborn et al. 2000
Parkes discovery, ATCA map
… and then some Cosmology
Perseus-Pisces Supercluster
~11,000 galaxy redshifts:
Arecibo as a redshift machine
Perseus-Pisces Supercluster
TF Relation Template
SCI
: cluster Sc sample
I band, 24 clusters, 782 galaxies
Giovanelli et al. 1997
“Direct” slope is –7.6
“Inverse” slope is –7.8
TF and the Peculiar Velocity Field



Given a TF template relation, the peculiar velocity of
a galaxy can be derived from its offset Dm from
that template, via
For a TF scatter of 0.35 mag, the error on the
peculiar velocity of a single galaxy is typically
~0.16cz
For clusters, the error can be reduced by a factor
, N , if N galaxies per cluster are observed
The Dipole of
the Peculiar
Velocity Field
The reflex motion of the LG,
w.r.t. field galaxies in shells of
progressively increasing radius,
shows :
convergence with the CMB dipole,
both in amplitude and direction,
near cz ~ 5000 km/s.
[Giovanelli et al. 1998]
The Dipole of the Peculiar Velocity Field
Convergence to the CMB dipole is confirmed
by the LG motion w.r.t.
a set of 79 clusters out to
cz ~ 20,000 km/s
Giovanelli et al 1999
Dale et al. 1999