Post on 12-Jan-2016
Overview of HI AstrophysicsOverview of HI Astrophysics
Riccardo GiovanelliRiccardo Giovanelli
A620 - Feb 2004
The Bohr Atom
o
e
o Er
Ze
m
pH )
2(
22Given a hydrogenic atom of nuclearcharge Ze, if the Hamiltonian dependsonly on r, i.e.
),()()/1( lmnlnlm YrRrThe wave function is
Where the Rnl(r) is an expansion in Laguerre polynomials and the spherical harmonicsYlm() are expansions of associated Legendre functions
n, l and m are integer quantum numbers
The bound energy levels depend only on n :
2222 )/)(2/()/)(( nZcmnZhcRE eon
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
of dipole moment: =(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. = P/2m (Kepler’s II)
so that: pcme e
)2/(
If we express the orbital angular momentum in units of h/2 /pL
then where is the Bohr magneton.L cme e2/
An electron is also endowed with intrinsic SPIN, of angular momentum
associated to which there is a spin magnetic moment
S
S
))(/( 3 vrcreH
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:
sinHHtorque
In order to change the angle , work must be done against the field:
HHdtorquework cos)(
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 theAppearance of FINE STRUCTURE in the atomic energy levels.
L
S
J
I
F
Atomic Vector model
Electron orbital angular momentum
Nuclear spin angular momentum
Electronic spin angular momentum
Total electronicangular momentum
Total atomic angular momentum
)(]2
)2()
2[()(
3
2
3
422
fso
ee
o EELSr
Z
cm
cp
r
Ze
m
pPH
Fine Structure
The effects of relativistic corrections and the spin-orbit interaction can be treated
as a perturbation term in the Hamiltonian.
The resulting fine structure correction to the atomic energy levels is (Sommerfeld 1916):
2/1
1
4
3
)12)(1(
)1()1()1(3
42
LnLLL
SSLLJJ
n
RhcZE fs
2)/)(( nZhcRE on Since
2/1
1
4
33
2
jnn
RhcE fs
which for the H atom reduces to:
52 10// nEE onfs
i.e. considering FS a perturbation is justified
Hyperfine Structure
The L-S coupling scheme leading to the fine structure correction can be appliedto the interaction between the nuclear spin and the total electronic momentum.This interaction leads to the so-called “hyperfine structure” correction.
As in the case of the electronic spin, the magnetic moment associated with thenuclear spin is proportional to the nuclear spin angular momentum:where the nuclear magneton
is 3 orders of magnitude smaller than the Bohr magneton.
Ig nIn
)/(2/ pepn mmcme
While the spin-orbit (L-S) perturbation term in the Hamiltonian is
The nuclear spin – electronic (I-J) perturbation term is
2n
The energy level hyperfine structure correction is (Fermi & Bethe 1933):
)12)(1(
)1()1()1()/)(( 32
LJJ
JJIIFFnmmRhcgE peIhs
So that:
p
ehsfs
on nm
m
nEEE
22
::1::
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:
)/(3
8
)12)(1(
12 23
2
peIp
eI mmcRgljj
j
mn
hcRmghE
Which corresponds to = 1420.4058 MHz
The upper level (F=1) is a triplet (2F+1=3) e and p have parallel spinsThe 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 byVan de Hulst in 1944. The transition was ~ simultaneously detected in 1951In the US, the Netehrlads and Australia (1951: Nature 168, 356).
E1
0
The transition probability forspontaneous emission 1 0 is
101
3
34
10 3
64S
ghcA
For the 21 cm line, 3121 Fg
210 3S
Hence: 1711510 10111085.2
yrsA
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
HI Line: transition probability
The transition is mainly excited by other mechanisms, which make it orders of magnitudemore 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
)/exp(11s
oo
kThg
g
n
n
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:
Lycoll
LyLykcollRs yy
TyTyTT
1
Where TR is the temperature of the radiation field at 21 cm, Tk is the kinetictemperature 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 Ts = Tk
levels are fully regulated by collisions.
2. Consider a warm, mainly neutral IS cloud: Tk = 5000K, nH = 0.5 cm-3, ne = 0.01 cm-3
no nearby continuum sources, no Lyman
Ycoll~1.5andTs ~ 3100 K levels still regulated by collisions but out of TE
3. Consider the vicinity of an HII region, with high Lyman flux:
Ts = Tk
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 = 2h3 /c2
Using these, it can be shown that the absorption coefficient , defined as thefractional loss of intensity of a ray bundle travelling through unit distance withinthe absorbing medium, i.e. dI = - I dscan be written as:
11142
210 )(1003.1)(
8
3 cmTnnkT
hcAsoo
s
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;
by Kirchhoff’s relation:
jIdsdI /
2
22)(
c
kTTBj
Integrating (*) and introducing the optical depth dsd
(*)
')/2()0( 22
0
)'(
dcTeeII s
Introducing “brightness temperature” Ik
cTb 2
2
2
')0(0
)'(
dTeeTT sbb … and if Ts is constant throughout:
)1()0( eTTT sbb
= 0I=I(0)
‘’
)1()0( eTTT sbb
HI 21 cm Line transfer-2
1. Suppose we observe a cloud of very high optical depth sb TT
2. Suppose the background radiation field is negligible ( Tb(0)~0 ) and the cloud is optically thin ( < 1). Then
0
dsTTT ssb Recall that 1114
2
210 )(1003.1)(
8
3 cmTnnkT
hcAsoo
s
)/exp(11s
oo
kThg
g
n
n and to show that
okTh
ooH neg
gnnnn s 4)1( /
0
11
Then:
dsnk
hcAT Hb
0
2
210 )(
32
3
21cm line, optically thin case: Column density
Converting frequency to velocity: where
dVVPd )()( )()/()( cVP
And integrating over the line profile, we obtain the cloud column density:
dVVTN bH )(1083.1 18 Atoms cm-2
Where V is in km/s
Caveat:We assumed the background radiation to be negligible, i.e. sb TT )0(
If Ts is comparable with TCMB, for example, then the correct expression for NH is
dVT
TTVTN
s
CMBsbH
1
18 )(1083.1
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
KTrms 03.0
Thus a 5-sigma detection limit will yield a minimum detectable brightnessTemperature of ~ 0.14 K
If we assume that the cloud “fills the beam”, and that the velocityWidth of the cloud is 20 km/s, then
218min, 105 cmNH
No detections of HI in emission are known below NH~1018
21cm line, optically thin case: Column density
dVVTN bH )(1083.1 18
Note that, for spin temperatures on order of 100K and cloud velocity widths onorder of 10 km/s, for > 1 column densities > than 1021
are required
Inverting
we can write, for theoptical depth at line center:
]/[][102.5 11219 skmVTcmN sH
Since the galactic plane is thin, face-on galaxies seldom exhibit evidence forsignificant optical thickness: the vast majority of the atomic gas is in opticallythin clouds. As disks approach the edge-on aspect, velocity spread to a largeextent 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
x
y dVVTN bH ),,(10823.1),( 18
The HI column density towards the direction ( is
dTN bH ),,(10848.3),( 14
In c.g.s. units (freq in Hz):
Dx /Dy /
If the galaxy is at distance D, then
So the total nr of HI atoms in the galaxy is
s
dNDdxdyN HH ),(2 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
dISs
),(
(over)
Total HI Mass: Disk Galaxies-2
We can express: dSkddTb
2),,(
2
So that dS
kDM HI )(2
10848.32
214
Converting from atomic masses to solar masses, expressing D in Mpcflux density in Jy [ 10-26 W m-2 Hz-1] and V in km/s:
dVSDMM JyMpcsunHI 251036.2/
This is usuallyreferred as theFlux Integraland is expressedin [ Jy km/s ]
Note that this measure of HI mass will always Underestimate the true mass, since it is computedAssuming and1
cmbs TT
1940
1950
1960
1970
1980
1990
2000
Van de Hulst & Oort make good use of wartime
1951: HI line first detected1953: Hindman & Kerr detect HI in Magellanic Clouds
Green BankNancayEffelsbergParkes, J.Bank
VLA and WSRT come on lineArecibo upgraded to L band;broad-band correlators, LNRs
1975: Roberts review1977: Tully-Fisher
Cluster deficiency, Synthesis maps,DLA systems, interacting systems Rotation Curves, DM, Redshift Surveys
Multifeed systems : large-scale surveys
Peculiar velocity surveys, deep mapping
First 100 galaxies
HI Mass FunctionHI Mass Functionin the local Universein the local Universe
HI Mass DensityHI Mass DensityParkes HIPASS survey: Zwaan et al. 2003 (more from Brian on this)
Visibility ofVisibility ofeven most even most massivemassivegalaxies isgalaxies islost at lost at moderately lowmoderately lowcosmic cosmic distancesdistances
ParkesHIPASSSurvey
Low mass systems are only visible in the very local Universe. Even if abundant, we only detect a few.
Very near extragalactic space…Very near extragalactic space…(more later from Erik)
High Velocity CloudsHigh Velocity Clouds
Credit: B. Wakker
?
The Magellanic StreamThe Magellanic Stream
Discovered in 1974 byMathewson, Cleary & Murray Putman et al. 2003
Putman et al. 1998 @ Parkes
ATCA map
Sensing Dark MatterSensing Dark Matter
M31M31 Effelsberg dataEffelsberg data
Roberts, WhitehurstRoberts, Whitehurst& Cram 1978& Cram 1978
[Van Albada, Bahcall, Begeman & Sancisi 1985]
[Swaters, Sancisi & van der Hulst 1997]
WSRT Map
[Cote’, Carignan & Sancisi 1991]
[Bosma 1981]
A page from Dr. Bosma’s Galactic Pathology Manual
HI Deficiency in groups and clustersHI Deficiency in groups and clusters
Virgo ClusterVirgo Cluster
HI DeficiencyHI Deficiency
HI Disk DiameterHI Disk Diameter
[Giovanelli & Haynes 1983]
Arecibo dataArecibo data
Virgo Virgo ClusterCluster
VLA dataVLA data
[Cayatte, van Gorkom,[Cayatte, van Gorkom,Balkowski & Kotanyi Balkowski & Kotanyi 1990]1990]
Solanes et al. 2002Solanes et al. 2002
Dots: galaxies w/ measured HI
Contours: HI deficiency
Grey map: ROSAT 0.4-2.4 keV
VIRGOVIRGOClusterCluster
Way beyond the starsWay beyond the stars
Carignan & Beaulieu 1989 VLA D-array
DDO 154DDO 154
Carignan & Beaulieu 1989 VLA D-array HI column density contours
Arecibo map outer extent [Hoffman et al. 1993]DDO 154DDO 154
Extent ofopticalimage
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, Westphal & Haynes
Van Zee, Skillman & Salzer
Haynes, Giovanelli & Roberts 1979 Arecibo data
NGC 3628
NGC 3623NGC 3627
Leo TripletLeo Triplet
SeeJohn Hibbard’sGallery of Roguesat
www.nrao.edu/astrores/HIrogues
… … and where there aren’t any starsand where there aren’t any stars
M96 RingM96 Ring
Schneider, Salpeter & Terzian 19Schneider, Helou, Salpeter &Terzian 1983
Arecibo map
Schneider et al 1989 VLA map
HI 1225+01HI 1225+01
Optical galaxy
Chengalur, Giovanelli & Haynes 1991 VLA data[first detected by Giovanelli, Williams & Haynes 1989 at Arecibo]
Kilborn et al. 2000 Parkes discovery, ATCA map
HIPASS J1712-64
M(HI)=1.7x10 solarm at D=3.2 Mpc
7
V(GSR)=332 km/s …. a Magellanic ejecta HVC?
… … and then some Cosmologyand then some Cosmology
Arecibo as a redshift machineArecibo as a redshift machine
Perseus-Pisces SuperclusterPerseus-Pisces Supercluster
~11,000 galaxy redshifts:
Perseus-Pisces SuperclusterPerseus-Pisces Supercluster
TF Relation TemplateTF 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 FieldTF and the Peculiar Velocity Field
Given a TF template relation, the peculiar velocity Given a TF template relation, the peculiar velocity of a galaxy can be derived from its offset Dm of a galaxy can be derived from its offset Dm from that template, viafrom that template, via
For a TF scatter of 0.35 mag, the error on the For a TF scatter of 0.35 mag, the error on the peculiar velocity of a single galaxy is typically peculiar velocity of a single galaxy is typically ~0.16cz~0.16cz
For clusters, the error can be reduced by a factor For clusters, the error can be reduced by a factor , , if N galaxies per cluster are observed , , if N galaxies per cluster are observedN
The Dipole The Dipole of the of the
Peculiar Peculiar Velocity Velocity
FieldField
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 The Dipole of the Peculiar Velocity FieldField
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 Giovanelli et al 1999
Dale et al. 1999Dale et al. 1999