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