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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 / 2me c 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 105 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 hcRme 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 1110 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 = 2h3 /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 ' 0 Tb Tb (0) Ts (1 e ) c2 2 k 2 I … and if 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 cm2 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 1019 N H [cm2 ]Ts 1V 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 ( , , )dd 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