Some recent work I. Cosmic microwave background, seeds of large scale structure (Planck) Formation and evolution of galaxies (Figure: Simpson et al.

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1 Radio astronomy Radio astronomy studies celestial objects at wavelengths longward of λ 100 µm (frequencies below ν 3 THz) A radio telecope can see cold gas and dust (Wien s displacement law of BB emision, λ max [mm]t [K 3) hot plasma (free-free emission, recombination lines, synchrotron radiation) very distant objects, λ = λ 0 (1 + z), redshifted lines, dust continuum near the radiation peak

2 Some recent work I Cosmic microwave background, seeds of large scale structure (Planck) Formation and evolution of galaxies (Figure: Simpson et al. 2015, ApJ 799, 81; The Scuba-2 Cosmology Legacy Survey, ALMA) Active galactic nuclei and their parent galaxies (Figure: Kimball et al 2015, MNRAS 452, 88; QSO J , CII 158µm at z=4.6, ALMA)

3 Recent work II Initial stages of massive star formation (Figure: Rathborne et al 2015, ApJ 802, 125; G near the GC, ALMA + SCUBA + Spitzer 24µm) Disks around young stars, planet formation (Figure: ALMA Partnership 2015, ApJ 808, L3; HL Tau, ALMA)

4 Recent work III Interstellar chemistry (Figure: Brünken et al. 2014, Nature 516, 219; para- and ortho-h 2 D + towards IRAS , SOFIA + APEX. For constraining o/p-h 2 and the age of a star forming core. Fundamental constants (Figure: Truppe et al. 2013, Nature Communications, accurate frequencies for the Λ-doublet transi- tions, sensitive to the fine structure constant α.

5 Radio astronomical observation data to information signal to data radio source atmosphere to receivers

6 Antenna temperature The power density (W Hz 1 ) received by a single-dish telescope is measured in terms of the antenna temperature, T A : T A = A e 2k S ν,obs = A e I ν P n dω 2k A e effective area of antenna k = Boltzmann constant S ν,obs observed flux density (Wm 2 Hz 1 ) I ν surface brightness (Wm 2 Hz 1 sr 1 ) P n normalized beam pattern Using the brightness temperature, T B = λ2 2k I ν: T A = 1 T B P n dω Ω A Ω A solid angle of the antenna beam

7 Coherent receivers Preserve the amplitude and phase of the incoming electric field Signal down-converted to an intermediate frequency (IF) front end, back end (Figure: et al. SOFIA/GREAT, Heyminck 2012, A&A, 542, L1; HEB mixer for 1-5 THz) Allow high spectral resolution Superconducting mixers (SIS, HEB) used at submm and far-infrared wavelengths Aims: low noise, wide IF band, high spectral resolution

8 Receiver temperature The noise added by the receiver is described by the receiver temperature Figures: J. Smuidzinas 2002, Monterey conference (top); T.L. Wilson, ALMA Newsletter (bottom)

9 Bolometer arrays Thermoelectric detection of incoming radiation in a wide frequency band The sensitivity is usually given in terms of NEP (noise equivalen power, W s 1/2 or W Hz 1/2, signal corresponding to the rms noise after 0.5 s integration) or NEFD (noise-equivalent flux density, mjy/beam, 1σ, 1s) Figure: ArTeMiS/APEX (left), SCUBA-2/JCMT (right)

10 Atmospheric transmission at radio wavelengths Affected primarily by water and oxygen lines Figure: ALMA transmission calculator

11 Sky noise

12 Sky subtraction in single-dish observations Position switching Beam switching Frequency switching On-The-Fly, scanning Sensitivity T = KTsys νtint, T sys = T sky + T rec

13 Radio spectroscopy

14 Information from spectral lines We are interested in the dynamical state and possible future developments of a gaseous object. These depend on the mass, gas kinematics (infall, outflow, rotation, turbulence, shocks), thermal support, and magnetic fields. Kinematics: LSR velocities and line shapes, v, v Temperature: symmetric and asymmetric rotors with metastable levels Density: excitation analysis of several rotational lines Column densities and chemical abundances: LTE analysis or radiative transfer modelling of spectral lines Ionization: abundances of molecular kations Magnetic field: Zeeman effect in HI, OH, CN, etc.

15 Famous radio lines I The λ = 21 cm line of HI (neutral hydrogen atom) - spin-spin interaction between the H nucleus and electron The fine structure lines of CI (neutral carbon) - coupling between the orbital angular momentum (L) and the spin (S) of electrons The Λ-doubling lines of the CH and OH radicals - coupling between orbital angular momentum Λ and molecule rotation N

16 Famous radio lines II The inversion lines of NH 3 (ammonia) - tunneling The rotational lines of CO, and other polar molecules (H 2 O, HCN, HCO +, N 2 H +, etc.) - change of the rotation angular momentum

17 Molecular states and energies Typical energy differences Electronic states: 1 ev K - UV and visible Vibrational states: ev K - infrared Rotational states: ev K - (sub)mm

18 The spectroscopic problem 1) How does the intensity of a line depend on the populations of the upper state u and the lower state l? radiative transfer 2) How do the populations depend on the physical conditions in the source? excitation

19 Radiative and collisional transitions u n u A ul n l B lu J n u B ul J n l C lu n u C ul l The probabilities of radiative transitions are described by Einstein coefficients, A ul (spontaneous emission), B lu (absorption), and B ul (stimulated emission) The collisional coefficients C ul depend on the gas density, n H2, the speed v of the colliding particles (kinetic temperature), and the collisional cross-section σ ul (microscopic properties), C ul = n H2 < vσ ul >

20 Excitation temperature In analogy with the Boltzmann equation (valid in TE), a quantity called the excitation temperature, T ex, is defined by Usually n u n l = g u g l e (Eu E l )/kt ex T bg T ex T kin

21 Radiative transfer ds I ν (s) I ν (s + ds) The intensity of radiation changes through absorption and emission in the medium (scattering ignored): di ν = κ ν I ν ds, κ ν absorption coefficient [unit m 1 ] di ν = ε ν ds, ε ν emission coefficient [W m 3 Hz 1 sr 1 ] This leads to the radiative transfer equation di ν dτ ν = I ν S ν, where we have defined the optical thickness, dτ κ ν ds, and the source function S ν εν κ ν

22 Antenna equation I The solution of the radiative transfer equation in homogeneous medium in terms of the brightness temperature (after background subtraction) is given by where T B = hν k [ Fν (T ex ) F ν (T bg ) ] ( 1 e τν ) F ν (T ) 1 e hν/kt 1 The calibration system of a single-dish telescope usually gives TA, the antenna temperature corrected for the atmosphere. This is related to T B by an efficiency factor η: T A = η hν k [ Fν (T ex ) F ν (T bg ) ] ( 1 e τν )

23 Antenna equation II The information of the column density and the velocity distribution is contained in τ. So we can write T A(v) = η hν 0 k [ fν0 (T ex ) f ν0 (T bg ) ] ( 1 e τ(v)) (τ(v) = λ3 A ul 8π F N ν(t ex) uφ(v)) Line-of-sight homogeneity is usually not a realistic assumption. Radiative transfer modelling together with a realistic source model is used more and more.

24 Linear polar molecules E rot = hbj(j + 1), J = 0, 1, 2,..., (rigid rotor approximation) J = ±1, B = rotation constant h 8π 2 I B

25 Symmetric top molecules E rot = hbj(j + 1) + h(b A)K 2 (prolate top) K = 0, ±1, ±2,..., ±J (projection of J on the molecular axis) J = 0, ±1, K = 0

26 Hyperfine structure Rotational energy levels can be split because of -interaction of the eletric quadrupole moment of a nucleus with spin I > 1/2 with the electric field of the electrons -interaction of the magnetic moments of nuclei with I > 0 with each other or with molecular rotation I = 0: 12 C 16 O, 18 O, I = 1/2: H, 13 C, 15 N I = 1: 14 N I = 5/2: 17 O diagram: Ho & Townes (1983)

27 Hyperfine structure II The splitting is very helpfull because it provides components wit different optical thicknesses Accurate determination of radial velocities and velocity dispersions diagram: Shirley (2003), spectrum: Caselli et al. (1995)

28 Summary Radio spectral lines provide information of the physical conditions of neutral and ionized gas in astronomical objects. In particular, rotational lines are the only direct probes of cool and dense gas where new stars originate Radio techniques enable very high spectral and angular resolution The selection of spectroscopic tools requires consideration of the excitation and radiative transfer We are normally observing tracer molecules (instead of H 2 ). Some knowledge of the chemical evolution is helpful when deciding which molecules to use.