1. Lecture 4 By Tom Wilson

2. Review page 1 Interferometers on next page Rayleigh-Jeans: True if h << kT S = measured: if  s <  B, T=T MB  s =  b, T = T S In mm / sub mm usually calibrations give T A * = “corrected antenna temperature” corrected for atmosphere, and telescope efficiency for very extended source T MB : corrected for atmosphere and beam efficiency

3. Grading Across the Aperture and Far E Field as limit of interferometer Review page 2

4. Above: the 2 antennas on the earth’s surface have a different orientation as a function of time. Below: the ordering of correlated data in (u,v) plane. Review page 3

5. Gridding and sampling in (u,v) plane

6. Review page 5 RECEIVERS (MM) Mix from sky frequency to IF frequency (4 GHz) and amplify signal 2 LIMITS:

7. Analog Coherent Receiver Block Diagram Review page 5 Time Frequency  f Total Amplification=10 16

8. Review page 6 In centimeters, the first stage of a receiver is a cooled transistor ampifier, a HEMT (InP, GaAs…). For HEMTs, T RX = 2 (n GHz ) with a minimum of 4 K, perhaps. The minimum noise for a coherent receiver is h n / k or about 5 K at 100 GHz. With mixers, the Rx noise is usually Double Sideband (DSB). For spectral lines want Single Sideband (SSB), where TSSB =2 TDSB. Bolometers- non coherent receivers. Noise quoted in NEP (watts Hz –1/2 ). For a given system on a telescope, performance is frequently given as “detectable source in Jy in 1 sec”. For HHT and 19 channel bolometer, 1 Jy in 1 sec. SCUBA/JCM this is 4 x better (2 x collecting area, 2 x rx efficiency). SCUBA has 37 beams at 0.87nm. INTERPRETATION Continuum dust thermal emission

9. Review page 7 Free-Free (Bremstrahlung) Synchrotron emission Radiation frequency is increased by beaming 1/ and doppler 1/ 2, so critical Frequency is  =10 4 for 10 GHz  : energy spectrum of cosmic rays

10. RELATE ATOMIC PHYSICS TO RADIO ASTRONOMY Einstein A & B coefficients and their role in Equation of radiative transfer A+B coefficients in a 2 level system. Start with: Lecture4 page 1 After some  manipulation, get Inserting numerical values of physical constants: N u A ul +B ul N u U=B lu N l U U =4  /c I U =4  /c I

11. Lecture4 page 2 In terms of column density, N l, get GROUND STATE OF HYDOGEN HI line from overlap of proton and electron wave functions—see next slide In Q. M., allowed transitions only between wave functions of opposite parity:

12. N=1 S P D F (From H. E. White, ‘ Introduction to Atomic Physics ’ )

13. Apply all this to HI: “21 cm line” hyperfine transition 0 = 1.420 405…GHz A ul = 2.87 · 10 -15 sec -1 A very non classical system!! Show For HI, h · / k = 0.06 K Lecture4 page 4

14. Lecture4 page 5 Frequency ( ) Frequency ( 0 ) A ul (sec -1 ) gugugugu glglglgl DI (deuterium) 327 MHz4.65 ·10 -17 42 3 He + 8.665 GHz 1.95 ·10 -1213 Similar transition are for D and 3 He + EXCITATION OF 2 LEVEL SYSTEM Competition of radiation and collisions Answer: For HI, T ex = T k, if n >1 cm -3 hk

15. Lecture4 page 6 HI Clouds assumed to be in pressure equilibrium HI: Used to obtain dynamics of galaxies, “HI masses” of galaxies, map rotation curve of our galaxy, … See absorption line if T BG > T ex (HI) = T k, geometry and cloud size relative to background continuum plays a role - - complex but solvable !

16. A=2.65 10 -7 sec -1 A=7.93 10 -8 sec -1 A=2.4 10 -6 sec -1 (Use two level excitation with collision rate of 10 -10 cm 3 sec -1 to get n*)

17. Lecture4 page 7 RADIO RECOMBINATION LINES These are “Rydberg Atoms” with Principal Quantum Numbers > 20 m = electron mass and M = nucleon mass Set z 2 = 1

18. Lecture4 page 7 Then, line intensity is proportional to N p N e From Bremsstrahlung, so is T c for HII regions Find e Saha Eq’n

20. Lecture4 page 9 NON-LTE EFFECTS N n : Actual population N n * : LTE population g u and g e are nearly equal for u, l > 20, so Then T ex < 0 population inversion typically T ex = -300K In Lecture 1, if |  | < 0, get

21. Lecture4 page 10 If lines are optically thin, what is amplified? On ‘Tools’, p. 342 is: Often lots of algebra !  < 0 and depends on density, and could be large!

22. Lecture4 page 11 APPLY TO AN ACTUAL HII REGION (ORION A) History 1965- 1967 From Radio Recombination Lines (RL), T e T e = 5800 K (6 cm, 5 GHz) optical is ~10 4 K 1968 Theory of RL broadening theory (Griem) 1969 2 components models with dense clumps 1970 Measured T e rises to 7000 K (6 cm) 1972 Brocklehurst & Seaton give complete theory At low frequencies core radiation broadened (large n) At high frequencies, cores dominates, but not much maser emission in diffuse foreground gas. Brown, Lockman & Knapp in Annual Reviews (1978) proposed a recombination line theory with large EM, low n e and lots of line masering. This is not matched by measurements. So unrealistic!

23. Lecture4 page 12 This is where MACROPHYSICS meets MICROPHYSICS Macrophysics: structure of a source on parsec Microphysics: cross sections, local populations of atoms Confluences of these – i.e. masering depends on atomic physics and source structure could be thought of as “Radiative transfer”

24. Lecture4 page 13 Quantum description: 2S+1 L J