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Lecture 3

Lecture 3. By Tom Wilson. Summary of Lecture 1 Noise in a Receiver. Receiver itself, atmosphere, ground and source. time on source. Analying bandwidth (for lines, need 3 resolution elements on the line above the ½ power point).

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Lecture 3

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  1. Lecture 3 By Tom Wilson

  2. Summary of Lecture 1 Noise in a Receiver Receiver itself, atmosphere, ground and source time on source Analying bandwidth (for lines, need 3 resolution elements on the line above the ½ power point) Temperatures from thermal hot and cold load measurements using the receiver.

  3. Hot-cold load measurements (to determine receiver noise contribution) Absorber at a given temperature Input to receiver OK for heterodyne receivers, but not for Bolometers

  4. Current Receiver Noise Temperatures Tmin=hn/k for coherent receivers TSYS=TRX e t Atmospheric optical depth

  5. Receivers • Heterodyne for spectral lines • High velocity resolution • flexibility, but not multi-pixel receivers in the mm/sub-mm • Bolometers for continuum • Multi-pixel cameras Noise Equivalent power (about 1)

  6. Types of Receivers Fractional Resolution

  7. Lecture 3 page 7 BOLOMETERS VS COHERENT RECEIVERS JCMT: 15 m sub mm dish, hA = 0.5 at l= 0.87 mm, n= 345 GHz With SCUBA, can detect a source with 0.16 Jy in 1second. So RMS is ¼ of this peak value or DSn=0.04 Jy in 1 sec. Compare to a coherent receiver: TSYS = 50 K, Dn= 2 GHz, integration time= 1 sec In antenna temperature. From Lecture 2: For JCMT, Or So comparable for 1 beam, but SCUBA has 37 beams & MAMBO has 117 beams.

  8. q(arc sec)=206 k l(mm)/D(m) of order 1.2 for single dishes Sn=3520 TA /(h A D2)

  9. Summary of Lecture 2 Rayleigh-Jeans Or (Show that these are consistent) In Jy True source size and temperature Gaussian beams: apparent source size and temperature

  10. Can make a relation for flux density similar to that for Main Beam Brightness temperature: S(total)=S(peak) . (q S2 + qB2 )/ qB2 Example: Orion A is an HII region with a total flux density of 380 Jy at 1.3 cm. The size is 2.5’ (FWHP). If the radio telescope beam size is 40” (FWHP), what is the peak flux density? Use the R-J relation to find the peak main beam brightness temperature. Solution: peak Jy/beam=9.5; TA=8.8K, TB=24 K

  11. Lecture 3 page 1 Far Field Diffraction and Fourier Transforms (radiation passing through an opening) (Exact calculations require programs such as GRASP)

  12. Lecture 3 page 2 Grading Across the Aperture and Far E Field

  13. Lecture 3, page 3 ALMA Technical Building ANTENNA Correlator Front-End Tunable Filter Bank Local Oscillator IF-Processing (8 * 2-4GHz sub-bands) Digital De-Formatter Digitizer Clock Digitizer 8* 4Gs/s -3bit ADC 8* 250 MHz, 48bit out Optical De-Mux & Amplifier Data Encoder 12*10Gb/s Fiber Patch-Panel From 270 stations to 64 DTS Inputs 12 Optical Transmitters 12->1 DWD Optical Mux Fiber

  14. Sketch of 2 element interferometer

  15. Earth Rotation Aperture Synthesis (u,v) plane and image plane • These are related by Fourier transforms • The distance between antennas varies, so we sample different source structures • On the next overheads, we indicate how structures are sampled. Following tradition, u represents one dimension distributions, with x as the separtion in wavelenghts u=2px/l andv=2py/l

  16. 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.

  17. Gridding and sampling in (u,v) plane Sensitivity: http://www.eso.org/projects/alma/science/bin/sensitivity.html

  18. VLA uv plane response

  19. Data as taken The radio galaxy Cygnus A as measured with all configurations of the VLA Data with MEM with MEM and Self- Calibration

  20. From W. D. Cotton (in ‘The Role of VLBI in Astrophysics, Astrometry, And Geodesy, ed Mantovani & Kus, Kluwer 2004)

  21. Lecture 3 page 16 • BROADBAND RADIATION • Black body (Moon, planets, 3K background) • Dust thermal emission • Bremsstrahlung (free-free) • Synchrotron (relativistic electrons in magnetic fields) • Inverse Compton Scattering (S-Z) • Dust: Mostly carbon, silicon with ice mantles “ground up planets” • From Hildebrand (1983)

  22. Lecture 3 page 17 For warm grains Use R-J get EXAMPLE: Dust emission from Orion KL The Orion “hot core” has the following properties:

  23. Lecture 3 page 18 Calculate the column density N(H2) = n L and the 1.3 mm dust flux density, S, if z = zSun, b = 1.9 If the value of L = diameter, use L (diameter in cm) x (size in radians) = = 7.5 1016 cm Them N(cm-2) = 7.5 .1016 cm x 107 cm-3 = 7.5 .1023 cm-2 for H2 N(H) = 2 N(H2) = 1.5 .1024 cm-2 So At 4 mm, S is 81 times smaller or 120 mJy. At 0.39 mm, Sis 81 times larger or 810 Jy

  24. Lecture 3 page 19 BREMSSTRAHLUNG (FREE-FREE) Hydrogen is ionized by O, B, electron and protons interact, electrons radiate. Classically: velocity Power radiated during encounter: ‘p’ is impact parameter Find From the Kirchhoff relation, get frequency

  25. Lecture 3 page 20 When n = n0, t = 1: For Orion A, t0 = 1 GHz, or 30 cm. But What is the Relation for TB? -

  26. Lecture 3 page 21 Orion A HII Region Te = 8500 K, q = 2.5’ (FWHP), so use t is much less than 1, at n = 23 GHz so T = Tet From 100-m, TMB (main beam) = 24 K in a 40” beam, so TMB (main beam) = T(true) 24 = (8500) .(8.235 10-2) .(8500)-1.35.(23)-2.1.EM so EM = 4 .106 cm-6 pc = Ne. Ni .L If L = 25’ = 0.33 pc converted to radians @ 500 pc get Ne = Ni = 3.5 .103 cm-3 This is the RMS density. Calculate the mass of ionized gas. Rough number since know Orion A is not spherical. From spectral lines know Ne= 104 cm-3, so L = 0.03 pc. Then M = 0.6 MSun in ionized gas

  27. Lecture 3 page 22 Free-Free Intensity and Flux Density as function of Frequency (Problem: Use the example of Orion to check these Curves)

  28. Lecture 3 page 4 Free-Free Emission from Planetary Nebulae NGC7027 (a PNe) has Sn= 5.4 Jy at 1.3 cm. What is the TMB (main beam brightness temperature) if the 100-m FWHP beam size is 43”? Use Where q0 is the telescope beam size in are min. Suppose the “true” gaussian source size is 10”, what is TB (true brightness temperature). Could use (Problem: Repeat for the 30-m, with beam 27’’, wavelength 3.5 mm, flux density 4.7 Jy)

  29. Lecture 3 page 5 Or And get We know that the electron temperature of NGC7027 is Te = 14000 K. Use equation of radiative transfer: To get This is a source which is thermal, so the radiation is free-free or Bremsstrahlung

  30. Lecture 3 page 23 SYNCHROTON RADIATION (NON-THERMAL) Highly relativistic electrons spiraling in a B field with a frequency P: Power radiated by electron (lab) P’: Power radiated by electron (rest frame) so P = P’ Transformation of acceleration So

  31. Lecture 3 page 24 Radiation patterns of an electron in a B field B Field, V about 0.2 c B Field, V about 0 Velocity

  32. Lecture 3 page 25 Then E: Particle energy Is difficult to separate energy of electron from B field strength To get spectral distribution, use Find a synchrotron spectrum n-m: (power law distribution of Cosmic Rays) Synchrotron radiation is found to be linearly polarized

  33. Lecture 3 page 26 SINGLE ELECTRON SYNCHROTRON EMISSION For relativistic electrons, the emitted pulse is 1/g shorter due to relativistic beaming while the Doppler effect gives rise to a factor 1/g2 wB: Frequency of rotation So for B = 10mG, wB is even lower when g<1 Thus in frequency reach a critical value So if B = 10 mG, wG = 176 Hz, to reach nC = 10 GHz, g = 1.6 104 In Synchrotron emission, we measure only the most relativistic particles

  34. Lecture 3 page 27 SYNCHROTRON ENERGY CONSIDERATIONS Allow one to determine the minimum or equipartion energy Inverse Compton effect When the radiation density is equal to magnetic energy density there can be energy losses in addition to synchrotron energy losses. R & W don’t do much, but Kellermann & Owen give: This is the basis of the statement: “1012 K is the highest source temperature possible”

  35. Lecture 3 page 6 Non-thermal sources Cas A: at 100 MHz, Sn= 3 104 Jy, qs=4’ (source size), l = 3 m = 300 cm Source Specral Index Thermal sources have limit T = 2.104 K Assume that for Cas A, T=7.5 108 (l(m) / 3) -2.8 What is the source temperature at 3 mm?

  36. Lecture 3 page 29 SUNYAEV-ZELDOVICH EFFECT Clusters of galaxies are filled with hot diffuse gas. Photons from the 3 K background are scattered in this cluster gas. More photons are given energy than lose energy on the low frequency side of the Planck curve. On the high frequency side, some photons are shifted to lower energies, but still a reduction in the 3 K background. At 160 GHz, have a cross over from absorption at longer wavelengths to emission at shorter wavelengths, so have zero absorption. The absorption is: When combined with X ray luminosity, which is Bremsstrahlung (free-free), proportional to Ne2 L, can solve for source distance. Given velocity of source, get HUBBLE CONSTANT. However there can be systematic effects such as clumping.

  37. Lecture 3 page 30 EXAMPLE OF S-Z EFFECT The cluster CL0016 +16 shows on S-Z absorption of –700 m K at 1 cm wavelength Z = redshift of CL0016 +16 is 0.541 X ray data: Te = 1.6 108 K Cluster size = 30“ to 19” RMS Ne = 1.2 10-2 cm-3 So

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