1. ATCA synthesis workshop - May 20031 ATCA – Calibration at mm wavelengths Rick Forster University of California, Berkeley Hat Creek Radio Observatory Berkeley-Illinois-Maryland Association Topics:Basics of interferometry The atmosphere Amplitude & phase calibration Atmospheric & instrumental effects Antenna effects

2. ATCA synthesis workshop - May 2003 2 L201.50.1933 S132.30.2422 C65.60.2210 X38.60.215 K1.220.50.532 W0.3587.52.700.6 Band cmGHzmJy/bbeam ATCA Bands

3. ATCA synthesis workshop - May 2003 3 V 2 or the total output power is T SYS = T R + T SKY + T A K (100+200+.04 K) Brightness B = 2k T B / 2 W/Hz m 2  Flux density S = B d  W/Hz m -2 Effective area A eff =  D 2 m 2 A few definitions Janskys/K S/T A = 3510/  D 2 Jy/K V (volts) Received power V A 2 = A eff S  Watts

4. ATCA synthesis workshop - May 2003 4 Tsys – ‘Paddle’ or Chopper Wheel method  s ~ RF LO GPBSampler Delay IF Digitized IF (V) Amb Sky T sys sets the flux scale and the noise level! Tsys = T amb - T sky V 2 amb – V 2 sky () V 2 sky -T sky n )  = sin -1 (n/s) s n =0.2 Jy  = sin -1 (0.2) ~ 12 o n = 2 k Tsys  Jy tbw  Tsys=300 K A=380 m 2 bw=128 MHz  =0.3 t=10 sec k=1380 Jy m 2 /K T amb T sky T sys V2V2 T

5. ATCA synthesis workshop - May 2003 5 Basic Interferometry _  g = B s ^ x B _ ^ s  g = geometrical delay correlation coefficient  = Ny–Nn N T sys = system temperature T ant = antenna temperature Ant 1 Ant 2 Correlator 1x2   Digitized IF from two antennas

6. ATCA synthesis workshop - May 2003 6 Tsys ~ 200 K Jy/K ~ 150  ~ 5 10 -4 S =  Tsys Jy/K ~ 15 Jy Correlation Coeffieient Ampl (Jy) & Phase 64 lag channels (+/- 32) 32 freq channels (amp & pha) Fourier Transform V = Ae i  Visibility Correlation Function

7. ATCA synthesis workshop - May 2003 7 Atmosphere T sky = T atm (1-e -  ) T A = T sou ( e -  ) T sys = T R +T sky +T A T sys = T R +T atm (1-e -  )+T sou (e -  ) T’ sys = T R e  +T atm (e  -1)+T sou delay absorption T’ sys = T sys e  Lay, 1997 for  = 1, e  = 2.7

8. ATCA synthesis workshop - May 2003 8 Opacity of the Atmosphere – O 2 & H 2 O H2OH2O O 2 50-70 GHz O 2 118 GHz H 2 O 180-190 GHz H 2 O 22 GHz Frequency (GHz) 50100 150 O2O2 84.9-87.3 H42  SO SiO 88.5-91.3 HCN HCO + CH 3 OH HC 3 N

9. ATCA synthesis workshop - May 2003 9 Log time  Power density 30 sec 3 hrs 10 min  D  Log  Log Distance (D) D saturation  = 1.0 (Gaussian)  = 5/6 (Kolmogorov)  = 1/2 (Lorentzian) Structure Function (  vs D) “Frozen Turbulence” Model (  power vs t)  = 5/6, 1km layer, 5km/s wind, 500m D Longer baselines shifts peak right Stronger winds shifts peak left Lay, 1997 Butler & Desai, 1999  ~ 0

10. ATCA synthesis workshop - May 2003 10 M87 data calibrated with 3C273 AmplitudePhase 80m 45m 15m

11. ATCA synthesis workshop - May 2003 11 Baseline Solution – C-array, March 2003 Phases BEFORE Correction Phases AFTER Correction

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17. ATCA synthesis workshop - May 2003 17 Absolute flux calibrationTest source MWC 349 (HII) 0909+013 (QSO) 1310+323 (QSO) cal source test Use a test source to help quantify the effects of atmospheric decorrelation in the image plane. Use a primary flux calibrator (planet or HII region) to check the value of Jy/K. Use your phase calibrator to monitor temporal gain changes.

18. ATCA synthesis workshop - May 2003 18 Passband – 32 visibility channels over 100 MHz Channel BW = 3.125 MHz (~11 km/s) n = 2 k Tsys  Jy tbw  k = 1380 Jy m 2 /K Tsys = 560 K A = 28 m 2  =  a  c =.70x.88 =.61 bw = 100/32 = 3.125 MHz t = 6m = 360 s n = 2.6 Jy (each 11 km/s channel) s/n = 12/2.6 ~ 4.6 phase noise ~ 11 deg 4 MHz = 14 km/s 64ch = 0.2 km/s At 0.2 km/s channel n = 8x2.6 ~ 21 Jy (ave 100 MHz ~ 6 times better)

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23. ATCA synthesis workshop - May 2003 23 30 min Az El

24. ATCA synthesis workshop - May 2003 24 A few final suggestions Calibrate Tsys often Check Jy/K on a flux cal Mosaic sources larger than ½ fwhm Use offset pointing for extended sources In a pinch total power correction might help Choose nearby calibrator if baseline is uncertain Choose integration time so S/N > 5 on calibrator Use a guest calibrator to gauge atmospheric effects Don’t push your observations beyond the seeing limit Avoid unnecessary PB calibration, & check sensitivity Monitor the atmosphere – abort 3mm in severe conditions Fast-switching might be worth a try in reasonable conditions

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