1. Calibration and Data reduction Strategies Cormac Purcell & Ned Ladd Mopra Training Weekend May 2005

2. I Calibration

3. Measuring Source Intensity

4. Source Atmosphere …  Opacity) Background Emission (CMB) Electronic Noise

5. Measuring Source Intensity P on-src = C [ I src e -  + J(T atm )(1-e -  ) + I bg e -  + I Rx ] P off-src = C [ J(T atm )(1-e -  ) + I bg e -  + I Rx ] SourceAtmosphereMicrowave Background Electronic Noise I src = (P on-source – P off-source ) (e  /C)

6. T A *  (P on-source – P off-source ) P off-source P off-source e  C T sys Measuring Source Intensity = C [ J(T atm )(1-e  ) + I bg e  + I rx ] e   C T sys = P off-source e  /C I src T sys = J(T atm )e  – J(T atm ) + I bg + I rx e   T sys is a measure of noise in the whole system.

7. Measuring T sys with a Hot Load Compare blank sky to a known temperature standard: P sky P load

8. Measuring T sys with a Hot Load P load = C[I load + I rx ] P off-src J(T atm )(1-e  ) + I bg e  + I Rx P load – P off-src I load + I Rx - J(T atm )(1-e  ) - I bg e  - I Rx = Compare power from blank sky and known load: Power measered from blackbody paddle:

9. Measuring T sys with a Hot Load P sky J(T atm )(1-e  ) + I bg e  + I Rx P load – P sky I load - J(T atm )(1-e  ) - I bg e  = Assume: T load = T atm i.e. I load = J(T atm ) P sky J(T atm )(1-e  ) + I bg e  + I Rx P load – P sky J(T atm ) e  - I bg e  =

10. Measuring T sys with a Hot Load P sky J(T atm )(1-e  ) + I bg e  + I Rx P load – P sky J(T atm ) e  - I bg e  = J(T atm )e  – J(T atm ) + I bg + I Rx e  J(T atm ) - I bg = T sys J(T atm ) - I bg = P sky P load – P sky MeasuredAssumed : 300 K & < 1K T sys

11. What if T load = T atm ? P sky J(T atm )(1-e  ) + I bg e  + I Rx P load – P sky I load - J(T atm )(1-e  ) - I bg e  = Cannot merge terms.

12. What if T load = T atm ? P sky J(T atm )(1-e  ) + I bg e  + I Rx P load – P sky (I load – J(T atm )) + J(T atm )e  - I bg e  = J(T atm )e  – J(T atm ) + I bg + I Rx e  (I load – J(T atm ))e  + J(T atm ) - I bg = T sys (I load – J(T atm ))e  + J(T atm ) - I bg = T sys no longer depends on Measurable Quantities

13. Calibration to T A * scale (P on-source – P off-source ) P off-source T sys T A * = T sys = P sky P load - P sky (J(T load ) – I bg ) Assumed 300 K (Ambient temperature) <1 K From CMB

14. T A * is Not Enough: Calibrating to a Telescope-Independent Scale T A * scale assumes source emission fills the forward hemisphere T A * = T source only if this is true In practice, one needs to consider the coupling between the source intensity distribution and the telescope response as a function of angle

15. Antenna Temperature from an Extended Source T A * =  source  P b  P b  22 22 need to know something about the beam…  T source (  ) Pb()Pb()

16. 2003 Beam Greyscale: 10% - 100% Contours: 1% - 10%

17. Greyscale: 10% - 100% Contours: 1% - 10% 2004 Beam

18. Pb()Pb()

19. Main Beam +/- 40’’ Extended beam +/- 80’’

20. Main Beam Efficiency,  mb T A * = 22 22  source  P mb  P mb  22 22 P b  T A * =  mb  source  P mb  P mb  22 22 T mb = T A * /  mb Main Beam brightness temperature

21. Main Beam Brightness Temperature Scale T mb = T source for a source which fills only the main beam @Mopra, this means sources with size ~80” –For smaller sources, need to consider beam dilution –i.e., T mb = over the main beam  mb = 0.4 @86 GHz in 2004

22. Extended Beam Efficiency,  xb T A * = 22 22  source  P xb  P xb  22 22 P b  T A * =  xb  source  P xb  P xb  22 22 T xb = T A * /  xb Extended Beam brightness temperature

23. Extended Beam Brightness Temperature Scale T xb = T source for a source which fills both the main and extended beams @Mopra, this means sources with size >150”  mb ~ 0.6 @86 GHz in 2003

24. Calibration of Mopra Data Frequent T sys measurements –Every 20 minutes in good weather –Always after changing target source –  T A * scale Knowledge of source size –Choose efficiency based on coupling between source intensity distribution and beam pattern –  T mb, T xb, or T source

25. II Data Reduction

26. Reduction Steps Remove band-pass (off position) Fit a polynomial to the baseline Average individual spectra Scale to required temperature scale Measure line profiles - e.g. fit with Gaussian

27. A TNF S ingle-dish A nalysis P ackage

30. Exporting your data Export from ASAP –Export as an ASCII text file (e.g. T A * vs V) Export from SPC –Export as FITS & use perl script to fix headers Import to CLASS –Read ASCII file & manualy fill headers –Use CFITS to convert from SPC-FITS

31. Exporting your data Direct export from ASAP to FITS coming soon!

32. Questions?