12M Manual Appendix C


Home
Up
Emergency Info
Proposals
Facilities
Instrumentation
Systems Status
Schedules
Observer Info
Science at ARO
ARO In The News
Weather
Staff
Education
ARO FAQ
Internal Docs
Tucson Info
Jobs
Photo Gallery
Search ARO
Contacts


Temperature Scales and Telescope
Efficiencies



The calibration mode used for essentially all spectral line observations at the 12m is the chopper wheel method (see Ulich & Haas, 1976, ApJS, 30, 247 for a detailed description of this technique). The chopper wheel technique corrects for atmospheric attenuation and several telescope losses. In the following, we describe the temperature scale used at the 12m and how it relates to temperature scales used at other millimeter wavelength observatories.

 

C.1 Definitions

 

In the following we define the terms used in the subsequent temperature scale and telescope efficiency discussion. we have tried to adopt a similar nomenclature to that used in Kutner & Ulich (1981, ApJ, 250, 341).  Note that throughout this discussion when we refer to a “temperature” we are actually referring to the effective source radiation temperature J(υ,Τ), which is defined as:

 

(C.1)

 


 

General Terms

 

s  Solid angle subtended by the source
d  Solid angle subtended by the central diffraction beam pattern of the telescope
Solid angle on the sky
Direction angle on the sky
Ρn Normalized antenna power pattern
Ρng Normalized Gaussian antenna power pattern
Βn Normalized source brightness distribution
Α Air mass toward which the measurement is made
0 Atmospheric optical depth at the zenith
G Maximum antenna gain

 


Efficiencies

         

r Radiative efficiency  
  (C.2)
       
       
       
rss Rearward Scattering and spillover efficiency  
  (C.3)
       
       
       
l r rss (C.4)
       
       
       
fss Forward scattering and spillover efficiency  
  (C.5)
       
       
       
mb Main beam efficiency  
  (C.6)
       
       
       
cmb Efficiency at which the source couples to the main diffraction beam of the telescope  
  (C.7)
       
       
       
c

Efficiency at which the source couples to the telescope beam

 
 

cmbmb

(C.8)
  (C.9)

 


 

Temperatures

TR Source radiation temperature  
       
       
TA Observed source antenna temperature  
  (C.10)
       
       
Observed source antenna temperature corrected for atmospheric attenuation  
  (C.11)
       
       
Observed source antenna temperature corrected for atmospheric attenuation, radiative loss and rearward scattering and spillover  
  (C.12)
       
       
Observed source antenna temperature corrected for atmospheric attenuation, radiative loss and rearward and forward scattering and spillover1  
  (C.13)
       
       
Source radiation temperature excluding any background emission (like the cosmic microwave background emission)  
   
  (C.14)
       
       

Source brightness temperature as measured by the main diffraction beam of the telescope

 
  (C.15
       
       

 

1 can also be defined as the source brightness temperature corrected for atmospheric attenuation, radiative loss, and rearward and forward scattering and spillover if the source is equal to or larger than the main diffraction beam.


 

C.2 Relations Between Temperature Scales

 

We can now combine the definitions above to derive the relations between the physical measurements and the temperature scale used at the 12m and the scales used at other telescopes. Combining the equations above, we can relate the source temperature corrected for atmospheric attenuation (T'A) to many of the antenna and source temperatures:

 

T'A (C.16)
       
  (C.17)
       
  (C.18)
       
  (C.19)
       

 


 

C.3 Telescope Efficiency Measurements

 

Telescope efficiencies are normally calculated using a measurement of the continuum brightness of a planet (for ) or the Moon (for ). In the following we give the relations used to calculate several telescope efficiencies. Since the source coupling between a disk source like the planets and a Gaussian telescope beam is given by:

 

                                                    (C.20)

 

We will use this term in the efficiency equation derivations given below.

 

C.3.1 Corrected Main Beam Efficiency

 

The efficiency factor which converts the 12m T*R scale to the Tmb scale is given by:

 

                 

                     

                                                 (C.21)

 

One can also calculate  using the Ruze equation:

 

                                                                          (C.22)

 

given that:

 

                                                                  (C.23)

 

                                                                                  (C.24)

 

                                                             (C.25)

 

where λ is the wavelength of observation, is the correlation scale size of the surface deviations (280 mm), a0 is the zero wavelength aperture efficiency (0.55), and is the surface accuracy (75 μm). Figure C.1 shows this relation with the actual measurements given in Table C.1.

 

C.3.2 Main Beam Efficiency

 

The efficiency factor which converts any source antenna measurement to the Tmb scale is given by:

 

 

                       

                                                       (C.26)

 

 

 

Figure C.1: Measured and theoretical estimates of  as a function of frequency.


 

Table C.1 lists the most recent measurements of  and  for the planets and frequencies given.

 

Table C.1:  12m Telescope Efficiencies

Frequency
(GHz)

Source

Source Size

(arcsec)

m

mb

Date Measured

72.0

Jupiter

37.4

x

35.0

1.04

±

0.13

0.66

±

0.08

April 1997

98.0

Venus

12.2

x

12.2

0.90

±

0.06

0.57

±

0.04

Nov 1996

98.0

Mars

8.5

x

8.4

0.83

±

0.07

0.53

±

0.04

Jun 1997

98.0

Saturn

16.9

x

15.3

0.93

±

0.11

0.59

±

0.07

Jun 1997

109.8

Venus

22.1

x

22.1

0.97

±

0.04

0.62

±

0.02

Aug 1996

109.8

Jupiter

43.4

x

40.6

0.97

±

0.05

0.62

±

0.03

Aug 1996

109.8

Saturn

19.2

x

17.3

0.97

±

0.06

0.62

±

0.04

Aug 1996

115.3

Jupiter

43.4

x

40.6

0.88

±

0.04

0.56

±

0.02

Aug 1996

115.3

Saturn

19.2

x

17.3

0.97

±

0.06

0.62

±

0.04

Aug 1996

140.8

Venus

13.4

x

13.4

0.73

±

0.05

0.47

±

0.03

Nov 1996

140.8

Mars

5.5

x

5.5

0.85

±

0.07

0.54

±

0.04

Nov 1996

140.8

Jupiter

35.5

x

33.2

0.82

±

0.09

0.52

±

0.06

Nov 1996

140.8

Saturn

19.1

x

17.2

0.92

±

0.09

0.59

±

0.06

Nov 1996

140.8

Uranus

3.5

x

3.5

0.80

±

0.10

0.51

±

0.06

Nov 1996

140.8

Neptune

2.2

x

2.2

0.76

±

0.10

0.48

±

0.06

Nov 1996

144.6

Saturn

17.4

x

15.7

0.76

±

0.04

0.48

±

0.03

Jun 1996

218.2

Saturn

18.0

x

16.1

0.58

±

0.03

0.37

±

0.02

Nov 1995

230.5

Saturn

19.5

x

17.6

0.43

±

0.11

0.27

±

0.07

Oct 1996

230.5

Uranus

3.6

x

3.5

0.46

±

0.15

0.29

±

0.09

Oct 1996

244.9

Mars

7.5

x

7.5

0.57

±

0.04

0.36

±

0.02

Dec 1996

265.9

Mars

5.5

x

5.5

0.48

±

0.03

0.31

±

0.02

Nov 1996

291.8

Mars

7.1

x

7.1

0.42

±

0.04

0.27

±

0.02

Dec 1996

291.8

Saturn

17.8

x

16.1

0.37

±

0.04

0.24

±

0.02

Dec 1996

 


 Copyright Arizona Radio Observatory.
For problems or questions regarding this web contact [tfolkers{at}email{dot}arizona{dot}edu].
Last updated: 11/08/11.