APEX Antenna Efficiencies

2017	2018	2019	2020	2021	2022	2023

Mars	Jupiter	Uranus	All

Instrument	Year-Month	Planet	θS ('')1	Frequency (GHz)	θmb ('')	ηa2,4	ηmb3,4	Jy/K5	# Scans
PI230	2018-09	JUPITER	33.2 ± 0.08	231.45	26.2	0.61 ± 0.05	0.75 ± 0.06	38 ± 3	6
FLASH460L	2018-06	JUPITER	43.1 ± 0.07	464.75	13.0	0.41 ± 0.03	0.50 ± 0.04	57 ± 5	6
FLASH345	2018-06	JUPITER	43.1 ± 0.07	334.75	18.1	0.53 ± 0.04	0.64 ± 0.05	44 ± 4	6
PI230	2018-06	JUPITER	43.0 ± 0.06	208.50	29.0	0.58 ± 0.05	0.71 ± 0.06	40 ± 3	8
PI230	2018-06	JUPITER	42.7 ± 0.23	230.80	26.2	0.45 ± 0.04	0.56 ± 0.05	997 ± 81	8
FLASH345	2018-06	JUPITER	43.1 ± 0.07	345.25	17.5	0.52 ± 0.04	0.64 ± 0.05	45 ± 4	6
PI230	2018-06	JUPITER	42.7 ± 0.23	218.80	27.7	0.58 ± 0.05	0.71 ± 0.06	40 ± 3	8
FLASH460L	2018-06	JUPITER	43.1 ± 0.07	452.75	13.4	0.37 ± 0.03	0.45 ± 0.04	64 ± 5	6
PI230	2018-06	JUPITER	43.0 ± 0.06	220.50	27.4	0.61 ± 0.05	0.74 ± 0.06	38 ± 3	8
FLASH460L	2018-05	JUPITER	43.3 ± 0.00	472.29	12.8	0.38 ± 0.03	0.47 ± 0.04	61 ± 5	6
PI230	2018-05	JUPITER	43.9 ± 0.02	225.03	26.9	0.60 ± 0.05	0.73 ± 0.06	39 ± 3	10
FLASH345	2018-05	JUPITER	43.3 ± 0.00	334.55	18.1	0.52 ± 0.04	0.64 ± 0.05	44 ± 4	6
FLASH345	2018-05	JUPITER	43.3 ± 0.00	345.05	17.5	0.52 ± 0.04	0.63 ± 0.05	45 ± 4	6
FLASH460L	2018-05	JUPITER	43.3 ± 0.00	460.29	13.2	0.42 ± 0.04	0.52 ± 0.04	55 ± 5	6
PI230	2018-05	JUPITER	43.9 ± 0.02	237.03	25.5	0.63 ± 0.05	0.77 ± 0.06	37 ± 3	10
PI230	2018-04	JUPITER	42.9 ± 0.01	254.20	23.8	0.62 ± 0.05	0.77 ± 0.06	37 ± 3	20
FLASH460L	2018-04	JUPITER	42.4 ± 0.28	459.25	13.2	0.41 ± 0.04	0.50 ± 0.04	58 ± 5	28
PI230	2018-04	JUPITER	43.6 ± 0.01	219.80	27.5	0.59 ± 0.05	0.72 ± 0.06	40 ± 3	8
FLASH460L	2018-04	JUPITER	42.4 ± 0.28	471.25	12.8	0.34 ± 0.03	0.41 ± 0.04	83 ± 8	28
FLASH345	2018-04	JUPITER	42.4 ± 0.29	338.75	17.9	0.54 ± 0.04	0.66 ± 0.05	43 ± 4	30
PI230	2018-04	JUPITER	43.6 ± 0.01	231.80	26.1	0.60 ± 0.05	0.74 ± 0.06	38 ± 3	8
PI230	2018-04	JUPITER	43.5 ± 0.03	215.10	28.1	0.59 ± 0.05	0.72 ± 0.06	40 ± 3	12
PI230	2018-04	JUPITER	42.9 ± 0.01	242.20	25.0	0.62 ± 0.05	0.76 ± 0.06	38 ± 3	20
FLASH345	2018-04	JUPITER	42.4 ± 0.29	349.25	17.3	0.53 ± 0.04	0.65 ± 0.05	44 ± 4	30
PI230	2018-04	JUPITER	43.5 ± 0.03	227.10	26.7	0.60 ± 0.05	0.74 ± 0.06	38 ± 3	12
FLASH345	2018-03	JUPITER	39.0 ± 0.00	346.55	17.5	0.46 ± 0.04	0.56 ± 0.05	51 ± 4	50
FLASH345	2018-03	JUPITER	38.4 ± 0.15	349.25	17.3	0.48 ± 0.04	0.59 ± 0.05	48 ± 4	14
FLASH460L	2018-03	JUPITER	38.4 ± 0.15	459.25	13.2	0.37 ± 0.03	0.45 ± 0.04	64 ± 6	14
PI230	2018-03	JUPITER	38.6 ± 0.12	208.00	29.1	0.56 ± 0.05	0.68 ± 0.06	42 ± 3	64
FLASH460L	2018-03	JUPITER	38.4 ± 0.15	471.25	12.8	0.34 ± 0.03	0.42 ± 0.04	69 ± 6	14
FLASH345	2018-03	JUPITER	38.9 ± 0.13	334.55	18.1	0.47 ± 0.04	0.58 ± 0.05	49 ± 4	52
PI230	2018-03	JUPITER	38.6 ± 0.12	220.00	27.5	0.58 ± 0.05	0.71 ± 0.06	40 ± 3	64
FLASH345	2018-03	JUPITER	38.4 ± 0.15	338.75	17.9	0.49 ± 0.04	0.60 ± 0.05	47 ± 4	14
FLASH345	2018-02	JUPITER	38.2 ± 0.00	334.55	18.1	0.47 ± 0.04	0.58 ± 0.05	49 ± 4	6
FLASH345	2018-02	JUPITER	38.1 ± 0.12	349.25	17.3	0.33 ± 0.03	0.40 ± 0.04	183 ± 16	6
PI230	2018-02	JUPITER	37.6 ± 0.26	242.54	25.0	0.46 ± 0.04	0.56 ± 0.05	54 ± 4	12
FLASH345	2018-02	JUPITER	38.2 ± 0.00	345.05	17.5	0.46 ± 0.04	0.56 ± 0.05	50 ± 4	6
PI230	2018-02	JUPITER	37.6 ± 0.26	230.54	26.3	0.45 ± 0.04	0.55 ± 0.05	54 ± 4	12
FLASH345	2018-02	JUPITER	38.1 ± 0.12	338.75	17.9	0.34 ± 0.03	0.41 ± 0.04	180 ± 15	6

Note 1: The planet sizes (θ_S) and fluxes from the planet models usually have < 5% uncertanties. The values given in the table above are the average planet size from selected scans (at least 5 scans at a given frequency; for data older than 2018, a minimum of 3 scans is used instead since there was no systematic observations of antenna efficiencies back then). If the planet size is smaller than 0.4 x HPBW (θ_mb) then θ_S, aperture efficiency (η_a) and the point source sensitivity (Jy/K) will be highlighted since the correction [1-exp(-Q)]/Q (with Q=ln(2)(θ_S/θ_mb)²) for non-pointlike source is < 5%.

Note 2: The aperture efficiency (η_a) intrinsicly includes the effects due to error beams, blockage, spillover, etc., because it is measured on sky toward a planet. Thus, it is lower than the expected aperture efficiency due exclusively to the surface accuracy as described by the original Ruze equation.

Note 3: Although the correction for the influence of the source size mentioned in Note 1 is only a first order correction (i.e, it asumes a clean Gaussian beam and does not take into account the effect of the sidelobes nor the error beams), we can consider our estimates a good approximation of the actual main beam efficiency (η_mb).

The spectra delivered by the APEX real-time calibration software (Muders et al. 2006, A&A, 454, L25) is in GILDAS/CLASS format (Pety J., 2005, in SF2A-2005, p. 721) in the corrected (for atmospheric attenuation, the forward efficiency and signal band gain) antenna temperature T_A^* scale (Ulich & Haas, 1976, ApJ, Suppl. Ser., Vol. 30, p. 247). The forward efficiency (η_fw) in the header is set to the actual value (<1.0). The beam efficiency (η_mb) is set to 1.0. In order to switch to the T_MB scale, one needs to multiply the data by η_fw/η_mb. Any further modification of η_mb after this switch of scale needs a multiplication by η_{mb_old}/η_{mb_new}. The "MODIFY BEAM_EFF" command in CLASS does the latter, i.e. it will use the existing eta_beam (=BEAM_EFF) as η_{mb_old} and the supplied value as η_{mb_new}. That is why the first step to switch to T_MB needs an initial BEAM_EFF set to FORWARD_EFF. Hence, for conversion of APEX data to main beam brightness temperature T_MB scale, we recommend using this CLASS script, after loading the data and getting a scan in the CLASS environment.

For point-like (relative to the beam size) science targets we recommend to use the η_mb values estimated from observations towards Uranus or Mars (when smaller than 0.4 x HPBW). For semi-extended sources (not point-like but unresolved by the beam) values estimated from Mars (when 0.4 x HPBW < θ_S < HPBW) are better. For extended sources (resolved by the beam) the values estimated from Jupiter or Mars (when larger than the beam) are recommended.

Note 4: Because of the new sub-reflector the forward efficiency (η_f=0.95) for 2018+ have smaller uncertainty of about 5% in contrast to the 10% uncertainty considered for previous years. Other efficiencies (η_a, η_mb and Jy/K) include the uncertainties of: the forward efficiency, the planet model (4%), the beam size (5%) and the uncertainty of the observed peak brightness temperature (usually < 10% for Uranus, and < 5% for Mars and Jupiter).

Note 5: The Jansky to Kelvin conversion factor for the APEX antenna can also be approximated by η_f24.4/η_a (Jy/K). According to the Ruze formula the aperture efficiency (η_a) and, hence, the main beam efficiency (η_mb), will degrade with shorter wavelength, λ, as

η_a (λ) = η_a (∞) exp(-16π²σ²/λ²)

where σ is the antenna surface RMS value (i.e. describing small scale deviations from a perfect surface).

Likewise, according to Downes (1989) the main beam efficiency can be estimated from the aperture efficiency as

η_mb (λ) = 0.8899 [θ_mb/(λ/D)]² η_a

with θ_mb ≈ k λ/D (assuming a Gaussian beam) where k is a factor that depends on the illumination taper and blockage of the aperture (e.g., Christiansen & Högbom 1985; Kraus 1986). For most APEX receivers we found k ≈ 1.17 which correspond to an edge tapering of about 13.9 dB (consistent with the value assumed by Güsten et al. 2006). Thus, the main beam efficiency can be approximated as: η_mb (λ) = 0.8899 (1.17)² η_a.

From the 2018 commissioning we recommend using θ_mb ≈ (9.0 ± 0.1) 658/f_GHz for the full frequency range of SEPIA660.

For the estimates we select only well focused and calibrated pointing scans toward Mars, Jupiter and Uranus (when available; during most of 2017 Mars was in sun avoidance). Pointing scans with offsets smaller than 10% of the beam size are selected for the estimates. Only the cross-scan in Azimuth are used and we discard the scans where the FWHM from the Azimuth and Elevation cross-scans differ by more than 10%. The aparent size and fluxes of the planets for a particular date and frequency are obtained from the corresponding models implemented in CASA ( CASA Guides: Solar System Models; ALMA memo #594). Comparing with other existing models (e.g., in GILDAS/ASTRO and in the work by Lellouch et al., 2006) we found they agree within 15%. Details of the theory and calculations used in our estimates can be found here. For a more elaborated explanation of the formulas we refer to the IRAM 30m internal documents cali_rep.pdf or spatial_response_framework_v1.8.pdf.

Efficiencies for the PI CHAMP+ instrument can be found at the corresponding web page at MPIfR.

The historical table below was adapted from Güsten et al. (2006, A&A 454, L13-L16). Beam sizes (θ_mb) were determined by deconvolving planet scans. The listed efficiencies are forward efficiency (η_f), aperture efficiency (η_a), main beam efficiency (η_mb), and Moon efficiency (η_M). The uncertainties of the listed efficiencies are expected to be 5-10%. For comparison with older values you can still find the former table of antenna efficiencies here.