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
HET345	2017-08	JUPITER	31.4 ± 0.00	346.55	17.5	0.50 ± 0.07	0.61 ± 0.09	46 ± 7	6
GARD180	2017-08	JUPITER	32.5 ± 0.04	178.01	34.0	0.60 ± 0.09	0.74 ± 0.11	38 ± 6	3
HET345	2017-08	JUPITER	31.4 ± 0.00	345.05	17.5	0.50 ± 0.07	0.61 ± 0.09	47 ± 7	3
GARD180	2017-08	URANUS	3.6 ± 0.01	207.25	29.2	0.60 ± 0.09	0.73 ± 0.11	39 ± 6	4
HET230	2017-08	JUPITER	32.2 ± 0.82	229.79	26.3	0.61 ± 0.09	0.74 ± 0.11	38 ± 6	4
NOVA660	2017-08	URANUS	3.6 ± 0.00	692.22	8.7	0.22 ± 0.04	0.26 ± 0.05	107 ± 19	5
HET460	2017-08	JUPITER	32.0 ± 0.03	460.29	13.2	0.32 ± 0.05	0.39 ± 0.06	73 ± 11	4
PI230	2017-07	JUPITER	33.3 ± 0.00	225.92	26.8	0.50 ± 0.07	0.61 ± 0.09	47 ± 7	3
HET230	2017-07	JUPITER	33.4 ± 0.03	214.15	28.3	0.60 ± 0.09	0.74 ± 0.11	39 ± 6	4
PI230	2017-07	JUPITER	34.1 ± 0.46	218.80	27.7	0.52 ± 0.08	0.64 ± 0.09	45 ± 7	4
PI230	2017-07	JUPITER	34.0 ± 0.23	230.80	26.2	0.53 ± 0.08	0.66 ± 0.10	43 ± 6	7
HET230	2017-07	JUPITER	36.0 ± 0.04	229.79	26.3	0.57 ± 0.08	0.69 ± 0.10	41 ± 6	6
NOVA660	2017-07	JUPITER	34.2 ± 0.97	692.22	8.7	0.25 ± 0.04	0.30 ± 0.04	95 ± 14	4
HET230	2017-07	JUPITER	36.0 ± 0.04	231.29	26.2	0.57 ± 0.08	0.69 ± 0.10	41 ± 6	3
HET460	2017-06	JUPITER	37.3 ± 0.00	460.29	13.2	0.30 ± 0.04	0.36 ± 0.05	79 ± 12	6
HET230	2017-06	JUPITER	37.6 ± 0.58	231.29	26.2	0.57 ± 0.08	0.70 ± 0.10	40 ± 6	20
GARD180	2017-06	URANUS	3.4 ± 0.00	207.25	29.2	0.58 ± 0.09	0.71 ± 0.11	40 ± 6	6
HET460	2017-06	JUPITER	37.3 ± 0.00	461.79	13.1	0.29 ± 0.04	0.35 ± 0.05	80 ± 12	3
GARD180	2017-06	JUPITER	38.1 ± 0.00	177.07	34.2	0.60 ± 0.09	0.73 ± 0.11	39 ± 6	3
PI230	2017-06	JUPITER	37.5 ± 0.56	230.54	26.3	0.51 ± 0.07	0.63 ± 0.09	45 ± 7	11
HET230	2017-06	JUPITER	37.6 ± 0.58	229.79	26.3	0.58 ± 0.09	0.71 ± 0.10	40 ± 6	40
PI230	2017-05	JUPITER	40.4 ± 0.00	230.54	26.3	0.55 ± 0.08	0.67 ± 0.10	42 ± 6	4
HET345	2017-05	JUPITER	40.6 ± 0.00	346.55	17.5	0.51 ± 0.08	0.63 ± 0.09	45 ± 7	12
GARD180	2017-05	JUPITER	41.7 ± 0.00	167.80	36.1	0.68 ± 0.10	0.84 ± 0.12	34 ± 5	3
HET345	2017-05	JUPITER	40.6 ± 0.00	345.05	17.5	0.51 ± 0.08	0.63 ± 0.09	45 ± 7	6
PI230	2017-04	JUPITER	42.9 ± 0.00	230.54	26.3	0.58 ± 0.09	0.72 ± 0.11	40 ± 6	8
HET230	2017-04	JUPITER	42.9 ± 0.00	229.79	26.3	0.64 ± 0.09	0.79 ± 0.12	36 ± 5	12
HET230	2017-04	JUPITER	42.9 ± 0.00	231.29	26.2	0.64 ± 0.09	0.78 ± 0.12	36 ± 5	6
PI230	2017-04	JUPITER	42.9 ± 0.01	228.10	26.5	0.55 ± 0.08	0.68 ± 0.10	42 ± 6	22
NOVA660	2017-04	JUPITER	42.6 ± 0.10	692.22	8.7	0.38 ± 0.06	0.47 ± 0.07	61 ± 9	4
HET230	2017-03	JUPITER	42.1 ± 0.00	229.25	26.4	0.66 ± 0.10	0.81 ± 0.12	35 ± 5	3
HET230	2017-03	JUPITER	42.1 ± 0.00	245.75	24.6	0.63 ± 0.09	0.77 ± 0.12	37 ± 5	4
HET230	2017-03	JUPITER	42.2 ± 0.21	229.79	26.3	0.65 ± 0.10	0.80 ± 0.12	36 ± 5	12
HET230	2017-03	JUPITER	42.1 ± 0.00	244.25	24.8	0.61 ± 0.09	0.75 ± 0.11	38 ± 6	5
HET230	2017-03	JUPITER	42.1 ± 0.00	230.75	26.2	0.66 ± 0.10	0.80 ± 0.12	35 ± 5	3
HET230	2017-03	JUPITER	42.2 ± 0.21	231.29	26.2	0.65 ± 0.10	0.79 ± 0.12	36 ± 5	6
HET345	2017-02	JUPITER	39.6 ± 0.00	351.75	17.2	0.48 ± 0.07	0.59 ± 0.09	48 ± 7	4
HET345	2017-02	JUPITER	39.6 ± 0.00	271.25	22.3	0.57 ± 0.08	0.70 ± 0.10	41 ± 6	4
HET345	2017-02	JUPITER	39.6 ± 0.00	312.75	19.4	0.51 ± 0.08	0.63 ± 0.09	45 ± 7	4

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.