Event Horizon Telescope
Memo Series

EHT Memo 2018-CE-01

Calibration & Error Analysis WG
James Clerk Maxwell Telescope Calibration Memo
Time dependence of the aperture efficiency and DPFU
S. Issaoun1 , H. Falcke1 , P. Friberg2 , M. Janssen1 , R. Tilanus1 and J. Wouterloot2
Jan 2, 2018 – Version 1.0
12Department of Astrophysics/IMAPP, Radboud University Nijmegen, 6500 GL Nijmegen, the Netherlands
East Asian Observatory, 660 N. A’ohōkū Place, University Park, Hilo, HI 96720, USAAbstract
We investigate a time dependence in the aperture efficiency of the James Clerk Maxwell Telescope (JCMT).
This time dependence indicates a loss of efficiency for the telescope during the daytime hours on Hawaii most
likely due to the dish surface heating from the Sun. We fit the nighttime dependence as a constant aperture
efficiency and the daytime dependence as a negative Gaussian (absorption curve) aperture efficiency as a function of local time on Hawaii (HST). This dependence propagates to the Degree Per Flux Unit (DPFU) scaling
factor needed for the station-based amplitude calibration as part of the Event Horizon Telescope. The JCMT
observed a number of hours in the daytime during the 2017 campaign, therefore the daytime contribution is anecessary factor to be included in the ANTAB tables for a priori amplitude calibration.

1Method

approximated as a Gaussian distribution, as in Fig. 2. The
median of the measurements is 0.514, which only differsfrom the mean by 0.04σ.

The JCMT staff provided aperture efficiency measurements
for the telescope at 230 GHz using planet calibrators. Overa hundred different measurements3 were performed from2006 to 2017 with Mars, Jupiter and Uranus, presented inFig. 1. Clear outliers from the general trend were flagged- efficiencies below 0.3 and above 0.7 - before any fit wasattempted on the data. We separated the nighttime and daytime data points based on average sunrise and sunset times
on Hawaii: the daytime measurements were chosen to be all
points measured between 6 HST (sunrise) and 19 HST (sunset), all other points were interpreted as part of the nighttime
trend. The conversion from local Hawaii time to UT is UT= HST + 10.
Figure 2: Histogram of the nighttime measurements approximatedas a Gaussian distribution.

The measurements of aperture efficiency before 6 HST andafter 19 HST correspond to the UT range of 5-16 UT, wheremost of the observations with the JCMT are performed in
the EHT schedules.

2.2

The daytime aperture efficiency trend showed a dip in efficiency during the day, due to the dish surface being affectedby heating from the Sun and e.g. an expansion of the main
support pillars of the backing structure. This trend is approximated as a negative Gaussian, and fitted to the daytimemeasurements. The daytime efficiency function is written as
follows, where xHST is the local time in the daytime range
and the fit parameters are presented in Table 1:

Figure 1: Aperture efficiency measurements from 2006 to 2017 atthe JCMT.

2

Results

2.1

Nighttime fit
ηA,day = 1 − Ae−

The nighttime aperture efficiency is expected to be very stable due to the dish having cooled down. We thus fitted thenighttime data points with a constant aperture efficiency
value. The nighttime efficiency obtained is:
ηA,night = 0.516 ± 0.054

Daytime fit(xHST −x0 )22σ2(2)Table 1: Daytime aperture efficiency fit parameters.

parameter
Ax0σ(1)The uncertainty on the nighttime value is determined by taking the standard deviation on the mean of the measurements

value
0.599 ± 0.014
13.55 ± 0.21
9.16 ± 0.45

3 The method used to derive the measurements is outlined in the A priori Calibration Memo by Issaoun et al. (2017) and will not be explained here.
See appendix for details on planet parameters.

2

Figure 3: Histogram of the daytime measurements approximatedas a Gaussian distribution.

Figure 5: Daytime and nighttime fits to the aperture efficiency
measurements.

Figure 4: Cumulative sum plot of the fit residuals compared to thecumulation of an analytical Gaussian distribution.

To determine the uncertainty on the fit as a whole, we subtracted the fitted aperture efficiencies from the measured
values at every daytime HST and the residuals were used for Figure 6: Main beam efficiency measurements at the JCMT (witherror estimation. Approximating the residual distribution as the RxA3 receiver) versus Hawaii Standard Time for all observaa Gaussian, a standard deviation of σ = 0.0547 was found, tions between 2010 and 2015.
as shown in Fig. 3. However, the distribution seems to have
two peaks and does not look entirely Gaussian. We thus
performed an additional analysis using cumulative statistics.
A similar behavior of the main beam efficiency for the teleThe standard deviation from the median of the residuals was scope, shown in Fig. 6, has been observed by JCMT staff
determined from the cumulative sum of the residuals, shown using measurements between 2010 and 2015. They havein Fig. 4. Here the median also lies very close to the meanfound that there is a significant decrease in the main beamof zero, and we see a broad agreement between the cumuefficiency during the day, and that this decrease is less onlative trend of the fit residuals and the analytical Gaussian. a cloudy day when the Sun has less effect on the surface of
Therefore it seems reasonable to use the Gaussian standard the dish.
deviation as the uncertainty on the fit. The average uncertainty from the positive and negative standard deviation
Comparing our fits to the main beam efficiency findings, thefrom the median in the cumulative plot is σavg = 0.0554.
points on the lower envelope of the daytime dip are likely
This value is taken as the overall uncertainty on the timedue to clear-sky days (with the Sun lowering the efficiency)
dependent negative Gaussian fit for the daytime apertureand the points on the upper envelope are due to cloudy days.
efficiency. Fig. 5 shows the two final fits as a function ofIn April 2017, daytime weather on Hawaii varied fromlocal time on Hawaii (HST).
mildly cloudy to clear in the afternoons, thus the error bud3

get is expected to be representative of varying observing
conditions at the telescope during EHT observations.

2.3

The cause of this dip in efficiency, however, remains to beexplained. At the JCMT, thermal models of the antenna(during the design and later by Fred Baas) predict surface
distortion caused by thermal gradients in the dish backup
structure originating from changes in temperature in thebuilding. The heavier elements in the backup structure heatup (or cool down) much slower than lighter pieces, generating these temperature gradients. The theoretical implications of the dish distortion have been studied but nevermeasured experimentally and were not pursued after thetelescope stopped daytime observing, although the JCMT
still keeps a temperature monitoring system.

The time-dependent DPFUThe DPFU for the JCMT carries forward the time dependence of the aperture efficiency. We have a constant nighttime DPFU and a daytime negative Gaussian fit DPFU4 ,where k is the Bolzmann constant and Ageom is the geometric area of the JCMT assuming a diameter of 15 meters:

Another effect on the efficiency is an absolute temperaturechange in the panels of the dish: the panels are made of thinaluminium layers on a stiff foam substrate, with different
expansion coefficients, so the panel shapes are expected toAgeom
DPFUnight =× ηA,night = 0.03304 ± 11%(3) change with temperature. This effect is aggravated if the2k
surface is under direct sunlight, such that the panels heat up
Ageom
DPFUday =× ηA,day = 0.0640 × ηA,day ± 14% (4) more than the building itself. Direct sunlight on at least part2kof the dish is also known to cause rapid focus changes.
The telscope building heats up during the day and telescope
staff generally aim to open the dome in the afternoon to
speed up the cooldown and limit the effect of dish distortionin the early evening. Therefore the time gap between theopening of the dome for cooldown and the first observations
The time-dependent trend for the aperture efficiency ofalso matters in the estimation of the aperture efficiency. The
the JCMT seems very stable through the years and wellconstrained by the two different fits. The scatter in the mea- seeing is also generally worse in the afternoon, worsening
surements, used here to derive an error budget for the JCMT, telescope performance.
are likely due to variations in the quality of the observing
While the fits presented here are of good practical use, it
conditions and telescope performance and likely not due
to a changing dish surface. The error budget however is ex- is generally preferable to complement them with direct
pected to be representative of varying observing conditions efficiency observations of planet calibrators and a monitorat the telescope during EHT observations. Provided that no ing of observing conditions such as: when the dome waschanges are made to the JCMT dish surface, these two rela- opened, how much cooldown time before the first observations should be suitable for practical use in future observing tions, possible effects of direct sunlight on the dish, clear
versus cloudy afternoons etc.
runs.

3

Conclusion

4 The relative error on the DPFU includes a 5% uncertainty on the planet brightness temperatures used for the planet calibration measurements addedin quadrature to the aperture efficiency error estimates.

4Appendix: JCMT planet calibration
Overview of planet brightness temperatures used at the JCMT by M. Currie.
Filename: scuba2.txt
scuba2.txt
Number of filters defined = 5
Number beams defined per filter =NF
12
3
4
5
6
7

Wavelength
850
450
1300
868
434

Freq.
350.0
677.0
234.5
345.8
691.5
0.0
0.0

Width
30.0
30.0
1.0
1.0
1.0
0.0
0.0

2HPBW
13.0
7.9
20.0
14.0
8.00.0
0.0

HPBW2
48.0
25.0
0.0
0.0
0.0
0.0
0.0

A1
0.98
0.94
1.00
1.00
1.00
0.00
0.00

A2
0.02
0.06
0.00
0.00
0.00
0.00
0.00

Planetary temperatures and errors:

850
450
1300
868
434

Mars
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0

Jupiter
163.8
4.0
148.5
5.0
170.0
5.0
163.8
4.0
148.5
5.0
0.0
0.0
0.0
0.0

Saturn
124.3
5.0
111.0
5.0
133.0
5.0
124.3
5.0
111.0
5.0
0.0
0.0
0.0
0.0

Uranus
82.71.0
68.4
0.5
96.9
0.5
86.6
0.0
70.2
0.0
0.0
0.0
0.0
0.0

Neptune
78.1
5.0
65.6
3.0
95.2
0.5
71.8
0.0
64.2
0.0
0.0
0.0
0.0
0.0

Notes these are revised numbers as of 20 Apr 2012:
The Uranus and Neptune brightness temperatures are from Moreno, R. 2010, "Neptune and Uranus planetary brightness
temperature tabulation, available from ESA Herschel Science Centre." The errors in brightness temperature are simply
an estimate from the variation over the filters and are not used by FLUXES. The Herschel calibration data indicatethat the SCUBA-2 filters are coincident with strong absorption lines. A more detailed analysis of the SCUBA-2 filtersin combination with the Neptune brightness temperatures is required before Neptune should be used for calibration.
The Jupiter brightness temperatures are obtained from the measurements of Griffin et al. 1986, Icarus 65, 244.
The errors in brightness temperatures are the rms internal errors of the observations. For MJD’s between 46040
through 50000 the Martian temperatures are derived from the model developed by Wright 1976, Ap.J., 210, 250.
Outside these MJD’s i.e., in particular after 10 October 1995 a simplified model of a rotating cratered asteroid isused Wright, E. L, 2007, astro-ph/0703640v1. Since the results for Mars are derived from models no errors are quoted;
however the Martian brightness temperatures are probably uncertain at the 5% level and this uncertainty must be added
to obtain the absolute errors. Over the interval for which both the original Wright model and the simplified model arevalid, the differences in brightness temperatures have an rms error of 0.13 K i.e. negligible. The flux densities for
Saturn are for the planetary disk only; an additional flux is expected when the rings present an open aspect, and atsuch times Saturn should not be used as a calibration object. Individuals using these data in published works shouldreference the appropriate papers as noted above. The filter frequencies are the effective frequencies for 1mm of water
vapour. These are the SCUBA-2 filters.
1300, 868, and 434 micron 234.5, 345.8, 691.5 GHz are for heterodyne receivers. Saturn, Mars copied from scuba.dat;
Uranus and Neptune from ESA4 values for 234.5 GHz are CO in LSB as normally observed with RxA3.

5