Guide to Spectral Line Observing at the JCMT

H.E. Matthews, J. Leech, P.Friberg

1 Introduction

Spectral line observations at the JCMT employ facility receiver systems currently operating in four frequency bands, `A', `B', `C' and `D', respectively covering about 211-276, 315-370, 430-510 and 625-710 GHz. All receiver systems employ SIS mixers. Spectral line polarimetry can currently be carried out at the longer wavelengths (A and B bands).

With these receivers, coverage includes the CO J=2-1, 3-2, 4-3, 6-5 and CI($^3$P$_1$-$^3$P$_0$) and lines at 492 GHz. An autocorrelation spectrometer (DAS) the serves as the backend for all of these receivers with spectral resolutions in the range of 95 kHz through 1.5 MHz, for which contiguous spectral coverage ranges from 125 to 1800 MHz.

A polarising FTS is offered on occasion contingent on demand, and the South Pole Imaging Fabry-Perot Interferometer system may be available on a collaborative basis. In the late development stages are an heterodyne array receiver for the 345-GHz band (HARP-B) and a new spectrometer designed for use of the latter (ACSIS). Participation with the Smithsonian Sub-Millimeter Array (SMA) is still forthcoming. Interferometry between the JCMT and the neighbouring Caltech Submillimeter Observatory is no longer offered. A new and significantly more powerful heterodyne instrument polarimeter, Rover, should be available collaboratively on the JCMT (commisioning expected 2nd quarter 2005).

2 Receiver Overview

For quick reference, Table includes the approximate operational parameters of the spectral line receivers available at the present time. Further particulars of these receivers are described in the subsections below. Each receiver is identified by its JCMT name, along with the number of independent channels (i.e., mixers), whether or not image sideband rejection is possible, and the approximate frequency tuning range. The most current situation for each receiver is maintained on the JCMT Web receiver summary and status pages.

Table: Overview of JCMT Spectral-Line Receivers

		Chan-		Image		Freq.	IF		$T_{rx}$	Bandw.	Efficiencies				HPBW
		nels		Rej'n?		(GHz)	(GHz)		(K)	(MHz)	$\eta_a$	$\eta _{mb}$	$\eta_{fss}$	$\eta_{tel}$	(arcsec)		Notes
A3		1		N		211-279	4.00		(80)	1800	0.57	0.69	0.80	0.91	19.7
B3		2		Y		310-370	4.00		$140$	1800	(0.53)	0.63	0.88	0.86	13.2
W/C		2		Y		430-510	4.00		150	1600	0.31	0.52	0.70	0.83	10.8		1
W/D		2		Y		630-710	4.00		350	1600	(0.20)	(0.30)	(0.60)	(0.65)	(8.0)		1,2
MPI		1		N		790-840	2.54		750	$>$1000	(0.15)	(0.25)	(0.50)	(0.60)	(7.0)		3
Notes:
(1) Characterisation ongoing
(2) Upgraded mixers installed in 2001 and 2002; re-commissioning still ongoing
(3) Available by collaboration with Ronald Stark, MPIfR, Bonn

Heterodyne mixing results in sensitivity to two `sidebands' separated in sky frequency to either side of the local oscillator (LO) frequency by the intermediate frequency (IF). One, the `signal' sideband, contains the line(s) of interest, and the other, the `image' sideband, should be suppressed if it does not also contain useful information, and if the receiver has the option to do so. Image sideband rejection can reduce the total system noise, as well as remove unwanted features from the image sideband. The intermediate frequency (IF) is 4 GHz for all systems. Table also gives representative values for the double-sideband `receiver temperature', $T_{rx}$, the likely instantaneous bandwidth, telescope efficiencies and losses (these and other related quantities are defined in Section ), and the full beamwidth to half-power.

Using the information given here, it is possible to derive a reasonable estimate of the system noise temperature $T_{sys}$ corresponding to any frequency and airmass which can be used in the calculation of sensitivity in any given instance (see Section ). In practice, I would recommend most users adopt the values given in Table , at least for commonly-observed lines.

2.1 `A-Band': 211-276 GHz

This frequency band is covered by Receiver A3, which replaced A2¹ in December 1998. A2 had been in service since March 1992. A3 was built at HIA, Victoria using most of the components of the highly successful receiver B3i.² In going to A3 from the B3i platform the basic design of B3i was retained, with some reorientation of the components. The major changes included a new tunerless mixer, replacement of the quadrupler by a tunerless tripler, and conversion of the IF to 4 GHz. Additional information on A3, its commissioning, and operational issues can be found on the A3 Web page.

For those contemplating using A3 the receiver provides a number of features which make it a very effective observing tool. Perhaps the most significant is its fully remote tuning capability, such that tuning between frequencies is usually completed within 20 seconds. With A3 it is routine, say, to tune to the CO 2-1 transition to establish pointing and focus offsets using a late-type star as a spectral line pointing target, and then retune back to the line of interest towards the program target. A second valuable feature is the instantaneous IF bandwidth of the receiver: with A3 one can make use of the full width of the spectrometer, which, at 1800 MHz, is well in excess of 2000 km/sec, and hence very suitable for extragalactic observations.

Note that A3 does not offer image sideband rejection; this can be used to advantage in some programs, while in others one may have to make some careful choices. Calibration is achieved by using two loads, one at ambient (cabin) temperature, the other nominally at liquid nitrogen temperature.

In Figure  the typical performance of A3 is shown and compared with that for A2. Both receivers have similar noise temperatures from the lower limit of the frequency range until about 245 GHz. At higher frequencies A2's noise temperature continued to increase to very high values by the high frequency limit of the receiver. A3 shows a strong hump for LO frequencies between 245 and 262 GHz and then returns to low values. In late 1998, in the laboratory at HIA, Victoria, the noise temperature was essentially flat at about 85 K across the band; the noise hump occurred after shipping and before installation on the JCMT; in the most recent complete tests in February 2002 the hump appears to be larger, although it does not appear to have expanded in terms of LO frequency. Because A3 is a double-sideband instrument some care is needed with calibration; in particular the sideband ratio estimated using HC$_3$N rotational lines has strong variations between about 245 and 260 GHz. With the exception of frequencies which include part of the ``hump'' within the passband under normal observing conditions the single-sideband system temperature of A3 is in the range 300-500 K.

A3 is now an old receiver, and if the mixer in A3, or some other component, fails there is presently no plan to continue to provide an A-band observing capability at the JCMT. There has been some discussion in Canada on this subject, and in due course there is a possibility that a replacement mixer may be installed, and that receiver noise temperatures will then be restored to around 80-90 K across the entire band.

Current status -Please refer to the spectral-line receiver webpages for the current status of receiver A3 Web

Figure: Double-sideband receiver temperatures ($T_{rx}$) for Receiver A3 as a function of local oscillator frequency, and derived from standard calibration measurements made at the JCMT. Recent observations (February 2002) are compared with data obtained in December 1998. The hump alluded to in the text is very clear, and seems to have increased in amplitude in the interim, but does not affect the majority of the spectral lines observed with A3. The dot-dashed line shows the performance of receiver A2, which was replaced by A3 in December 1998. The continuous curve indicates the atmospheric attenuation for relatively poor conditions (5.0mm pwv; full vertical scale equals 100%). The horizontal bar at the bottom of the figure shows the present useful tuning range of A3 in rest frequency. Also shown are a selection of the more important spectral lines in this window.

2.2 `B-Band'; 315-370 GHz: Receiver B3

Receiver B3 is an automated heterodyne receiver for the 345-GHz (0.8-mm wavelength) band.³ It employs two low-noise niobium SIS junctions which are normally used to simultaneously detect orthogonally polarised radiation. B3 replaced the single-channel receiver B3i in early 1997. B3i had been in service since November 1991, and was reincarnated as A3 (see Section ).

Current status (July 2002): B3 has seen extensive use in the past year and has been reliable and stable in that time for the most part with some minor problems. We continue to see reduced line intensities on occasion, the cause of which remains under investigation.

In general the change in 1999 to tunerless mixers was a major step toward greater reliability and ease of use of B3, although there has been some inevitable sacrifices as regards tuning range and the potential for optimisation. The multiplier failed during a storm in December 2001, and its replacement has different characteristics, the result being that the upper end of the frequency range is now about 370 GHz, slightly lower than previously. The Gunn oscillator on occasion locks to a frequency offset 50 MHz from the expected value; for the time being we monitor the LO frequency with a counter pending a more permanent solution.

The receiver is usually tuned under remote computer control. A dual-beam interferometer allows either single-sideband (SSB) or double-sideband (DSB) operation, using either one or the other, or both, channels -- i.e. single- or dual-polarity. In SSB mode the detectors look into a cold load at the image sideband frequency, thereby enhancing sensitivity under all sky conditions except the very best. There is only one local oscillator so the two channels will be tuned to the same frequency. B3 has good baseline stability and bandwidths of up to the full spectrometer coverage of 1.8 GHz can be used. Calibration is achieved via on-board cold and ambient loads.

In Figure the double-sideband receiver temperatures for receiver B3 are plotted as a function of LO frequency.

Figure: Recent values for the double-sideband receiver temperatures ($T_{rx}$) of receiver B3 as a function of frequency are shown. The values are derived from single-sideband tunings obtained at the telescope in February 2002, following the replacement of the multiplier (see text). There are two mixers; $T_{rx}$ for channel A is indicated by connected $\bullet$'s, and for channel B by $\triangle$'s. Other details as for Figure . The variation of atmospheric transmission across the band (excluding weak absorption features) is shown for 1mm pwv.

The extreme tuning range of the receiver is approximately 310-370 GHz (in sky frequency). For frequencies within a few GHz of the tuning limits, mixer performance is less good, and one or both mixers may not show true heterodyne performance.

On the sky, SSB system temperatures well below 500 K are routine for B3 under normal conditions. However, the receiver window includes strong atmospheric absorption lines at 325 and 369 GHz (cf. Figure ); in these regions, it is may be difficult or impossible to observe sometimes even under good conditions.

Receiver B3 (and receiver W, discussed next) offers a wide range of options to the observer. To help in choosing between these options some additional comments may be useful:

• Because the backend spectrometer (the ``DAS'') has a fixed number of channels (2048; see Section ), the resolution in dual-polarisation mode with B3 will be half of that available when only one mixer is being used. Hence if one wishes to achieve the best spectral resolution (about 95 kHz) only one mixer must be used. At the other end of the scale, up to 920 MHz of bandwidth is currently available with the DAS using both mixers simultaneously with a spectral resolution of about 750 kHz. One can achieve a frequency coverage of about 1800 MHz (1500 km/s) using just one of the mixers, with a resulting spectral resolution of about 1.5 MHz. When only one mixer is to be used, it is recommended to use the second channel (`B').
• Some thought may be needed regarding whether to choose SSB or DSB operation. Using the SSB mode usually yields a better sensitivity and is the better choice when one is interested in a line or lines in one sideband. However, with an appropriate choice of sky frequency and setup of the spectrometer it is possible to observe lines originating from both sidebands simultaneously. In such cases one would choose to observe in DSB mode, and the cost in system sensitivity and reduced calibration accuracy may be outweighed by the increased observing efficiency. Under the right circumstances the best observing efficiency can be had by using both mixers in DSB mode and employing frequency switching. A factor of about eight in observing time could be gained in this way over that using a single mixer in SSB mode with, say, beamswitching. Examples of important pairs of lines which can be observed in this way are CO(3-2) and HCN(4-3), HCN and HNC(4-3), C$^{17}$O and C$^{18}$O(3-2), and CO and CO$^+$(3-2). One final caveat concerns intensity calibration: line intensities are less well-calibrated in DSB mode, and one should plan on observing a well-known ``standard line'' source in the same mode if using the DSB configuration, and subsequently making the necessary intensity correction off-line.
• Care needs to be exercised in cases where one wants to carry out line observations free from contamination from the other sideband using the SSB mode. The image sideband rejection is not absolute; typically it is in the range 12-14 dB, or a factor of not better than, say, 25. Thus a 1 K line in the rejected image sideband will still appear as a 40 mK line in the spectrum of the signal sideband, and one should be aware of this potential source of confusion. An example of what happens when one has a bright line in the image sideband is shown in Figure .

Figure: An example of line ``leakage'' from the image sideband. The spectrum shows an observation of H$_2$CO at 362.736 GHz in the upper sideband in single-sideband mode. H$_2$CO is, as is well known, not seen in the circumstellar envelope of IRC+10$^\circ$216 at the expected velocity of $-$26km/s. Two other lines are seen, however; one, at about $-$50 km/s, is due to HNC(4-3) in the signal sideband, while the second, at about $-$100 km/s, arises from imperfect cancellation of the image sideband, and is HCN(4-3), at 354.5 GHz. The latter is normally about 40 K in peak intensity, but is heavily attenuated by the sideband filter. Nevertheless, a very significant fraction of the signal is still received.

2.3 Receiver W; C- and D-bands

Receiver W, developed at MRAO in Cambridge, is the facility instrument for the higher-frequency spectral lines at the JCMT. The receiver has four SIS mixers: two for observations at C band (built by MRAO) with a tuning range from about 430 to 510 GHz, and two for D band (built by SRON in The Netherlands), covering from about 630 to 710 GHz. All mixers use SRON junctions. The pairs of mixers receive orthogonally-polarised radiation, so that one or the other mixer, or both mixers, at either C- or D-band may be used. Note that since only one local oscillator is provided, both mixers will be observing the same frequency range, and also that it is not possible to observe at C- and D-band simultaneously. The C-band coverage considerably increases the frequency regime accessible around the CO 4-3 and CI($^3$P$_1$-$^3$P$_0$) lines at 461 and 492 GHz, compared with that for the previous receiver C2. D-band observations, including the J=6-5 transition of CO and its isotopomers, had not been possible with the JCMT for some time prior to the arrival of receiver W.

Current status (July 2002): Prior to the current engineering shutdown extending through July 2002, both C-band mixers were working well with typical values for $T_{rx}$ (DSB) of 150-250 K. D-band history is somewhat more mixed: in 2000 the original mixers were replaced with new (and also tunerless) versions from SRON. One of the D-band mixers exhibited relatively poor performance especially at the higher frequencies, and was subsequently replaced twice more. The frequency synthesizer unit also failed, and was eventually replaced. A failed circuit in the LO control has been replaced. The most recent complete tests indicated good performance for both D-band mixers, with $T_{rx}$(DSB) about 320-450 K across much of the band.

Receiver W is normally operated in single-sideband (SSB) mode with the unwanted sideband terminated on a cold load. Dual-sideband (DSB) operation is possible, although untested. Tuning is partly automatic; the LO chain needs to be tuned manually by the operator, and although the C-band mixers and both sets of diplexers are tuned remotely, some manual fine adjustment is usually needed. Switching between C- and D-band is manual also.

The receiver was delivered to Hilo in Summer 1998, and during August 1998 commissioning began at the JCMT and remains ongoing. The receiver has performed well to date, with frequency coverage and sensitivity close to those anticipated in both frequency windows. Those ``standard'' lines (to be truthful, there are not enough samples to define ``standards'', but representative examples are available) which have been observed show decent agreement in both intensity and line shape with available data.

Commissioning receiver W has proven to be slow and full characterisation of the receiver is still far from complete, and mixed results have been obtained for aperture and beam efficiencies. The main difficulty has been in obtaining sufficient observing time during the necessarily good conditions when suitable test targets (Uranus, Mars, especially) are also available. Thus not all receiver parameters are well known and users should allow time to measure efficiencies. As new information becomes available, it will appear on the Receiver W Web pages.

2.3.1 `C-Band': 430-510 GHz

The C-band section of W replaced receiver C2. The latter⁴was a single-channel SIS receiver built by the RAL group, covering frequencies from about 450 to 505 GHz, and which was in service since May 1993. W offers significant improvements in sensitivity for observers of `C-band' spectral lines. Not only are the two mixers lower in noise, but unlike the one mixer in C2, they are capable of single-sideband operation, resulting in more accurate calibration.

Nevertheless, the 430-510-GHz (600-$\mu$m) band is a difficult one in which to work, since the transmission is rarely more than 50% at the zenith, and the region is sharply divided into a number of atmospheric ``windows''. This situation is shown in Figure , where the transmission for 0.5 mm of precipitable water vapor (equivalent to CSO tau about 0.03) is shown as a function of frequency. This represents the best observing conditions at Mauna Kea, essentially.

Figure: Variation of sky transmission for 0.5mm of precipitable water vapour over the frequency ranges covered by the C-band mixers in receiver W is shown as a continuous curve (full scale corresponds to 100%). Important spectral lines within this region are indicated (the CI($^3$P$_1$-$^3$P$_0$) line is identified by `${\rm C}^0$'). The tuning range at C-band is shown by the lower horizontal bar and compared with that for the earlier receiver `C2'. Double-sideband receiver temperatures of about 150-250 K are normal within this range; recently measured values are shown above, where the different symbols correspond to values obtained for the two channels of the receiver, those for channel A being linked by the dot-dashed line.

As indicated in Table  for practical purposes it is not productive to attempt to observe at 461 GHz for a zenith optical depth at 225 GHz (as given by the CSO `tau-meter') greater than 0.10. Conditions are more restrictive still at 492 GHz; the 225-GHz optical depth should not exceed 0.06 for useful data to be taken. If the program sources are at low declinations, if one is interested in broad lines, or if the frequency of the line being observed falls in a region of especially low transmission, even more restrictive limits are appropriate. In any case, one should not be tempted to `push' these limits. It is rarely productive and much better to revert to a lower-frequency program.

2.3.2 `D-Band'; the 660-692 GHz window

Until April 1995 an agreement with Reinhard Genzel and his group at the Institut für extraterrestrische Physik in Garching permitted a high-frequency heterodyne capability (`Receiver G') to be used at the JCMT. The receiver covered the band 650-692 GHz (including the CO(6-5) and $^{13}$CO(6-5) transitions) using an SIS mixer receiver⁵. Results from this receiver and its predecessors demonstrated the ability of the JCMT to make unique observations at these high frequencies.

Receiver W provides once again for observations in the D-band. In Figure  the tuning range of receiver W/D is indicated, together with the transmission as a function of frequency and a number of potentially important molecular lines.

Figure: The frequency region covered by the upper (`D') band of receiver `W', the continuous curve showing the behaviour of the zenith atmospheric transmission for 0.5 mm pwv ( $\tau_{225}\approx0.03$). DSB receiver temperatures (derived from SSB measurements and assuming the sideband ratio is unity) have recently been obtained for the new tunerless D-band mixers at a few frequencies, and are plotted here (as indicated by the symbols $\bullet$ and $\triangle$ for the two mixers, and in the case of channel A joined by a dotted line). There is a significant increase in noise temperature at the upper end of the band. Some transitions of common molecules (e.g. HCN, HCO$^+$) are shown which are included within the range of receiver `W', as indicated by the horizontal bar. The tuning range of receiver G (Harris et. al. 1994) is shown for comparison.

3 Line Polarization Observations

By installing the polarimeter originally used with the retired bolometer system UKT14 equipped with the appropriate waveplate in the beam waist of either A3 or B3, observations of the linearly polarized component of spectral lines are possible by making line observations at a series of waveplate angles. This is a non-standard facility, but it appears to work very well. There is no waveplate suitable for use in the frequency bands of receiver W. Further details can be obtained from the polarimeter Web pages.

4 IF Switch

The IF switch (IFS) automatically switches on demand between the outputs of heterodyne receivers and maintains power levels to the spectrometer at preset optimum values. This removes any need for manual switching when changing receiver setups. The operation of the IFS is completely transparent to the user, and usually, even to the telescope operator; information is included here only for completeness. The real functionality of the IFS lies in its ability to accommodate dual-channel systems such as B3 and W. The IFS also allows extra-wideband modes to be used with all extant heterodyne receivers; it splits the broad receiver passband into two overlapping bands which can then be processed by the DAS in two 920-MHz sections (see Table ).

5 Spectrometer Backend: the DAS

The `Dutch' (or Digital) Autocorrelation Spectrometer (DAS) became available at the JCMT in 1992. Properties of the basic modes of the DAS are summarized in Table , and some additional notes are given below. The DAS is soon to be replaced by a new versatile correlator system (ACSIS; designed for use with the multi-element receiver HARP) in 2004.

Table: Basic Spectrometer (DAS) Configurations

	No. of	Channel	Spectral	Channels
Bandwidth	Sub-	spacing	Resolution	per	Notes
(MHz)	systems	(kHz)	(kHz)$^a$	subsystem$^b$
Single Polarization (all receivers)
125	1	78	95	1600	1
250	1	156	189	1600
500	1	313	378	1600
760	1	625	756	1216	2
920	1	625	756	1472
$\sim$1800	2	1250	1513	736	3
Dual Polarization (receivers B3, W only)
125	2	156	189	800	4
250	2	313	378	800
500	2	625	756	800
760	2	1250	1513	608	2
920	2	1250	1513	736	5
$^a$Spectral resolution assumes natural weighting (the default)
$^b$Actual number of channels per subsystem will be somewhat greater due
to edge effects
Notes:
1) Best achievable resolution; for receivers used in single-channel mode only.
2) Compressed 920-MHz-band option with an increased overlap between
the subbands.
3) Widest band available overall (single polarization only).
4) Best resolution for receivers used in dual-polarization mode.
5) Widest band available overall in dual polarization mode

 		Note, 1 MHz is equivalent to 		 1.30 km/s at 230 GHz, 


0.87 km/s at 345 GHz, 


0.65 km/s at 461 GHz, 


0.43 km/s at 690 GHz, 


and    00.37 km/s at 810 GHz.

The DAS is a versatile hybrid autocorrelation spectrometer employing 3-level (2-bit) sampling logic and having 2048 delay channels. The latter are divided into 16 modules of 128 channels each. The IF/video and A/D sections consist of 16 `sub-bands' each with a total width of 160 MHz. Via a crossbar switch sub-bands can be associated with correlator modules in a large number of ways. The sub-bands are grouped together in two main sections<sup>6</sup> with IF inputs at most 920 MHz wide. Thus, for receivers offering `dual-channel' (i.e. dual polarisation) operation, such as B3 and W, signals from both may be received simultaneously and combined in data reduction. The DAS can also operate in cross-correlation mode for interferometry.

Each association of a set of sub-bands with a group of correlator modules is known as a `subsystem'. The most common and basic possibilities are given in Table . Many of these (all those with one subsystem) are for single-polarization observations using all the correlator modules of the DAS; others (with two or more subsystems) offer the possibility of dual-channel observing, wideband configurations, split-frequency modes, or combinations of different spectral resolutions. The maximum bandwidth using one subsystem of 8 sub-bands is about 920 MHz (reduced from the theoretical maximum of 1.28 GHz to circumvent aliasing within the DAS), and the minimum bandwidth using a subsystem of one sub-band is 125 MHz.

The narrowest channel spacing that can be obtained results from using all 16 correlator modules (all 2048 channels) for a single instrumental polarisation with a total bandwidth of 125 MHz is about 78 kHz. When two or more sub-bands are combined in a single subsystem, the sub-bands overlap in frequency space; the default spacing between subbands in such instances is 125 MHz.

At the other extreme, as noted in Section  one can use the IF switch to split a wide-bandwidth signal from a single-polarisation input into two overlapping regions fed into both subsystems of the DAS; the resolution in this instance would be 1.25 MHz, sufficient for many extragalactic projects. In this last mode input from only one mixer is be used; for dual-channel receivers this sacrifices resolution and sensitivity to achieve the maximum frequency coverage.

Using two inputs to the DAS results in only 1024 channels being used for each subsystem instead of the 2048 available for a single input. Thus for a given total bandwidth this leads to a factor of 2 reduction in spectral resolution. For instance, the signals from the two channels of B3 or W can be observed simultaneously, but only with a best spectral resolution of 156 kHz. The gain in sensitivity may be worth sacrificing some spectral resolution, depending on the astronomical goals.

The spectral resolution given in Table  is for uniform (natural) weighting; this is also the default weighting. This results in the best spectral resolution, but pronounced `ringing' of sharp features. The default can be changed in the spectrometer configuration setup during observing. For instance, if Hanning weighting is used, this results in a resolution of 2.0 times the channel spacing, but with considerably reduced sidelobe levels.

Table  shows only the most basic configurations of the DAS. The intent is to demonstrate the range of possible total bandwidths and frequency resolutions. However, as noted above the subsystems may be offset in frequency from the nominal central IF, and from each other, according to fairly complex rules; both coarse (in steps of 125 MHz) and fine (in steps of 1.25 MHz) LO offsets may be specified. The IF tuning range around the central IF is $\pm0.5$ GHz less the bandwidth being used; hence subsystems having a bandwidth nominally of 1 GHz cannot be tuned in the IF stage. The IF internal tuning capability of the DAS allows many possibilities, e.g.:

• One can have one broad band (of, say, almost 1 GHz) covering a complete spectral region, and one narrow band (say, 125 MHz) covering a specific region of interest with higher resolution.
• There is also the possibility of observing two or more spectral lines simultaneously with the same or different resolutions; whether this is possible may depend on the instantaneous IF bandwidth and IF of the receiver being used (see Table ). Aside from the trivial case of lines having frequencies differing by less than the spectrometer bandwidth,⁷ lines in opposite sidebands can be observed by offsetting the observing rest frequency and using a `non-standard' DAS observing setup. In general the latter is possible for two lines separated in rest frequency in the range $2\nu_{IF}\pm\Delta\nu$, where $\nu_{IF}$ is the IF frequency and $\Delta\nu$ the IF bandwidth (see Table  for these numbers). Special configuration files are set up to make use of non-standard modes.

These more complicated arrangements are beyond the scope of this guide, but are not inherently obscure. Individuals wishing to use more esoteric setups should contact one of the JCMT staff scientists before submitting a proposal.

6 Spectrometer backend: ACSIS

The replacement for the DAS, the ACSIS digital autocorrelation spectrometer is due for commissioning in the first quarter of 2005. More details can be found at the ACSIS website.

7 Observing Techniques with Heterodyne Receivers

Point-by-point spectral line observations can be made using either position-switching, beamswitching or frequency-switching. The spectral-line raster mapping technique can be used to rapidly and efficiently map larger areas of bright emission, and observe occultations.

7.1 Position-switching

Here the telescope observes alternately the source and a nearby reference position, from which pair of spectra the software obtains a calibrated result from which most instrumental and atmospheric effects have been eliminated. The integration time spent on a single signal or reference position is a compromise between observing efficiency and the rapidity with which conditions change, but is typically 30 seconds or less. If baseline ripples are found to be a problem then users may wish to experiment with modifying the focus position by a suitable fraction of a wavelength between subscans; most ripples appear to be the result of cable flexures and will therefore not be improved by focus modulation however.

7.2 Beam-switching

In this technique, the secondary mirror is `chopped' (usually at 1 Hz, and in the azimuth direction, although chopping in any direction is possible) with the source in one beam. At a slower rate, typically every 10-30 seconds, the telescope is moved by an amount equal to the chop throw, to bring the source into the other beam. Thus a negative line signal is obtained when the source is in the reference beam, and a positive one when it is in the signal beam. Both signal and reference phases are necessary; if one attempts to omit the reference part of the cycle, standing waves are the likely result. Generally the technique is effective for sources of small angular size (i.e. smaller than the beam throw -- see the telescope overview for limits on this), and should produce better results whenever sky noise is a problem (most of the time).

7.3 Frequency-switching

In this case the frequency of the local oscillator is switched between two values of the LO frequency separated by, say, 16 MHz. Although for the time being `true' frequency-switching (i.e. at a rate of up to a few Hz) is implemented only for receiver A3, the advantages of the technique are such that procedures have been developed which mimic the process, by switching the frequency once every subscan (or `phase' in JCMT-talk), that is, typically every 20-30 seconds. This `slow' frequency-switching works well with A3, B3, and, as far as it has been used to date, with W.

For certain types of observations, frequency-switching is the observing mode of choice:

• It is very efficient for observing narrow-line (less than a few MHz in width), spatially-extended objects. Telescope motion is no longer part of the observing process, and the line is observed almost continuously. Thus the observing of suitable objects is speeded up by a factor of somewhat more than two.
• Searching for a reference position free of line contamination. This is often difficult and time-consuming in the position-switched mode.
• Spectral line identification. Since lines in opposite sidebands move in opposite directions as the LO changes, frequency-switching automatically identifies the sideband in which a line appears because upper and lower sideband lines have mirror-image profiles in the unprocessed data. Note however that the technique may not be well-suited to sources with a high density of spectral lines, due to the overlapping of the ``ghosts'' produced by the reduction of the data. However, it seems to me that it should be possible to disentangle the resulting spectrum even then.
• Telluric lines can be observed directly; these are naturally cancelled out by position- and beam-switching. However, this can be a curse if you do not want to see these features; for instance, CO rotational lines from the Earth's atmosphere are quite strong ($\sim$2-10 K T$^*_A$ in emission). Ozone lines are in absorption, rather wide due to pressure-broadening, and can be very strong; they make a real mess of the baseline when working in frequency-switched mode.

The total frequency switch should be kept to a minimum, and although switches of up to 50 MHz have been used with some success, I would not recommend such a large switch for most purposes. In order to minimize the ripples in the baseline caused by this technique, it seems one should adopt a frequency switch which is an integral multiple of $\pm$8.2 MHz or so.

7.3.1 Point-by-point mapping

One can map an extended source by observing points defined via offsets from a central position. The points may be observed using any of the standard single-point observing modes (see above). The most convenient way to make such observations is by setting up a grid of positions. Any number of grids may be combined to make the map. Sequences of individual points may be observed using a `pattern' definition file to fill in additional points in your map. If position-switching is used, the reference position is defined with respect to the map centre and remains unchanged throughout the map, unless you change it.

7.4 Raster mapping

For extended fields with relatively bright line emission, the raster mapping technique is a sensible choice. In this mode the telescope is scanned along a line of constant latitude (usually RA, but as modified by the coordinate frame definition) while the DAS continuously integrates the incoming signals, forming the average once every few seconds and saving the result. Typically it is possible to map 0.5 K T$^*_a$ emission when the system temperature is as high as about 1000K (the image should be fairly heavily oversampled). The on-source observing efficiency is up to 75%, which compares with about 30% with regular grid maps. Maps of total time up to $\sim 1$ hour can be made easily without a break in observing at longer wavelengths when the sky is stable, and a data rate approaching $\sim$1000 spectra per hour can be achieved using this technique. Raster mapping runs only in the position-switched mode, with an integration at a user-supplied reference position once at the end of every row.

In preparing a time estimate for raster mapping the following points should be noted:

• Normally the sampling interval (`cell') should be less than half the HPBW to avoid smearing the map in the scan direction. One-third HPBW sampling is a good default choice. If you want to cover a larger area you can set the sampling interval (corresponding to the distance the telescope moves between spectra) to a larger number (say, one beamwidth), as long as some beam smearing is acceptable. A rotated (wrt the normal coordinate frame) cell may be used if you want to map along a particular direction. Some observers prefer to use a sampling interval in the scan direction of half that in the perpendicular direction; e.g. by using a cell of $3\times6''$.
• The integration time per point ($T$) should be 3-6 seconds per point; 2 seconds is the minimum time set by the hardware, but loading of the control system has increased this to 3 seconds for practical purposes. If you want to obtain more than 6 seconds/point, then repeat the map at the same position as often as necessary and average them together (this will give better baselines and calibration than a longer integration time per point).
• The number of points ($N$) along a row (in the scan direction) should be an odd number, and not greater than 59.
• The time on the reference position is automatically set to $T\sqrt{N}$. This gives the optimum signal-to-noise ratio over the map in a given time.
• The number of rows (i.e. in the direction perpendicular to the scan) can be any (preferably odd) number. The practical limit to the size of the complete raster is set by the atmosphere; calibrations should be done at regular intervals, say once per 30, 60 or 90 minutes, depending on the sky conditions. Raster maps containing more than 1000 points are routine. Larger maps can be constructed by mosaicing sub-maps together in data reduction.

7.5 Observing Lunar Occultations

The raster procedure can be used also for observing lunar occultations by making the sampling interval very small (e.g. 0.01 arcseconds), and thus effectively setting the scan rate to zero. This is the only way that a suitably fast sampling can be obtained. See the article by Dent and Coulson in the JCMT Newsletter for more details.

8 Estimating Time Requirements and Sensitivity for Heterodyne Receivers

On the JCMT Web pages, there is an Integration Time Calculator tool, which will do your calculations for you. Below, I explain the details in case you want to do it yourself, or understand a little more about what goes into these calculations.

For position- or beam-switched⁸ observations, the rms value of the temperature fluctuations observed in a spectrum, expressed in Kelvin, is given by the expression:

$$T_{A}^{*}(rms) = (2.0 \times T_{sys} \times \kappa) / \sqrt{t \times \Delta\nu}$$ (1)

The `antenna temperature' $T_{A}^{*}$ is that which would be measured outside the atmosphere (i.e. corrected for absorption by the Earth's atmosphere). To convert this to the internationally accepted $T_{r}^{*}$ scale, it will be necessary to make a further correction:

$$T_{r}^{*}(rms) = T_{A}^{*}(rms) / \eta_{fss}$$ (2)

The equivalent flux density sensitivity in Janskys (applicable to point sources) is:

$$S(rms) = 15.6 \times T_{A}^{*}(rms) / \eta_{a}$$ (3)

In these expressions, the various parameters have the following meanings:

• The backend degradation factor, $\kappa$.

  This allows for the inherent inefficiency in the detection of signals by the spectrometer. For a 2-bit digital correlator, such as the DAS (see Section ) $\kappa$ = 1.15.

• The total integration time, $t$, in seconds.

  This includes the time spent on the reference position, but not telescope movement time etc, when the backend system is not integrating. Since equal times are spent on the signal and reference positions (with the exceptions of frequency-switching and raster mapping), only $t$/2 seconds are spent actually integrating on the source position.

• The noise bandwidth, $\Delta\nu$, in Hz.

  This is the effective frequency resolution of each channel in the spectrometer backend. It is not the same as the channel spacing; the normal minimum resolutions are given in Table ; if you intend to smooth your spectra to some greater effective channel bandwidth, this is the value you should use in eqn. ().

• The system noise temperature, $T_{sys}$, in Kelvin.

  This is the effective single-sideband noise temperature of the receiver taking into account losses in the receiver, atmosphere and telescope, and the fact that a spectral line is observed in only one of the two sidebands. The system temperature is calculated from the relation:

  $$T_{sys} = 2 \times [T_{rx} + \eta_{tel}T_{sky} + T_{tel}] / [\eta_{sky} \times \eta_{tel}]$$ (4)

  
  

  where the factor 2 comes from the assumption (sometimes very definitely approximate) that the receiver has the same equivalent noise temperature in both sidebands. For single-sideband systems where the image sideband is `looking' into a cold load of effective temperature $T_{im}$, eqn. () should be replaced by:

  $$T_{sys} = [2T_{rx} + \eta_{tel}T_{sky} + T_{tel} + T_{im}] / [\eta_{sky} \times \eta_{tel}]$$ (5)

  
  

  In B3 and W $T_{im}$ is about 30-40 K; i.e. considerably smaller than $(T_{sky} + T_{tel})$. In Table  I give calculated values assuming observations are to be done in single-sideband mode where possible (receivers B3 and W). In eqns. () and ():

  $T_{rx}$ is the double-sideband receiver noise temperature (the number usually quoted by the builders of the receiver -- see also Tables  and and Figures , , and );

  $T_{sky}$ and $T_{tel}$ are the additional noise contributions from the sky and telescope respectively;

  $\eta_{sky}$ is the fraction of radiation transmitted by the atmosphere at the zenith angle ($Z$) in question. This is a strong function of frequency, and depends on the pathlength through the atmosphere (that is, on the `airmass', $A$). The transmission at the zenith, $\eta_{sky,zen}$, is related to the optical depth at the zenith ( $\tau_{zen}$) by:

  $$\eta_{sky,zen} = \exp[-\tau_{zen}]$$ (6)

  
  

  and hence the transmission at airmass A is

  $$\eta_{sky,A} = \exp[-\tau_{zen} \times A] \simeq \exp[-\tau_{zen} \times \sec(Z)]$$ (7)

  
  

  In practice the sky contribution is derived by measuring the emission from the sky and then using

  $$\eta_{sky} = 1 - T_{sky}/J_M$$ (8)

  
  

  where $J_M$ is the mean radiation temperature of the atmosphere, typically 260 K.

  $\eta_{tel}$ is the receptive efficiency of the telescope after accounting for ohmic losses and spillover, and is related to the mean radiation temperature of the telescope enclosure $J_{tel}$ (usually about 265 K) by

  $$\eta_{tel} = 1 - T_{tel}/J_{tel}$$ (9)

  
  

  Values for $\eta_{tel}$ are given in Table .

• The forward spillover and scattering efficiency, $\eta_{fss}$; beam efficiency $\eta _{mb}$

  This is a measure of what fraction of the forward antenna pattern is coupled to an extended source. That is, it is a correction for the radiation scattered from large angles by spill-over past the subreflector, scattering by the support legs, etc. It is conventional to define $\eta_{fss}$ as the coupling to a source of 0.5$^{\circ}$ diameter, so that it can be measured by observing the Moon. The quantity `beam efficiency' ($\eta _{mb}$) measures the extent to which the beam pattern is non-gaussian, or the fraction of power contained within the main lobe of the beam pattern⁹. Approximate values of $\eta_{fss}$ and $\eta _{mb}$ are given in Table , where these have been determined.

• The aperture efficiency, $\eta_{a}$

  This factor (see Table ) defines the response of the telescope to a point source of radiation; it is the ratio of the strength of the signal actually received to that which would have been received by a `perfect' telescope of the same diameter, i.e. a telescope with no losses or blockage, having uniform illumination and no surface errors.

Hence, in order to calculate the time required for a given observation, one must first decide on the frequency resolution $\Delta\nu$ required by the measurement and the desired rms sensitivity in Kelvins $T_{a}^{*}$ or $T_{r}^{*}$ or flux density. $T_{sys}$ can be taken from Table , and the backend degradation factor $\kappa$ from the notes above. The inversion of eqn.  then leads to the total integration time, $t$, for the observation alone (i.e., with no overhead for telescope movement, pointing, calibration and set-up of equipment).

8.1 Examples: Approximate rms sensitivities after one hour's integration.

In Table  I give examples of the calculated rms noise $T_A^*(rms)$ in Kelvin after a total observation time of 1 hour (this assumes 30 minutes on source, 30 minutes on a reference position), generally for three different values of the atmospheric transmission. For all receivers calculations are given based on the expected or known performance. I have chosen three cases, for transmission values which correspond to `typical', `exceptional', and `not at all good' sky conditions for the frequency in question, and assumed a mean observing elevation of 60$^\circ$. Clearly this is rather subjective, but the calculations do seem to reflect reality. In preparing proposals I would suggest using the `typical' numbers, and these are given in bold face in the first of the three lines presented for each frequency. `Exceptional' conditions (the second line for each frequency) are not the best that have ever been seen on Mauna Kea, but not far from it. In the third line, the `not at all good' sky conditions are the upper limits for which observations may be useful. For worse conditions than useful for the observations at hand one would be well advised to switch to a lower-frequency receiver.

For the most part Table  is self-explanatory. The optical depth of the sky at 225 GHz ( $\tau_{225}$; as obtained from the CSO radiometer) is used to derive the transmission at each frequency, via the scaling from $\tau_{225}$ to water vapour pressure and using the ATM routine . The system temperature $T_{sys}$ is then derived from relations given in Section . The rms noise $T_a^*$(rms) then follows, assuming the DAS to be configured in the standard single-subsystem 500-MHz mode, which gives a spectral resolution of 378 kHz.

Table: Rms Noise Values for Common Frequencies after 1 Hour's Integration$^a$

Frequency	Transition	Receiver	$T_{rx}$	$\tau_{225}$	$T_{sys}$	$T_A^*$(rms)	DSB/	Notes
(GHz)		System	(DSB;K)	(nepers)	(K)	(mK)	SSB
231	CO(2-1)	A3	65	0.10	281	18	DSB	1,2
				0.03	220	14
				0.20	384	24
266	HCN(3-2)	A3	60	0.10	280	17	DSB	1,2
				0.03	213	13
				0.20	385	24
331	$^{13}$CO(3-2)	B3	120	0.07	660	41	SSB	1,2,3
				0.03	457	28
				0.15	1245	78
345	CO(3-2)	B3	120	0.10	660	41	SSB	1,2,3
				0.03	425	27
				0.20	1140	71
461	CO(4-3)	W/C	150	0.05	1395	87	SSB	3
				0.03	1190	74
				0.10	3550	220
492	CI($^3$P$_1$-$^3$P$_0$)	W/C	185	0.05	2140	133	SSB	3
				0.03	1210	76
				0.08	4700	290
692	CO(6-5)	W/D	400	0.05	5020	310	SSB	1,3,4
				0.03	2880	180
				0.08	11500	720
$^a$ The integration time includes equal time spent on the signal and reference phases. Either position-
or beam-switching is assumed. A spectral resolution of 378 kHz is used in these estimates; this corre-
sponds to the 500-MHz mode of the autocorrelation spectrometer in single-mixer mode. Using either
of B3 or W in dual-mixer mode should normally reduce $T_A^*$(rms) by a factor of $\sim\sqrt{2}$. Frequency-
switching reduces $T_A^*$(rms) by a further factor of $\sqrt{2}$ for the same integration time.
Notes:
(1) Equipped with tunerless mixers.
(2) Fully remotely tuneable.
(3) $T_{sys}$ given for SSB mode; DSB value will be somewhat greater.
(4) D-band mixers have been replaced with tunerless versions in March 2000 and further upgraded in 2001.

Except in pathological cases the rms noise decreases as the square root of the integration time. One could therefore use this table to scale your sensitivity estimates to any resolution and integration time for the lines given. For other frequencies, estimates should be based on a reasonable value of the transmission and the $T_{rx}$ at the frequency in question.

8.2 Estimating Overheads for Spectral Line Observations

The actual elapsed time for any given observations will of course be greater than the requested integration time due to operational overheads, which depend on the exact observing technique and hardware used.

Overheads during integration

For position- and beam-switched modes in general one can expect to spend of the order of 30% more time in telescope movement and software overheads, including calibration, above the raw integration time. Shortening the time spent on the individual signal and reference phases can increase the overhead significantly; 10 seconds per phase is fairly normal.

Use of the frequency-switching and raster mapping techniques reduce the overheads considerably, to typically about 15% of the total integration time. If one further notes that all or most of the time in these modes is spent integrating on source, then it is clear that the `on-source-efficiency' can be more than doubled over that achieved for the normal modes above. I have discussed these questions in a JCMT Newsletter article,¹⁰ although improvements in the software have since significantly reduced some of the overheads mentioned there.

Allowing for Receiver Tuning Time

The user may find it useful to have practical estimates of the time required to both set up and tune each of these receivers; if frequent retuning is expected during a program, allowance should be made for this in estimating the total time for the program. Assuming that the requested receiver is cooled and operational, initial startup usually takes no more than a few minutes; retuning the receiver within the available frequency range is usually accomplished in less than 30 seconds for A3 and B3 (both are remotely tuned and do not involve going to the receiver cabin). On the other hand Receiver W (C and D band) needs some manual optimisation and may take 20 minutes or so to complete the tuning procedure sometimes, including time spent by the Telescope Operator running up and down the telescope stairs.

Pointing and Calibration.

How often pointing and focusing observations should be performed during an observing run depends primarily on the beamwidth (frequency) in use and the type of observation being carried out. The fraction of time spent in this exercise increases dramatically at the higher frequencies.

Generally pointing is carried out using strong continuum targets, but since there are relatively few of these, it is worth mentioning that spectral line pointing and focusing is an extremely valuable additional option, especially for receivers A3 and B3, where remote tuning is the norm. Spectral line pointing and focusing uses bright spectral line targets (mostly circumstellar envelopes of late-type stars); CO and sometimes HCN lines are often bright enough for this to be used. See the JCMT spectral line web page for further information. In principle any compact target with a bright line can be used; this includes, say, the recombination line maser in MWC349, and, with a suitable wider band (up to 920 MHz), external galaxies. For objects not already included in our catalog as spectral line pointing targets, it will be necessary to add the velocity range of emission to the source catalog as well as the central velocity to allow proper use of the spectral line pointing routine.

Calibration will be required more often at higher frequencies, during less stable atmospheric conditions, and for sources at low elevations. As a rough practical guide, one should dedicate about 10-20% of the total observing time to these activities at the lower frequencies, and about 30% at the higher frequencies.

All in all, the overhead for spectral line observations due to all possible causes seems to amount to somewhere in the region of 50% of the elapsed time; that is, if one multiples the anticipated total integration time (signal and reference both included) by a factor of two or slightly less, then one should obtain a total time close to that really needed to complete the observations. Programs consisting mostly of raster mapping have low overheads, perhaps 30% or so.

9 Calibration of spectral line data

To obtain a calibrated intensity (in Kelvin T$^*_A$) scale corrected for the sky and telescope losses vanes (chopper wheels) in each receiver system are used to allow the mixer to sequentially `see' the hot (i.e. ambient temperature usually) and cold (liquid nitrogen) loads, and the sky. However, using the average across the receiver bandpass of the total power response to each load to derive values for the sky, receiver and system temperatures is strictly inappropriate, since there is significant frequency-dependent structure, both instrumental and telluric in origin, in the IF bandpasses of the receivers.

For this reason, under normal observing conditions the operating system carries out a a full channel-by-channel calibration which accounts automatically for any receiver bandpass gain changes with frequency and time. This (so-called `continuous calibration') is the recommended (and default) calibration method. Generally the results are excellent; in fact we recommend using the DAS to obtain a spectrum of a planet in order to determine telescope efficiencies. In `continuous calibration' the atmospheric contribution in each sideband is calculated on-line during the observing using the ATM atmospheric model. The off-source sky spectrum is used to update the calibration on every reference phase. Thus variations in the sky noise during an integration are accommodated. Note two points regarding the latter: (a) at some time before the first spectrum a normal calibration off-source must be carried out, in order to derive the receiver and zenith sky temperatures, and (b) this method cannot be used during frequency-switching or raster mapping, since there is no suitable off-source phase in these modes.

To summarise, the spectral line observer at the JCMT does not need to worry too much about calibration of the data to the T$^*_A$ scale - the telescope operator will issue the appropriate calibration commands for the type of observation being undertaken. In general, the data will be well calibrated to the standard T$^*_A$ antenna temperature scale. All the remains for the observer is to transform this antenna temperature into an astrophysical brightness temperature - this is usually achieved by observing a suitable planet (see below).

9.1 Standard Spectra

As noted elsewhere, at the start of each observing shift at the telescope it is good practice (and one followed in any case by seasoned radio astronomers) to obtain a `standard spectrum'. A number of sources have been chosen to provide these spectra of commonly-observed lines. Details of these sources, together with specifications as to how each source should be observed (e.g. beam-switch 300$''$) can be found here. The integration time is up to you, but, so that your result may be usefully added to the cumulative set of spectra, 2 to 5 minutes is appropriate. The sources are distributed over the sky, and at any time, at least one should be visible. It is recommended that at the beginning of each observing shift, and every time one makes a major change in observing frequency, that a spectrum of a standard is taken so that the result can be compared with the official standard to verify system performance. These `reference spectra' data can later examined by local staff, who will be looking for notable changes in the spectra over time.

The standard spectra can be displayed via the JCMT home page on the Web. If you want the original data sets (SPECX files) and descriptions, those may be downloaded also. Note that these web-based ``standard spectra'' are presented only calibrated to the standard T$^*_A$ antenna temperature. One should not be using the standard spectra to calibrate to astrophysical brightness temperatures - here planetary observations are more suitable. One should also bear in mind that some the some of the standard sources are extended on the scale of typical heterodyne beam sizes, and may not have a well determined brightness distribution on the sky. Nevertheless, observations of standard sources are a very useful check on observations - they confirm both the tuning and the approximate sensitivity of the receiver. If the line strengths of the spectral standards observed on the same nights as your data do not agree to within 20-30% this a cause concern, and will typically be commented on by the Telescope Operator at the time.

9.2 Factors affecting line intensity and profile

Over the years we have probably encountered all the known problems which can lead to erroneous spectral line data. Most are described below.¹¹

Even if no specific faults exist in a receiver, there are many other possible sources of error in the line intensities. Some of the more significant are given below, with estimates of their impact on the data.

1. Sky variations. Mainly caused by atmospheric transmission changes between the time of the calibration and the sample. This is negligible under good conditions; test measurements on a source with repeated calibrations and integrations with a stable sky gave $\sim$3% variation with A2 and $\sim$6% with B3i. Under variable sky conditions (not necessarily correlated with poor sky transmission) this effect can introduce factors of 2 variation in the line brightness. Some work will be done in Fall 1994 to improve this by using the reference position in each sample as the `sky' for the calibraton.
2. Baselines. For linear baselines, the signal:noise ratio in the integrated line intensity is decreased by the ratio of [linewidth(MHz)]/[baseline(MHz)]. For example, a s:n of 5-sigma in $T_a^*.dv$ will be reduced to 3.3-sigma if the line covers 60% of the useful IF passband. This will obviously be worse for higher-order polynomial baselines. Larger s:n is better. No baseline subtraction is also better (i.e. use beamswitching in azimuth).
3. Standing waves. These could result from reflections off the dewar windows or filters in the receiver (even when working properly, there will always be some reflection. Signals will also reflect off the hot load, mixer and the secondary mirror. The level can be estimated by observing continuum sources, and variations of as much as 5% can be seen.

4. Beam size. These are measured periodically ***LINK***. Note that a 2% variation in beam size would result in $\sim$4% error in the line brightness for a point source, although an extended source would show no change.

5. Sidelobes. The integrated emission over the inner sidelobes becomes significant at higher frequencies when the accuracy of the dish surface is low. For extended sources, this provides a significant uncertainty. At 690 GHz, this may contribute 50% , and even at 490 GHz, there may be $\sim$10% error. This can be corrected by careful measurement of the coupling to compact and extended planets. It causes an excess in $T_a^*$.

6. Receiver sideband ratio. Note that the sensitivity of each sideband of a dual sideband receiver will only be approximately equal, and that sideband suppression for a single-sideband receiver such as B3 will not be perfect. See here for more details.

7. Receiver tuning reliability. Repeated retunings and integrations on the same line under good conditions using the prescribed tuning technique result in variations in line intensity of around 3% - 5% depending on the receiver, although these variations may actually have been caused by (1) above.
8. Pointing. This can be a major culprit; e.g. for a compact source, a 16% decrease in line intensity can be introduced if you are pointed only one-quarter beam off source.
9. Focussing. This is usually most important around sunset or sunrise when the telescope temperature is changing. An error of 0.5 mm in the z-focus will give about a 10% error in the intensity of a compact source at 345 GHz.
10. Errors in the atmospheric model. We use the IRAM ATM model online to determine the sky transmission in the two sidebands. Any errors will be largest when the ratio of transmission ($R$) is largest. It is difficult to quantify the possible error, but tests with C2 at 460 GHz (worst case) over a range of $R$ show less than a 10% error. It is probably under 3% at 345 or 230 GHz, where $R$ is close to unity. One should beware of the 320, 330 and 370 GHz regions for B3 though.
11. Telluric ozone or CO lines. These are not included in the current atmospheric model, but are taken out, to first order, with the (normal) DAS channel-by-channel calibration. The lines are not usually bright, so this effect is negligible. You will see these lines if you frequency-switch ($\rm {O}_3$ in absorption, CO in emission) or observe bright continuum sources such as planets (when both species will be in absorption).

12. Variation in the physical temperature of calibration loads.

    COMING SOON.

13. DAS sampler non-linearity. Improvements to the DAS have reduced this down to a level of $\pm$1% .

14. Emission in reference beam. Underlines the need for careful selection of observing mode, and of reference position.
15. Poor signal:noise in the line. One should integrate longer(!).

With the above list, it might appear that you stand no chance of ever getting calibrated data. But it's not as bad as all that. Under good conditions, and assuming you're pointed and focussed etc, the errors combine to a total of $\sim$ 20 %.

We have been collecting standard spectra from known sources for some time now, using data from scheduled observers, and obtained during engineering tests. These data therefore represent a normal range of observing conditions. These can be found here.

9.3 Obtaining telescope efficiencies using the DAS

Spectra produced by the DAS are generally well-calibrated provided the usual care has been taken regarding IF levels, pointing and so forth. This applies also to any offset from the zero level, of course. Thus if one arranges to position- or beam-switch in azimuth (so as to avoid sky emission differences) the observed power level differential arises only from the difference in sky radiation between the signal and reference beams after correction for telescope losses. By observing a discrete source of known continuum strength (such as a planet) one can therefore derive the beam efficiency of the telescope. Using a small source, it is possible also to determine the aperture efficiency. Conversely, if you know the efficiency and the source size, you can determine an object's flux density or brightness temperature from the measured zero-level offset using the DAS. We encourage all spectral line observers, having used a planet for pointing, to take advantage of this possibility. At the time of writing, the correct place to specify what sort of calibrations need to accompany your science observations is in the ``Show to Observer'' note of your MSBs.

=5.0in

Figure: A spectrum obtained towards Mars at 492 GHz with C2 using the 500-MHz DAS configuration. The vertical scale has been truncated for clarity. The fact that the signal level is not constant with frequency (or velocity) is a result of standing waves within the system. However, the relative variations are small and the mean level represents the continuum antenna temperature of the source.

First determine the average brightness temperature over the passband (using the f-s-s command in SPECX , or, as is often sufficient, by eye). Remember that, for a dual sideband reciever such as A3, the calibration algorithm assumes that line emission appears in only one sideband, whereas the planet continuum arises from both sidebands. Thus one must first divide the mean continuum level obtained by 2.0, approximately,¹² to get the observed planet brightness temperature $T_a^*$.

9.4 Getting the main-beam efficiency $\eta _{mb}$

From the fluexes program obtain the planet physical temperature $T_{phys}$ and planet full diameter $D$ (note that the program output give semi-diameter). Then:

1. Apply the Rayleigh-Jeans correction to get the planet brightness temperature $T_b$. To a good approximation at frequencies in use at the JCMT
   $$T_b = T_{phys} - \frac{h\nu}{2k}$$
   The second term (the `Rayleigh-Jeans correction') is about 5.5K at 230 GHz, 8.3K at 345 GHz and 12 K at 492 GHz.
2. The expected antenna temperature $T_A^{*\prime}$ is reduced from the planetary brightness temperature by a factor

   $$\eta_{gauss} = 1 - \exp\left[-\ln 2\left(D/B\right)^2\right] = 1 - 2^{-(D/B)^2}$$ (10)

   
   
   which is the theoretical coupling between a gaussian beam of half-power width $B$ and a planetary disk of diameter $D$. Using this correct the brightness temperature to obtain the expected antenna temperature for a perfect dish using the known beamsize $B$ (see e.g. the relevant fact sheet):
   $$T_A^{*\prime} = T_b \eta_{gauss}$$

3. Then the main beam efficiency for a object of the same size as the planet is simply the ratio of the observed antenna temperature to that predicted i.e. $\eta_{mb}=T_a^*/T_a^{*\prime}$.

If all is well, you should be getting something close to the fact sheet values for the frequency you are using.

In the case of the above example (Figure ), I measure a mean level in the spectrum of 126.1 K, which gives $T_a^*=70.0$ K, taking into account the ratio (0.8) of the signal and image sideband system temperatures ¹²(taken from the operator's screen at the time). From fluxes the value of the physical temperature of Mars is 208 K, and the Rayleigh-Jeans correction 12 K, leading to a corrected brightness temperature of 195 K. The size of Mars at the time was $13.68''$, and the beamwidth to halfpower $10.38''$. Thus $eta_{gauss}=0.70$ and the expected antenna temperature of Mars is $T_a^{*\prime}=0.70\times195=136.5$K, leading to a main-beam efficiency referred to an object of size $13.7''$ of $\eta_{mb}=70.0/136.5=0.51$. Since the fact sheet gives $0.53\pm0.05$ this is very satisfactory.

9.5 Aperture efficiency and surface accuracy

From observations of the same type as above, but for an object (e.g. Uranus¹³) considerably smaller than the beam it is possible to deterine the aperture efficiency $\eta_a$. This is defined to be the ratio of the effective area to the physical area; i.e. $\eta_a = A_e/A_p$. If we measure an antenna temperature $T_a^*$ (corrected for telescope and atmospheric losses as above) from a source which has a flux density $S$ within the beam of the telescope (so a source much smaller than the beam is best used for this), then

$$S = \frac{2kT_a^*}{A_e} = \frac{2kT_a^*}{\eta_a A_p}$$ (11)

For the JCMT this reduces to

$$S/T_a^* = 15.625/\eta_a\;\;\;\;{\rm (Jy\:K^{-1})}$$ (12)

For the special case of a planet of disk diameter $D$, the total flux $S$ has to be corrected for the coupling to the beam. Assuming the beam is gaussian (a good approximation at the lower frequencies at least) the corrected flux is

$$S' = S\frac{x^2}{1-\exp(-x^2)}$$ (13)

where

$$x = \frac{D}{1.2B}$$ (14)

and $B$ is the FWHM of the beam.

The flux density of a planet can be calculated by knowing its brightness temperature; usually this information can be obtained by running the fluxes or fluxnow program and there is no need to make the calculation. If not, the total flux density for an object of uniform brightness temperature $T_b$ is:

$$S = \frac{2h\nu ^{3}}{c^{2}}\frac{\Omega(p)}{\exp(h\nu/kT_b) - 1}$$ (15)

where $\Omega(p)$ is the solid angle subtended by the planet in steradians; this is available from the output of fluxes and fluxnow.

The aperture efficiency $\eta_a$ is related to the rms deviation $\sigma$ of the telescope surface from a paraboloid by the `Ruze formula'¹⁴:

$$\eta_a = \eta_{a,max} \exp\left[ -16\left( \frac{\pi\sigma}{\lambda}\right) ^2\right]$$ (16)

where $\eta_{a,max}$ is the maximum aperture efficiency after correcting for geometric blocking and other effects, such as membrane reflection loss. $\eta_{a,max}$ is about 0.70 for the JCMT at the longer wavelengths. $\eta_a \sim 0.75\eta_{mb}$ for well-behaved telescopes, if $\eta _{mb}$ is defined for a source the same size as the half-power beamwidth.

10 Continuum Observations with Heterodyne Receivers

There is a separate backend for continuum observations with the heterodyne receivers which uses a phase-sensitive lockin amplifier. Pointing and focus observations are routinely made using the chopping secondary mirror and this hardware. Because of advances in SIS mixer technology the JCMT's heterodyne receivers are now almost as sensitive as was the retired UKT14 bolometer¹⁵ in this mode at equivalent wavelengths, at least for A3 and B3 (approximate equivalent `NEFD's' are about 0.8 and 1.0 Jy Hz$^{-1/2}$ for A3 and B3 respectively under good conditions). To obtain the maximum sensitivity for continuum data observing in double-sideband mode is recommended; this would not normally be the preferred mode for spectral line observations. Now that SCUBA is available it seems unlikely, but should one find a need to do photometry observations with one of the heterodyne receivers, calibration should be carried out by observing sources of known flux density at a range of airmasses, and/or by spectral line calibration measurements. (Photometric observations can be reduced using the COADD program¹⁶).

Generally the only use for continuum mapping observations with heterodyne receivers in the SCUBA era is to obtain beam maps. These are almost always made in an `on-the-fly' mode, where the telescope is scanned along one coordinate, and stepped in the other, rather than point-by-point. For those with experience of UKT14 this will be familiar, and this is the standard method of making maps of the beam response. For such observations the data are sampled by a microcomputer in one of the IF sections after synchronous detection. The secondary mirror is made to chop in the scanning direction. In order to make a map, therefore, one chooses a spatial sampling interval (the `cell'), a chop throw, and an area over which one wants to map. In the normal chopping mode the map should be elongated in the scanning direction by an angular distance equal to the chop throw in order to obtain a resultant square map after restoration.

As a rule of thumb the cell (i.e. the sampling interval) should be set to not larger than about one-third the beam size, and the chop throw should be about two to three times the beam size in a normal application. This is somewhat arbitrary, and there may be reasons to adopt different standards in some cases. It is possible to combine in the processing stage (with JCMTDR, for instance) maps made with different chop throws; this can be desirable in practice to allow better sampling of spatial frequencies.

Table: Typical `On-the-fly' Map Parameters for Heterodyne Receivers

Receiver	Frequency	HPBW	Cell	Chop	Map size	Map size	Sens.	Time
	(GHz)	(arcsec)	(arcsec)	(arcsec)	(arcmin)	(cells)	(Jy)	(mins)
A3	230	21	6	72	$4.2\times3.0$	$43\times31$	0.8	28
B3	345	14	4	40	$2.7\times2.0$	$41\times31$	1.0	26
W/C	461	10	3	30	$2.0\times1.5$	$41\times31$	6.5	26
W/D	690	7	2	24	$1.4\times1.0$	$43\times31$	12.0	28

In Table  I give some typical values for cell sizes, chop throw, a