Spectral-Line Observing

We will consider the rms, $\sigma_{{\rm T}}$(K), for observations with a receiver of system temperature, T$_{sys}$, frequency resolution, $\beta$ per polarization, and total integration time per observing cycle, $\tau$. Note that $\beta = B/N$, where $B$ is the total bandwidth of the spectrometer per polarization, and $N$ is the number of independent points in the computed spectrum (e.g. the number of spectrometer channels for an unsmoothed spectrum.) If the spectrum has been Hanning smoothed, then the effective frequency resolution is broadened by a factor of about 1.67. The sensitivity calculations given below represent the analog case, and it should be remembered that 9-level operation of our spectrometer achieves 96% of the signal-to-noise of analog correlation, whereas 3-level operation achieves 81%. For the following observing modes, the theoretical sensitivities are;

• Total-Power Observations: Here, all the observing time is spent looking at the target (``Point-and-Shoot''). This gives, $\sigma_{{\rm T}} = {\rm T}_{sys}/\sqrt(\beta \tau)$ per polarization, or $\sigma_{{\rm T}} = {\rm T}_{sys}/\sqrt{2\beta \tau}$ if both polarizations are averaged to obtain the final spectrum. Pure total-power observations are found to be adequate for many Arecibo observation, especially if narrow total bandwidth observing is to be used (say less than 1 MHz total), and has even been used for relatively short integrations on Galactic HI. Note that this is also the case for total-power continuum observations.

• ``In-Band'' Frequency switching: NOTE: Frequency switching is NOT presently supported, although investigation of its efficacy at Arecibo is being investigated.

  For ``in-band'' frequency switching, the line under investigation is always in the observing band. For each of the two positions where the line falls, only one half of the time is spent looking at the line, with noise being present all the time. Using a ``flip, shift and average'' operation on the raw frequency-switched spectrum, gives, $\sigma_{{\rm T}} = \sqrt{2}{\rm T}_{sys}/\sqrt {\beta \tau}$ for a single polarization, or $\sigma_{{\rm T}} = {\rm T}_{sys}/\sqrt(\beta \tau)$ if both polarizations are averaged to obtain the final spectrum.

• Position Switching or ``Out-of-Band'' Frequency Switching: Here the line is only observed for one half of the time, with noise being present all of the time. This gives, $\sigma_{{\rm T}} = 2{\rm T}_{sys}/\sqrt {\beta \tau}$ per polarization, or $\sigma_{{\rm T}} = \sqrt{2}{\rm T}_{sys}/\sqrt {\beta \tau}$ if both polarizations are averaged to obtain the final spectrum. Note that this is also the case for simple Dicke-switched continuum observations.

• Position Switching on a Target Source, and a Band-Pass Continuum Calibrator: When the simple position-switched technique is used to measure the emission or absorption line spectrum of a source that also has significant continuum emission, problems can arise due to residual standing waves for any telescope with a partially blocked aperture. An extreme case of aperture blockage occurs with the Arecibo 305-m radio telescope, where the feed support platform and a good fraction of its support cables are situated within the volume traversed by the incoming rays focused on the telescope feed. This large structure can also scatter significant amounts of radiation from the surrounding hills, and other sources of radiation arising outside the telescope main beam.

  The usual solution, to employ simple ON/OFF position switching, breaks down when the target is observed against significant continuum radiation. Under these circumstances, the component of the standing-wave pattern due to the continuum emission from the direction of the target source is not cancelled at all by subtracting the source-free OFF data from the ON, and a standing-wave residual whose amplitude is proportional to the source intensity remains to degrade the spectrum. To minimize the effects of the residual standing wave when observing a strong continuum source, another (reference) continuum source (preferably chosen to have different redshift to avoid its possessing an emission or absorption line near the same frequency as the target) is also observed in the same ON/OFF position-switched mode. The azimuth-zenith angle track followed during this observation should be made to be as near as possible to that for the target source. Division of the target spectrum by that of the reference source then cancels the residual standing wave, and results in a spectrum whose magnitude is proportional to the ratio of the target and reference flux densities across the observing bandwidth, including any spectral-line component that may be present in the target.

  Here, the line is observed for one quarter of the time, but noise is observed all the time. This gives, to first approximation, $\sigma_{{\rm T}} = 4{\rm T}_{sys}/\sqrt {\beta \tau}$ per polarization. Note that T here is not just the ``blank-sky'' system temperature, but should allow for the contribution due to the continuum reference emission of the target and reference sources, i.e. if both have a flux density, SJy, then T$_{sys}$ should be increased by $\Delta {\rm T}_{sys}(K) = S/2 * {\rm G}(za)$, where ${\rm G}(za)$ is the telescope gain (in K/Jy) at zenith angle, $za$.

  For full description of the technique and the detailed sensitivity considerations, see
  http://www.naic.edu/~astro/aotms/performance.shtml, and then click on report ``2001-02.ps''.