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The German REceiver for Astronomy at Terahertz Frequencies (GREAT) is a dual channel heterodyne instrument that will provide high resolution spectra (up to R = 10^{8}) in several frequency windows in the 1.25–5 THz range.
The front-end unit consists of two independent dewars that operate simultaneuosly. Each dewar contains one of the following channels:
The GREAT instrument uses Fast Fourier Transform (FFT) spectrometers as backends. Each XFFTS spectrometer has a bandwidth of 2.5 GHz and 64,000 channels, providing a resolution of 44 kHz. The beam size is close to the diffraction limit—about 14 arcsec at 160 μm.
A detailed description of the GREAT instrument and its performance during Basic Science can be found in the GREAT special issue (Heyminck et al. 2012, A&A, 542, L1). The LFA is described in Risacher et al. 2016 (A&A, 595, A34). Because the instrument is regularly being upgraded and its performance improved, always check the GREAT website for the latest information.
Heterodyne receivers work by mixing the signal from a source at a given frequency ν_{s} with that from a local oscillator (LO) at a specified (and precisely controlled) frequency ν_{LO} and amplifying the result. The mixing results in two frequency bands, called the signal and the image bands, located symmetrically on either side of ν_{LO} and separated from ν_{LO} by the intermediate frequency ν_{IF} = |ν_{s }– ν_{LO}|. GREAT operates in double sideband mode, i.e. both the image and signal bands are equally sensitive to incoming radiation. By definition the spectral line of interest is always placed in the signal band, which can be chosen to be either above (Upper Sideband, USB) or below the LO frequency (Lower Sideband, LSB); see Figure 7-1. For sources rich in spectral lines, care has to be taken so that a spectral line in the image band does not overlap or blend with the line in the signal band.
The channels that are currently operational are listed in Table 7-1. Not every frequency in each tuning range has been checked, so there may be gaps where the LOs do not provide enough power to pump the mixer.
Front-End | Frequencies (GHz) | Lines of Interest | DSB^{5} Receiver Temperatures (K) |
---|---|---|---|
upGREAT LFA | 1830–2006 | [CΙΙ], CO 16-15, OH ^{2}Π_{1/2} | 1000 |
upGREAT HFA | 4744.77749 | [OI] | 1100 |
4GREAT | 490–635^{1} | NH_{3}, [CI] | -- |
890–1100^{2} | CH, CS | -- | |
1240–1500^{3} | [NII], CO, OD, SH, H_{2}D^{+} | 800 | |
2490–2590^{4} | ^{18}OH ^{2}Π_{3/2} | 1500 |
In Cycle 6, GREAT offers two configurations:
Each of the two installed mixers is provided with XFFTS Fast Fourier Transform spectrometers. The XFFTS has a 2.5 GHz bandwidth and 64,000 channels, providing a resolution of 44 kHz.
The usable instantaneous bandwidth is generally less than that covered by the XFFTS, generally about 1-1.5 GHz. The tuning range of the HFA is limited because the LO (a Quantum Cascade Laser) can only be tuned in discrete steps.
The GREAT sensitivities and integration times are calculated with the GREAT time estimator. Presented here are the background of these calculations and some worked out examples. Because of the way a heterodyne receiver is calibrated (by measuring the receiver temperature, T_{rx}, with a hot and a cold load), the logical intensity unit for a heterodyne observation is temperature, expressed in Kelvin (K). Either the antenna temperature, T_{A}^{*} (the asterisk refers to values after correction for sky transmission, telescope losses and rearward spillover, see e.g. Kutner and Ulich, ApJ, 250, 341 (1981)) or the main beam brightness temperature, T_{mb}, are used. Similarly, the noise is expressed in temperature units as well, ΔTA * or ΔT_{mb}, and the sensitivity (or signal-to-noise ratio) of the observations is given by the ratio of the source temperature and the rms temperature of the spectrum. In order to calculate these quantities, we first must estimate the single sideband (SSB) system temperature, T_{sys}, which also includes losses from the atmosphere and the telescope. T_{sys} is given by:
The factor 2 in Equation 7-1 assumes that the noise temperature is the same in both signal and image band, which is true for the HEB mixers used by GREAT. The transmission of the atmosphere, η_{sky}, at the altitude, observing frequency, and airmass that we plan to observe at can be estimated using the atmospheric transmission code ATRAN. The GREAT time estimator calls ATRAN directly, so those estimating the integration time needed by using the time estimator have no need to run ATRAN separately. T_{sky} depends on η_{sky} and the ambient temperature of the sky (T_{amb}) where the signal is absorbed and can be derived from Equation 7-2.
(Eq. 7-2)
T_{sky} = J(T_{amb}) x (1 - η_{sky})
where J(T_{amb}) is the mean Rayleigh-Jeans (R-J) temperature of the atmosphere, which we assume to have a physical temperature of 220 K at 41,000 ft, resulting in J(T_{amb}) = 177.5 K at 1.9 THz. Likewise the telescope temperature, T_{tel}, is related to η_{tel} by Equation 7-3:
(Eq. 7-3)
T_{tel} = J_{tel} x (1 - η_{tel})
where J_{tel} is the radiation temperature of the telescope, with a physical temperature ~ 230 K (J_{tel} = 187.4 K at 1.9 THz). If we assume an η_{tel} of 0.92, then T_{tel} = 14.8 K.
As an example, let us calculate the system temperature at the [CII] fine structure line at 157.74 μm (1.9005369 THz). In this example we calculate what we would have at the beginning of a flight, when we are still at low altitude. We therefore assume that we fly at an altitude of 39,000 ft and observe at an elevation of 30 degree. For a standard atmospheric model this corresponds to a transmission of ~ 76%, which gives T_{sky} = 42.6 K. For a receiver temperature T_{rc} = 1100 K, Equation 7-1 therefore predicts a single sideband system temperature T_{sys} = 3301 K when observing the sky.
Now we are ready to calculate the sensitivity. The rms antenna temperature, (corrected for the atmospheric absorption, and telescope losses), ΔT_{A}^{*}, for both position switching
and beam switching is given by Equation 7-4
(Eq. 7-4)
ΔT_{A}^{*} = (2 x T_{sys} x κ ) x (t x Δν)^{-0.5}
where k is the backend degradation factor, t is the total integration time of the number of on and off pairs that we plan to take, and Δν is the frequency resolution of our spectra. Strictly speaking, Δν is the noise bandwidth, which can be slightly different than the frequency resolution, depending on the design of the spectrometer. For our example we expect the Full Width Half Maximum (FWHM) of the line to be a few km/s, and we will therefore calculate the rms for a velocity resolution of 1 km/s, corresponding to a frequency resolution of 6.3 MHz. Since the GREAT backends have much higher resolution, this is not a problem. We can easily bin the spectrum to our desired velocity resolution. For an observation with three pairs of 40 seconds in each beam, or t = 4 min, and assuming the backend degradation factor k=1, we then find ΔT_{A}^{*} = 0.17 K, which is the one sigma rms antenna temperature.
To convert antenna temperature to brightness temperature T_{R}^{*}, we have to make one more correction as shown in Equation 7-5:
(Eq. 7-5)
T_{R}^{*} = T_{A}^{* }/ η_{fss}
where η_{fss} is the forward scattering efficiency, usually measured for a very extended source (like the Moon). For GREAT η_{fss} = 0.97. Therefore our brightness rms temperature, ΔT_{R}^{*} = 0.18 K^{5}. Note: The GREAT time estimator assumes the line temperature in T_{R}^{*}, and not in main beam brightness temperature, T_{mb} = T_{R}^{*}/η_{MB} , which is for a source that just fills the main beam.
If we want to express our results in flux density, Sn, rather than brightness temperature, we can convert antenna temperature, T_{A}, to flux density, S_{ν}, using the standard relation given in Equation 7-6:
(Eq. 7-6)
S_{ν} = 2 x κ x η_{fss} x T_{A}^{* }/ A_{eff}^{ }
where κ is the Boltzmann constant, and A_{eff} is the effective area of the telescope. A_{eff} is related to the geometrical surface area of the telescope, Ag, by the aperture efficiency, η_{a},
i.e. A_{eff} = η_{a} x A_{g}. For the measured main beam efficiency in early April 2013 (0.67) and a Half Power Beam Width (HPBW) of ~ 14.1 arcsec (+/- 0.3 arcsec) an aperture efficiency^{6} of 55 +/- 2 % is derived. Equation 7-7 yields the following simple form for the 2.5 m SOFIA telescope:
(Eq. 7-7)
S (Jy) = 971 x T_{A}^{* } (K) or within errors ~ 1000 x T_{A}^{* }(K)
Normally we use Jy only for spatially unresolved sources, but we can also use Equation 7-7 to convert line intensities into W/m^{2}, which maybe a more familiar unit for the far infrared community. If we assume that the [CII] line we are observing is a Gaussian with a Full With Half Maximum (FWHM) of = 5 km/s, i.e. 31.8 MHz, the integrated line intensity is given by 1.065 x T_{peak} x Δν, where Δν = 31.8 MHz. If we take T_{peak} equal to our rms antenna temperature, we find using Equation 7-7 that our four minute integration therefore corresponds to a one sigma brightness limit of ~ 6.1 10-17 W/m^{2} for a 5 km/s wide line observed with 1 km/s resolution. If we only aim for a detection, we can probably degrade the resolution to 2 km/s. In this case we gain a square root of 2, and therefore our one sigma detection limit is 4.3⋅10^{-17} W/m^{2}.
This is the reverse of what is typical when writing a proposal, when the proposer has an estimate how wide and how bright the line is expected to be and knows what signal to noise is needed for the analysis. Assume we want to observe the [CII] 158 μm line in T Tauri, a young low-mass star. Podio et al. (2012, A&A, 545, A44) find a line intensity of 7.5 ⋅10^{-16} W m^{-2} for the Herschel PACS observations, which are unresolved in velocity (the PACS velocity resolution is ~ 240 km/s for [CII]). Here we want to velocity resolve the line to see if it is outflow dominated or whether it is emitted from a circumstellar disk or both. We therefore need a velocity resolution of 1 km/s or better. If we assume that the line is outflow dominated with a FWHM of say 20 km/s (127.2 MHz; little or no contribution from the circumstellar disk) we get a peak antenna temperature (using Equation 7-7) of 0.52 K or a radiation temperature T_{R}^{*} = 0.55 K. In this case we want a SNR of at least 10 and a velocity resolution of 1 km/s or better. Let’s check whether it is feasible. If we plug in the values we have in the GREAT time estimator (assume 40 degrees elevation, standard atmosphere, and we fly at 41,000 ft) or we can estimate it from the equations given above.
With these assumptions ATRAN gives us an atmospheric transmission of 0.86 integrated over the receiver band-pass. The receiver temperature is 1100 K (DSB). Using Equation 7-2, we find that the sky only adds 24.9 K to the system temperature and from Equation 7-1 we therefore get T_{sys} = 2881 K. Since we want to reach a signal to noise of 10, the rms antenna temperature ΔT_{A}^{*} = 0.052 K. We can now solve for the integration time using Equation 7-4, where we set Δν = 6.338 MHz (1 km/s resolution). In this case t = 1937 sec or 32.3 min. The PACS observations show the emission to be compact, so we can do the observations in Dual Beam Switching Mode (DBS; see Section 7.2.1.1), with a chop throw of 60 arcsecond. Both DBS and Total Power (TP) modes are currently estimated to have an overhead of 100% and a setup time for tuning and calibration of two minutes (which get added when entering the observations in USPOT, the SOFIA proposal tool). Our observation would therefore take 60 minutes, which is completely feasible. The GREAT exposure time calculator gives t = 1930 sec. The difference is negligible.
Sensitivity calculations for an On-the-Fly (OTF) map, when data are taken while the telescope is scanning), are done a bit differently. For example, for an OTF map of the [CII] line (Half Power Beam Width, HPBW ~ 14 arcsec), we need to sample the beam about every 7 arcsec. If we read out the average once per second, for example, this means that we scan with a rate of 7 arcsec/second. To do a 3 arcmin scan will therefore take 26 sec, resulting in 26 map points, let us make it 27, to get an odd number of points. We therefore need to spend (1 second) * (√27) = 5.2 seconds on the reference position in total power mode. We ignore the time it takes the telescope to slew to the next row and any time needed for calibration. For a 3 x 3 arcmin^{2} map, i.e. 27 x 27 positions with a cell size of 7 x 7 arcsec^{2}. The integration time for each row is therefore 5.2 +27 seconds or 32.2 seconds/row. The total integration time for the map is therefore 14.5 minutes. We definitely want to do one repeat, so the total integration time is therefore 29 minutes. For all observing modes, we assume a 100% overhead and 2-minute setup for tuning and calibration. The total duration of the two maps is therefore 61.9 minutes. Thus, a 3 x 3 arcmin^{2} map in the [C II] line is entirely feasible.
Our 3 by 3 arcmin^{2} map with one repeat has an integration time of 2 seconds per map point. For typical observing conditions (41,000 feet, 30 degrees elevation) the GREAT time estimator (settings: TP OTF map, Non=27, Classic OTF; see Section 7.2.3) gives us an rms temperature/map point of 0.9 K for a velocity resolution of 1 km/s.