5.2 Performance

5.2.1 Spectral Resolution

The blue spectrometer operates in 1st and 2nd order. An order-sorting filter blocks the unwanted order. The red spectrometer only operates in 1st order. The spectral resolution of FIFI-LS depends on the observed wavelength. It ranges from R = λ/Δλ ~500 to 2000. That corresponds to a velocity resolution of 150 to 600 km/s. The top panel of Figure 5-3 shows the spectral resolution in velocity resolution and in R vs. wavelength as measured in the lab.

FIFI-LS has 16 pixels in the spectral direction. The wavelength range covered by these 16 pixels also depends on the observing wavelength. The bottom panel of Figure 5-3 shows the instantaneous spectral coverage or bandwidth (BW) in micron.

Throughput of optical system

Figure 5-2. Throughput of optical system -- here the transmission of the overall optical system is shown for the six possible optical configurations using two dichroic beam splitters (D105 and D130) and both grating orders (blue channel only).

Spectral Resolution

Instantaneous spectral coverage

Figure 5-3: Top: The spectral resolution in km/s and λ/Δλ for both channels; Bottom: The instantaneous wavelength coverage in km/s of the 16 spectral pixels vs. wavelength.

5.2.2 Integration Time Estimates

FIFI-LS will operate such that the detectors are always background-limited, infrared photodetectors. Under this assumption, the overall performance of FIFI-LS as a function of wavelength has been estimated. Further assumptions about the emissivity of the telescope, optics, and baffling, the efficiency of the detectors had to be made. Figure 5-3 shows the resulting sensitivities for continuum and unresolved lines as minimum detectable fluxes per pixel, i.e. detected with a signal to noise ratio (SNR) of 4 and an on-source integration time of 900 s or 15 min.

The FIFI-LS on-line exposure time estimator should be used to estimate the on-source exposure times used in proposals and observing preparation. The time estimator requires the following input:

  • Observatory Altitude (in feet; < 60,000 ft): default 38,000 ft
    This value is used in ATRAN to derive the atmospheric absorption. For more details about ATRAN (see Sect. 3.6).
    On a typical SOFIA flight, observations start at 38,000 ft or 39,000 ft and 43,000 ft are reached 3.5 h before the observations end. The default value of 38,000 ft ensures that time estimate does not underestimates the water vapor overburden. If an observations is rather sensitive to the water vapor, a higher altitude can be entered and justified in the proposal. In Phase II, select "Low" or "VeryLow" for "Requested WV Overburden" in the "Observing Condition"-panel in SSPOT, if the altitude used in the time estimation is 41,000 ft or 43,000 ft, respectively. Note, that this limits the schedulability of the observation to the last 5.5 h or 3.5 h of observations.
  • Water Vapor Overburden (in microns; 0 if unknown): default 0 If a value of 0 is given, ATRAN assumes a typical amount of water vapor to derive the atmospheric absorption.
  • Telescope elevation (between 20 and 60 deg): default 40 For northern sources an elevation of 40° is okay, but sources south of a declination of -15° will most likely be observed at a respectively lower elevations unless an observation from the southern hemisphere is required.
  • Signal to Noise Ratio or Integration Time (s): default SNR of 5 Specify either a requested SNR and the required on-source exposure time is returned, or specify an on-source exposure time and the resulting SNR is returned.
  • Wavelength (in microns, between 51 and 203): default 157.741 μm (rest wavelength of [CII] line) Specify the rest wavelength of the requested transition.
  • Source: default 2.087e-17 W m-2 line flux (MDLF per pixel for [CII]) Specify the expected source flux per FIFI-LS pixel either as integrated line flux in W/m^2 or as continuum flux density in Jansky. Make it obvious in the technical feasibility section of the proposal that the referenced flux estimates have been converted to FIFI-LS pixels sizes.
  • Velocity correction (source VLSR, in km/s): default 0 km/s Enter the source velocity relative to the local standard of rest. The resulting Doppler-shift is important to estimate the atmospheric extinction.
  • Bandwidth: default 0 km/s Enter the desired width of the spectrum. The width should allow for sufficient baseline on both sides of the expected line/spectral feature to allow a good estimate of the underlying continuum telluric or astronomical. This value enters the time estimate only, if the requested bandwidth is larger than the instantaneous bandwidth. The time estimator calculates the on-source integration time per map position for a source flux, F and a desired SNR using,

equation

where MDF(λ) is either the Minimum Detectable Continuum Flux (MDCF) in Jy per pixel or the Minimum Detectable Line Flux (MDLF) in W m-2 per pixel at the entered wavelength (see Figure 5-4). The factor α is the transmission of the atmosphere for the observing wavelength derived by ATRAN. The on-line time estimator includes a plot of the transmission smoothed to the spectral resolution of FIFI-LS at the observing wavelength over the bandwidth from ATRAN. If the desired spectrum is wider than the instantaneous bandwidth, I is the ratio of the requested width of the spectrum and the bandwidth (Figure 5-3). Otherwise I is equal to 1.

The exposure time estimator returns the on-source exposure time per map position ton. If mapping is planned, this values has to be multiplied with N, the number of map positions, to derive the total on-source observing time. More on mapping can be found in Sect. 5.3.5. The total on-source observing time N x ton has to be entered into SPT during phase I of the prosal process. The overhead depends on the observing mode (Sect. 5.3.5) and gets automatically added by SPT.

Be conservative with the time estimates! Unforeseen issues like thunderstorms or computer crashes may cut the observing time short. Better to aim for 5σ and get a 4σ result, than aim for a 3σ and then wonder, if there is a 2.4σ signal.

Minimum detectable continuum flux

Minimum detectable line flux

Figure 5-4: Continuum and emission line sensitivities for a monochromatic point source: The values are calculated for a SNR of 4 in 900 s. The MDCF is in Jy per pixel and the MDLF is in Wm-2 per pixel. Both sensitivity values scale as SNR / √(t), where t is the on-source integration time.