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.
  • Source velocity (in km/s): default 0 km/s
    Enter the radial velocity of the source relative to the local standard of rest (LSR).
  • Input Observer Velocity (VLSR in km/s): default 0 km/s
    In many, but not all cases, the default value of zero can be used. However, if the observing wavelength is near a strong narrow telluric feature, the earth's velocity relative  to the LSR becomes important, eg. for galactic sources and the [OI] line at 145.525µm. Then either enter the velocity directly or have it computed by entering time, date, source coordinates, and SOFIA's location. The Doppler-shift due to the source's and the observatory's velocity is important to estimate the atmospheric extinction. See also Atmospheric Transmission
  • 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 and astronomical. This value enters the time estimate as the factor l. 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 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).

Atmospheric Transmission

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 of the atmosphere at full spectral resolution and smoothed to the spectral resolution of FIFI-LS at the observing wavelength over the bandwidth. Two integration times are calculated using the transmissions from each curve. The value derived from the unsmoothed curve applies to an observation of a very narrow line, while the value from the smoothed curve applies to a continuum source or a line broader than the instrument's spectral resolution. If the atmospheric transmission is smooth near the observing wavelength, the two values will not differ much and the more conservative or appropriate observing time should be chosen. Furthermore, the observing time will not depend strongly on the source velocity. The velocity correction can be rounded to 100km/s and the earth's velocity can be ignored.

However, if there is a telluric feature near the observing wavelength, one has to carefully check the feasibility of the observation (a special warning is displayed if the ratio of the derived observing times exceed 1.5). This usually happens when the observing wavelength is near a strong and narrow atmospheric feature. A typical example is the [OI] line at 145.525µm, which is near a narrow and strong telluric feature at 145.513µm or at -25km/s relative to the [OI] line. In such a case, it is crucial to enter a good estimate of the source velocity accurate to ~1km/s. The source velocity needs to be the combination of the source velocity relative to the LSR or another reference frame and earth's velocity relative to that reference frame, which depends on the observing date and target location. Therefore the time estimator includes a calculator for the earth's velocity relative to the LSR. It may be necessary to add a time constraint for the observation to avoid an adverse earth's velocity relative to the source.

If the observing line is near a strong and narrow telluric feature, not only the observing time estimate needs greater care, but the correction for the atmospheric absorption of an observed line flux will have a large uncertainty. To derive the correction factor, the atmospheric transmission curve would need to be integrated while weighted with the intrinsic line profile of the observed emission line with the correct relative Doppler-shift. In most cases FIFI-LS will not be able to resolve the line profile and cannot resolve the atmospheric feature. Any attempt to correct the measured line flux would depend strongly on assumptions of the source's line shape and position and assumptions of the water vapor content and shape of the telluric feature. In short, expect a large uncertainty of a line flux measured near a strong and narrow telluric feature.

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 proposal 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 3σ result, than aim for a 3σ and then wonder, what to do with a 1.8σ 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.

Download the PDF Version

Share This Page