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Sensitivity Estimates

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The values below are based on measurements at the telescope. These values are similar to what is estimated by the T-ReCS Integration Time Calculator. The overall accuracy of the ITC S/N values is of the order of a factor of 1.2 to 1.4, since conditions at the telescope may vary during an observation, and since for faint targets the assumed square-root of time scaling will not hold exactly. For faint targets we advise people to be conservative in their exposure times to ensure that the desired S/N is obtained. Sensitivity estimates are available for

All sensitivities are 5 sigma in one hour of observation assuming an on-source efficiency of 50%, i.e. half the time on-source and half on-sky, in roughly average summer sky conditions (thus sensitivities are somewhat better when conditions are very good) and at low airmass (<1.2 airmasses).

In actual operation, including acquisition overhead, the time needed for such an observation will be a bit less than 2 hours for imaging because the on-target efficiency of T-ReCS is near 30% rather than 50% when observing in chop-nod mode. For spectroscopy the efficiency is a bit lower and the time needed for a 30 minute on-target exposure time is about 2.5 hours .

Imaging Sensitivity

The last column in the table below gives the N-band magnitude (or Q-band magnitude, in the case of the Qa filter) that the ITC predicts will give S/N of 5 in 30 minutes on-source, for a hot star spectrum--specifically the alpha Car template. A hot star will have nearly the same magnitude in all of the filters.

The only significant discrepancy between the ITC calculation and the observed values is in the N filter, where the observed sensitivity is somewhat worse than predicted. This type of discrepancy is also observed for the analogous filter on the VISIR instrument at the VLT, and we do not know the cause of this difference. There is also some disagreement for the Qa filter, but the Q-band observations are especially sensitive to the water vapour content of the atmosphere so it is more difficult to compare the ITC values to the observed values for Q-band filters than it is for the filters in N-band.


Filter Name Wavelength 
Point Source Sensitivity 
S/N=5, 30 min. on source 
Optimum Aperture Diameter (pixels) Magnitude Equivalent ITC N magnitude (S/N=5, 30 minutes)
Si-1 7.77 6.7 3 9.9 9.82
Si-2 8.73 1.4 3 11.4 11.35
Si-3 9.68 3.4 5 10.2 10.21
Si-4 10.37 2.2 5 10.5 10.79
Si-5 11.63 1.6 5 10.5 10.49
Si-6 12.29 2.7 7 9.9 10.05
N 9.83 1.4 5 11.1 11.65
Qa 18.06 21 9 6.8 6.59

The observed values (PS sensitivity and Magnitude Equivalent) in the table are a result of analysis (by Tom Hayward) of T-ReCS images of standard stars obtained in late 2003/early 2004. The images used were chosen to have good PSF shape and minimal detector noise problems. The values are approximate mean values for two to six observations, depending on how many observations were available for each filter when the analysis was carried out. 

What was done to produce these estimates was to first find the noise level in the image choosing a clean region of the T-ReCS detector away from hot pixels and other known artifacts of the detector. Given this noise level then a series of apertures were defined with diameter 1, 3, 5, and so on pixels. The total counts from the target was set equal to the counts in the aperture, corrected for the general background level in a larger aperture surrounding the source. The signal-to-noise (S/N) value was calculated for each aperture and the one that gave the highest S/N value was chosen to estimate the detection limit. The optimum diameter tends to increase with wavelength because the stellar point spread function becomes wider.

One might initially think that the total signal would just continue to increase with aperture size and this the S/N value would increase to an asymptotic value. This does not happen because there a general background noise per pixel, on the average, whose contribution thus increases proportional to the aperture size, and thus for apertures significantly larger than the stellar point spread function the S/N goes down somewhat since the stellar contribution levels off. Thus there is a optimum aperture size for the detection of point sources.

Once a maximum S/N value was estimated, this value was used with the known flux density of the standard at the filter wavelength to find the expected flux density value where S/N would be 1 in the particular exposure time. Then the total on-source time was used to scale to S/N of 1 in 1 second, or S/N of 5 in 25 seconds. This was then divided by 8.5 to get the value for S/N of 5 in 1800 seconds. This assumes strict scaling of the noise by the square-root of the exposure time. As noted above, 30 minutes on-source corresponds to a little under 2 hours actual observation time due to acquisition and the chop-nod efficiency of the instrument.

The values are given in mJy. These are converted to magnitudes using the Cohen spectral energy distribution and adopted magnitudes for alpha CMa. The magnitudes are also given in the table. Stars without circumstellar dust shells will have essentially the same magnitude in all filters.

For stars the most sensitive filter is the Si-2 filter since it is located in a clean part of the N-band window and stars have a higher mean flux density in the Si-2 filter than on the average over the N filter. For intrinsically cooler objects the Si-5 filter may produce slightly better results than the Si-2 filter or N-band filter, again because of being in a clean part of the N-band window. These trade-offs are dependent on the shape of the object spectrum, as values are given in terms of flux density rather than in-band flux. The colour correction effects are minor for the Si and narrow-band filters, but may be significant for the N and Q broad filters. The Qa filter sensitivity is critically dependent on atmospheric conditions, rather than any assumptions about the shape of the object spectrum.

Under the best conditions the point source sensitivities can be somewhat better (by a few tenths of a magnitude) than the values in the table above.

The Q-band sensitivity is significantly worse that that for any of the N-band filters. The above value corresponds to the best seasonal conditions, and in local winter the Q-band conditions are typically rather worse than the above values which were measured in summer. The Qb 24.56 micron filter sensitivity is again much worse than the Qa filter sensitivity values given above. As a very rough rule of thumb, a source needs to be at least 10 times brighter in Qa than in N for approximately the same signal-to-noise value in a Qa observation as in an N filter observation, for a given on-source time, and two or three times brighter still in Q-band for good signal-to-noise Qb observations to be possible.

Comparison with the Michelle sensitivity values shows differences in sensitivity. (The on-source time is the same for both tables so the values can be directly compared.) For the Si2 and Si5 filters, where the atmospheric effects are the smallest, the sensitivities of the two instruments are about the same. The differences in values are thought to be due to having slightly different methods of calculating the S/N from the images. In those filters where atmospheric effects are stronger, such as the Si1 and Si6 filters at the edges of the N-band window, the Michelle sensitivities are a bit better than those for T-ReCS. The Q-band sensitivity of Michelle is clearly much better than that of T-ReCS. We believe that all of these differences are due to the difference in the site characteristics, due to Mauna Kea being higher and dryer than Cerro Pachon. The intrinsic sensitivities of the two instruments under the same atmospheric conditions are thought to be the same.

The continuum emission sensitivity can be approximately estimated in two ways. On a per pixel basis the sensitivity is found from the point source sensitivity divided by the square-root of the number of pixels in the aperture, which is 0.89 times the aperture diameter given above. Thus for example the N-band sensitivity per pixel is 0.31 mJy per pixel or 39 mJy/square arc-second. One can actually do better if the images are binned, since one cannot resolve continuum structure on a scale much smaller than the stellar FWHM. Three by three binning would improve the detection limit for continuum emission by a factor of about 3 to near 13 mJy/square arc-second.

Spectroscopic Sensitivity

Some estimates of the T-ReCS spectroscopic sensitivity have been obtained from analysis of standard star observations. There will be some variation in the actual sensitivity for any given observation depending upon the slit width to be used, the seeing at the time of the observation, the centering of the target in the slit, and the stability of atmospheric conditions during an observation. In particular for faint targets the stability of the atmosphere over a long observation is an issue. The standard stars are bright, so they are observed for only 2 or 3 minutes and for these sources the background subtraction is less of an issue. Thus it is possible that the results shown below will overestimate the sensitivity for targets near the limit. For faint sources near the detection limit the theoretical square-root of time variation in signal-to-noise ratio may not apply, and these calculations will then be somewhat in error.

All values given are estimates of the 5 sigma detection limit in Jy for 30 minutes on-target time.

The N-band sensitivity is about 15 mJy at 8.8 microns and about 25 mJy at 11.7 microns. In terms of magnitudes these are 8.8 and 7.6 respectively. A reasonable rule of thumb is that the sensitivity for T-ReCS low-resolution spectroscopy is close to 10 times worse than the imaging sensitivity at the same wavelength. The Q-band sensitivity is roughly 10 times worse than that at N-band for either imaging or spectroscopy.

As noted below these values are for the 0.35 arc-second slit, giving better wavelength resolution. If the widest slit is used the sensitivity will be about a factor of 2 better at the cost of poorer wavelength resolution.

We do not have much basis for estimating the sensitivity of the highres10 grating as yet. The sensitivity of T-ReCS in this mode appears to be strongly limited by the detector dark current and read noise, in which case we can estimate that it will be of order 3 to 5 times worse than for the low resolution N-band spectroscopy mode.

The ITC gives values similar to the values shown here for the low resolution spectral modes of T-ReCS.

The following plot shows the derived detection limit over the N-band. This is specifically for the 0.35 arc-second slit, values of order 2 times better would be obtained for a relatively compact target when using the 1.3 or 0.7 arc-second slits. Note the reduced sensitivity in the ozone band region. The actual situation in the band is actually worse than suggested by the plot because there may be systematic residuals from the ratioing with a standard star to remove the telluric features.

The analogous plot for Q-band is given below. The uncertainties here are larger because the Q-band conditions are much more variable than those for N-band. We may be able to do better than this under exceptionally dry conditions. Again this estimate is for a narrower slit and better sensitivity would be obtained with the wide slits. As the quality of the Q-band window is not good, there are tremendous variations in sensitivity over the 17 to 26 micron wavelength range.


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