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At these wavelengths a survey is more sensitive to detecting relatively cool disks (T<100k), but would a telescope operating in the sub-millimeter be less sensitive to warm debris disk than say, a mid IR telescope?

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Such surveys are designed to detect an excess of emission over that expected from a stellar photosphere.

The emission from a circumstellar disk is often modelled as a blackbody at lower temperature than the stellar photosphere. A hotter blackbody with the same emitting area emits more flux than a cooler blackbody at all wavelengths.

Therefore, if you had a disk of fixed emitting area, it would be easier to detect a hotter disk at sub-mm wavelengths than a cooler disk.

However, if you have a lot of cold disk material and no warmer regions, then because the Wien tail of the blackbody distribution is so steep, it emits almost no radiation at near- and mid-infrared wavelengths, and sub-mm detection is the best way to detect it.

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