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The SN 1572 remnant, also called Tycho's supernova remnant, is beautiful in X-ray images. It seems to be rather dim in visible light. Are there any amateur photographs of this object? How long are the exposure times needed to get a nice picture?

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As you say, SN 1572 is not very bright in the optical. There are some Hα regions that have been observed with world-class optical telescopes, but they do not look like the X-ray and infrared images that you normally see. In fact, images from the Palomar Optical Sky Survey 2 (with a limiting magnitude of ~22) do not reveal any nebular emission from this object at all:

POSS2 of SN 1572

Therefore, the optical emission must be fainter than 22nd magnitude. I do not think there are amateur photographs of an object this faint and I believe a CCD on an amateur telescope would saturate from noise before revealing any of the nebular emission.

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It does not appear to be practical to photograph with amateur equipment. According to the Wikipedia article the remnant was viewed visually with Palomar telescope. Links to studies of the remnants were done using 2m + telescopes. So trying to get a visible light photo would require an extremely large telescope.

This table does not list a magnitude for the remnant (B CAS) http://maps.seds.org/Const/Data/cassiopeia_tab.html So it appears that it might be extremely faint.

And this list of deep sky objects does not list the remnant either. http://www.dibonsmith.com/cas_con.htm

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There are two faintly visible areas of nebulosity on the above image taken from the Palomar Sky Survey, that correlate with the remnants of Supernova 1572. Sidney van den Bergh imaged this object in 1970 with the Palomar 200 inch telescope, comparing this with similar images taken by Walter Baade in 1949, 1955 and 1957. His findings were published in the Astrophysical Journal (168: 37-39, 1971 August 15). Using my 32" telescope, two areas of nebulosity were recovered visually in August, 2006. These were at: 00h 25m 06.9s, +64d 11m 37s; and 00h 25m 51.4s, +64d 09m 19s.

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