NavList:

Consider "extinction."

It is not possible to observe any star setting or rising, right on the horizon due to extinction. This is also the reason that you can view a sunset without going blind, because the intensity of the sunlight has been attenuated so much by this effect. So you certainly will not be able to observe Polaris as a negative altitude. 

HO 249 volumes two and three provide computed altitudes as low as negative seven and a half degrees to allow observations of the sun at a sextant altitude of negative 4 degrees from B-52s flying at 55,000 feet  which results from applying the refraction correction of minus 60 minutes. They get to a negative  seven and a half degree possible computed altitude because the observed sextant altitude with a bubble sextant from that altitude is negative 4 degrees to which you apply the refraction correction of negative 1 degree gets you to a negative 5 degrees. If it was an upper limb of the sun then, the observed altitude is  negative 5 degrees. I assume that the very low computed altitudes are to allow for use of an assummed position several degrees away from the position of the aircraft. 

I believe that such low observation could also be of the moon even with extension of its much lower light. I remember when flying accross the Atlantic at 10,000 feet  in a Cessna 172 that I was surprised by a small bright orange light in the middle of the night. It was unexpected! Then it slowly grew and became the rising moon. 

HO 249 volume, use for star observations,  does NOT contain negative values for Hc.

It is clear that you can't observe polaris at a negative altitude of even planets. 

http://fer3.com/arc/m2.aspx/Latitude-Polaris-visibility-FrankReed-oct-2014-g28937

http://fer3.com/arc/m2.aspx/Visibility-rising-setting-Schmidt-apr-2000-w2818

http://fer3.com/arc/m2.aspx/Longitude-Sunset-LaPook-may-2012-g19417

gl