Pope Emeritus Benedict XVI (formerly known as Joseph Cardinal Ratzinger) is depicted above wearing what is known as a "cappello romano," which is Italian for "Roman hat."
It does not originate from papal attire, but was simply a fashionable hat worn by 17th century clergy.
A cappello romano (literally Roman hat in Italian) or saturno (because
its appearance is reminiscent of the ringed planet Saturn) is a hat
with a wide, circular brim and a rounded crown worn outdoors in some
countries by Catholic clergy, when dressed in a cassock. It is made of
either beaver fur or felt, and lined in white silk. Unlike many other
articles of ecclesiastical attire, it serves no ceremonial purpose,
being primarily a practical item. The cappello romano is not used in
liturgical services. Since the general abandonment of the cassock as
street dress, it is uncommon even in Rome today, though it was quite
popular there and in some other countries with a Catholic majority
population from the 17th century until around 1970.
There are some, mostly minor, differences in the designs of cappelli,
depending on the rank of the wearer. The pope wears a red cappello
with gold cords. Cardinals formerly also had the privilege of wearing
a red cappello, but this rule was overturned by Paul VI, and now
Cardinals' cappelli are black, as are those of all other clerics.