Sea pumpkin

On beach, low spring tide: hundreds of these "pumpkins" lying in shallow water. It is apparently important to note that the beach sand was deeply washed away. It was night.

Pumpkins as in pictures. Enormous, fleshy things. The one collected and shown here was one of the smallest; size up to double this. Flesh really juicy, no smell, no taste -- seems to be all fresh water. Is this a plant's underground storage organ?

Twig with leaves came along later, donated by a stranger. If the leaves do not belong to the pumpkin, I shall remove them.

First opinion was that the pumpkins were washed ashore from the coral reefs. That lead to the identification of the pumpkins as algae.

Second opinion was that the twig & leaves, dug up from the beach sand, belong with the pumpkins. A stranger gave me the gift of a small sample of his larger sample.

Third opinion, by another stranger, was that these pumpkins belong to the Asteraceae. I have no idea why.

What are sea pumpkins?

EDIT HISTORY

• Observation originally posted 2014-11-06.
• Pictures of leaves removed 2014-12-26 (see below for why).