A few words about taking care of adult sea urchins, because improper care can result in the animals dying or spawning out before they are needed.
Upon receiving new animals, let then float in their plastic bags on top of the water of your set up aquarium for approximately 20 minutes. This will allow them to adapt to any temperature difference. It is better for them to go from warm to cold, than from cold to warm. The latter will often kill the animals and very likely to induce spawning before you are ready.
It is best if new animals are allowed to "rest" in their new surrounding for approximately 3 days before use. If you do not have a permanent aquarium setup and hope to use the animals the day of arrival, go ahead. Letting them sit in a warm enviroment without proper circulation, filtering, etc. is worse than using then right away.
I use the formula, crude, of 1 inch of urchin width per gallon of water. The limiting factor for short term is oxygen use. Adding too many animals will reduce the oxygen level below survival level. The weaker animals will die first, with their rotting corpses polluting the tank to the extent that the other healthier animals will succumb also. Long term problem is waste build up. This is assuming that you have an active filtration and aeration system going. Even the best filtration system cannot handle over crowding for long. Ammonia and other waste products will build up to toxic levels.
No water circulation = death if the water level is higher than height of the sea urchin [approximately one inch]. Good circulation/filtration means the tank can be any height.
Each species has an optimum temperature range.
To maintain the correct temperature is important. This can best be accomplished using an aquarium with a refrigeration system, but is not always available.
Some species of sea urchin are used to warmer temperatures (L. pictus & A. punctulata) and can be maintained without refrigeration at room temperature.
If you only need to keep them for a few hours, you may be able to rig a makeshift water bath. Place the sea urchins in a container which is sitting in a second container of water to which you add ice as needed to maintain the proper temperature. (Don't add ice directly to seawater as this will dilute the salinity).
Placing them in a refrigerator is BAD NEWS. This does weird things to the eggs making normal development impossible.
There are no fresh water sea urchins. Sea urchins must be maintained in a narrow range of salt concentration. If you use seawater from the ocean, you should have no problems. If you use a mix, such as Instant Ocean, make sure you follow the directions carefully. Too low or too high salinity will result in a reabsorption of gametes or death. See seawater formulations.
Sea urchins are used as indicator organisms in public aquariums to determine if the system is functioning properly. This is because they are very "picky" about water quality. If the water is contaminated, the sea urchins will be the first to show signs of stress, spines laying down or falling off. Do use an aquarium filter and do clean up the day after feeding. Any metal exposed to the seawater will corrode and poison the tank. A dying sea urchin will often spawn out and rot out, causing the others in the tank to spawn and die as welll.
Sea urchins will eat each other, so it is important to feed if you plan on having them around for more than a few days. If you do not feed over a long period of time the sea urchins will reabsorb their gametes. Most sea urchins are vegetarians, with a few omnivores thrown in. The easiest foods are the brown seaweeds like giant kelp, laminaria or egregia. However, for land based use, carrots or potatoes will substitute for kelp. It is best to avoid meat, the omnivores will subsist on kelp or carrots and meat is messy and easily fouls the tank (see above). OR you can make up our famous "Urchin Cookie" recipe.
If it all possible you should maintain a light cycle that matches the height of the species' season. If you have a sea urchin that is gravid in the winter, use a short day. If you have a sea urchin that is gravid in the summer, a long day. A fluorescent light (low heat) hooked to a 24-hour timer works well.
IF the above is not enough and you are still getting die off before you can use the urchins. Here are some suggestions from our own Professor Steve Palumbi.
1) His setup consists of a tank with an oversized filtration system. That is, the filter capacity is many times larger than the size the tank of that volume would normally need. Sea urchins are not efficient consumers and the fecal material will support a large bacteria population.
2) All the water in the tank passes a UV sterilization unit at least once every half hour. This may mean a pretty good sized circulation pump for the UV and filter units.
3) One tenth of the seawater is removed each week and replaced with new seawater. This water is removed at the same time the fecal material is removed from the bottom of the tank by means of a siphon tube. He does not use any sand or other material on the bottom of the tank, which makes cleaning easier.
4) The lower the number of animals per tank the higher the level of success.
All the above conditions mentioned still apply. Don't over feed. Remove rotten food and sick or dead animals promptly.
I have noticed and used an interesting little sensor available at pet supply stores. It has a round dot approximately one centimeter in diameter in the center surrounded by a color guide. The center starts out yellow and if there is ammonia or nitrates in the water it gradually turns blue. Sticks to the side of the tank and is visible through the glass/plastic. This provides another way of keeping track of water quality.
I would recommend a thermometer of course, and checking the pH. The pH of normal seawater is between 8 and 8.3. The water will tend to go acidic as bad bacteria build up.
Also at pet stores are bacterial preparations for 'seeding' your biological filter. I have found this helps quite a bit to push a new tank to carrying capacity.
Steve said, if you do everything right, you should be able to keep animals for years without having to resort to antibiotics.
There are two antibiotics that might work, if all of the above fails and you really need your animals to survive. Understand that this is a last gasp effort that may also fail.
Ampicillin, sodium salt - use at 100mg/Liter or 3.85 grams per 10 gallons. After three days you will probably need to change the water in the tank.
Chloramphenicol - 30mg/Liter or 1.16 grams per 10 gallons. This antibiotic is a suspect carcenogen. So only use as a last resort and keep students away from the tank. You really are better off with the UV sterilizer mentioned above. After three days you will probably need to change the water in the tank.
NOTE: There may be a temptation to autoclave your seawater. Autoclaved seawater will KILL your sea urchins. They really hate this stuff. Autoclaving does something to the water to make it lethal. Filter sterilizing does work however, if you can afford the filter units to do large volumes.
Pet stores may have other formulas available. Be sure it is safe for invertebrates and echinoids. Some are not safe and will kill your sea uchins.