I'm sorry Neptune is throwing up for the past three days. He must be dehydrated, which is dangerous to his health. Because he spends time outside, he could have licked, chewed, ingested something toxic or a non-food item and this is the cause of the vomiting. Here is more information about vomiting in cats:
Due to the color of his vomit, if he is not eating anything or his stomach is empty, due to the vomiting, this can be caused by bile mixed with excess acid in his stomach, which makes him nauseated. For the moment, you can give him 1/4 of a 10 mg. tablet of Pepcid AC (generic=Famotidine), which is an over the counter acid controller every 12 hours and see if this helps to soothe his stomach and quell any nausea. It's a very small pill, so 1/4 is quite tiny. You can give it to him in the traditional way and follow it with some water (dropper fed water from the side of the mouth, if he is not drinking on his own). They sell Pepcid AC in all pharmacies, Walmart, Target, supermarkets, etc.
Neptune should be seen by his (or any) vet, as soon as possible, to find the cause of the vomiting and be treated. He also may need I.V. or sub-Q (under the skin) fluids, if he is dehydrated.
I hope all will be well with Neptune!
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