Hi, welcome to GoY, Aster is a genus of about 250 species of annuals, biennials, perennials and sub shrubs, they're divided into 3 groups, depending on their cultivation needs, Derek.

Of the popular ones though if you mean the big michaelmas daisies that are in flower now they are perennial. If you mean the small bedding ones they are annual.

Hi, there are also the so called china asters, which although they're in the family Asteraceae / compositae, they are a different genus, of just 1 species, but lots of varieties, these are half hardy annuals, and are usually much larger flowers than true Asters, and vary in height from about 8 " up to about 30", Derek.

To add more confusion I think there are some Asters that are perennials, but are grown as annuals over here because they are not fully hardy.

If you have no idea which they are leaving them in the ground and seeing if they reappear next year will answer your question!