Celery: why do I need a broker for periodic tasks?

As the Celery documentation explains:

Celery communicates via messages, usually using a broker to mediate between clients and workers. To initiate a task, a client adds a message to the queue, which the broker then delivers to a worker.

You can use your existing MongoDB database as broker. see Using MongoDB.

Celery architecture is designed to scale and distribute tasks across several servers. For sites like yours it might be an overkill. Queue service is generally needed to maintain the task list and signal the status of finished tasks.

You might want to take a look in Huey instead. Huey is small-scale Celery "Clone" needing only Redis as an external dependency, not RabbitMQ. It's still using Redis queue mechanism to line the tasks in queue.

There also exists Advanced Python scheduler which does not need even Redis, but can hold the state of the queue in memory in-process.

Alternatively if you have very small amount of periodical tasks, no delayed tasks, I would just use Cron and pure Python scripts to run the tasks.