During the festival, the daily sacrificial service includes a goat brought as a sin offering, which is offered in addition to the regular daily burnt offering and its accompanying grain and drink offerings. A close look at the details of these festival sacrifices reveals a unique pattern. During other holidays, the instructions for the sin offering explicitly state that it is meant to provide atonement for the people. However, during this specific festival, that detail is entirely absent [חזקוני].
There are two ways to understand this omission. The first approach points to the universal nature of the holiday. The bulls offered during this time are meant to atone for all the nations of the world. Because the focus of these sacrifices is global, the resulting atonement is not limited strictly to the Israelites.
A second explanation focuses on the festival's timing. This holiday takes place immediately following the Day of Atonement. Since the people have just been completely purified from their sins, they do not require any additional atonement at this stage. Because of this recent and thorough cleansing, any mention of atonement for the people is deliberately avoided in the instructions for the offerings from the Day of Atonement onward [חזקוני].