The keyword term is a noun phrase, "Patriots Day," modified by an adverb, "online." In this construction, "Patriots Day" is a proper noun functioning as the direct object of an implied action verb (such as watch, stream, or find). The word "online" is an adverb of place or manner that modifies this unstated verb, specifying that the action is to be performed via the internet.
Grammatically, "Patriots Day" operates as a single conceptual unit, naming a specific entity (either the holiday or, more likely, a film title). The term "online" is an adverbial that indicates the medium or environment for the interaction with that noun. Search engine queries are frequently elliptical, meaning they omit words that are understood from context. The user's query omits the verb, but the syntactical relationship persists: the adverb modifies the understood action being performed upon the noun.
For the purpose of structuring an article, the primary part of speech to treat as the main point is the noun, "Patriots Day." This noun represents the core subject matter. The adverb "online" serves as a crucial qualifier, narrowing the article's focus to the digital availability, streaming options, or virtual observance of that subject. The article's central theme is the noun, framed within the specific context provided by the adverb.