An adverbial participle is anarthrous and usually in the nominative case. While it will still modify some noun (principle 7), its emphasis is more on the verb than on its noun.
- If it is present, you can translate it in a temporal sense using “while” as the keyword or in a causal sense using “because” as the keyword.
- If it is aorist, you can translate it using the key word “after”.
For more detailed analysis, see GGBB p. 758. cf. adjectival participle, attributive participle, substantival participle.