• vidyām-āsthāya — applying his mystic knowledge
  Compound: vidyā (knowledge) + āsthāya (resorting to). Arjuna employs a celestial vidyā — instantaneous transit. Gauḍīyas note: the highest yogic powers are still bounded; only Kṛṣṇa's cakra crosses the unbounded.
• phālgunaḥ — Phālguna (Arjuna)
  Arjuna's star-name. The verse uses it deliberately — he is operating as a stellar warrior with celestial credentials. And still the sons are not there.
• saṁyamanīm — to Saṁyamanī
  From saṁyamana (restraint). Yamarāja's city — the place of restrained souls. Arjuna's first stop. The Bhāgavatam follows him through every standard cosmographic location to demonstrate exhaustively that the sons are off the standard map.
• bhagavān yamaḥ — Lord Yama
  Yamarāja honored with the title bhagavān — proper Vaiṣṇava etiquette. He is a mahājana (cf. SB 6.3.20), one of the twelve authorities on dharma; even his city does not contain the sons.

While the curses continue, Arjuna invokes a mystic vidyā and leaps to Saṁyamanī — Yamarāja's city. The kṣatriya is now operating at full astra-yoga capacity; no one else in this birth could do what he does. And the brāhmaṇa's sons are not there. The chapter is methodically eliminating every available rescue except the one it intends to reveal.