Perrin reaches Rand's rooms in time to get the Aiel guarding the door to find Moiraine for Healing. She arrives just in time to keep Rand from bleeding to death from the wound in his side taken at Falme. Rand's rooms are crowded with bystanders: Perrin, Lan, and Rhuarc, with other Aiel just at the doors.
Rhuarc surveyed the room with sharp blue eyes, as if he suspected enemies hiding behind a drape or an overturned chair. The clan chief of the Taardad Aiel had no visible weapon except the heavy-bladed knife at his waist, but he carried authority and confidence like weapons, quietly, yet as surely as if they were sheathed alongside the knife.
Rhuarc, The Shadow Rising, p. 69
"Don't try to harry me, Moiraine." He was blood filthy, half naked, more than half leaning on Callandor to stay sitting up, but he managed to fill those words with quiet command.
Rand, The Shadow Rising, p. 73
Both Rhuarc and Rand have an expectation of obedience - the quiet confidence that radiates from them. For Rhuarc, it's likely from many years as a clan chief; overcoming challenges for the survival of his clan. For Rand, it's less on such experience, and more the comfort in the knowledge that, with Callandor, he has the authority to back the expectation. He's still struggling to find his way, but has settled on the path of accepting his role as Dragon Reborn. That takes a burden off his shoulders and allows him to assume the role and all the expectations that go with it. There is a certain comfort from accepting a task that lays the foundation for continued confidence in its execution.