The Facial Expression
Looking at the face of Naṭarāja one gets immediately aware of a special feature viz. "the third eye" set vertically in the forehead. The vertical extremes of this tilaka-shaped "eye" touch the rim of the head-dress at the top, and the point between the two eyebrows at the bottom. The pupils of all the three eyes, Śrīraṅgamahaguru noted, appear equidistant. It is common to refer to the two eyes of the Lord as the Sun and the Moon.( Cf. dhyāna-śloka of Viṣṇusahasranāman , or even the much older Muṇḍakopaniṣad 2.1.4.) The third eye, known as the "eye of knowledge," is commonly represented as the Eye of Fire. This trinity of eyes thus represents the trinity of luminaries viz. the Sun, the Moon, and the Fire.
The third eye is closed, while the horizontal eyes are depicted as open. This combination suggests a special yogic condition. It is known in yogic literature as "eyes open but gaze turned inwards," which is a reference to the peak of yogic experience called Śāmbhavī-mudrā. Refer Śāṇḍilyopaniṣad 1.7.14:
antar lakṣyaṁ bahir dṛṣṭir nimeṣonmeṣa-varjitā | eṣā sā śāmbhavī mudrā sarva-tantreṣu gopitā || अन्तर् लक्ष्यं बहिर् दृष्टिर् निमेषोन्मेष-वर्जिता । एषा सा शाम्भवी मुद्रा सर्व-तन्त्रेषु गोपिता ॥
The left eyebrow of Naṭarāja is considerably raised. This indicates a high state of mind. Kālidāsa makes a reference to this as a culmination in the particular positioning of the eyebrow. Kumārasambhava 3.47: bhrū-vikriyāyāṁ virata-prasaṅgaiḥ. This is also the way to attain the high yogic state(s) called unmanī/samunmanī/ manonmanī. This is confirmed by Śāṇḍilyopaniṣad 1.17:
tāraṁ jyotiṣi saṁyojya kiñcid unnamaya bhruvau |
pūrvābhyāsasya mārgo'yam unmanī-kārakaḥ kṣaṇāt |
तारं ज्योतिषि संयोज्य किञ्चिद् उन्नमय भ्रुवौ ।
पूर्वाभ्यासस्य मार्गोऽयम् उन्मनी-कारकः क्षणात् ।
The connection between the raising of the eyebrow and the state of mind is a matter of yogic experience, as the Upaniṣad sets it forth.
The ecstatic state of Naṭarāja is borne out by His facial expression. An ineffable, gentle smile adorns His face. There is an asymmetry noticeable in the smile, recognized only upon a close observation: the left portion of the smile has a certain femininity, with a visible dimple on the left cheek, while the right portion is somewhat tinged by restraint, as the dimple is hardly obvious. The lower lip is a little projected forward, as against the upper one which is a little drawn back. The nostrils betray features of deep inhalation, followed by the retention of breath; thus these nostrils show the stillness attained by what is spoken of as Kevala-kumbhakāvasthā "the state of Kevala Kumbhaka, "Stilled Retention" in yogic texts.