Several arguments in identification of penance panel at Māmallapuram have been presented by scholars. The arguments are well documented in the following link which is sufficient for reference.
Nevertheless, I would like to cite some more references to clarify the details of the relief and its identification. Both the scenes – Bhagīratha’s penance and Arjuna’s penance are depicted in the Vana parva of Mahābhārata. The suggestion is elucidated with verses and their meaning for a wider audience. I intend to draw conclusions based on observations and correlating them with the textual description.
The epic refers to Arjuna and his journey with arms; reads as below,
दिव्यं तद्धनुरादाय खड्गं च पुरुषर्षभः।
He, the bull amongst men, took his divine bow and a sword. It is further emphasized that he held the Gāṇḍīva during the conversation with Śiva who was in the disguise of a hunter.
गाण्डीवमाश्रयं कृत्वा नाराचाश्चाग्निसन्निभान्।
निवसामि महारण्ये द्वितीय इव पावकः ।।
I dwell in this great forest with the Gāṇḍiva and fire-like arrows which stand in comparison subsequent to the Agni deva.
Next reference also substantiates our understanding that Arjuna attacked Śiva with his bow and his sword.
संप्रायुध्यद्धनुष्कोट्या कौन्तेयः परवीरहा।
तदप्यस्य धनुर्दिव्यं जग्राह गिरिगोचरः ।।
ततोऽर्जुनो ग्रस्तधनुः खङ्गपाणिरतिष्ठत।
युद्धस्यान्तमभीप्सन्वै वेगेनाभिजगाम तम् ।।
Hence it is obvious to construe that Arjuna was with his bow and sword even during his penance.
Now we would introspect on the description of the retinue that followed Lord Śiva.
कैरातं वेषमास्थाय काञ्चनद्रुमसन्निभम्।
विभ्राजमानो वपुषा गिरिर्मेरुरिवापरः ।।
निष्पपात महार्चिष्मान्दहन्कक्षमिवानलः ।
देव्या सहोमया श्रीमान्समानव्रतवेषया।
किरातवेषसंछन्नः स्त्रीभिश्चापि सहस्रशः।
अशोभत तदा राजन्स देशोऽतीव भारत ।
He took the disguise of a hunter and shone like the Meru Mountain. The handsome God of Gods was accompanied by Umā, in guise of a Kirāta woman, accompanied by the Bhūtas, and thousands of women too in disguise of Kiratās. O King, that region suddenly blazed up in beauty, in consequence of the arrival of the God of Gods in such company. And soon enough a solemn stillness pervaded the place. The sound of springs, water-courses, and birds suddenly ceased.
It is evident from the description that the Lord was surrounded by thousands of women including his consort.
Now we cite the description of the Lord during the penance of Bhagīratha.
संवृतः पार्षदैर्घोरैर्नानाप्रहरणोद्यतैः ।
Lord Śiva comes with his Bhūtas who held various weapons. Then Bhagīratha offers his prayer to the Lord to hold Gaṅgā. Seeking his approval, Bhagīratha prays to Gaṅgā and she descends on the forehead of the Lord. She flows through the land, follies in it, while Bhagīratha stands beside the Lord. Later she turns and addresses Bhagīratha, to show her the path.
एवंप्रकारान्सुबहून्कुर्वती गगनाच्युता ।
पृथिवीतलमासाद्य भगीरथमथाब्रवीत् ॥
दर्शयस्व महाराज मार्ग केन व्रजाम्यहम् ।
Thus Bhagīrtha is shown beside the Lord even after Gaṅga had started flowing. Then the Lord returns to his abode Kailāsa.
To witness the Gaṅgāvataraṇa, the immortals like Devas, Gandharvas, Nāgas, Yakṣas and mortals like sages assemble. But it should be noted that they assembled after the journey of the God to Kailāsa.
तां प्रच्युतामथो दृष्ट्वा देवाः सार्घं महर्षिभिः ।
गन्धर्वोरगयक्षाश्च समाजग्मुर्दिदृक्षवः ॥
Keeping these points in mind, now we focus our analysis of the panel. The man in penance is not presented with the bow, quiver or a sword. He is in a state of penance in proximity to the Lord. A flowing river too is shown nearby. Gathered audiences from the three worlds throw light that the relief portrays Bhagīratha, because only in this scene that in the presence of the Lord the celestials assembled. It is important to note the subtler detail that the celestials gather to shower on Arjuna after Lord leaves to his abode and not during his presence.
Hence it is unambiguous that the sculptural representation at Mallai suits the episode of Bhagīratha and not that of Arjuna.
Can we now analyse the two sculptures from Kailāsanātha temple, Kāñcīpuram. The first panel clearly depicts the Kirātārjuna yuddha and the other one, the penance of Bhagīratha.
The Kirātārjuna panel contains the figures of the Lord and Arjuna. It is interesting to note that the Arjuna is depicted with Kirīṭa (crown) as he is known as Kirīṭī (a surname of Arjuna). He bears the bow, two quivers (as mentioned in Mahābhārata since he is a Savyasāci) and an arrow. But the sword is not depicted here. Other representations follow the dictum in Mahābhārata. Hence it is clear that depicting Arjuna with crown was the custom of Pallava sculptors even during the penance.
The next panel which has the Bhagiratha’s penance resembles the posture in Māmallapuram. He stands in Yogic posture with lifted arms. The Lord is depicted as the bearer of Gaṅgā.
Comparing the panels with the Māmallapuram penance panel and analyzing it in the light of texts from Mahābhārata, it is very clear that the depiction is Bhagīratha and not Arjuna.
it is pertinent to note that both the unfinished and finished penance panel at Māmallapuram is sculpted with gathered audience facing the flow of the river, quietly delineating it to be crux of the content. Had the appearance of Lord Śiva been the soul, the spectators should have rapt attention towards the Lord and the devotee, which has not happened. So this strengthens that it is Gaṅgāvataraṇa.
Hence I conclude that the penance panel at Māmallapuram is the sculptural representation of Bhagīratha and not of Arjuna.
Pictures courtesy : Sri. Arunkumar Pankaj