My Personal, philosophical and scientific speculations for the Indradhanush verse.
Atharva Veda 15.1.:
He grew, he became great, he became Mahādeva.
He gained the lordship of the Gods. He became Lord (Ishāna).
He became Chief (Ekā) Vrātya. He held a bow, even that Bow of Indra.
His belly is dark-blue (neela), his back is red (lohita).
With dark-blue he envelops a detested rival, with red he pierces the man who hates him: so the theologians say.
To be honest, though the wordings are almost same but for the 6th verse i ike the hindi one much better as it fits perfectly with my explanation n makes much more sense.
वहीं व्रात्यसमूह के एकमात्र अधिपति हैं, उनके द्वारा जिस धनुष का स्पर्श किया गया (धारण किया गया), वहीं इन्द्रधनुष के नाम से कहा गया ॥६॥
He is the only ruler of the Vratya group, The bow which was touched (held) by him was called Indradhanush. 6.
Now, in the above verse we see, He became Mahadeva and Ishana and touched/held a bow which was called Indra-Dhanush. Plus, his colour is Neela-Lohita.
The Neela-Lohita or Krishna-Pinglam are the words use to signify the Ardhanarishwara form of Bhagawan Shiva and Mata Parvati which implies the Agni-Soma nature of the Universe. With Neela (Maya/Prakriti), he envelops with maya and with Lohita (Ishwara/Purusha), he impales thus gives moksha (sometimes also by killing them).
Rudra is the embodiment of all Devas. All devas are merely different manifestations (parts) of Sri Rudra Himself. On the right side of Rudra, there is the sun, then the four-headed Brahma, and then three Agnis (fires). On the left side, there exist Sri Umadevi, and also Vishnu and Soma (moon). (Rudra hridhaya upanishad).
Uma Herself is the form of Vishnu. Vishnu Himself is the form of the moon. Therefore, those who worship Lord Vishnu, worship Lord Siva Himself. And those who worship Lord Siva, worship Lord Vishnu. Those who envy and hate Sri Rudra, are actually hating Sri Vishnu. Those who decry Lord Siva, decry Lord Vishnu Himself. (Rudra hridhaya upanishad).
Rudra is the generator of the seed. Vishnu is the embryo of the seed. Siva Himself is Brahma and Brahma Himself is Agni. Rudra is full of Brahma and Vishnu. The whole world is full of Agni and Soma. The masculine gender is Lord Siva. The feminine gender is Sri Bhavani Devi. All the mobile and immobile creation of this universe, is filled up with Uma and Rudra. The Vyakta is Sri Uma, and the Avyakta is Lord Siva. (Rudra hridaya upanishad).
MBH Anusashana Parva, SECTION CLXI.:
"Vasudeva said, '. . . Brahmanas conversant with the Vedas say that that god has two forms. One of these is terrible, and the other mild and auspicious. Those two forms, again, are subdivided into many forms. That form which is fierce and terrible is regarded as identical with Agni and Lightning and Surya. The other form which is mild and auspicious is identical with Righteousness and water and Chandramas. Then, again, it is said that half his body is fire and half is Soma (or the moon). . .'
So, the right Agni side have elements like Fire (obviously), Sun, Lightning and the left Soma side have Moon and Water.
Mahadeva.:
He said to him, “Thou art Mahan Devah (the Great God).” And because he gave him that name, the moon became suchlike, for the moon is Prajapati, and Prajapati is the Great God (MahabDev). He said, “Surely, I am mightier than that: give me yet a name!” (Śatapathabrāhmaṇa 6.1.3.16).
Ishana :
He said to him, “Thou art Ishana (the Ruler).” And because he gave him that name, the Sun became suchlike, for Ishana is the Sun, since the Sun rules over this All. He said, “So great indeed I am: give me no other name after that!” (Śatapathabrāhmaṇa 6.1.3.17).
Conclusion.: When the Agni Particles (Sunrays) touches Soma Particles (Water Droplets), it creates the bow, the Rain Bow or The Indra Dhanush.
As for why it's called Indra Dhanush.?
It's because Indra means King, Ishana also means Ruler/King and MahaDeva also means Prajapati/King.
The bow can also symbolises the bending and dispersions of the light.
Interestingly, Shatapatha Brahmana 6.1.1 says the following verses for Indra and Agni respectively.:
- This same vital air (prana) in the midst doubtless is Indra. He, by his power (indriya), kindled those (other) vital airs from the midst; and inasmuch as he kindled (indh), he is the kindler (indha): the kindler[3] indeed,--him they call 'Indra' mystically (esoterically), for the gods love the mystic. They (the vital airs), being kindled, created seven separate persons (puruṣa).
- He verily is composed of seven persons, for this Person (Agni) is composed of seven persons, to wit, the body (trunk) of four, and the wings and tail of three; for the body of that (first) Person (was composed of) four, and the wings and tail of three. And inasmuch as he makes the body larger by one person, by that force the body raises the wings and tail.
So, Indra divides himself into 7 Purushas by kindling himself with Indriyas plus these 7 Purushas are Agni only.
As for indriyas, we hava 5 karma indriyas and 5 jnana indriyas and the 11th manobuddhiahamkara.
Check the following answers for Indriyas.:
This, this and this.
These Indriyas/Pranas/Rudras are also associated with the Ashtamoorti forms as Nose signifies Air, Eyes Sun, Vocal cord Fire, Mind Moon, Body Earth, Hairs Herbs, Blood/Semen Water and so on. So here also the concept of Agni-Soma can be applied.
Thus, Indra/Agni divides itself by kindling from Indriyas into 7 Purushas can be linked with the dispersion of the 7 colours of the Rainbow after refrating from water droplets. The white light divides itself into 7 different colours.
(P.S.: I know Ashtamoorti form have different names for different elements which also varies from scripture to scripture. But my answer is fully from the Agni-Soma PoV.).
I hope this helps. Prd..