THEORY 1
1. Drupada didn't want simply a son. He wanted a son who could kill Drona, a brahmana. According to rules, only a brahmana could kill another brahmana. ie, he needed to adopt a brahmana boy who was exceptional in battle tactics and weaponry. Dhrishtadyumna was said to have been born with armor and weaponry, skilled in his knowledge of battle/war.
2. Panchali probably came as package deal. If Dhrishtadyumna were an orphan, and Panchali were his sister/twin, he'd not going to leave her behind.
This is where the Agni Angirasa possibility comes in. Because Mahabharata states several times Angirasa is Agni.
In some oral Nepali versions of Mahabarata, Panchali leaves the Pandavas after war and goes on a pilgrimage of fire. ie, to her home with the Angirasas.
Since Ghora Angirasa was Krishna's guru according to Chandogya Unpanishad, this explains his connection to Panchali.
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THEORY 2
Shikhandi, I believe, was Amba's child. She is said to have left a "flower" at Panchal's doorstep. Panchal was her maternal family, so it stands to reason.
If you take that further, it is entirely possible Drupada could not have children and adopted Shikhandi first. When the king realized the boy was gay/trans, he wanted another son.
Combine this with THEORY 1, you have an answer.
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THEORY 3
There is a Buddhist jataka which bluntly states the king of Kashi (who was also king of Panchal as stated in other Buddhist jatakas) killed the king of Kosala (strangely, Amba's land, again). Kosala prince was an infant at the time and hidden. He was later found when he had the Kashi king's life at his mercy and decides to forgive him. Then the king of Kashi adopts the prince, the son of king of Kosala.
This is where things get interesting. The queen of Kosala was pregnant at the time of the Kasi-Kosala clash with her 2nd child. The victor, the king of Kashi married her and brings her home as he didn't have any children of his own.
A girl was born who they named KANHA. This girl marries the sons of Pandu.
Now, the jatakas call Panchali a *****, but their judgement of her morality aside, it is the only place I have seen Panchali's (and Dhrishtadyumna's) origins bluntly stated.
https://www.sacred-texts.com/bud/j5/j5029.htm
Back to Mahabharata. Asita, Nandagopa's brother, had two sons - Devala and Dhaumya. Yes, the Pandava priest. Devala had a scholarly daughter called Sannati who was married to Brahmadutta, the king of Panchal. Elsewhere, Bheeshma also calls the king of Panchal as Brahmadutta. My guess is it was a title.
So there you go, Panchali's father and mother.
Biological father - king of Kosala, adoptive father - king of Panchal/Kashi.
Mother - Sannati, the daughter of Devala, the niece of Nandagopa.
This would also explain Panchali's connection to Krishna WITH OR WITHOUT Buddhist jataka portion.
FYI, though Sannati would've technically been Krishna's niece, she was of Pandu's gen as Asita once proposed marriage to Satyavati before she married Shanthanu.😆 So Asita was Shanthanu's gen, Devala was Bheeshma's, Sannati was Pandu's. But technically, she was Krishna's foster niece😆
I'm not going searching through links for MBH parts. If you have CE in Kindle format, run a search😆.
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@CaptainSpark. I think you might be quoting Prof. Bandhopadhyay's theory. There are lots of holes in it.
1. Drupada is actually said to have paid the sages a lot of money. There was no reason to say it.
2. The queen bluntly refused to go an participate.
3. Dhrishtadyumna was supposed to have trained under Drona. And at his birth, he was supposed to have been fully trained, so it occurred before the yajna.
It is not likely that Drupada did not deploy a fully trained Dhrishtadyumna in the battle with the Pandavas.
4. Where was Drupada at the beginning of the exile? Only Dhrishtadyumna (maybe Shikhandi, too) shows up with Krishna. No parent on earth will sit comfortably at home if they hear such news. Unless of course they didn't care. Panchali's description of her father (sitting on her father's lap, learning while the sages were teaching her brother, as she states to Yudhishtira) does sound like a loving relationship. I do not think Drupada was her biological father.
5. Pandavas are revered for their "divine" birth NOW. Suyodhana openly mocks it at the time. There was no need for Panchali to have a matching story. She would've been mocked for claiming a fire birth.
6. MOST IMPORTANT POINT. Sexual fire is Prof. Bandhopadhyay's interpretation. KRISHNA DWAIPAYANA VYASA contradicts the good professor as MBH states over and over Agni is Angirasa. Vyasa doesn't say Agni is sex.
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If we disregard the Buddhist jatakas, Angirasa brahmana children would be the most likely probability for Panchali and Dhrishtadyumna.
Now, one possibility exists that the king of Kosala who died was an Angirasa. I'm still researching on that.
I mentioned the Krishna-Panchali connection. She was a child of his guru's clan, perhaps. But she definitely was the daughter (adopted or otherwise) of Sannati, who was Krishna's foster relative.