The roles of the Þorgerðr Hölgabrúðr and Irpa in these sources and the implications of their names has been the topic of some scholarly discourse and conjecture.
[1] According to Skáldskaparmál chapter 42, Hölgi (a traditional eponym of the northernmost Norwegian province Hålogaland) is also Þorgerðr's father.
[3] Þorgerðr is referred to as Gerðr in Tindr Hallkelsson's 10th century drápa on Haakon, quoted in chapter 43 of Óláfs saga Tryggvasonar, found in the Heimskringla.
[4] McKinnell says that the variety of stories and names suggest that the tradition of Þorgerðr Hölgabrúðr was wide spread, and that she was venerated in more than one area.
[4] The name Irpa may derive from the Old Norse term jarpr "dark brown", which has led to a number of theories about the goddess.
[7] On the island, Haakon falls to his knees, and, while looking northward, prays to what is described as his patron goddess, Þorgerðr Hölgabrúðr.
The weather becomes thick in the north, the clouds cover the sky, daylight becomes sparse, thunder and lightning ring out, and it begins to rain.
The Jomvikings fleet fights facing the storm and cold, and they have trouble standing due to the heavy wind.
The Jomsvikings throw weapons, missiles, and stones at Haakon's fleet but the winds turn their projectiles back at them.
The saga describes this attack: And then it grew dark again with a squall, this time even stronger and worse than before.
[10]Sigvaldi tells his men to retreat, and reasons that this is not what he vowed to fight, especially since there are now two women, whom he refers to as "ogresses" and "trolls".
Hrapp plunders a seated depiction of Þorgerðr; he takes a large gold ring from her plus the linen hood she is wearing.
They enter the house with a few men, and find that it is lit from glass windows in the ceiling, so that the daylight illuminates the room and there are no shadows to be seen due to this.
Following their advice, Haakon has a wooden man (Old Norse trémaðr) built out of driftwood and endows it with a human heart.
Haakon and the two sisters then bring the trémaðr to life, arm him with a halberd, and send him to Iceland to kill Þorleifr, which he does.
[20] Davidson points out that Haakon may have later turned to the same goddess soon before he met his death, when he hid in the earth beneath a swine in Óláfs saga Tryggvasonar (collected in Heimskringla) chapter 48, and that this could symbolize a mound of Freyja, one of whose names means "sow" (Old Norse sýr).
[20] Davidson theorizes that the account of Olaf I of Norway dragging Þorgerðr's image out of its temple after Haakon's death, and burning it next to a depiction of Freyr (Freyja's male twin), further supports this view.
[24] Lotte Motz (1993) proposed that Þorgerðr was a rare instance of a giantess who was the recipient of cultic worship in her own right in heathen Scandinavia.