We know that Sól (Sunna) is a goddess, the life giver, worshipped and aknowlegded as a primary Natural force and a main deity, the building stone of the three elements - containing other deities and their attributes as well. We know from The Deluding of Gylfi (Gylfaginning) that Sól will give birth to one daughter only after being eaten by the wolf Fenrír during Ragnarök.
From Vafþrúðnirmál during the battle of wisdom between Óðinn and the giant Vafþrúðnir, it is testified;
Óðinn kvað:
"Hvaðan kemr sólá inn slétta himin,
er þessa hefr Fenrir farit?"
Vafþrúðnir kvað:
"Eina dóttur berr Alfröðull, áðr hana Fenrir fari;
sú skal ríða, þá er regin deyja, móður brautir, mær."
Yes, "the new sun" is named Álfröðull, after Ragnarök - the new beginning. This name is, as everything else in our dear mythology, not a coincidence.
Alfr is Elf - and is of course not only related to ancestors, they are your ancestors (the light-elves) - and the sum of all your ancestors is you - Óðinn. The name Álfröðull is thus Sól incarnated - translated as "elf-beam", "elf-glory". She is the sun rising and setting every day - giving a new incarnated sun the next. She is the increasing sun in spring and the dying sun eaten by the powers of winter (Fenrír) every year, with the symbolic name Álfröðull at the solstice. Álfröðull is Sól and Sól is Álfröðull in eternal cycle.
She is pulled by two horses Árvakr (very alert) and Alsviðr (very quick) - in a chariot. She is chased by the wolf (the symbol itself for female re-production) Sköll (wich is a kenning for Fenrír). The same way our other deities are pulled by totem animals in chariots - like Þórr, Freya, Freyr etc., the symbolism for Sól is identical. It is connected to the elves and re-incarnation - ancestral cult. It symbolizes the reið - the ride every child of Nature must do, to overcome its ancestor to be re-born. They are mytologically and symbolically protected by the shield of Svalín ("the cooler") being the protective layer in the atmosphere at a comsoligical level, the walls and roof of a burial mound or the "walls" of a pregnant mother on a human level.
Alfröðull contains Freyr (the King of the elves, the seed) and Baldr (the bright, shining, the returning one) - the child, the new beginning, the new King/Queen, the returning one, the re-incarnated. There is no coincidense that Sól and Mání (her mythological brother) is the two deities that every other deity spring out of, togehter with Jörð. There is no coincidense that the first pagan day of the week is the day of Sól and the second the day of Mání.
Sól/Alfröðull is represented by the rune ᛋ*sōwilu (sól ). The rune is figuratively the one part of the sun wheel and the thunder bolt (bringing fire/the suns power to Jörð). The other part in combination with the first gives the swastika - the sun wheel - in eternal cycle. As mentioned earlier, the rune ᚱ*raidu (reið) represents the ride - the circular pattern itself, while ᛋ*sōwilu is the fuel that ignite - the fire.
It is no suprise that the herb of ᛋ*sōwilu is the mistletoe - the evergreen symbol of re-incarnation, of Baldr, of the solstice and everything re-born! It is the symbol of growth and movement, thus, the rune ᛁ*īsaR (iss) (ice) is the counterpart, representing the frozen seeds and fertility dwelling - that can be ignited to grow again by the fires of Sól and the water of ᛚ*laguR (logr). This is why ᛋ*sōwilu is the accumulations of the second ætt of runes - bringing you over in the third ætt - the divine! The divine level of "God-Making", to become divine in the fields of Ásgarðr - the home of the breathing.
The fire is kept alive - and it is re-kindeled not only on the sky, but the spirits of our ancestors are re-kindlled in us. Like a new dawn, from the rays of Sól - like a new birth, a new day, a new life, a new solstice. So is also your own life. You have risen from the realm of death yourself, decended, after a ride and a struggle, you have seen the light of the rays of Sól again - accumulating you to the third cycle; to find the golden tablets of your ancestors in the green gras reflected by Alfröðull. The cycle of self improvement. The cycle of becoming an honorable re-born ancestor. The cycle of Óðinn incarnated.