During his travels, Ibrāhīm ibn Yaqūb Visited Hedeby. He noted:
Schleswig (Hedeby) is a very large town at the extreme end of the world ocean. In its interior one finds fresh water sources. The inhabitants worship Sirius, except for a minority of Christians who have a church of their own there. They celebrate a feast at which all get together to honor their god and to eat and drink. He who slaughters a sacrificial animal puts up poles at the door to his courtyard and impales the animal on them, be it a piece of cattle, a ram, billygoat or a pig so that his neighbors will be aware that he is making a sacrifice in honor of his god.
My questions then are: what is the significance of Sirius? Is this just that ibn Yaqūb wasn’t there long enough to get all the details so just put down the name of the star as he knew it and gave it no more thought? The quote also seems to imply monotheism; is this likely? I believe Hedeby is quite well excavated - do we have any material evidence of religious practices in the town?
The significance of Sirius is close to zero; it's just a way of expressing that the inhabitants of Hedeby were Pagans. Sirius, al-shi'rā, is mentioned in the Qu'ran in sura 53, Al-Najm ("The Star"). Qu'ranic exegesis is diverse, but according to Bassel A. Reyhari, there is one line of reasoning common to all exegetes: that Sirius had been worshipped by tribes of pre-Islamic Arabia. This is the exegetical interpretation that informs ibn Yaqūb al-Tartushi's little nugget of information. The translation given in Anders Winroth's The Age of the Vikings includes all a reader needs to know in brackets:
The inhabitants worship Sirius [they are pagan], except for a small number of Christians.
As for monotheism, I think that's highly unlikely. Religion in Hedeby was a diverse phenomenon. Hedeby was a large trade emporium that attracted traders from all directions, and you could expect to find Norse Pagans from diverse locations in Scandinavia, Christians and traders coming from all directions. It's a possibility that Norse Paganism was monolatrous, as argued by Terry Gunnell, but the minutiae of Norse religion in Hedeby remain in the realm of speculation.