I’ve had a quick look and census suggests Aaron was born in leeds, looking on ancestry I found a baptism which could be him.
Horbury, St Peter and St Leonard Yorkshire England
born 6 June 1840 baptised 21 Feb 1845
Aaron son of William and Mary Rushworth of Horbury miner
there were also entries on the same day for his siblings Thomas born 18 Jul 1838 and Martha born 18 Nov 1843.
This seems to fit with the details on his marriage detailing his father as being William Rushworth a miner.
Hope this helps