It looks like Michael died before daughter Julia was born, which raises the question, whose daughter is Ann Callahan, living with Bridget and Julia in 1910.
Julia's marriage record said she was born in Roxbury, which is a neighborhood and post office in Boston.
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Births registered in the city of Boston, 1871
January 27, 1871
Julia Callahan, at 53 Vale Street, parents William and Bridget, both born in Ireland, residing in Boston. no occupation listed for William
[this is the city's copy, you can see by looking at image 1 in the set. also the book only includes records from Boston]
https://www.familysearch.org/ark:/61903/1:1:FH9T-BJP"Massachusetts Births and Christenings, 1639-1915," database, FamilySearch (
https://familysearch.org/ark:/61903/1:1:FH9T-BJP : 10 February 2018), Julia Callahan, 27 Jan 1871; citing Boston, Suffolk, Massachusetts, ; FHL microfilm 592,872.
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Births registered in the city of Boston, 1871
January 27, 1871
Julia Callahan, at 53 Vale Street, parents William, deceased, and Bridget, both born in Ireland, residing in Boston.
[this might be the state's copy, since the record set includes other cities besides Boston]
https://www.familysearch.org/ark:/61903/1:1:FXZP-MSD"Massachusetts Births, 1841-1915," database with images, FamilySearch (
https://familysearch.org/ark:/61903/1:1:FXZP-MSD : 11 March 2018), Julia Callahan, 27 Jan 1871, Boston, Massachusetts; citing reference ID #7677, Massachusetts Archives, Boston; FHL microfilm 1,428,074.
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Some city directories. I need to go back and look for William
1872 Boston City Directory
Callahan Bridget, widow, house 53 Vale
[Vale St is in Roxbury]
https://bcd.lib.tufts.edu/view_text.jsp?urn=tufts:central:dca:UA069:UA069.005.DO.00019&chapter=d.1872.su.Callahan 1873 only found a business directory
1874 only found a business directory
1875 Boston City Directory
no Bridget
1876 Boston City Directory
Callahan, Mrs Bridget house 930 Harrison Avenue
1885 Boston City Directory
Callahan Bridget, widow, h. Taylor Nep.
[in the 1876 book Nep. = Neponset, a section in Dorchester, which is a neighborhood in Boston. Taylor St is near Neponset Circle, on Google Maps]
1885 also came from the Tufts.edu site.