What is the closest star to the Sirius system, excluding Sirius B?
Procyon, Alpha Canis Minoris, is very probably the closest star to Sirius, Alpha Canis Majoris, in physical location in three dimensional space.
The nearest star to Sirius would have to have a small difference of no more than a few light years in their distances from Earth. In our part of the galaxy the average distance between stars is about 5 light years, so it is unlikely that the closest star to Sirius will be more than about 6 light years closer or farther from the Sun than Sirius is.
And the nearest star to Sirius should have a small difference in direction as seen from Earth. For example, if a star is on the opposite of the sky from Sirius as seen from Earth, then the Sun will be closer to Sirius than that star is.
So that immediately suggests that Procyon, Alpha Canis Minoris, may be the closest star to Sirius, since it is in a similar direction as seen from Earth and at a similar distance to Sirius.
I have a copy of an astronomy textbook, Exploration of the Universe Brief Edition George Abell, 1964, 1969. Appendix 12 on page 464 lists the nearest stars to the Sun.
They include in order of increasing distance from the Sun: Alpha Centauri, Bernard's Star, Wolf 359, Lalande 21185, Sirius, etc., including a total of 37 solitary stars and multiple star systems out to 40 Eridani.
The table lists the stellar distances from the Sun in parsecs. A parsec is approximately 3.26164 light years.
Instead of converting parsecs to light years, I assume that a candidate star's distance from the Sun must be less than two times the distance of Sirius from the Sun, otherwise the Sun must be closer to Sirius than the other star. The distance of Sirius is 2.67 parsecs, and twice that is 5.34 6arsecs. Unfortunately the table only goes out to 5.00 parsecs, but that should be enough.
The direction to Sirius is given as 6 hours, 42.9 minutes, latitude minus 16 degrees 39 minutes in the equatorial coordinate system. An hour angle is equal to 15 arc degrees, so an hour minute is equal to 0.25 arc degrees or 15 arc minutes.
Procyon has equatorial coordinates of 7 hours 36.7 minutes latitude plus 5 degrees 21 minutes n the table.
So a star would have to be between 7 hours 36.7 minutes, and 5 hours 49.1 minutes to have closer equatorial longitude to Sirius than Procyon does.
BD+5 degrees 1668 has longitude 7 hours 24.7 minutes, and Ross 614 has longitude 6 hours 26.8 minutes.
A star would have to be between latitude plus 5 degrees 21 minutes and minus 38 degrees 39 minutes to have a closer latitude to Sirius than Procyon does.
A number of stars in the list have closer latitudes than Procyon. But of the two stars which have closer longitudes than Procyon, only Ross 614 has a closer latitude, at minus 2 degrees 46 minutes.
Sirius is 2.67 parsecs from the Sun, and Procyon is 3.47 parsecs from the Sun. So the difference in their distances is 0.8 parsecs. Assuming that a star has to be less than one parsec closer or farther than Sirius to be closer to Sirius than Procyon, that gives about 20 star possibilities.
All in all, Procyon seems to be the best candidate to be the closest star to Sirius. But BD+5 degrees 1668 and Ross 614 may also be contenders.
There are more modern lists of nearby stars, which have more precise distances and include recently discovered nearby stars, mostly dim red dwarfs and brown dwarfs which are not really stars but are considered to be intermediate between planets and stars.
Wikipedia has a "List of nearest stars and brown dwarfs", for example.
Assuming that a star should be less than 45 degrees of declination and less than 3 hour angles of longitude (equal to 45 arc degrees) from the direction to Sirius to be a possible candidate, that narrows down the Wikipedia list a bit. The epoch 2000 coordinates of Sirius are longitude 6 hours 45 minutes and declination - 16 degrees 43 minutes. So a candidate star or brown dwarf on the list should be between 3 hours and 45 minutes and 9 hours and 45 minutes, and between declination + 28 degrees 49 minutes and - 61 degrees 43 minutes.
And its distance should be less than 6 light years closer or farther than Sirius - with a listed distance of 8.659 light years, and so be between 2.659 and 14.659 light years from the Sun.
The candidate stars on the Wikipedia list would be Epsilon Eridani, Procyon, DX Cancri (G 51-15), Gliese 1061, Luyten's star (whch is also known as BD+5 degrees 1668), Kapteyn's Star (CD-45 degrees 1841), Ross 614, and the brown dwarf UGPS J072227.51−054031.2.
I have actually calculated the actual distances between stars based on their coordinates and their distances from the Sun, but it is rather complicated.
There is a site called Wolfram Alpha Widgets which has a widget for calculating the distances between two stars.
The widget didn't recognize UGPS J072227.51−054031.2.
But it gave the distance of DX Cancri from Sirius as 9.167 light years (LY) which is farther than the Sun at 8.659 LY, Gliese 1061 as 8.597 LY, Epsilon Eridani as 7.844 LY, Kapteyn's Star or CD-45 degrees 1841 as 7.475 LY, Luyten's star or BD+5 degrees 1668 as 5.763 LY, Ross 614 as 5.528 LY, and Procyon as 5.221 LY.
So it is my opinion that Procyon is very likely to be the known star that is closest to Sirius.
It is possible that the brown dwarf UGPS J072227.51−054031.2 might be closer to Sirius than Procyon is.
But a brown dwarf is not exactly a star, so even if it is closer to Sirius than Procyon is, some people wouldn't consider it the closest star to Sirius. In fact, the mass of UGPS J072227.51−054031.2 is estimated to be between 5 and 40 times the mass of Jupiter according to the Wikipedia article on UGPS J072227.51−054031.2.
The dividing line between planets and brown dwarfs is approximately 13 times the mass of Jupiter. So there is a possibility that UGPS J072227.51−054031.2 could actually be a rogue planet in interstellar space, which would make it certainly not a star nor the nearest star to Sirius.
Assuming you mean the "closest in the sky" you could find its neighbors at https://gea.esac.esa.int/archive/. From here I can find Gaia DR3 source id: 2947050466531872640 at RA: 101.29146384626932, DEC: -16.722798831098476 at less that 25 arc sec. Fore more "normal" targets you can have a look at Simbad: http://simbad.u-strasbg.fr/simbad/sim-coo?Coord=06+45+08.91728-16+42+58.0171&CooFrame=ICRS&CooEqui=2000.0&CooEpoch=J2000&Radius.unit=arcmin&submit=Query+around&Radius=2 .
The winner: Procyon (1.6015 parsecs or 5.2233 ly)
I used the Simplified Hippcarcos Catalog and wrote a program to use the RA, Dec, and Parallax. Convert those to rectangular coordinates, and compute the distance between Sirius and every star in the Hipparcos catalog. And some help debugging from JamesK. It's possible another catalog might produce a different winner.
A photo of the winner:
#!/usr/bin/python #Greg Miller (email@example.com) #Released as public domain import re import math d2r=math.pi/180.0; def polarToRect(lat,lon,r): lat=math.pi/2-lat*d2r; lon=lon*d2r; x=r*math.sin(lat)*math.cos(lon) y=r*math.sin(lat)*math.sin(lon) z=r*math.cos(lat) return [x,y,z] def parseStarData(line): fields=line.split(",") id=int(re.sub(r"[\[ ]","",fields)) ra=float(fields) dec=float(fields) parallax=float(fields) if(parallax>0): parsecs=1/(parallax/1000) else: parsecs=100000000 return [id,ra,dec,parsecs] def distanceBetween(a,b): x=a-b y=a-b z=a-b return math.sqrt(x*x + y*y + z*z) def main(): f=open("hipparcos_full.js",'r') siriusRADEC=parseStarData('[ 32349, " ", -1.44, 2, 101.28715539, -16.71611582,"+", 379.21,') sirius=polarToRect(siriusRADEC,siriusRADEC,siriusRADEC) line=f.readline() min=1000000000 while line: if(len(line)>100): star=parseStarData(line) xyz=polarToRect(star,star,star) distance=distanceBetween(sirius,xyz) if((star!=32349) and (distance<min)): min=distance print(star,distance) line=f.readline() f.close() main()