Note About The PGC Designations: Aside from the designations for the individual galaxies, PGC also has an entry for the pair (as Arp 57 = CGCG 101-019), namely PGC 3167645; however, a search of the LEDA database for that PGC designation returns no result, so it can be thought of as merely a "place-keeper", and of no other use.
Usage By The Arp Atlas: PGC 46225 is used by the Arp Atlas as an example of a spiral galaxy with a small high-brightness companion (PGC 1457659), with the note "Small companion connected to end of arm."
Physical Information: Since this galaxy and its companion are interacting, they must be at about the same distance, and the best number to use for an estimate of their Hubble Flow distance is the average of their individual recessional velocities. For PGC 46225, the recessional velocity relative to the Cosmic Microwave Background is about 18345 km/sec, while for its companion, the measured value is about 18195 km/sec (all astronomical data have at least a small range of uncertainty, so "about" is more accurate than any specific number), yielding an average of about 18270 km/sec (the 150 km/sec difference between the two values is the "peculiar velocity", or actual motion of the objects relative to each other, and has nothing to do with the Universal Expansion). Given that average (and H₀ = 70 km/sec/Mpc), a straightforward calculation indicates that Arp 57 is about 850 million light-years away. However, for objects at such distances we should take into account the expansion of the Universe during the time it took their light to reach us. Doing that shows that the galaxy was about 790 to 795 million light-years away at the time the light by which we see it was emitted, about 815 million years ago (the difference between the two numbers being due to the expansion of the intervening space during the light-travel time). Given that and its apparent size of about 0.69 by 0.43 arcmin (from the images below), PGC 46225 is about 160 thousand light-years across.
 Aside from its obvious companion, PGC 46225 is in the same direction and at nearly the same distance as PGC 46234. The difference in their recessional velocities is small enough that it could be due to peculiar (non-Hubble Expansion) velocities, so although the two galaxies may be unrelated, they may be part of a triple system of gravitationally bound objects.

Usage By The Arp Atlas: See PGC 46225 for a note about that.
Physical Information: As discussed in the entry for PGC 46225, Arp 57 was about 790 to 795 million light-years away at the time the light by which we see it was emitted, about 815 million years ago (the difference between the two numbers being due to the expansion of the intervening space during the light-travel time). Given that and its apparent size of about 0.21 by 0.14 arcmin (from the images shown in the previous entry), PGC 1457659 is about 45 to 50 thousand light-years across (or was, about 815 million years ago; the interaction between the two galaxies during that interval may have slightly changed its appearance and dimensions).

Note About Error In HyperLEDA: In the LEDA database, PGC 46234 is shown as part of Arp 57 and CGCG 101-019 (which is Arp 57). This is a blunder. Although it is possible that PGC 46234 is a companion of Arp 57, and it is shown in the photograph in the Arp Atlas, it is definitely not part of the Arp object.
Physical Information: Based on a recessional velocity of about 17940 km/sec relative to the Cosmic Microwave Background of 17940 km/sec (and H₀ = 70 km/sec/Mpc), a straightforward calculation indicates that PGC 46234 is about 835 million light-years away. However, for objects as such distances we should take into account the Universal expansion during the time it took their light to reach us. Doing that shows that the galaxy was about 780 million light-years away at the time the light by which we see it was emitted, about 800 to 805 million years ago (the difference between the two numbers being due to the expansion of the intervening space during the light-travel time). Given that and its apparent size of 0.5 by 0.25 arcmin (from the images below), the galaxy is about 110 to 115 thousand light-years across.
 As noted in the entry for PGC 46225, it is possible that PGC 46234 and Arp 57 are more closely related than their slightly different recessional velocities might imply, as the roughly 400 km/sec difference in their recessional velocities is only slightly larger than typical "peculiar velocities" (random motions of galaxies relative to each other that are not related to the Universal Expansion), but whether they are part of a gravitationally bound triple system cannot be known, and they are most likely not gravitationally bound companions; but if nothing else, the slightly peculiar appearance of PGC 46234 might be explained by a moderately close passage of the galaxy with the now (apparently) more distant pair at some time in the past.

Physical Information: Based on a recessional velocity relative to the Cosmic Background Radiation of 10450 km/sec (and H₀ = 70 km/sec/Mpc), a straightforward calculation indicates that PGC 46423 is about 485 to 490 million light-years away. However, for objects at such distances we should take into account the expansion of the Universe during the time it took their light to reach us. Doing that shows that the galaxy was about 465 to 470 million light-years away at the time the light by which we see it was emitted, about 475 million years ago (the difference between the two numbers being due to the expansion of the intervening space during the light-travel time). Given that and its apparent size of about 1.4 by 0.25 arcmin (from the images below), the galaxy is about 190 thousand light-years across. The galaxy is classified as an HII emitter, indicating that it has regions of relatively rapid formation of hot, bright stars that are heating up the gases out of which they formed.
 The faint galaxy to its west, PGC 790153, is a probable companion, as it has a similar recessional velocity, but the north-south galaxy on its eastern side, PGC 790216, has an unknown distance, and is probably merely a background galaxy. Nothing is known about 6dFJ1319096-242505 ("PGC 4681588"), the small galaxy immediately to its east, so whether it is in any way related to PGC 46423 is also unknown.

Physical Information: Since PGC 46461 and 46464 are an interacting pair, they must be at essentially the same distance, so the best Hubble Flow recessional velocity is the average of their individual measurements. For PGC 46461, that is about 10135 km/sec, and for PGC 46464, it is about 10795 km/sec. Note that if those velocities were only related to the Universal Expansion, its higher recessional velocity would place PGC 46464 behind PGC 46461; but since the image of the pair clearly shows that PGC 46464 is in front of its companion (as seen from our location), the difference of nearly 600 km/sec in their recessional velocities must represent a real motion (a "peculiar velocity") of the spiral galaxy toward its elliptical companion, so they will be even closer together (and probably "collide" with each other) at some future date.
 Based on their average recessional velocity relative to the Cosmic Background Radiation of about 10465 km/sec (and H₀ = 70 km/sec/Mpc), a straightforward calculation indicates that PGC 46461 and 46464 are about 485 to 490 million light-years away, in reasonable agreement with a single redshift-independent distance estimate of about 465 million light-years (which, as shown below, is probably very close to their actual distance). However, for objects at such distances we should take into account the expansion of the Universe during the time it took their light to reach us. Doing that shows that the pair was about 465 to 470 million light-years away at the time the light by which we see it was emitted, just over 475 million years ago (the difference between the two numbers being due to the expansion of the intervening space during the light-travel time). Given that and its apparent size of about 1.05 by 1.05 arcmin (from the images below), PGC 46461 is about 140 to 145 thousand light-years across.

Physical Information: Based on the discussion in the entry for PGC 46461, the pair of interacting galaxies must have been about 465 to 470 million light-years away at the time the light by which we see it was emitted, just over 475 million years ago (the difference between the two numbers being due to the expansion of the intervening space during the light-travel time). Given that and its apparent size of 1.45 by 0.45 arcmin (from the images above), PGC 46464 is about 195 to 200 thousand light-years across, counting the extended dust lanes silhouetted against its elliptical companion.