Regular readers of my Blog will know that I come more from the data analysis side of astronomy than the pretty pictures side.  So this month just for a change, we’ll have some wonderful images as well as data. So, let’s start off with … a pretty picture!

In fact, Figure 1 is far from being  ‘just a pretty picture’ – this stunning image shows two galaxies, NGC2788 and NGC2789 which are in collision. 
How do we know these galaxies are interacting and that what we are seeing is not just a trick of perspective?  If we look at the NASA Extragalactic database, we see the data in Table 1:

 The first thing we can see is that both galaxies should be visible in modest sized amateur telescopes.  The two galaxies have similar magnitudes, as shown above, although remember that each order of magnitude decreases brightness by approximately 2.5. 
 The fact that NGC2798 and NGC2799 are close together is revealed by two parameters: their redshifts are similar within two parts in 10,000. And their Hubble distances with respect to the Cosmic Microwave Background (CMB) are approximately only 2.78% different.
 
Will stars collide? 
The NASA/ESA press release that accompanied this picture states  “While one might think the merger of two galaxies would be catastrophic for the stellar systems within, the sheer amount of space between stars means that stellar collisions are unlikely”.  How can that be established?
As a first approximation, we can model a spiral galaxy such as our Milky Way (MW) as a disk where the radius of the disk, is about 50,000 light-years or 15.33 kpc  and the thickness of the disk is about 0.5kpc. The number of stars in the MW is estimated to be N ~ 10¹¹
We are now interested in parameter called the number density of stars - simply, the number of stars divided by the volume of the disk.
However, we can’t work out the volume of the disk simply by calculating the volume of an equivalent cylinder.  In reality, the disk of a spiral galaxy is not homogenous – it has been known since the’60s that the spiral arms are density waves (Lin & Shu, 1964).  Let's assume 70% of stars are in the spiral arms; there are no stars in the voids between the arms; and that the arms make up 50% of disk.  These are of course gross assumptions, good only as a first approximation.  The results (calculations are available in Excel® if you are interested) are shown in Table 2 below:

In the ‘Single galaxy’ column the number density of stars is less than one star per cubic parsec; expressed differently: in one cubic parsec of space, there is on average less than one star.  In fact, on average we’d need to search 2.63 cubic parsecs of space to find a single star.
In the ‘Two similar colliding galaxies’ column, we imagine two spiral galaxies colliding head on.  Here, the number density is doubled as the spiral arms collide.  Correspondingly, the volume of space on average we expect to encounter a star is still 1.31 one cubic parsecs. 
Let’s just remind ourselves how large a volume of space a cubic parsec is.  Imagine a cube of space one parsec on each side.  That’s 3.26 light-years on each side or, if you prefer,  3.1*1013 km on each side.

Even a very large star such as the red supergiant Betelgeuse is a very small object in all that space, so even in a galactic collision, as the NASA press release says, the chances of two stars colliding is very small.

How common are galaxy collisions? 
The answer is – not uncommon.  The next two images show some well-known examples.

The image in Figure 3 shows the distorted disk of NGC4631.  This is caused by NGC4631’s interaction with two much smaller galaxies, NGC 4627 and NGC 4656.

The plot in Figure 4 shows the results of radio emissions of NGC4361 reported in Neininger & Dumke (1999).  The small dark object above the disk of NGC4631 is the dwarf elliptical galaxy NGC 4627 with which NGC4631 is interacting.

Another source of data about colliding galaxies is Galaxy Zoo, a project that enables citizen scientists to categorise and analyse images of galaxies taken by professional observatories.  One of Galaxy Zoo’s initiatives is the Galaxy Merger project (Holinchech 2016).  The data collection phase is now complete and comprises 62 colliding galaxy pairs (I have this data as an Excel table for anyone interested).
 
A good example from the Galaxy Zoo merger table Is ARP148 in Ursa Major (Galaxy Zoo mergers table ID49).   This is also called Mayall’s Object, named after American astronomer Nicholas U. Mayall (not John Mayall), who discovered the object in 1940.

Can it happen here? 
There is a short answer: ‘Yes’.  For example, the Sagittarius Dwarf galaxy has been involved  in multiple collisions with our Milky Way galaxy and this is the probable reason for the warped nature of the Milky Way’s disk (Law & Majewski, 2010).
A recent determination of the radial velocity of the Andromeda galaxy, M31 with respect to the Milky Way indicates a velocity of −109.3 ± 4.4 kms per second, the negative sign indicating M31 is moving towards the Milky Way.  The same research indicates a low transverse velocity of 17 km per second, indicating the probability of a head-on collision between the two galaxies (van der Marel, 2012)

The end result of this collision will be a very massive elliptical galaxy.
 
 
Acknowledgements 
This Blog is not a scientific paper, although it lists various scientific papers as sources in the References section.  I am indebted to Hugh Allen for drawing my attention to the paper by Neininger & Dumke  (1999).
Data used in Table 1 was obtained from the NASA Extragalactic Database.  The NASA/IPAC Extragalactic Database (NED) is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

References 
Holincheck et al (2016).
Galaxy Zoo: Mergers – Dynamical models of interacting galaxies. 
MNRAS459,720–745 (2016). doi:10.1093/mnras/stw649
 
Law, D;  Majewski, S (2010). The Sagittarius dwarf galaxy: a model for evolution in a triaxial Milky Way halo.
2010 ApJ 714 1.  DOI: 10.1088/0004-637X/714/1/229
 
Lin, C & Shu, F (1964).
 On the Spiral Structure of Disk Galaxies.  ApJ, vol. 140, p.646 .  DOI: 10.1086/147955 
 
Neininger, N; Dumke, M  (1999). Intergalactic cold dust in the NGC 4631 group.
DOI: 10.1073/pnas.96.10.5360
 
van der Marel, R et al (2012). The M31 Velocity Vector.II. Radial Orbit Towards the Milky Way and Implied Local Group Mass.
ApJ, 753:8 (14pp), 2012 July 1.  DOI: 10.1088/0004-637X/753/1/8   https://iopscience.iop.org/article/10.1088/0004-637X/753/1/8/pdf