Amount of Information of a Galaxy? Just like the title suggests, how much data/information does a galaxy have in (bits)? Like the Milky Way galaxy for example?
For example, this is based on the Bekenstein Limit formula where mass can give an approximate amount of information within a given space.
 A: It depends. 
None of the  numbers below should be taken too seriously. 
The Bekenstein bound gives an upper bound on how much information could be inside a galaxy-sized object without it imploding. If we assume the galaxy has mass $10^{12}M_\odot$ and has radius 30 kpc, I get $4.7449\times 10^{106}$ bits. 
The actual amount of information stored is another matter. Largely because it depends on what we mean with information. One way to define it is as the logarithm of the number of ways microstates could make up the galactic macrostate, that is, the total entropy of the galaxy. This gets contributions from black holes and gas (a lot), much less from the stars, and a small part from things like planets. It seems likely that most entropy resides in supermassive black holes: if we assume nearly all entropy is in the central black hole Sag A* I get $3.2146\times 10^{68}$ bits - but this is rather different from how we normally think of information!
A more everyday form of information can be estimated like this: atoms in solid molecular matter can store information (by which isotope or element they are, how they are bound etc.) at about 1 bit per atom. Condensed matter in neutron stars and white dwarfs may also count. Looking at the contents of the universe, maybe there is about 20% such matter per main sequence star mass. So in the milky way, if we assume all of this mass is carbon (this will be very much an order of magnitude guesstimate), we get $0.2(300\cdot 10^9 M_\odot) (N_A / 0.012) = 5.9893\times 10^{66}$ potential bits. If we more conservatively leave out the neutron stars and white dwarfs we get $5.0909\times 10^{64}$ bits. Assume a lower atomic weight and it goes up, at most a factor of 10.
Another approach would be to see how many bits are needed to describe all the matter in the galaxy. If we assume it needs to have Planck-length precision in position we need 186 bits per particle and dimension (log2 of the width of the galaxy divided by the Planck length), use the same number of bits for momentum, and (say) 10 bits for other quantum numbers we have 1126 bits per particle. This is likely an overestimate (especially since the uncertainty relations add a cell size of volume $\hbar^6$ in phase space). If we guess that there are $(300\cdot 10^9 M_\odot)(2/m_p)=7.1353\cdot 10^{68}$ particles (that is, 300 billion star masses mostly composed of protons and an equal number of electrons), we get $8.0343\cdot 10^{71}$ bits. For each baryon there is also $10^9$ to $10^{10}$ photons, so the actual number could be 9 or 10 orders of magnitude larger. Of course, we have ignored dark matter completely here. Still, it is worth noticing that it is not even close to the Bekenstein bound. 
In the end, how much information there is depends on what counts as information ("a difference that makes a difference"). Should we count the photons between the stars that are transmitting visual information? What about data compression - maybe only unique information counts? What about meaningful information? A system like a galaxy can represent many different things by being in different configurations, but much hinges on what should be represented.
