# What is the average mass of galaxies according to Hubble Deep and Ultra Deep field observations?

It is very widely known among people interested in astronomy that there are 100-400 billion stars in the Milky Way galaxy and there are ~ 100 billion galaxies in the observable universe, which is usually calculated as $10^{22}$ stars in the observable universe. I have also seen estimates an order or even two orders of magnitude higher than this.

What I am thinking here is why it is assumed that the Milky Way is the average galaxy ? One way to check whether or not the Milky Way is an average galaxy in mass and so in stellar mass is to check the results of the Hubble deep and ultra deep field images. While searching for information, I came across this page, which I somehow doubt its source of information, and it states: "Within the Hubble Ultra Deep Field there are approximately 10,000 discrete objects. Most of these objects are very small and likely have masses in the range of $10^5$ to $10^7$ solar masses. Note the mass of the Milky Way galaxy is $10^{12}$ solar masses."

So if "most" of the 10,000 galaxies seen in the Hubble ultra deep field image are that small in mass, then it is completely incorrect to consider the Milky Way an average mass galaxy. It is also clear from this diagram that the Hubble deep field extends to the "Normal Galaxies", while the Ultra deep field extends to the "First Galaxies". So it is expected to observe many small irregular and dwarf galaxies in the HUDF. As far as I understand, these small galaxies merge to form more massive spiral and elliptical galaxies that we see today. So again, if we are observing 10,000 small galaxies that should merge to form normal galaxies, we shouldn't be thinking that the image contains 10,000 galaxies similar to the Milky Way.

So, am I correct that the Milky Way is not an average mass galaxy in the observable universe and that we should use a smaller number when referring to the number of stars in the universe ?

• Who thinks the Milky Way is an average galaxy? It isn't. – Rob Jeffries Dec 17 '14 at 23:13
• Might want to read Phil Plait and Emily Lackdalwalla's blogs. – Carl Witthoft Dec 17 '14 at 23:16

I think the following image, which comes from Tomczak et al. (2014) and the so-called ZFOURGE/CANDELS galaxy survey should do the trick.

It shows how the galaxy stellar mass function (i.e. the number of galaxies per unit mass per cubic megaparsec that have a certain stellar mass) evolves as a function of redshift. As you might imagine this is not just a case of counting galaxies and estimating their masses - you have to account for the fact that it is harder to see low-mass galaxies.

Anyway, these are their results and they clearly show that a galaxy like the Milky Way that has about 200 billion stars and a stellar mass of about $5\times10^{10}M_{\odot}$ (note that the total mass of the Milky Way is dominated by dark matter), is quite a massive galaxy (note the logarithmic y-axis).

In other words, small galaxies dominate the statistics. However, when you look at the Hubble Deep or Ultradeep fields, it is quite difficult to use this information. You will always tend to see the most luminous and most massive galaxies and the low-mass galaxies will not be represented as shown in the mass functions shown in this picture. So there are actually two separate things here, and I'm not sure I can definitively answer either. (i) What is the average mass of a galaxy; (ii) what is the average mass of a galaxy seen in the Hubble Deep fields?

The answer to (ii) will obviously be much bigger than the answer to (i). Fortunately you can see from the plot that the straight(ish) line section below about the mass of the Milky Way are a power laws with slope $\sim -0.5$. That means that $M\Phi(M) \propto M^{+0.5}$ and when you integrate this over some range, it is the upper limit that dominates. So low-mass galaxies, do not dominate the stellar mass. In fact, it is galaxies about the size of the Milky Way that dominate the stellar mass. Galaxies with $M>10^{11}M_{\odot}$ (in stars) become increasingly rare, so these do not contribute so much. Therefore, very roughly, the number of stars in the Universe will be given by the number of galaxies with mass within a factor of a few of the Milky Way multiplied by the number of stars in the Milky Way.

I cannot provide an answer for the average mass for a galaxy in the UDF or any other survey volume because it is unclear how many of the lowest mass objects there are or what lower mass cut-off to work with. The plots shown for the CANDELS field below will be perfectly representative of the UDF or any other deep observation, the cosmic variance should not be an issue for order of magnitude estimates. EDIT: As an example, let's take the average space density of $5\times 10^{10}M_{\odot}$ galaxies to be $10^{-2.5}$ per dex per Mpc$^{3}$ in the low redshift universe and assume galaxies over a 1 order of magnitude (1 dex) range of mass contribute almost all the stellar mass. If the observable universe if 46 billion light years ($\sim 15,000$ Mpc - see Size of the Observable Universe) and the average star is $0.25M_{\odot}$; there are: $$N_* = 10^{-2.5} \times 5\times10^{10} \times \frac{4\pi}{3} \times (15000)^3/0.25 \simeq 10^{22}$$ stars in the observable universe.

• Great, that's exactly what I am looking for. But honestly I seem to be unable to read the plots so I hope you can help me with this. There are two things that should answer my question. 1) If there is a certain number of galaxies at redshifts < 3, what is the percentage of this number that should be in galaxies with stellar masses > $5\times10^{9}$ Solar masses ? 2) Is there a way to find the number of galaxies in the HUDF image with redshifts less than 3 ? – Abanob Ebrahim Dec 18 '14 at 0:35
• @AbanobEbrahim Your (1) could be quite difficult. Where do you make the low-end cutoff? For a warmup, how many satellite galaxies orbit the Milky Way? This number was revised not long ago, and is still debated. And what is a galaxy anyway? Do you count globular clusters? – user10851 Dec 18 '14 at 4:37
• @AbanobEbrahim You need to convert the differential frequency distributions to cumulative frequencies by integrating the mass functions. As Chris says, difficult unless you define a lower mass limit. Second point: you need to find papers on the UDF that do this - I'm sure you will find some. – Rob Jeffries Dec 18 '14 at 7:33
• Let me try to make this a easier. Are there any examples for stellar masses of ANY galaxies in observed in the UDF ? I just need a general idea about how the stellar masses change with increasing redshifts. – Abanob Ebrahim Dec 18 '14 at 20:49
• Why would you think the UDF is different to the CANDELS fields? The redshift distribution might be different, but the mass function at a given redshift will be the same. – Rob Jeffries Dec 18 '14 at 21:21