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When the weather is clear, we can look at the stars. And we normally would see several thousands of them, they all being more than a $\textrm{pc}$ away from us.

Now, there are globular clusters, which consist of some $10^5$ stars concentrated is a few $\textrm{pc}$ area. From oustside they look like this:

A globular cluster

Now, how do they (and the whole sky) look from inside? Imagine that solar system is inside such a cluster. Would it be a big change? Would there be a significant difference between night and day? Would it be easier or harder to study astronomy there?

P.S. The credits for the question go to Ross Church.

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I'm not sure, but I would think that there is no stable habitable zone within a globular cluster (GC), except perhaps in its outer parts. The stellar density is so high that Solar-system-like objects will be destroyed/destablised by stellar encounters. Hence life as we know it may never form there. Moreover, the fraction $Z$ of non-primordial elements ("metals" in astronomy slang) is very low, at least in the old GCs of the Milky Way. Low $Z$ stars are much less likely to host planets. Thus, there may be nobody so observe the GC night sky. –  Walter Dec 25 '13 at 13:51
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Dear @Walter, yes, this is correct. Solar system would not be stable for more than some $10^3$ years and would not even have formed there. However, I am still curious to know, how would the sky look like if one managed to take the Sun and the Earth and put them into such a cluster. –  Alexey Bobrick Dec 25 '13 at 14:05
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The Asimov story Nightfall describes this very situation. –  dotancohen Dec 27 '13 at 9:05
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Globular clusters occupy an interesting place in the spectrum of composite stellar systems. As you point out, they are highly concentrated populations of stars, and seem to lack any dark matter component, unlike more massive dwarf galaxies.

Binary interactions become very important in simulating globular clusters, and interestingly enough (maybe unsurprisingly), the one example of a discovery of a planet found in a globular cluster has been around a binary star system (see: PSR B1620-26 b; this circumbinary planet was found orbiting a pulsar and a white dwarf.). This is not to say there are not other examples, however, this was the easiest for me to come across. I would be interested to know how common this situation is, and in addition, how stable it is given the potentially highly chaotic environment it lives in. These speculations don't answer your question, but I thought it interesting enough to bring up as evidence in favor of your question not being an unreasonable one to ask.

From the wiki page:

Globular clusters can contain a high density of stars; on average about 0.4 stars per cubic parsec, increasing to 100 or 1000 stars per cubic parsec in the core of the cluster.[26] The typical distance between stars in a globular cluster is about 1 light year,[27] but at its core, the separation is comparable to the size of the Solar System (100 to 1000 times closer than stars near the Solar System).[28]

This seems to indicate to me that location within the globular cluster would matter quite a bit. If at the core the average distance between stars is about three thousand times closer than our nearest neighbor is to our sun (my estimate to give some perspective: a few lightyears to Proxima Centauri divided by 100 is about 3000AU (about 100 times further than Pluto from the sun)), then stable orbits may be shifted inward, or simply may not exist due to two-body interactions.

However, if life were to exist (an assumption we're going to make for the purposes of your question), one would see a very different night sky. According to this paper, the number density profile of stars within the globular cluster M92 follows a Wilson Profile fairly well, which has the form:

$$ f_{W} = A\{ e^{-aE} - e^{-aE_{0}} [1 - a(E-E_{0}) ] \} $$ where $E \le E_{0}$. E is the specific energy of the star:

$$ E = v^{2}/2 + \Phi(r) $$

and where $\Phi(r)$ is the mean-field gravitational potential, determined from the Poisson equation. For each family of models, the constants A, $E_{0}$, and a in the above distribution function define two dimensional scales (a typical radius and a typical mass or velocity) and one dimensionless parameter, the central depth of the potential well (related to the concentration parameter) (all of the information is taken from the paper I've linked).

It seems to be the case that globular clusters are not "simple stellar populations", in that they are usually made of multiple generations (sources: 1,2). However, globular clusters generally consist of population II stars and are older stellar systems when compared to other star clusters. I bring all of this up because in addition to the number density of stars, the stellar distribution of stellar types would certainly be an important factor in how the night sky would look. If you lived a thousandth of a lightyear from a blue supergiant, you could imagine that that would make a huge difference in what you would see on a day to day basis. At the same distance, a supergiant star is on the order of $10^{5}$ times the luminosity of our sun (and therefore is $10^{5}$ the flux, since $L \propto f$ holding $D_{L}$ constant). At the same distance as our sun, the magnitude of a star with $10^{5}$ times the flux would have an apparent magnitude of about -38 (I used Rigel as my test case; this produces a star in our sky which is 12 magnitudes brighter than our sun). Moving this to the average distance between stars at the center of a globular cluster we would get an apparent magnitude of:

  • $M = -6.43 $ from $m=-38$ at distance of $d=1$AU.
  • $m=-26.43$ from $M=-6.43$ at a distance of $d = .00326 ly$ (the new average distance between stars at the center of a globular cluster)

In other words, a blue supergiant at an average distance between stars within a globular cluster would appear to be as bright as our sun is to us! This is absolutely crazy. Depending on where it is in relation to the sun, it could effective cause two days, or potentially one day which is greater than half the time it takes your planet to rotate once. I would image that this would certainly interfere with observing in optical (and shorter wavelengths).

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Great answer, thank you very much! I think you can easily expand it a bit to make it complete. I am not sure if supergiants are important in cluster cores. In any case, I don't think they dominate in total luminosity. A relevant one-liner here would be just to get the total flux from all the stars within half-mass radius as seen from the core and compare it to that of the Sun. Then one other small thing, which seems confusing is the usage of $m$ and $M$, former is typically used for apparent and latter for absolute magnitudes. Thank you very much again, it was very interesting and informative! –  Alexey Bobrick Dec 26 '13 at 19:01
    
Sure - supergiants are probably not the most common stellar type, but I wanted to point out that there could potentially be a drastic change in what you might see at the core of a globular cluster. I am also using M for absolute magnitude and m for apparent magnitude. I just presented it in reverse order. Also, I couldn't find values of A, $E_{0}$, and a for a typical globular cluster, though I will look for them. Once I do find them I can do exactly as you say - finish off the calculation regarding how many stars and of what types within some volume from the test observer's point of view. –  astromax Dec 26 '13 at 20:21
    
I guess, it would be "hard" to do, because you will need then to get the grav.potential, which you don't yet know. At least, it wouldn't be a one-liner. A simpler approach would be to take a gaussian cluster (in velocities and positions), or take an isothermal model. In any case you will find that the relevant flux will be coming from a sunlike star located at $R_{core}/N_{*,core}^{1/3}$. –  Alexey Bobrick Dec 26 '13 at 21:00
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Just as a sidenote, another interesting question would be whether anything would change if the cluster were or were not core-collapsed. Also, you are right, stars leaving post-MS would make a difference now and then, when viewed from within the cluster. –  Alexey Bobrick Dec 26 '13 at 21:02
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In a typical position in a globular cluster (maybe halfway between center and edge), there'd be many more bright stars in the sky due to the star density. These would be distributed unevenly in the sky, with more light coming from the center of the globular cluster.

Depending on the globular cluster's orbit, we might be able to see the Milky Way face-on. This would be beautiful and would take up a large fraction of the sky. However, it wouldn't be particularly bright--the apparent magnitude would be $\approx -3$, the brightness of Jupiter.

If our alien eyes were good at discerning wavelengths, the sky would seem redder. Globular clusters have many old stars (more red), and very few massive stars (fewer blue) since they are not sites of active star formation.

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Let us assume the data for a globular cluster to be equivalent to that of M13.

Given 300,000 stars and a radius of 1 ly, let us assume uniform density.

Another assumption is to consider all stars to be Sun-like.

The number density can be calculated as $$\rho = \frac{300000*3}{4\pi(1\ ly)^3} \approx 9 \times10^{-44}\ m^{-3} $$

Now, using the formula for mean free path $$\lambda = \frac{1}{\sqrt{2}\pi D^2 \rho}$$, and using $D = 14 \times 10^{8}\ m$, we have $$\lambda \approx 10^{24}\ m \equiv 10^{8}\ ly$$.

Now you don't have to be a genius to see how the sky will look if the nearest stars to you are this far. It will be almost like our own sky but just a lot of stars in every direction. There will be no special hike in flux received.

The number density is much higher at the centre. But even if you assume the density at centre to be orders higher than the average value, the uninteresting view exists! As Zack pointed out, we'll have a lot of long wavelength light due to abundance of old stars.

It is mentioned that the optical view won't be too attractive, but there is a certain thrill in being at the centre of a globular cluster. It is very difficult to stay there for a long time avoiding collisions or surviving the radiation and stellar winds from collisions and novae which are frequent for globular cluster.

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Many thanks! As a comment, I don't see why would mean free path estimate would be relevant here. Perhaps you mention it for estimating the maximum possible lifetime of a planetary system. But then you need to account for gravitational attraction, which will decrease $\lambda$ significantly. Then also, the average distance between the stars will be in fact of order $pc/N^{1/3}\approx 10^{-2} pc$, which is a few thousands of AU, which is not too much, but not too little, given that you have quite many stars here. –  Alexey Bobrick Dec 26 '13 at 14:35
    
No, I use it as a rough estimation of the order of mean distance between any two stars in the globular cluster. –  Cheeku Dec 26 '13 at 14:38
    
but then it gets really brainexploding: if the cluster is a parsec in size, how can you imagine the stars been separated by $10^8$ parsec in it? –  Alexey Bobrick Dec 26 '13 at 14:48
    
Yes, this particular estimate is highly dependent on number density which I have assumed to be uniform. I searched through lots of articles and have lengthy calculations on my notebook but then you needed an idea of how it would "look" so... –  Cheeku Dec 26 '13 at 15:05
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@AlexeyBobrick Now, I see. I got something to learn from my own answer. Good! –  Cheeku Dec 26 '13 at 23:47
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