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Astronomical spectroscopy can be used to determine the chemical composition of far away bodies. In the related question Can we detect atmosphere on exoplanets? we learned that even now we are studying exoplanet atmospheres.

We know that currently the atmosphere of Earth is about 21% Oxygen and about .035% Carbon Dioxide. As I understand it Earths early atmosphere had a much higher level of Carbon Dioxide created by volcanic activity.

What level of oxygen (O2 or O3) can be explained by tectonic or chemical actions, what level could only be achieved by some kind of life?

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I would argue that no specific level of molecular or atomic oxygen in atmosphere is indicative of carbon-based life (i.e. life as we know it on Earth). A planet could have oxygen rich atmosphere which could be due to naturally occurring thermo-chemical reactions (e.g. Sabatier/Bosch reaction), loss of hydrogen in water vapor through atmospheric escape and managing to hold onto the heavier oxygen, even by thermal / magmatic release of oxygen in oxide minerals.

On the other hand, we also know of anaerobic organisms, some of which (obligate anaerobes) don't tolerate oxygen rich environment and are essentially killed by its presence in notable concentrations. So we have both control ends with a non-indicative correlation; carbon-based life could exist even without molecular or atomic oxygen present in the environment and life forms develop that don't utilize it directly in their metabolism, and don't release it as a metabolic byproduct, and at the same time high concentrations of atmospheric oxygen could be due to other, inorganic causes.

More interesting than measuring atmospheric composition and amount of oxygen in it on average might however be measuring changes in atmospheric composition during planet's diurnal cycles, seasonal changes, and otherwise finding that it potentially has a role in metabolism of carbon-based life. Other metabolic byproducts might potentially be more indicative of activity of life, such as trace amounts of methane that could originate via methanogenesis that change in concentration as the environment changes daily or seasonally. Periodically changing ratio of other atmospheric gases, even in trace amounts and the changes can't be explained by inorganic processes, could also be more indicative of life than the presence of oxygen itself.

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The linked Wikipedia pages confirm that it isn't realistic to assume that Sabatier/Bosch could produce free oxygen in a planetary atmosphere: it's quite hard to do so in a controlled, engineered micro-environment. The basic problem remains: if there's free oxygen on a planet, then where's the carbon? –  MSalters May 2 at 11:43
    
@MSalters Don't take Wikipedia articles for granted, they can quite frequently be self-contradicting from one article to another. E.g. regarding Sabatier / Bosch reactions in particular, the article on Terraforming of Venus suggests introduction of hydrogen into its atmosphere. Now, if that hydrogen came from water, say icy asteroids and comets, the whole reaction releases plenty of oxygen. You'd just need a bit higher temperatures / more energy to make it work, say explosive evaporation on impact should do it. ;) –  TildalWave May 7 at 3:32
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The first third of Earth's own existence had neglible atmospheric oxygen. (Simple) life existed during a few hundred million years of this period. Thus, atmospheric oxygen does not correlate with life on a planet.

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+1 valid point, but while I grant you can have life without atmospheric oxygen, the question is "can you have a level of atmospheric oxygen without life". –  James Jenkins May 1 at 10:34
    
Some kinds of life existing in absense of oxygen does not mean there's no correlation. That's only true is just as many oxygen-less planets as oxygen-rich planets have life. For all the planets of which we currently know the atmospheric composition, oxygen correlates very strongly with life, even if we know that exceptions are possible. –  mcv May 1 at 11:26
    
Veering into philosophy: we don't know the absence/presence of life on planets other than Earth. Even robot-infested Mars hasn't been declared lifeless. (I know which way I'd bet my money, though.) –  Camille Goudeseune May 1 at 16:50
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As @TidalWave said, no specific level of oxygen is by itself sufficient to potentially indicate life. However, based on this article, what astronomers are looking for is the combination of both oxygen and methane in a single atmosphere.

Both oxygen and methane can be created independently by nonliving processes, so their individual presence is of little interest. What scientists are looking for is both of them in the atmosphere of a single body. If these reactive gases are not constantly replenished by living things, they will react with each other, creating carbon dioxide and water. As a result, we should not observe them in the same atmosphere without a large, living source.

The article itself is about a study which suggests that we can be fooled by detecting both signatures from an exoplanet with an exomoon with opposite atmospheres (i.e. one is O2, the other is CH4), and is quite interesting.

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Oxygen is a highly reactive element. Gaseous oxygen rapidly combines with other elements. If there's any large amount of free oxygen in the atmosphere, after any significant amount of geological time, it's reasonable to assume that there is some process continuously releasing it to make up for what's being lost in oxidation.

On our planet, that process is photosynthesis done by living plants.

That doesn't mean no other mechanism is possible, but it does suggest that SOMETHING unusual and interesting is going on which is driving a reaction backward against its natural flow.

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Oxygen is about 1% of the universe's mass. So that suggests that looking at any random sample of mass throughout the universe you would expect to see 1% oxygen. Now of course you wouldn't be surprised to see higher concentrations and lower concentrations in any given sample, but the larger your sample size the more likely it is that the value will approach 1%.

The atmosphere of a rocky planet like Earth is a tiny fraction of the planets mass (8.6134×10^-5% for Earth). However if we assume that oxygen content in the core and on the surface of a rocky planet without life is similar we can easily assume that any given lifeless planet should have around 1% oxygen in the atmosphere.

Now finding out the variance or standard deviation of oxygen in planetary atmosphere is a problem. I've found this paper that seems to be based on data for a large number of exoplanets, the problem is the data isn't shared, just the results. In Table 1 of that paper data is shown for three different types of exoplanet. We could calculate the variance based on this but variance from 3 data points isn't very accurate.

It comes down to two aspects in my eyes. First can you attribute the oxygen content to another source? Second is the oxygen content high enough to suggest life. It will never be a guarantee from this type of observation, so you really need to know how confident you want to be. Once you know you're confidence level you could calculate your confidence interval based on standard deviation of exoplanets oxygen content. However even this is dependent on how likely you think exoplanets are to support life, if it's very unlikely then you can be more confident if you have just a few similar oxygen content observations; if it's very likely then you would expect the majority of observations to have a high oxygen content.

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It's not explicitly stated in the question, but I suspect the question is about signatures that explicitly indicate the presence of O2 or O3 rather than (for example) carbon dioxide. –  David Hammen Apr 30 at 20:22
    
@DavidHammen: Agreed. Within the Solar System, Venus and Mars have plenty of oxygen in the form of CO2, but only Earth has significant amounts of O2 in its atmosphere. Titan's atmosphere has only trace amounts of oxygen-containing compounds; I think most of the oxygen combined with the excess hydrogen to form water, which at that temperature is effectively a mineral. –  Keith Thompson Apr 30 at 21:39
    
@DavidHammen, you are correct. –  James Jenkins May 1 at 11:45
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