Merging Stars, Star Formation, and Planetary Nebulae

I was reading the latest issue of Sky and Telescope this week and came across an article by Monica Young talking about the formation of massive stars (here a link to the highlights, you’ll need an account to actually read it). The gist of the article is that forming massive stars is difficult – as mass accumulates and nuclear reactions begin, the radiation pressure from the young (not yet massive) star will tend to blow material away, halting the growth. This happens around 10 solar masses, so it’s a bit mysterious how we end up with more massive stars then that (and we do – although they are rare, Type O stars are over 15 solar masses, and the most massive stars are over 25). The article covers a few modern approaches, mostly which involve particular dynamics by which material is accumulated in a different physical location then the photon flux from the new star. But, it was also mentioned that some massive stars are simply caused by merging younger stars, which was the topic of my master’s thesis! Since I’ve never written about it here (and it’s only been published at the academic library), I thought I would give a quick overview on the cute idea and nice results we worked out (“we” being myself and my adviser at the time, Robin Ciardullo).

The problem we were tackling had to do with the Planetary Nebula Luminosity Function (PNLF – there is even a Wikipedia page about this now!). As medium-sized and smaller (under 10 solar masses or so) stars reach the end of their life, they turn into really pretty objects called Planetary Nebula (PNe, and here are some cool Hubble pics). Massive stars a) evolve faster and b) make brighter PNe then their less massive siblings, so over time less and less bright PNe should be produced by any given population of stars. Further, the luminosity from a PNe is primarily due to excitation from the central white dwarf, which also dims over time. Therefore, PNe in a single population of stars should be generally getting less luminous over time. Problem is, that is not observed, at all!

The Brightest PNes in a population are the same luminosity, regardless of the age of the population.

The Brightest PNes in a population are the same luminosity, regardless of the age of the population.

The figure above comes from Ciardullo (2006), and demonstrates the problem – all the brightest PNe have the same absolute magnitude, regardless of the age of the stellar population (which goes old to young from top to bottom). This allows you to use PNe as a secondary method to find astronomical distances, but it also shows that there is something fundamentally incorrect with the nice picture of stellar evolution I’ve presented above. The idea explored in my thesis was that as the population aged, stellar mergers produced a ready supply of massive blue stars (called “Blue Stragglers”) which would form the brightest PNe. The advantage of a model like this is that it does not require a significant amount of detailed physics, such as the effects of stellar rotation, wind, or other micro-astrophysics. It is simply a population synthesis approach – we essentially created stellar populations, used standard stellar evolutionary models, but included a small fraction of stars (around 10%) which merged to form more massive stars.

First, let’s take a look at the “standard picture”, with no Blue Stragglers:

Simulated PNLFs with no merging stars.

Simulated PNLFs with no merging stars.

The ages of the stellar populations are shown in the upper lefthand corner (1-10 Gyr). It clearly displays the effect I talked about – the brightest PNe fade over time as the population ages.

Now let’s take a look at our basic model, including 10% blue stragglers into a population of several different ages:

The PNLF single burst models with 10% blue straggler fraction.

The PNLF single burst models with 10% blue straggler fraction.

As we expected, the brightest PNe held pretty constant for a variety of stellar population ages (1-10 Gyr, shown in the upper corner, with the 1 Gyr being a bit of an outlier). The absolute magnitude ended up being a little high, and the initial shape was more shallow then the observations, but it was clear that the blue stragglers were able to keep the maximum luminosity of the PNLF relatively constant over a wide range in population ages.

It’s worth noting that the two populations of blue stragglers which we are discussing here are actually disjoint. Since PNe form from stars under 10 solar masses, the usual formation scenarios have no trouble making them. It’s only for the stars over 10 solar masses that the merging scenario is invoked for a creation mechanism. On the other hand, both of these merger scenarios are based on stars which form in binary systems, and then merge at a later time. So although the end masses are different the formation mechanism from a blue straggler point of view is the same. It would be interesting to see if one could reproduce the required blue straggler fraction by using the initial binary population. Using both the PNLF and mass star formation considerations, one might be able to check this over the entire mass range of the initial mass function of binaries. Not something I can see spending time on at the moment, but an interesting question which even might make a nice undergraduate project!

If you are interesting in reading the whole thesis, you can check it out here. What I’ve talked about above the only half the story – there is also the “dip” found in some PNLFs (but not M31, for instance), which the model tried to address as well.


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