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Evolution of Supermassive Population III Stars

Taylor Varilly

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Table of Contents

The fates of massive stars

Black hole formation

Population III

Pair-instability supernova

New findings

Simulations of supermassive metal-free stars

What are the applications?

The search for primordial stars

Sources and questions

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Stellar black holes

Usually over 5 M☉

TOV limit for neutron degenerate matter

Triggered by lack of fuel or by addition of matter
Supermassive stars spawn supermassive black holes

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Population-III

Entirely composed of primordial gasses

[Z/H] ~ -10

“First generation” stars
At least 30 M☉
None observed: extinct

Lifetime ~ 10^6 years

3 really rough categories of stellar classifications:

population 1 are metal rich

population 2 are comparatively more metal poor- the metallicities of these still far exceeds the metallicities of the gas left over from the big bang

Pop-III on the other hand are made entirely of hydrogen and helium with tiny amounts of lithium-7: essentially metal free: at most [Fe/H] ~ -2.5

This makes these stars first generation, or the first population of stars to emerge after the big bang: would have emerged about 1-10 million years after the big bang

These then would go on to fuse the metals seen in many population II stars and would have provided the first ionizing radiation in the universe

These stars would have been extremely massive and also likely quite isolated

Actually entirely hypothetical. None have been directly observed, which makes sense because most would have been quite massive and would have had relatively short lifetimes. However, it’s a bit of a mystery because theoretically, the very least massive of these should still be visible

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Population III mass limits

How were these stars supported by radiation pressure?
Upper mass limits

H2 is possibly the main coolant
Jeans Instability

Consensus on mass divided

It is thought that molecular hydrogen cooling may have been occuring in the centers of population iii stars. We know this because a star needs to “cool” in order to condense and form, which you normally need heavier elements to do- because gravity

Obviously the matter heats up again as it gets pulled together, so for a stable star, you need radiation pressure to balance the internal pressure

When a heavier element releases a photon in a star like the sun, it’s more likely to be absorbed by an element similar in energy to the one that released it. So if a heavy element emits a photon in the center of the star, it isn’t very likely to get absorbed by the hydrogen or helium in the outskirts. However, these population iii stars don’t have heavier elements, so you’re going to have

hydrogen atoms releasing photons and then other hydrogen atoms quickly reabsorbing them after very short mean free paths

This isn’t a very efficient cooling method, so by this logic we should have had really large large massive stars that don’t condense very much because they would become far too hot

However, it was found that there may be cooling in the center of the star by molecular hydrogen: the cooling theoretically puts a constraint on the mass. Which is good because jeans Instability, which you may be familiar with tells you the point at which the molecular gas cloud collapses into a star: (depends on jeans length, which depends on temperature) also analagous to the TOV limit which was mentioned before. With a really hot star that doesn’t have an efficient cooling method, the jeans mass is going to be huge (10^5M). But the upper mass limit would be constrained to about 2 times their jeans mass if hydrogen cooling were occuring.

lambda = sqrt(15kbT/4pi mu rho)

R=½ lambda

M=4/3pi rho R^3

Although theoretically we may now have a more constrained mass, which means all the population iii that are any greater than 1000 solar masses are going to very quickly collapse and form black holes, there is still a huge lack of agreement on the actual range of masses for these. The interstellar medium would have been warmer back then and there was a lack of heavy elements, so it would have been much easier to form stars with a greater total mass. Computer simulations show that they would have typically been on the order of several hundred solar masses. But looking at population ii stars, the concentrations of heavy metals indicate that they may have been smaller, like on the order of 20-150 solar masses. This isn’t helped by the fact that we can’t observe any.

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So here is a chart which shows the initial stellar mass versus the remnant mass for a star of no metallicity

Although actual mass ranges are not agreed upon, what is agreed upon is that any population iii with mass greater than 100M is going to end as a black hole with no supernova explosion at all and those with masses between 10 and 50 solar masses are going to have a fairly high energy supernova explosion while also ending in a black hole. There’s an interesting band right here which indicates a range of masses where the entire star is completely disrupted in what’s called a pair instability supernova and there is no remnant at all. I’m going to be discussing simulations related to that phenomenon later.

What I want you to take away here is that the extremely supermassive stars are expected to simply collapse rapidly after a very short lifetime and generally, any with an initial mass above 30 Mo is expected to end as a black hole. In fact, many of the supermassive holes which sit in the center of galaxies today are thought to be a result of these massive population iii stars

You also might be asking how these more massive stars could have been stable enough in the first place to even last millions of years without immediately collapsing under their own pressure. But the star’s own rotation would have kept it stable enough for a few million years before it collapsed

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Pair-instability Supernova

Pair production
Gamma ray pressure in core is reduced
No black hole remnant!

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Why study an “extinct” star?

Big bang metallicities
Later creation of Population-II stars

Dispersion of heavy metals

Important aspect of reionization in post-big bang universe
Early black hole formation
For fun

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New research in Population III evolution

KEPLER
CASTRO
Simulations of population III stars above 10,000M☉
Narrow window found where supermassive stars completely annihilate, leaving no black hole remnant

University of California, Santa Cruz

University of Minnesota

Department of Energy’s computing center

1-D stellar evolution code (spherically symmetric) called Kepler: takes into account nuclear burning, stellar convection, special relativity, electron-positron pair production, and photo-disintegration of element (which happens when the star rapidly collapses into a black hole): they accounted for general relativistic effects as well, since these stars are far over 1000 solar masses

Kepler basically provided all the initial conditions for the star and then the simulations were also run in 2D in CASTRO, which is a code developed at Berkley Lab

These simulations showed that for stars in the narrow window between 55,000 and 56,000 solar masses, their lives ended in a highly energetic supernova explosion rather than as a black hole

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What drives such a collapse?

General relativistic effects!
Stars in 55,000-56,000M☉ range begin to collapse after ~1.69 million year lifetime
Energy released in rapid synthesis > binding energy
~10^55 ergs of energy released in explosion

The star lives to be about 1.69 million years old before general relativistic effects make them unstable, and they begin to collapse. Helium starts synthesizing in the core and then other heavy elements like oxygen, neon, magnesium, and silicon are rapidly synthesized

The explosion is triggered by thermal photons contributing to the core’s gravity, causing the core to contract and subsequently burn rather explosively.

What happens is, at the very high temperature and low density of the core, even the most energetic photons are unable to make electron-positron pairs.. So instead, the photon energy is contributed toward the source term in einstein’s field equation, where they act as an additional source of gravity. So this changes the relativistic density and the core contracts

The energy released is greater than the binding energy of the star and the collapse completely halts, turning into a supernova explosion

The explosion itself is mostly powered by helium burning and gives off roughly 10^55 ergs of energy: this is more than 10,000 times the energy of a type 1a supernova: this ejects at least half the mass far into interstellar space

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Simulations in KEPLER

Both Newtonian and general relativistic effects accounted for
Mass loss neglected for initial conditions
Pressure and effective gravity calculated using TOV equation with relativistic density

star was partitioned into 1201 zones in mass giving an effective resolution of 46.2Mo

mass loss was neglected for determining the initial conditions because massive population iii stars don’t really lose any of their mass throughout their lifetime

and here’s the equation that was used for finding the effective gravity. The g without the tilde on it is actually the Newtonian gravitational field and the rho naught was the relativistic density

The Kepler conditions are then put through Castro, which models the hydrodynamics of the particles

One issue with the initial conditions that leads to a greater lack of accuracy in the simulations is the fact that they did not model the evolution of the protostar from much lower masses, but instead assumed it just started at the main sequence. More importantly, the star was assumed to be not rotating, which is a false assumption from what we know of any population iii star.

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Initial conditions as determined by KEPLER
Radius	1.73 x 10^13 cm
Surface temperature	7.19 x 10^4 K
Luminosity	5.70 x 10^42 erg/s
Lifetime of star prior to collapse	1.69 Myr

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This graph was done with CASTRO simulations. And this is at the beginning of the castro simulation, so before core collapse

It shows elemental masses as functions of radius: the x-axis is showing how much mass is enclosed within that radius

The core is 31,000 solar masses, so the “edge” of the core is where this line is

As you leave the core, you’ll see an increasing amount of hydrogen and a decreasing amount of helium

And at the end of the star’s life cycle, we do see a larger amount of heavy elements in the core

So much like the Kepler simulation, we have the core collapse reversed by energy release, but castro is a hydrodynamic software and accounts for fluid instabilities as well.

So now, after core collapse and during the explosion, we’re going to have violent fluid instabilities in the core because the helium burning creates pressure gradients that oppose the density and mass fraction gradients. This creates enormous rayleigh taylor instabilities

And if you don’t know, a rayleigh taylor instability is when you have two fluids with different densities in contact, but the lighter fluid is pushing the heavier fluid

The high pressure gradients end up mixing a lot of elements, even the heavier ones, throughout the star during the explosion

So then the burning continues until the shock reaches the hydrogen envelope

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Total loss of 3M☉ due to stellar envelope diffusing out of simulation domain

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Here is a comparison of the properties of the pair instabilities supernova explosion that I discussed previously and the general relativistic explosion. I think this is a pretty nice summary. The most significant difference between the two is the trigger for collapse

in kepler, if the simulation did not include general relativistic effects, the star just collapses into a black hole without exploding because you’re going to have the same effects of pair instabilities with the core collapse as any other supermassive star

We’re also working with significantly more massive stars here than with pair instability supernovae and subsequently a much much greater release of energy

While PSNe produce a small amount of nitrogen at the oxygen burning shell, as we saw in the previous tables and charts, no significant amount of nitrogen was produced from the GSNe

For the GSNe, when the shock wave reaches the hydrogen envelope, it does not plow up and accumulate mass there because the hydrogen envelope is not as extended as in the red supergiants. So it only creates a very weak reverse shock and continues burning outward

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Finding Evidence of Population III

Gravitational lensing
SEGUE
SDSS
James Webb Space Telescope
Wide-Field Infrared Survey Telescope

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Why are these results important?

Such supermassive explosions distribute matter great distances
This could help explain

The early creation of many heavier metals
The distribution of metals throughout galaxies
The presence of heavy metals in early solar system formations

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Sources

Abel, T., et al. "The Formation of the First Star in the Universe." (2001). Science Magazine. Web. Oct 2014.

Bombaci, I., et al. (1995). "The Maximum Mass of a Neutron Star." Astronomy & Astrophysics. Web. 1 Oct. 2014.

Castellani, V., 1999, The First Stars

Chen, Ke-Jung, et al. (2014). "The General Relativistic Instability Supernova of a Supermassive Population III Star." The Astrophysical Journal. Web. Oct 2014.

http://www.jwst.nasa.gov/images_artist13532.html. 2009.

http://www.sciencedaily.com/releases/2014/09/140929090559.htm. 2014. By Ken Chen.

http://theeternaluniverse.blogspot.com/2010/07/massive-early-stars-and-molecular.html. 2010.

http://en.wikipedia.org/wiki/Metallicity#mediaviewer/File:NASA-WMAP-first-stars.jpg. 2007.

Kreckel, H., Bruhns, H., Cizek, M., Glover, S., Miller, K., Urbain, X., & Savin, D. (2010). Experimental Results for H2 Formation from H- and H and Implications for First Star Formation. Science

Nakamura, F., & Umemura, M., 2000, ApJ

Schaerer, D., 2002, A&A

http://science.nasa.gov/media/medialibrary/1999/08/25/ast26aug99_2_resources/CXO_CasA.mid.jpg

Phillips, A.C. The Physics of Stars. 2nd ed. West Sussex: John Wiley & Sons, 1994. Print.