Brown Dwarfs at the Boundary

by Paul Gilster on December 10, 2013

We spend a lot of time probing the borderlines of astronomy, wondering what the boundaries are between a large gas giant and a brown dwarf, for example. The other end of that question is also intriguing: When does a true star get small enough to be a brown dwarf? For main sequence stars don’t operate the same way brown dwarfs do. Add hydrogen to a main sequence star and its radius increases. But brown dwarfs work the opposite way, with additional mass causing them to shrink. We see this beginning to happen at the high end of the brown dwarf mass range, somewhere between 60 and 90 Jupiter masses.

Electron degeneracy pressure, which occurs when electrons are compressed into a very small volume, is at play here. No two electrons with the same spin can occupy the same energy state in the same volume — this is the Pauli exclusion principle. When the lowest energy level is filled, added electrons are forced into higher energy states and travel at faster speeds, creating pressure. We see this in other kinds of objects as well. A star of less than four solar masses, for example, having gone through its red giant phase, will collapse and move off the main sequence until its collapse is halted by the pressure of electron degeneracy — a white dwarf is the result.

New work out of the RECONS (Research Consortium on Nearby Stars) group at Georgia State has now found observational evidence that helps us pinpoint the distinction between very low mass stars and brown dwarfs. Let me quote from the preprint to their upcoming paper, slated to appear in The Astronomical Journal, to clarify the electron degeneracy issue:

One of the most remarkable facts about VLM [Very Low Mass] stars is the fact that a small change in mass or metallicity can bring about profound changes to the basic physics of the object’s interior, if the change in mass or metallicity places the object in the realm of the brown dwarfs, on the other side of the hydrogen burning minimum mass limit. If the object is unable to reach thermodynamic equilibrium through sustained nuclear fusion, the object’s collapse will be halted by non-thermal electron degeneracy pressure. The macroscopic properties of (sub)-stellar matter are then ruled by different physics and obey a different equation of state… Once electron degeneracy sets in at the core, the greater gravitational force of a more massive object will cause a larger fraction of the brown dwarf to become degenerate, causing it to have a smaller radius. The mass-radius relation therefore has a pronounced local minimum near the critical mass attained by the most massive brown dwarfs…

With these facts in mind, the RECONS team used data from two southern hemisphere observatories, the SOAR (Southern Observatory for Astrophysical Research) 4.1-m telescope and SMARTS (Small and Moderate Aperture Research Telescope System) in Chile, to take measurements of objects thought to lie at the star/brown dwarf boundary. Says Sergio Dieterich, lead author of the paper:

“In order to distinguish stars from brown dwarfs we measured the light from each object thought to lie close to the stellar/brown dwarf boundary. We also carefully measured the distances to each object. We could then calculate their temperatures and radii using basic physical laws, and found the location of the smallest objects we observed. We see that radius decreases with decreasing temperature, as expected for stars, until we reach a temperature of about 2100K. There we see a gap with no objects, and then the radius starts to increase with decreasing temperature, as we expect for brown dwarfs.“

The diagram below makes the distinction clearer:

Brown-Dwarf_2

Image: The relation between size and temperature at the point where stars end and brown dwarfs begin (based on a figure from the publication). Credit: P. Marenfeld & NOAO/AURA/NSF.

Notice the temperature drop as the size of main sequence stars declines, then the break between true stars and brown dwarfs. The RECONS research indicates that the boundaries can be precisely drawn: Below temperatures of 2100 K, a radius 8.7 percent that of the Sun, and a luminosity of 1/8000th of the Sun, we leave the main sequence. The team identifies the star 2MASS J0513-1403 as an example of the smallest of main sequence stars. Is the gap between true stars and brown dwarfs right after 2MASS J0513-1403 real or is it the effect of an insufficient sample? To find out, the team is planning a larger search to test these initial results.

Note, too, the interesting distinction in the ages of these objects. Small M-dwarfs can live for trillions of years. Brown dwarfs, on the other hand, have much shorter lifetimes, continually fading over time. Whether they could produce a habitable zone over timeframes sufficient to support life is an open question, one that we’ve looked at in Brown Dwarf Planets and Habitability. Our study of small, dim objects and astrobiology is only beginning.

The paper is Dieterich et al., “The Solar Neighborhood XXXII. The Hydrogen Burning Limit,” accepted at the Astronomical Journal and available as a preprint. See this NOAA/SOAR news release for more.

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{ 9 comments… read them below or add one }

Alex Tolley December 10, 2013 at 11:58

If you keep adding mass to a brown dwarf, wouldn’t it eventually ignite fusion and then expand again? Is there some boundary that is unstable where there is a state change between the 2 types of objects?

Thomas Mazanec December 10, 2013 at 13:36

I was just about to ask this, Alex. As I recall, a story by Poul Anderson, as well as “Habitable Planets For Man”, postulated the possibility of objects which would start fusion in their core, expand from the added heat, go out and cool, contract and heat up to fusion again, etc.
I would love to know if this is possible.

Eniac December 10, 2013 at 23:26

Alex and Thomas: Interesting question. My guess would be that the increase in temperature from fusion energy would outweigh any decrease in density from expansion, at least at the core, where fusion would first occur. Thus, once fusion is ignited, it would not stop and the object would be classified as a normal low-mass star.

Sergio Dieterich December 11, 2013 at 0:39

Hi Alex and Thomas, this is Sergio Dieterich, lead author of this study. I think the question you ask, whether a brown dwarf can become a star if more mass is added and whether there exists a zone of instability between the two realms is a very interesting one. To answer the first question, there is some evidence that this can occur if gas accretion (the process by which a star or brown dwarf absorbs gas from its originating cloud) lasts more that several million years. It is believe that most accretion happens during the first million years, where it really makes little sense to call the object either a star or a brown dwarf — it hasn’t really finished forming yet. However if there are episodes of extended accretion, it is possible that some objects that began as brown dwarfs may then jump the gap and ignite fusion. This is probably extremely rare, given the very unique circumstances needed.
About the second question, is there a zone of instability between stars and brown dwarfs? A more precise definition of a star is that not only must it undergo hydrogen fusion, but it must be able to sustain it in the long term and reach an equilibrium state. So, almost by definition, any such unstable object would be a brown dwarf. There is a very interesting twist here. If you look at Figure 9 of the paper (there is a link in the story above), you will see the variability analysis we did for all the targets in the survey. We find a spike in variability at temperatures just above 2100K, where we determined the hydrogen burning limit to be. Could these small stars be varying because they are on the edge? While stellar atmospheric effects are more likely to be the culprit here, it is still an interesting hypothesis. We are trying to device a larger variability study to try to get to the bottom of this. Thank you for your interest! And may I also thank the author of this new story for a very clear and accurate portrayal of our work.

andy December 11, 2013 at 13:45

What about post-common envelope binaries? Is it possible that some of the M-dwarfs in such systems may be former brown dwarfs that were engulfed by the companion star during the giant star stage?

steven rappolee December 11, 2013 at 15:22

” We find a spike in variability at temperatures just above 2100K, where we determined the hydrogen burning limit to be.”

so we need find a new born object precisely this mass that also seems to have finished with its debris disk.This might be an object still oscillating with its battle between gravity and thermal expansion?

steven rappolee December 11, 2013 at 15:44

or does this variability of temperatures ocer in all stars of This small mass regardless of age? IE an ageless battle between thermal expansion, a tapering off of Fusion reactions followed by gravitational contraction with an uptick of the fusion reaction, repeat.
What role would Lithium play?

ljk December 17, 2013 at 12:06

Nearby Failed Stars May Harbor Planet, Astronomers Find

Dec. 16, 2013 — Astronomers, including Carnegie’s Yuri Beletsky, took precise measurements of the closest pair of failed stars to the Sun, which suggest that the system harbors a third, planetary-mass object.The research is published as a letter to the editor in Astronomy & Astrophysics.

Full article here:

http://www.sciencedaily.com/releases/2013/12/131216142805.htm

Paul Hellings January 22, 2014 at 7:30

Does the electron degeneracy only occur at the very core of throughout the complete brown dwarf (except some outer layer such as the atmosphere) ?

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