# Is stellar ignition all-or-nothing?

The boundary between brown dwarfs and stars is around 80 Jupiter masses. Only stars generate a self-sustaining hydrogen fusion, although brown dwarfs sometimes fuse lithium and deuterium.

Is hydrogen ignition all or nothing? If so, there should be a mass overlap. For example, a 79 Jupiter mass star may achieve ignition by forming faster and thus with a higher core temperature, or by having a bit more deuterium or lithium kindling than normal. Conversely, a slowly-forming 81 Jupiter mass brown dwarf may stay below ignition temperatures.

The heaviest brown dwarf we know has about 90 Jupiter masses, while the lightest star has about 73 Jupiter masses, which suggests a mass overlap, although these masses are approximate values. Is there any estimate to how big this mass overlap is?

Edit: To clarify my question: Stars above about 0.35 solar masses have a radiative envelope so end their life with some unburnt hydrogen. Stars below 0.35 solar masses burn all of their hydrogen b/c they are fully convective. Brown dwarfs (say of 0.05 solar masses) don't burn any light hydrogen. Are there individual objects (presumably around 80 Jupiter masses) that are between 0.05 and 0.35 solar masses and are destined to one day end their life with 10% of their hydrogen burnt? Or with 25%? Or with 50%? This is of course barring any outside catastrophic event like being torn apart by a black hole.

• Why would the heavier object collapse slower if it's cooler? Jan 5 at 18:49
• @ChristopherJamesHuff in my scenario it forms more slowly because the gas cloud is thinner or faster rotating or some other reason. As a result it ends up slightly cooler. Jan 5 at 18:58
• I’m not 100% sure here but I’ve heard often that metallicity can come into play at critical values like these, as well as other stages of fusion, so that may have something to do with the overlap? Jan 5 at 21:49

No fusion isn't all or nothing. Given the same chemical composition of constituents then there will be a smooth ramping down of the nuclear fusion rate as the mass decreases. The lower mass objects will also take longer to contract and heat up, and so at any given mass, an older object will have more nuclear fusion.

So there is some blurriness to the definition of the boundary. You could try to define it as the mass where the radius contraction ceases at some point and the luminosity is provided by nuclear fusion, but even in objects with slightly lower mass that continue to contract there will be some nuclear fusion going on.

Fortunately this is of little actual consequence. The interior structures and observational properties of a "brown dwarf" just below the boundary and a "star" just above the boundary are quite close until they have lived for many billions of years although the brown dwarf will be smaller and have a higher surface gravity at a similar age.

One issue that does inject a significant amount of blurring to the boundary is initial chemical composition. It is predicted that the boundary between stars and brown dwarfs will be at higher masses for lower metallicity objects.

The classic work on this is Chabrier & Baraffe (1997). They define the hydrogen-burning minimum mass to be the lowest mass where thermal equilibrium is attained and the luminosity of the object is provided by nuclear reactions. The HBMM is about 0.072-0.075 solar masses at solar metallicity but 0.083 solar masses for metallicities about 30 times lower and could reach 0.092 solar masses for brown dwarfs born from primordial gas with no metals (Burrows et al. 2001).

Thus if you have a spread of metallicities in a sample then the boundary between stars and brown dwarfs will be blurred by this.

Note that initial abundances and subsequent burning of deuterium and lithium have almost no effect on the HBBM because all D and Li is burned before the onset of hydrogen (protium) burning. i.e. Whatever it started with, an object close to the HBMM will have no D or Li by the time it contracts close to the H-burning temperature, so it has no bearing on the question. In fact, Li-burning is energetically negligible and D-burning only delays the contraction by some ~10 million years (compared to a timescale for possible H ignition of more than a billion years).

Edit: Let me answer your new question. Once hydrogen has ignited, it doesn't stop until all the available fuel is consumed. The increasing mean particle mass in the core, means it will contract and get hotter in order to maintain hydrostatic equilibrium, which increases the fusion rate.

Stars with mass less than 0.35 of the Sun are fully convective and thoroughly mixed. If they are massive enough to begin nuclear fusion, then it will burn to completion. The mass will determine how long that will take.

As the OP accurately summarises:

That means that each individual object is either a star or not a star with no in-between "the fire got started but it burned out early" objects? However, the mass-cutoff is fuzzy and there is a mass overlap between "star" and "not-a-star" objects and there is no clear way to tell them apart without waiting billions of years? – Kevin Kostlan

• Brown dwarfs will burn very little hydrogen through their evolution, while red dwarfs will burn almost all of it. Are there any objects that will end their life with 10% of their hydrogen burnt? 25%? 50%? Mar 17 at 9:30
• @KevinKostlan yes, early M-dwarfs that have a radiative core. Mar 17 at 11:19
• @KevinKostlan anything lower mass than 0.35 solar masses doesn't have a radiative core. Only M dwarfs more massive than 0.35 will preserve any hydrogen. May 29 at 15:11
• @KevinKostlan Everything with less than 0.35 solar masses is fully convective and will burn all of its hydrogen if it is able to (I e. also $>0.075$ solar masses). May 30 at 5:01
• That means that each individual object is either a star or not a star with no in-between "the fire got started but it burned out early" objects? However, the mass-cutoff is fuzzy and there is a mass overlap between "star" and "not-a-star" objects and there is no clear way to tell them apart without waiting billions of years? May 30 at 6:47