<p>The &quot;lithium test&quot; for a brown dwarf involves measuring two things - the lithium content and the spectral type (a proxy for surface temperature) or luminosity. But you may also need to know (or assume) something about the age of the object. The method is useful because the tracks of low-mass stars and brown dwarfs run together very closely in the usual luminosity versus Teff plane of the Hertzsprung-Russell diagram. In addition to the considerable uncertainty in the placement of these tracks, one really needs to know the <em>age</em> of an object in order for its luminosity or Teff to lead to even a crude mass estimate and hence the Li-test is pursued.</p>
<p>Li is completely and rapidly burned in a fully convective, low-mass object, once the core temperature reaches about 3 million degrees. The time it takes for a contracting pre main sequence star (or some brown dwarfs) to reach this temperature is mass-dependent. It takes about 20 million years at 0.2 solar masses, about 120 million years at 0.075 solar masses (roughly the boundary between stars, and brown dwarfs that will never become hot enough to fuse <em>hydrogen</em>), and if the object is below 0.06 solar masses, it <em>never</em> gets rid of its Li. The physics of this process is well understood and hence it has become a very useful and trusted tool for mass and age estimation.</p>
<p>At the same time as this happens, the surface temperature and luminosity are also diagnostic of mass, but in an age dependent way. An M7 spectral type is on the brown dwarf limit at about 120 Myr, but a similar spectral type in an older and more luminous object would mean it was more massive.</p>
<p>Historically then, the Li test was applied to low-mass objects in the Pleiades cluster (see <a href="https://arxiv.org/abs/astro-ph/9607002" rel="nofollow noreferrer">Rebolo et al. 1996</a>), which has an age of about 120 Myr. Objects with spectral types cooler than M7 <em>at that age</em> should be brown dwarfs. This was confirmed by finding Li in their atmospheres.</p>
<p>The Li test is not a completely unambiguous indicator of whether an object of unknown age is a star or a brown dwarf. Both stars and brown dwarfs can have spectral types M6.5-L2, but a star would be older at the same spectral type. If you have measured the luminosity (or spectral type) of an object and know whether it has lithium or not, then this provides a constraint on both mass and age. The diagram below, from <a href="http://adsabs.harvard.edu/abs/1998ASPC..134..394B" rel="nofollow noreferrer">Basri et al. (1998)</a>, is I think as clear as it can be made.</p>
<p><a href="https://i.sstatic.net/GKXLd.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/GKXLd.png" alt="Li-temperature relation" /></a></p>
<p>The more-or-less diagonal curves are the tracks along which low-mass stars and brown dwarfs of the labelled mass evolve (getting cooler with age). The diagonal dashed region shows the area of the temperature versus age plot where Li is expected to be depleted. I have labelled the equivalent spectral types. The stippled (dotted) area marks where the presence of Li <em>guarantees</em> that you have a brown dwarf with mass <span class="math-container">$&lt;$</span> 0.075 solar masses.</p>
<p>Thus an M6.5 object with Li could either be a brown dwarf or a star younger than about 140 Myr, but an M6.5 object without Li is a star. An M8 dwarf with Li is a brown dwarf with an age less than 200 Myr, but an M8 dwarf without Li could either be a more massive brown dwarf with age just over 200 Myr or an older low-mass star. At spectral type L0-L2 then an object with Li will be a brown dwarf if its age is less than 500-1000 Myr, but could still be a brown dwarf with mass above 0.06 solar masses with an age just a little older than this, or an even older low-mass star. Objects cooler than L2 are always brown dwarfs and always have Li - but this test may fail at much cooler temperatures (cooler than abut L8) because the Li atoms form LiCl and LiOH molecules, the atomic Li I line at 6708A disappears from the spectrum, and the molecular features are too weak/confused to be identified.</p>
<p>A similar diagram can be made with luminosity on the y-axis and actually, that is more secure, since Li depletion as a function of luminosity is much easier to
predict than the behaviour of effective temperature, which depends a lot on the details of the atmosphere. Of course to measure a luminosity you need the distance to the object though.</p>
<p>Nowadays, the presence of Li in a low mass objects atmosphere is more likely to be used as an age, rather than mass indicator. For example, if one sees Li in an M7 object, then it is likely to be younger than 120 Myr (and vice versa). The prediction of Li depletion, particularly as a function of luminosity or spectral type is thought to be more secure than predicting the position of such an object in the HR diagram. This forms the basis of the
<a href="http://www.astro.keele.ac.uk/%7Erdj/pages/ldb.pdf" rel="nofollow noreferrer">lithium depletion boundary</a> age determination method for clusters.</p>
<p><strong>To sum up</strong>.</p>
<ol>
<li><p>An object with a spectral type of M8 or cooler <em>with Li</em> is a substellar brown dwarf.</p>
</li>
<li><p>An object with Li but a warmer spectral type must be a brown dwarf if it is younger than some threshold age (e.g. about 50 Myr for type M6).</p>
</li>
<li><p>An object younger than <span class="math-container">$\sim 150$</span> Myr <em>without</em> Li must be a star.</p>
</li>
<li><p>An object cooler than about spectral type L2 must be a brown dwarf whether it has Li or not.</p>
</li>
</ol>

CC BY-SA 3.0
2017-04-15T10:24:20.017Z
old+ Li means brown dwarf, right? About `cooler than M7 should be bds`, could you give some reference? I think there are L-type stars. see https://en.wikipedia.org/wiki/Category:L-type_stars
questionhang
CC BY-SA 3.0
2017-04-15T13:54:30.800Z
@questionhang See the edit, I think the picture makes things much clearer.
ProfRob
CC BY-SA 3.0
2017-04-16T08:45:10.830Z
Basri's paper is just for young bds. http://adsabs.harvard.edu/abs/1998ASPC..134..394B. `guaranteed limit for lithium brown dwarfs` means we tell Li bds apart in bds. When we talk about cool stars and bds together, it will become complicated. When can we use Li test to tell cool stars and bds apart?
questionhang
CC BY-SA 3.0
2017-04-16T10:17:10.410Z
@questionhang You are asking for a simple answer that doesn't exist. The answer is complex. You will have to read my answer carefully and follow up the references. I have added a very clear summary. If that doesn't meet your high (some might say unrealistic) expectations then you will have to hope that another expert on Li depletion in low-mass objects reads your post.
ProfRob
CC BY-SA 3.0
2017-04-16T10:48:17.923Z
I talk about bds and cool stars together from the very beginning.
questionhang
CC BY-SA 3.0
2017-04-16T12:38:08.123Z
TRAPPIST-1 is an example. `high-resolution optical spectroscopy failed to detect significant absorption at the 6,708 Å lithium line36, suggesting that the object is not a very young brown dwarf, but rather a very-low-mass main-sequence star. ` (http://adsabs.harvard.edu/abs/2016Natur.533..221)  Then why is not TRAPPIST-1 an old brown dwarf?
questionhang
CC BY-SA 3.0
2017-04-16T14:52:46.210Z
@questionhang The logic of that statement fits perfectly with my answer. TRAPPIST-1 is not an old brown dwarf because it has a spectral type of M8. So it is either a young brown dwarf or a star older than about 250 Myr. It could *just* be a brown dwarf without Li if its age is just  below 250 Myr. Obviously if the age is random between 0 and 10 Gyr, then it is most likely a low-mass star.
ProfRob
CC BY-SA 3.0
2017-04-17T11:30:22.860Z
I do not understand `RAPPIST-1 is not an old brown dwarf because it has a spectral type of M8`.  From the figure above, we can see a M8-type bd older than 250Myr does not have Lithium either.
questionhang
CC BY-SA 3.0
2017-04-17T12:15:09.293Z
@questionhang As is *clearly* apparent from the figure above, the *minimum* mass of an M8 object older than 250 Myr is 0.075 solar masses and therefore it is *not* a brown dwarf.
ProfRob
CC BY-SA 4.0
2017-04-15T08:14:55.410Z
2021-11-27T17:43:22.720Z
2021-11-27T17:43:22.720Z
ProfRob
<p>Both low-mass PMS (pre-main-sequence) stars and young brown dwarfs can fuse lithium in their cores and the lithium can be depleted throughout the star/brown dwarf very quickly. <a href="https://en.wikipedia.org/wiki/Lithium_burning" rel="nofollow noreferrer">Wiki</a>. Then the Li I 6708A absorption line disappears from the object's spectrum. </p>

<p>Why and how can the Lithium test be used as an indicator to distinguish between young brown dwarfs and young low-mass stars?</p>

<p>Can somebody summarise in what cases we can tell whether an object is a brown dwarf or a low-mass star?</p>

CC BY-SA 3.0
2017-04-11T22:24:10.423Z
By the rest of the spectrum? Position in HR diagram? There are many methods.
AtmosphericPrisonEscape
CC BY-SA 3.0
2017-04-13T11:46:55.930Z
Could you list several reliable methods?
questionhang
CC BY-SA 3.0
2017-04-13T12:09:51.217Z
I'm not sure what you're asking. Did you read the wiki page for brown dwarves? Quite a few things of what you've asked for are explained there.
AtmosphericPrisonEscape
CC BY-SA 3.0
2017-04-13T13:37:22.103Z
Are you talking about low-mass stars or pre main sequence stars? You question is confusing as it is.
Py-ser
CC BY-SA 3.0
2017-04-15T13:57:33.337Z
@AtmosphericPrisonEscape The position of a very low-mass object in the HR diagram does not unambiguously tell you its mass. Aside from the severe model-dependencies in the evolutionary models, there is a close-to mass-age degeneracy in the L vs Teff plane.
ProfRob
<star><stellar-evolution><brown-dwarf><elemental-abundances>
Using the "Lithium test" to distinguish low-mass stars and brown dwarfs
questionhang
# Using the "Lithium test" to distinguish low-mass stars and brown dwarfs

(Asked by: username_0 on 2017-04-11)

Both low-mass PMS (pre-main-sequence) stars and young brown dwarfs can fuse lithium in their cores and the lithium can be depleted throughout the star/brown dwarf very quickly. [Wiki](https://en.wikipedia.org/wiki/Lithium_burning). Then the Li I 6708A absorption line disappears from the object's spectrum.

Why and how can the Lithium test be used as an indicator to distinguish between young brown dwarfs and young low-mass stars?

Can somebody summarise in what cases we can tell whether an object is a brown dwarf or a low-mass star?

**Tags:** star, stellar-evolution, brown-dwarf, elemental-abundances
> **Comments:**
> **username_1**: By the rest of the spectrum? Position in HR diagram? There are many methods.  
> **username_0**: Could you list several reliable methods?  
> **username_1**: I'm not sure what you're asking. Did you read the wiki page for brown dwarves? Quite a few things of what you've asked for are explained there.  
> **username_2**: Are you talking about low-mass stars or pre main sequence stars? You question is confusing as it is.  
> **username_3**: @AtmosphericPrisonEscape The position of a very low-mass object in the HR diagram does not unambiguously tell you its mass. Aside from the severe model-dependencies in the evolutionary models, there is a close-to mass-age degeneracy in the L vs Teff plane.  

---

## 1 answers

### Answer by username_3 on 2017-04-15. Score: 6

The "lithium test" for a brown dwarf involves measuring two things - the lithium content and the spectral type (a proxy for surface temperature) or luminosity. But you may also need to know (or assume) something about the age of the object. The method is useful because the tracks of low-mass stars and brown dwarfs run together very closely in the usual luminosity versus Teff plane of the Hertzsprung-Russell diagram. In addition to the considerable uncertainty in the placement of these tracks, one really needs to know the *age* of an object in order for its luminosity or Teff to lead to even a crude mass estimate and hence the Li-test is pursued.

Li is completely and rapidly burned in a fully convective, low-mass object, once the core temperature reaches about 3 million degrees. The time it takes for a contracting pre main sequence star (or some brown dwarfs) to reach this temperature is mass-dependent. It takes about 20 million years at 0.2 solar masses, about 120 million years at 0.075 solar masses (roughly the boundary between stars, and brown dwarfs that will never become hot enough to fuse *hydrogen*), and if the object is below 0.06 solar masses, it *never* gets rid of its Li. The physics of this process is well understood and hence it has become a very useful and trusted tool for mass and age estimation.

At the same time as this happens, the surface temperature and luminosity are also diagnostic of mass, but in an age dependent way. An M7 spectral type is on the brown dwarf limit at about 120 Myr, but a similar spectral type in an older and more luminous object would mean it was more massive.

Historically then, the Li test was applied to low-mass objects in the Pleiades cluster (see [Rebolo et al. 1996](https://arxiv.org/abs/astro-ph/9607002)), which has an age of about 120 Myr. Objects with spectral types cooler than M7 *at that age* should be brown dwarfs. This was confirmed by finding Li in their atmospheres.

The Li test is not a completely unambiguous indicator of whether an object of unknown age is a star or a brown dwarf. Both stars and brown dwarfs can have spectral types M6.5-L2, but a star would be older at the same spectral type. If you have measured the luminosity (or spectral type) of an object and know whether it has lithium or not, then this provides a constraint on both mass and age. The diagram below, from [Basri et al. (1998)](http://adsabs.harvard.edu/abs/1998ASPC..134..394B), is I think as clear as it can be made.

[![Li-temperature relation](https://i.sstatic.net/GKXLd.png)](https://i.sstatic.net/GKXLd.png)

The more-or-less diagonal curves are the tracks along which low-mass stars and brown dwarfs of the labelled mass evolve (getting cooler with age). The diagonal dashed region shows the area of the temperature versus age plot where Li is expected to be depleted. I have labelled the equivalent spectral types. The stippled (dotted) area marks where the presence of Li *guarantees* that you have a brown dwarf with mass $<$ 0.075 solar masses.

Thus an M6.5 object with Li could either be a brown dwarf or a star younger than about 140 Myr, but an M6.5 object without Li is a star. An M8 dwarf with Li is a brown dwarf with an age less than 200 Myr, but an M8 dwarf without Li could either be a more massive brown dwarf with age just over 200 Myr or an older low-mass star. At spectral type L0-L2 then an object with Li will be a brown dwarf if its age is less than 500-1000 Myr, but could still be a brown dwarf with mass above 0.06 solar masses with an age just a little older than this, or an even older low-mass star. Objects cooler than L2 are always brown dwarfs and always have Li - but this test may fail at much cooler temperatures (cooler than abut L8) because the Li atoms form LiCl and LiOH molecules, the atomic Li I line at 6708A disappears from the spectrum, and the molecular features are too weak/confused to be identified.

A similar diagram can be made with luminosity on the y-axis and actually, that is more secure, since Li depletion as a function of luminosity is much easier to
predict than the behaviour of effective temperature, which depends a lot on the details of the atmosphere. Of course to measure a luminosity you need the distance to the object though.

Nowadays, the presence of Li in a low mass objects atmosphere is more likely to be used as an age, rather than mass indicator. For example, if one sees Li in an M7 object, then it is likely to be younger than 120 Myr (and vice versa). The prediction of Li depletion, particularly as a function of luminosity or spectral type is thought to be more secure than predicting the position of such an object in the HR diagram. This forms the basis of the
[lithium depletion boundary](http://www.astro.keele.ac.uk/%7Erdj/pages/ldb.pdf) age determination method for clusters.

**To sum up**.

1. An object with a spectral type of M8 or cooler *with Li* is a substellar brown dwarf.
2. An object with Li but a warmer spectral type must be a brown dwarf if it is younger than some threshold age (e.g. about 50 Myr for type M6).
3. An object younger than $\sim 150$ Myr *without* Li must be a star.
4. An object cooler than about spectral type L2 must be a brown dwarf whether it has Li or not.

> **Comments:**
> **username_0**: old+ Li means brown dwarf, right? About `cooler than M7 should be bds`, could you give some reference? I think there are L-type stars. see https://en.wikipedia.org/wiki/Category:L-type_stars  
> **username_3**: @questionhang See the edit, I think the picture makes things much clearer.  
> **username_0**: Basri's paper is just for young bds. http://adsabs.harvard.edu/abs/1998ASPC..134..394B. `guaranteed limit for lithium brown dwarfs` means we tell Li bds apart in bds. When we talk about cool stars and bds together, it will become complicated. When can we use Li test to tell cool stars and bds apart?  
> **username_3**: @questionhang You are asking for a simple answer that doesn't exist. The answer is complex. You will have to read my answer carefully and follow up the references. I have added a very clear summary. If that doesn't meet your high (some might say unrealistic) expectations then you will have to hope that another expert on Li depletion in low-mass objects reads your post.  
> **username_0**: I talk about bds and cool stars together from the very beginning.  
> **username_0**: TRAPPIST-1 is an example. `high-resolution optical spectroscopy failed to detect significant absorption at the 6,708 Å lithium line36, suggesting that the object is not a very young brown dwarf, but rather a very-low-mass main-sequence star. ` (http://adsabs.harvard.edu/abs/2016Natur.533..221)  Then why is not TRAPPIST-1 an old brown dwarf?  
> **username_3**: @questionhang The logic of that statement fits perfectly with my answer. TRAPPIST-1 is not an old brown dwarf because it has a spectral type of M8. So it is either a young brown dwarf or a star older than about 250 Myr. It could *just* be a brown dwarf without Li if its age is just  below 250 Myr. Obviously if the age is random between 0 and 10 Gyr, then it is most likely a low-mass star.  
> **username_0**: I do not understand `RAPPIST-1 is not an old brown dwarf because it has a spectral type of M8`.  From the figure above, we can see a M8-type bd older than 250Myr does not have Lithium either.  
> **username_3**: @questionhang As is *clearly* apparent from the figure above, the *minimum* mass of an M8 object older than 250 Myr is 0.075 solar masses and therefore it is *not* a brown dwarf.  

---

