Metal production with protium

[chornedsnorkack]

What happens if environment with abundant protium but little metals is heated to a high temperature? Are there any paths for metal synthesis besides triple alpha?

Obviously triple alpha is the only option if protium has been thoroughly exhausted.

But it is a difficult process:
first, alpha+alpha -> Be-8+gamma
usually Be-8 undergoes alpha fission in 7*10ˇ-17 seconds
rarely next step within these 10ˇ-16 seconds:
Be-8+alpha -> C-12+gamma

Now, if protium is not exhausted, what are the branches of pp chain?

Up to He-3, pp chain is standard:
p+p -> d+e++nue
or
p+p+e -> d+nue
rapidly followed by
d+p -> He-3+gamma
But from He-3 there are 4 options:
He-3+p -> alpha+e++nue
He-3+p+e -> alpha+nue
He-3+He-3 -> alpha+p+p
He-3+alpha -> Be-7+gamma
From Be-7, there are 2 main branches:
Be-7+e -> Li-7+nue
Li-7+p -> alpha+alpha
or
Be-7+p -> B-8+gamma
B-8 -> alpha+alpha+e++nue

But note that all these Be and Li isotopes are long-lived compared to Be-8!
Even B-8 has lifetime of 0,8 seconds, and Be-7 has lifetime in months (depending on electron abundance).

So, considering alpha is abundant, could you have side branches of these reactions?

Like:
Be-7+alpha -> C-11+gamma
Be-7+alpha -> B-10+p
Li-7+alpha -> B-11+gamma
Li-7+alpha -> B-10+n
Li-7+alpha -> Be-10+p
B-8+alpha -> N-12+gamma
B-8+alpha -> C-11+p?

[antoniseb]

I had also wondered about this, but I don't have an answer for why He-3 should be a trace species in a Helium star. Perhaps one of our star-guys will know.

[korjik]

It is called Hydrogen

I think it is the very different temperature between hydrogen and helium burning that keeps abundant helium from burning before the triple alpha starts up. You should have all those side chains burn off the remaining lithium, beryllium, boron and helium-3 as the temp heads up to helium burning temps tho.

Basically, while you still have hydrogen burning, the temp is going to be too low to get much helium burning, but as the temp rises after hydrogen burning ceases all the trace elements between helium and carbon will react with helium as the temperature rises. It will never be anything more than a very minor energy source tho.

[Celestial Mechanic]

It is called Hydrogen {Snip!}

A quick Google search turns up several sites (among them Wikipedia, Merriam-Webster, and Brittanica) defining protium to be the isotope of hydrogen consisting of a single proton, to distinguish it from deuterium and tritium. There's also a drug (generic name pantoprazol) of that name, but we can safely disregard that.

[chornedsnorkack]

Do lower metallicity stars have higher temperature for the same luminosity?

[korjik]

IIRC, at the same temp, a low metal star is smaller than one with more metals. I think that works out to be higher temp for same luminosity.

[chornedsnorkack]

And does it also mean lower luminosity for the same mass?

[antoniseb]

Do lower metallicity stars have higher temperature for the same luminosity?

What are you asking? Photosphere temperature? Two stars with the same luminosity but different temperatures simply have different diameters in such a ratio that the luminosities are the same. So, are you asking if two stars, regardless of mass, but only looking at luminosity and diameter are different according to metalosity? My understanding that the answer to this depends on the spectral class. e.g. M8 stars with high metalicity are darker while (IIRC) B0 stars with high metalicity are brighter.

[chornedsnorkack]

I thought about core temperature.

At the same temperature, lower metallicity star should have lower luminosity because of less CNO cycle operation. Right?

[antoniseb]

... At the same [core] temperature, lower metallicity star should have lower luminosity because of less CNO cycle operation. Right?

I inserted the word core into your quote for clarity of what I'm saying... Yes, For stars in a mass range where CNO matters.

[chornedsnorkack]

For lower temperature stars, the CNO cycle is irrelevant even at solar metallicity. For example, Sun is said to have 1,1% proportion of CNO somewhere.

What causes the differences of subdwarfs of low mass from dwarfs of same mass? Is it just the atmospheric effect (less metallic atmosphere is more transparent and light comes from deeper and hotter levels, right?) or is a subdwarf different all the way down to the core because the more transparent interior leaks away heat from the core?

[chornedsnorkack]

How low metallicity and massive would a star need to be to produce carbon while still having core hydrogen?

[Van Rijn]

A quick Google search turns up several sites (among them Wikipedia, Merriam-Webster, and Brittanica) defining protium to be the isotope of hydrogen consisting of a single proton, to distinguish it from deuterium and tritium.

Sometimes you'll also see them listed as hydrogen-1 (protium), hydrogen-2 (deuterium), hydrogen-3 (tritium).

[Romanus]

Metallicity affects size and surface temperature, but not actual luminosity, since the mass and composition are roughly the same (the metals being a minor component). Hence, the reason subdwarfs are considerably hotter than field stars of the same mass; the uppermost main sequence stars in the oldest globular clusters are all less massive than the Sun, but also much earlier in spectral type (often well into class F).

[chornedsnorkack]

Metallicity affects size and surface temperature, but not actual luminosity, since the mass and composition are roughly the same (the metals being a minor component).

Do metals have a significant effect on the interior opacity?

[ctcoker]

Not interior opacity, no, since everything is completely ionized. It's the surface opacity that increases quite a bit with metallicity. The surface opacity change is why more metal-rich stars tend to be redder at the same luminosity.

[chornedsnorkack]

Not interior opacity, no, since everything is completely ionized. It's the surface opacity that increases quite a bit with metallicity.

It takes a lot of heat to ionize, say, the last electron of uranium.

Roughly above which temperature does the opacity of the remaining metal ions become insignificant compared to non-metal opacity, for solar metallicity?

[ctcoker]

Probably around the helium ionization temperature of ~50,000 K. By that point, electron scattering is by far the dominant opacity source in stars. Although metal atoms can have many more electrons than hydrogen or helium ones, they make up a small fraction of the total atoms, so the dominant contributors of electrons are hydrogen and helium. So while you're right that the metals aren't completely ionized until you get very deep in the star, they're ionized enough to not contribute many spectral lines. At the surface, however, unionized and lightly ionized metals can be very strong absorbers.

[chornedsnorkack]

Probably around the helium ionization temperature of ~50,000 K. By that point, electron scattering is by far the dominant opacity source in stars. Although metal atoms can have many more electrons than hydrogen or helium ones, they make up a small fraction of the total atoms, so the dominant contributors of electrons are hydrogen and helium.

I am surprized that the temperature is so low.

Thus, in low mass stars, the differences between dwarfs and subdwarfs are confined to a very thin layer just under the photosphere - the tachocline and most of the convective zone are not appreciably affected.

What causes tachocline, if not the addtional opacity due to metals?

[ctcoker]

Hold up a sec. A quick read of the relevant sections of Kippenhahn and Weigert showed that my previous post probably isn't correct. I'll get back to you on that.

However, I'm fairly confident that tachocline is mostly due to the opacity jumps from the helium and hydrogen ionization zones in lower mass stars. These change the adiabatic exponent, which is important... somehow. Give me a couple days to read up in K&W, and I'll get back to this subject.

EDIT: Disregard the second part of this post too. The tachocline is the transition between the convective and radiative zones deeper in the Sun's interior, long after the helium and hydrogen ionization zones have been passed. K&W does extensively go over stellar convection and stuff, so I'll still be able to get back to you.

[ctcoker]

I am surprized that the temperature is so low.

Thus, in low mass stars, the differences between dwarfs and subdwarfs are confined to a very thin layer just under the photosphere - the tachocline and most of the convective zone are not appreciably affected.

What causes tachocline, if not the addtional opacity due to metals?

And, as promised, here I am. It turns out that complete ionization does not occur until ~few*10⁷ K, and it is at that point that electron scattering opacity takes over. Lower than that, free-free opacity (bremsstrahlung, basically) is the dominant opacity source deep in stellar interiors, and there is a metallicity effect there. A good approximation for full ionization in cgs is given by Eq. 17.5 in K&W:

Here, X is the hydrogen fraction, Y the helium fraction, X_i the metal fractions, Z_i the nuclear charge (i.e., atomic numbers), and A_i the atomic masses. However, the effect due to metals in solar metallicity stars is only an additional 10-20% according to my estimate. This would change the location of the tachocline, but not by too much. At the surface, the bound-bound transitions (aka spectral lines) become very important, and so metals can have very large effects on the surface opacity, which will set the color of the star and its effective temperature.

The tachocline itself is caused by the rise in opacity with falling temperature; you can see from the above equation that the free-free opacity is a steeply falling function with increasing temperature. This, combined with the changes in pressure, density, and temperature as you go further out into the star, set the location of the tachocline and the CZ depth.

[chornedsnorkack]

And, as promised, here I am. It turns out that complete ionization does not occur until ~few*10⁷ K, and it is at that point that electron scattering opacity takes over. Lower than that, free-free opacity (bremsstrahlung, basically) is the dominant opacity source deep in stellar interiors,

Is it a non sequitur or a coincidence?

and there is a metallicity effect there. A good approximation for full ionization in cgs is given by Eq. 17.5 in K&W:

Here, X is the hydrogen fraction, Y the helium fraction, X_i the metal fractions, Z_i the nuclear charge (i.e., atomic numbers), and A_i the atomic masses. However, the effect due to metals in solar metallicity stars is only an additional 10-20% according to my estimate. This would change the location of the tachocline, but not by too much.

That is for the free-free reverse bremstrahlung.

At the surface, the bound-bound transitions (aka spectral lines) become very important, and so metals can have very large effects on the surface opacity, which will set the color of the star and its effective temperature.

How about bound-free transitions?

The tachocline itself is caused by the rise in opacity with falling temperature; you can see from the above equation that the free-free opacity is a steeply falling function with increasing temperature. This, combined with the changes in pressure, density, and temperature as you go further out into the star, set the location of the tachocline and the CZ depth.

So tachocline is caused by the strong temperature dependence of free-free transitions even in low metallicity gas.

What could be a good comparison set for stars of equal mass and age but very different metallicities?

[ctcoker]

Apologies for the late reply, I was on vacation for the past two weeks.

Is it a non sequitur or a coincidence?

Coincidence, I'd say. Not sure why you would use "non sequitur" here, though...

That is for the free-free reverse bremstrahlung.

Yes, and?

How about bound-free transitions?

Typically they don't contribute too much at the very surface as I understand it until you get to hotter stars, but they are responsible for the jumps in opacity you get at the hydrogen and helium ionization zones.

So tachocline is caused by the strong temperature dependence of free-free transitions even in low metallicity gas.

What could be a good comparison set for stars of equal mass and age but very different metallicities?

For low-mass stars, yes. I'd have to review K&W again for the high-mass case where you get convective cores and radiative envelopes.

I'm not sure what you mean by "good comparison set." Do you mean observables like effective temperature, luminosity, radius, and so on?

[chornedsnorkack]

Apologies for the late reply, I was on vacation for the past two weeks.

And then I was.

Coincidence, I'd say. Not sure why you would use "non sequitur" here, though...

I was trying to figure whether a causal relationship was implied.

Yes, and?

Typically they don't contribute too much at the very surface as I understand it until you get to hotter stars, but they are responsible for the jumps in opacity you get at the hydrogen and helium ionization zones.

Do bound-free transitions of metals have significant contributions to opacity in the hotter zones below helium ionization, compared to reverse bremsstrahlung?

For low-mass stars, yes. I'd have to review K&W again for the high-mass case where you get convective cores and radiative envelopes.

I'm not sure what you mean by "good comparison set." Do you mean observables like effective temperature, luminosity, radius, and so on?

Observables and also harder to observe things like age. Because for a field star, the age is hard to tell... Comparing the low metallicity globular clusters (mean metallicity -1,6) and the high metallicity ones (-0,6), do they also differ in age?

[ctcoker]

I was trying to figure whether a causal relationship was implied.

Oh, okay. No, there's no causal relationship; the extra electrons enhance the free-free opacity, but the temperature at that point is so high that electrons and nuclei aren't close enough to each other for long enough for a free-free transition to take place.

Do bound-free transitions of metals have significant contributions to opacity in the hotter zones below helium ionization, compared to reverse bremsstrahlung?

Judging from what I could find, they have the same sort of effect as they do for the free-free dominant zone: Not too much, but it's not a tiny effect either.

For reference, these are the dominant opacity sources in the Sun from the surface inward: Bound-bound -> H ionization -> He ionization -> bound-free -> free-free. In hotter stars, electron scattering takes over in the core.

Observables and also harder to observe things like age. Because for a field star, the age is hard to tell... Comparing the low metallicity globular clusters (mean metallicity -1,6) and the high metallicity ones (-0,6), do they also differ in age?

For the globs, not necessarily (!). Take a look at Marin-Franch, et al. (2009). Assuming I understand their Figure 10 correctly, the very metal poor globs ([M/H] ~ -1.5 and lower) are all around the same age, but the scatter increaes as you get more metal-rich. Young globulars appear to universally more metal-rich as you would expect, but many old globulars are comparatively metal-rich too! I wasn't expecting that result, though looking back on it, it shouldn't be too surprising - the metal-rich globulars are almost universally much closer to the galactic center than the metal-poor ones.

Going to back to your original question, a good set of comparison variables for stars with identical luminosities and ages but wildly different metallicities would be the metallicity itself (of course), but also color and magnitude (if the distance is known). The combination of those factors along with an isochrone model would be able to say that two stars are (roughly) the same age, as well as give their masses and radii, probably to within 5-10%.

[chornedsnorkack]

For reference, these are the dominant opacity sources in the Sun from the surface inward: Bound-bound -> H ionization -> He ionization -> bound-free -> free-free. In hotter stars, electron scattering takes over in the core.

And obviously, in low metallicity stars, there are no metals for bound-free absorption below the (second) He ionization.
As implied, in Sun, the tachocline is in the bound-free dominated region (rapidly decreasing opacity with increasing temperature) below the metal bound-free dominated region. Correct?

For the globs, not necessarily (!). Take a look at Marin-Franch, et al. (2009). Assuming I understand their Figure 10 correctly, the very metal poor globs ([M/H] ~ -1.5 and lower) are all around the same age, but the scatter increaes as you get more metal-rich. Young globulars appear to universally more metal-rich as you would expect, but many old globulars are comparatively metal-rich too! I wasn't expecting that result, though looking back on it, it shouldn't be too surprising - the metal-rich globulars are almost universally much closer to the galactic center than the metal-poor ones.

Which means it should be possible to compare old metal-poor globulars with old metal-rich globulars from inner Milky Way, and compare stars of known equal age and equal mass whose only difference is metallicity (and its effects on radius, spectrum, convection etc.).

What is the metallicity value defining the dividing line between a dwarf (class V) and a subdwarf (class VI)?

[ctcoker]

And obviously, in low metallicity stars, there are no metals for bound-free absorption below the (second) He ionization.
As implied, in Sun, the tachocline is in the bound-free dominated region (rapidly decreasing opacity with increasing temperature) below the metal bound-free dominated region. Correct?

Don't forget that you can still end up with cases where the electron recombines briefly; bound-free opacity doesn't go away just because the default state of the gas is ionized. Past the He ionization zones (there are two - one for each electron), the ionization fraction is quite large, but it is not exactly 1 until you get much hotter.

I'm not sure which opacity region the tachocline of the Sun is in. It could be in the free-free or bound-free zones, but I don't have the time to research that more thoroughly right now. There should be a whole wealth of literature out there on this subject - try searching "solar convection zone depth" and similar on ADS.

Which means it should be possible to compare old metal-poor globulars with old metal-rich globulars from inner Milky Way, and compare stars of known equal age and equal mass whose only difference is metallicity (and its effects on radius, spectrum, convection etc.).

What is the metallicity value defining the dividing line between a dwarf (class V) and a subdwarf (class VI)?

The effects of metallicity on main sequence stars are well known from stellar models; all else being equal, more metal-rich stars are redder and colder at fixed mass and age due to the higher opacity, especially at the surface. They are also more luminous and larger due to the higher mean molecular weight in the core, which leads to increased energy production and faster evolution.

I don't know the exact cutoff between the dwarf and subdwarf populations. A quick search turned up a lot of scientific hemming and hawing, but no real straight answer to this. At a guess, it's probably somewhere down around [M/H] = -1.5, and certainly lower than -1.

[chornedsnorkack]

I don't know the exact cutoff between the dwarf and subdwarf populations. A quick search turned up a lot of scientific hemming and hawing, but no real straight answer to this. At a guess, it's probably somewhere down around [M/H] = -1.5, and certainly lower than -1.

Meaning that no young subdwarfs exist in Local Group... neither Large Magellanic Cloud ([M/H]=-0,6) nor the Small ([M/H]=-0,9) qualify.

Does I Zwicky 18 consist of subdwarfs?

[ctcoker]

Those are average metallicities; the actual observational cut is not metallicity, but magnitude and color. The cool subdwarfs are classified as stars that are a couple magnitudes dimmer than they should be given their color; the hot subdwarfs are a different class of stars entirely. Given their lower metallicities, there may be younger subdwarfs in the Magellanic Clouds, more likely in the Small than the Large.

I do not know if I Zwicky 18 consists mostly of subdwarfs, but given its mean metallicity [M/H] ~ -1.2, it seems a good bet that there are quite a few.

[chornedsnorkack]

The effects of metallicity on main sequence stars are well known from stellar models; all else being equal, more metal-rich stars are redder and colder at fixed mass and age due to the higher opacity, especially at the surface. They are also more luminous and larger due to the higher mean molecular weight in the core, which leads to increased energy production and faster evolution.

Mean molecular weight depends not only on metal fraction, but on helium fraction.

Sunīs exterior is, and always has been (due to radiative core), 2% metals, 27% He-4 and 71% protium by mass. The core still has 2% metals, but only something like 36% protium left.

What is the He-4 fraction of subdwarfs, which have 0,2% or less metals?