How much hydrogen has been consumed?

[iced199]

With our stars consuming hydrogen to make helium, how much has been consumed since the Big Bang? I know 73 or so percent of the total mass of the visible universe is hydrogen, so how much has been consumed? IE, what was the original proportion of hydrogen to helium to other elements? I know we are not in any danger of stars using up all our hydrogen in the near future, but still, just curious. Thanks.

 

[marcus]

I don't have any very precise figures, maybe someone can supply some more accurate.
I think there is rough agreement on the primordial abundances.
In mass terms:
"Without major changes to the Big Bang theory itself, BBN will result in mass abundances of about 75% of H-1, about 25% helium-4, about 0.01% of deuterium..."
http://en.wikipedia.org/wiki/Big_Bang_nucleosynthesis

As I recall the mass abundance of hydrogen is STILL around 73 or 74%. So a vague qualitative assessment would be that not very much has been used up. There are still these big clouds of gas (mostly hydrogen) which haven't even formed stars yet.

And fusion only occurs in the inner cores of stars, so even in stars a lot of the hydrogen is just sitting around in the outer layers providing weight to squeeze the inner 10% core so there is enough density and temperature to support fusion.

I'll try to find a more precise reliable source, but in the meantime my guess would be that percentagewise we have hardly made a dent--probably no more than 1 or 2% of the original hydrogen has been used up. Possibly more but I doubt it. Have to check

 

[Chronos]

It is believed that about 90% of the baryons expected to exist are unaccounted for in the local universe (z~0). That leaves a lot more hydrogen available for future star formation than the amount currently claimed by stars. It is likely much of this exists in the IGM and is mostly ionized, making it difficult to detect. An enormous mass of hydrogen was recently detected bridging Andromeda and the Triangulum galaxy [possibly on the order of 500 million or more solar masses]. See http://arxiv.org/abs/1205.5235

 

[Orion1]

With our stars consuming hydrogen to make helium, how much has been consumed since the Big Bang? I know 73 or so percent of the total mass of the visible universe is hydrogen, so how much has been consumed?

The Universe is capable of burning both hydrogen and helium as nuclear fuel. In about 5 billion years, the Sun will enter a red giant phase and begin burning helium in the core.

λCDM Universe heavy baryonic matter and neutrino density:
$$\Omega_h = 0.0033$$
λCDM Universe baryon density:
$$\Omega_b = 0.0456$$
Percentage of hydrogen and helium burned into heavy baryonic matter by the Universe:
$$P_u = \frac{\Omega_h}{\Omega_b} = 0.0723 = 7.23 \; \%$$
$$\boxed{P_u = 7.23 \; \%}$$

It is believed that about 90% of the baryons expected to exist are unaccounted for in the local universe (z~0).

$$P_u = \frac{\Omega_h}{10 \cdot \Omega_b} = 0.00723 = 0.723 \; \%$$
$$\boxed{P_u = 0.723 \; \%}$$

Reference:
λCDM model parameters - Wikipedia
Sun - Possible long-term cycle - Wikipedia
Universe - size, age, structure, and laws - Wikipedia
The End of Stars? - Orion1 #8

 

[Chalnoth]

The Universe is capable of burning both hydrogen and helium as nuclear fuel. In about 5 billion years, the Sun will enter a red giant phase and begin burning helium in the core.

λCDM Universe heavy baryonic matter and neutrino density:
$$\Omega_h = 0.0033$$
λCDM Universe baryon density:
$$\Omega_b = 0.0456$$
Percentage of hydrogen and helium burned into heavy baryonic matter by the Universe:
$$P_u = \frac{\Omega_h}{\Omega_b} = 0.0723 = 7.23 \; \%$$
$$\boxed{P_u = 7.23 \; \%}$$


$$P_u = \frac{\Omega_h}{10 \cdot \Omega_b} = 0.00723 = 0.723 \; \%$$
$$\boxed{P_u = 0.723 \; \%}$$

Reference:
λCDM model parameters - Wikipedia
Sun - Possible long-term cycle - Wikipedia
Universe - size, age, structure, and laws - Wikipedia
The End of Stars? - Orion1 #8

Where are you getting $\Omega_h$ from? Because these numbers seem extremely unlikely. I don't think that much matter has even collapsed to form stars yet.

 

[jimgraber]

http://en.wikipedia.org/wiki/Abundance_of_the_chemical_elements
suggests heavy elements are more like 2% than 7% by weight.
By atom number count, it is much less of course.

Jim Graber

 

[Orion1]

Where are you getting $\Omega_h$ from? Because these numbers seem extremely unlikely. I don't think that much matter has even collapsed to form stars yet.

$\Omega_h$ is cited from post#4, reference 3. Only around 0.5% of all 'baryonic' matter is presently in the form of stars, relative to all matter and energy in the total Universe.

Heavy Elements: (baryonic)
$$\Omega_H = 0.003 = 0.3 \; \%$$
Neutrinos: (baryonic)
$$\Omega_{\nu} = 0.0003 = 0.03 \; \%$$

$\Omega_h$ is actually the addition of:
$$\Omega_h = \Omega_H + \Omega_{\nu} = 0.003 + 0.0003 = 0.0033 = 0.33 \; \%$$
$$\boxed{\Omega_h = 0.0033}$$

Only about 2% (by mass) of the Milky Way galaxy's disk is composed of heavy elements.

2% is relative to the Milky Way galaxy's disk, not to the Universe as a whole.

My calculation in post#4 is relative only to 'baryonic' matter in the λCDM model, i.e. hydrogen and helium, and not to all the matter and energy in the total Universe.

Reference:
Universe - size, age, structure, and laws - Wikipedia
Abundance of elements in the Universe - Wikipedia

 

[Chalnoth]

$\Omega_h$ is cited from post#4, reference 3. Only around 0.5% of all 'baryonic' matter is presently in the form of stars, relative to all matter and energy in the total Universe.

Heavy Elements: (baryonic)
$$\Omega_H = 0.003 = 0.3 \; \%$$
Neutrinos: (baryonic)
$$\Omega_{\nu} = 0.0003 = 0.03 \; \%$$

$\Omega_h$ is actually the addition of:
$$\Omega_h = \Omega_H + \Omega_{\nu} = 0.003 + 0.0003 = 0.0033 = 0.33 \; \%$$
$$\boxed{\Omega_h = 0.0033}$$


2% is relative to the Milky Way galaxy's disk, not to the Universe as a whole.

My calculation in post#4 is relative only to 'baryonic' matter in the λCDM model, i.e. hydrogen and helium, and not to all the matter and energy in the total Universe.

Reference:
Universe - size, age, structure, and laws - Wikipedia
Abundance of elements in the Universe - Wikipedia

Perhaps you mean from this graph?
http://en.wikipedia.org/wiki/File:Cosmological_Composition_-_Pie_Chart.png

This shows heavy elements as 0.03% of the universe by mass, which is roughly 1% of the total baryon fraction. The neutrino mass fraction almost entirely comes from the early universe, and shouldn't be added here.

 

[Orion1]

heavy elements as 0.03% of the universe by mass, which is roughly 1% of the total baryon fraction. The neutrino mass fraction almost entirely comes from the early universe, and shouldn't be added here.

λCDM Universe heavy baryonic matter mass fraction:
$$\Omega_h = 0.0003$$
λCDM Universe baryon matter mass fraction:
$$\Omega_b = 0.0456$$
λCDM Universe neutrino baryonic matter mass fraction:
$$\Omega_{\nu} = 0.003$$
λCDM percentage of hydrogen and helium burned into heavy baryonic matter by the Universe:
$$P_u = \frac{\Omega_h}{\Omega_b - \Omega_{\nu}} = 0.00704 = 0.704 \; \%$$
$$\boxed{P_u = 0.704 \; \%}$$

Reference:
Cosmological Composition - Pie_Chart - Wikipedia
λCDM model parameters - Wikipedia

 

[Chalnoth]

A fraction of those neutrinos would have been produced from nuclear fusion and heavy element radioactive decay, insufficient data available for further differentiation.

Yes, but that number is completely inconsequential compared to either the current heavy baryonic matter density or the primordial neutrino fraction.

λCDM Universe heavy baryonic matter and neutrino density:
$$\Omega_h = 0.003$$

Heavy baryonic matter density is roughly $\Omega_H = 0.0003$, a factor of ten less than you paint here.

 

[Orion1]

Heavy baryonic matter density is roughly $\Omega_H = 0.0003$, a factor of ten less than you paint here.

Corrected, see post#9.

 

[Chalnoth]

Corrected, see post#9.

Yeah, that's much more reasonable. However, you still shouldn't be considering the neutrino fraction, as that really doesn't have anything to do with the elements being burned in stars, nor is it part of the baryon fraction. There's also too many significant digits kept, as the heavy element fraction is only quoted with one significant digit. So given the information presented so far in this thread, "a bit less than 1%," is the accurate way to state the fraction of baryons in heavy matter by mass.

 

[Orion1]

you still shouldn't be considering the neutrino fraction, as that really doesn't have anything to do with the elements being burned in stars, nor is it part of the baryon fraction.

λCDM Universe heavy baryonic matter mass fraction:
$$\Omega_h = 0.0003$$
λCDM Universe baryon matter mass fraction:
$$\Omega_b = 0.0456$$

λCDM percentage of hydrogen and helium burned into heavy baryonic matter by the Universe:
$$P_u = \frac{\Omega_h}{\Omega_b} = 0.0065 = 0.65 \; \%$$
$$\boxed{P_u = 0.65 \; \%}$$

Reference:
Cosmological Composition - Pie_Chart - Wikipedia
λCDM model parameters - Wikipedia

 

[Impaler]

On a related note what is the current Rate of burn in the local-galactic-group environment? I've read recently that high red-shift galaxies have been observed that have metal content close to that of present galaxies. This has been interpreted as indicating that the rate of burn was very very high just beyond our limit of observation and that it then slowed down and stayed slow for most of the rest of the universes history.

I'm wondering what kind of time-line we would get if we looked at only the burn-rate extrapolated from luminosity (something we can do with high confidence) and the changing galactic enrichment (also high confidence). Dose it jive?

PS: Orion, dose your heavy Baryon mass fraction include the content still inside of stars, or is it just what's been released into dust/planets etc? At anyone time the next batch of heavy Baryons are hidden from view inside Stars but we should be able to estimate this fairly accurately, it might not be inconsequential.

 

[Orion1]

Orion, does your heavy Baryon mass fraction include the content still inside of stars?

Affirmative, the stellar heavy baryonic matter mass fraction inside stars is included and determined by the emission spectrum and metallicity of stars. It may be more meaningful to simply calculate the lifetime of the Universe, which includes the totality of all the different events occurring inside the Universe up to the present time and beyond.

$H_0 = 2.3298 \cdot 10^{- 18} \; \text{s}^{- 1}$ - Hubble parameter (WMAP)
$\Omega_h = 0.0003$ - λCDM heavy baryonic matter mass fraction
$\Omega_b = 0.0456$ - λCDM baryonic matter mass fraction

Universe heavy baryonic matter stellar burn rate integration by substitution:
$$R_b = \frac{d \Omega}{dt} = \Omega_h H_0 = 6.989 \cdot 10^{-22} \; \frac{d \Omega}{\text{s}}$$

Universe heavy baryonic matter stellar burn rate:
$$\boxed{R_b = 6.989 \cdot 10^{-22} \; \frac{d \Omega}{\text{s}}}$$

Universe baryonic matter stellar epoch burn lifetime integration by substitution:
$$T_s = d \Omega \cdot dt = \frac{\Omega_b}{R_b} = \frac{\Omega_b}{\Omega_h H_0} = 6.524 \cdot 10^{19} \; \text{s} = 2.067 \cdot 10^{12} \; \text{y}$$

Universe baryonic matter stellar epoch burn lifetime:
$$\boxed{T_s = \frac{\Omega_b}{\Omega_h H_0}}$$

Universe baryonic matter stellar epoch burn lifetime:
$$\boxed{T_s = 2.067 \cdot 10^{12} \; \text{y}}$$

Universe age:
$$T_u = \frac{1}{H_0} = 4.292 \cdot 10^{17} \; \text{s} = 1.36 \cdot 10^{10} \; \text{y}$$

$$\boxed{T_u = 1.36 \cdot 10^{10} \; \text{y}}$$

Number of present Universe ages required to complete baryonic matter stellar epoch burn lifetime:
$$n_a = \frac{T_s}{T_u} = \frac{\Omega_b}{\Omega_h} = 152$$

The Universe will be producing stars for a very long time...

Reference:
Universe - Wikipedia
Cosmological Composition - Pie_Chart - Wikipedia
λCDM model parameters - Wikipedia
Heat death of the Universe - Wikipedia

 

[Impaler]

No I was asking what the burn rate is derived from observation of present local space (z = 0), not form extrapolation of theorized age. As I said the burn rate is believed to be changing over time quite substantially, simply dividing the total burn by the total time would almost certainly over-estimate the present rate.