Cosmology · Baryons, gas and cosmic neutrinos

An inventory of ordinary matter

Classify one supplied hydrogen–helium mass account by both environment and nuclear species, then separate baryon count from ionization-dependent particle count.

Preparation: ratios, powers of ten and ordinary arithmetic. Physical quantities and notation are introduced as they are needed.

Back to the chapter

After reading, you can

State the mass convention and selection behind an ordinary-matter inventory.
Avoid double counting when two classifications describe the same material.
Distinguish conserved nuclear inventory from charge state, free-particle count and a complete energy account.

An inventory starts with a convention and a domain

An ordinary-matter census connects observations with quantities such as stellar mass, gas mass and composition. Each conversion needs a definition of the material counted, the region or epoch, and the mass or energy convention.

Nuclear species and physical environments provide different classifications. The same hydrogen nucleus belongs both to a species category and to an environment such as a stellar or diffuse-gas reservoir.

A precision mass–energy inventory must account for electron rest mass, nuclear and atomic binding, radiation and other energy terms as appropriate. A nuclear mass proxy can illustrate bookkeeping while leaving those corrections outside its definition.

Here choose a finite account containing only hydrogen and helium nuclear mass proxies. The numbers are invented for the exercise; the reservoir labels and fractions are not a current cosmic census or observational completeness claim.

Rows and columns partition the same supplied mass

Let M_* be an arbitrary positive mass unit for this imposed nuclear proxy. Define four disjoint environmental reservoirs with total masses 25, 15, 35 and 25 M_*.

The stellar row contains hydrogen proxy 15 and helium proxy 10. Cold neutral gas contains 13 and 2; warm ionized gas 28 and 7; hot ionized gas 19 and 6, all in M_*.

Row sums give 100M_* across environments. Column sums give 75M_* hydrogen and 25M_* helium, also totaling 100M_*. Adding both sets of totals would count the same supplied material twice.

The environmental names are disjoint by stipulation in this ledger. Real tracer-selected reservoirs can overlap, so their observational labels do not automatically define a clean partition.

Invented finite nuclear-mass-proxy account; environmental rows and species columns describe the same 100M_*
Reservoir	Hydrogen / M_*	Helium / M_*	Row total / M_*	Share of supplied total
Stellar	15	10	25	1/4
Cold neutral gas	13	2	15	3/20
Warm ionized gas	28	7	35	7/20
Hot ionized gas	19	6	25	1/4
Total	75	25	100	1

A selected subtotal is different from the full account

Select only the stellar and cold-gas rows. Their subtotal is 25+15 = 40M_*, leaving 60M_* outside that chosen selection. The two-fifths share is a property of this supplied ledger.

Calling the other 60M_* outside the selection does not establish that an actual survey has missed that fraction. A real completeness statement would require observing and tracer-to-mass models.

Now prescribe a reassignment of 8M_* hydrogen and 2M_* helium from the warm row to the hot row. The warm entries become 20 and 5, and the hot entries 27 and 8.

The warm and hot totals exchange ten units, becoming 25 and 35, while hydrogen remains 75, helium 25 and the full account 100M_*. This is a change of assigned categories; no heating law, transition rate or physical time history has been calculated.

Ionization changes the number of free particles

Consider a separate parcel containing eight hydrogen nuclei and two helium-4 nuclei, with no nuclear transmutation. It contains 8+2×4 = 16 baryons, counting the protons and neutrons in the nuclei.

As neutral atoms, the parcel has ten atomic particles. Fully ionizing it leaves ten bare nuclei and releases twelve electrons: one from each hydrogen atom and two from each helium atom.

The resulting free-particle count is 22, while the baryon count remains 16. Electrons are not baryons. The separate parcel is an illustration of particle accounting, not an extra row to add to the 100-unit ledger.

Under an ideal nuclear proxy assigning one mass unit to a hydrogen nucleus and four to helium-4, the parcel’s proxy remains 16 units. Ionization exchanges binding energy with radiation or other material in a full physical account; constancy of this proxy is not a claim that every mass–energy contribution stays fixed.

This is a finite invented nuclear-mass-proxy account, not a current baryon census. Four stipulated disjoint environmental rows use arbitrary positive mass unit M_*. Stellar H 15 plus He 10 gives 25; cold gas H 13 plus He 2 gives 15; warm gas H 28 plus He 7 gives 35; hot gas H 19 plus He 6 gives 25. All bars share a linear mass axis zero to 40 M_*. Blue hydrogen portions on the left have centered circles; orange helium portions on the right have centered squares, matching the legend. Direct left-H/right-He numerical captions identify every actual segment without color. Row totals are 25, 15, 35, 25 and sum 100 M_*. Column totals H 75 and He 25 partition that same 100 M_*, so adding both sets does not make 200. Explicit SELECTED labels identify stellar plus cold gas as a 40 M_* subset;60 M_* lies outside this chosen selection, which is not survey incompleteness. A separate prescribed reassignment of 8 H plus 2 He M_* from warm to hot changes those row totals to 25 and 35 while H 75, He 25 and full 100 remain fixed; no heating dynamics are calculated. The lower illustration is a distinct parcel, never an extra ledger row. Eight H labels and two helium-4 labels are shown as ten neutral atoms in one row and ten fully ionized bare nuclei in the next. Circles and squares distinguish the two labels; their drawing sizes are schematic, not physical particle radii or masses. Twelve additional small electron dots, in two rows of six, belong to the ionized parcel only. Eight H nuclei plus two helium-4 nuclei retain 8+2×4 =16 baryons in either charge state. There are ten neutral atomic particles, or ten nuclei plus twelve free electrons =22 free particles after full ionization. Electrons are not baryons, and no electron orbits are depicted. An imposed nuclear proxy assigning 1 to H and 4 to helium-4 also remains 16 for this parcel. Ionization changes binding-energy exchange in a full physical account; electron rest mass, binding and radiation are outside this declared proxy. No measured reservoir fraction, cosmic missing-matter percentage, complete energy conservation law or actual survey conversion is inferred. Original Ark teaching model.

A real census carries the tracer conversions

Starlight becomes an inferred stellar mass through population, extinction and mass-to-light assumptions. Gas absorption or emission becomes an inferred mass through species abundance, ionization, temperature and geometry.

Diffuse gas can contain substantial column or mass while producing a weak selected signal. Different physical phases favour different tracers, and their selection functions must be compared before combining inferred reservoirs.

A historical source inventory can help explain those methods without supplying current fractions. The finite ledger here deliberately avoids adopting its empirical percentages, fitted masses or numerical energy-density estimates.

A useful ordinary-matter inventory therefore states the accounting convention, disjointness assumptions, observing selection, conversion models and uncertainties. The next lesson isolates why fixed gas column can coexist with changing recombination-line emission.

Worked reasoning

Avoid counting the same mass twice

Why do the species total 75+25 and the reservoir total 25+15+35+25 not make 200M_*?

The species columns partition the supplied nuclear proxy into hydrogen and helium, totaling 100M_*.
The environmental rows independently partition that same proxy, also totaling 100M_*.
The classifications are two axes of one table, so their totals describe the same material.

The account contains 100M_*. Its selected stellar-plus-cold-gas subtotal is 40M_*, not an additional mass on top of the full account.

Try the reasoning

Does the fully ionized eight-H-plus-two-helium-4 parcel have 22 baryons because it has 22 free particles?
Show the answer and reasoning
No; it has 16 baryons.
The twelve liberated electrons change free-particle count but do not add baryons.
Does the prescribed warm-to-hot reassignment change the hydrogen and helium totals?
Show the answer and reasoning
No; they remain 75M_* and 25M_*.
The same imposed species masses move between environmental labels.
Does the chosen 40-percent selected subtotal measure a current cosmic baryon fraction?
Show the answer and reasoning
No.
It belongs to an invented finite ledger with a stipulated selection and no observational inference.

What to carry forward

An ordinary-matter inventory needs a mass convention, domain and tracer selection.
Species and environmental classifications can partition the same mass and must not be added as separate material.
Ionization changes charge state and free-particle count while a declared nuclear account keeps baryon bookkeeping distinct from total energy.

References

Sources supporting the explanations, physical distinctions and examples in this lesson.