A quasar beam through intergalactic hydrogen

Lyman-alpha Forest: Gas, Velocities and Absorption

Why does one beam of quasar light acquire a forest of dark lines? Neutral hydrogen removes light near its Lyman-alpha transition. Expansion and gas motion shift the absorption from different places to different wavelengths. Density sets how much hydrogen contributes, while temperature changes both the neutral fraction and line width.

Drag a beam through a three-dimensional gas field. Follow the same hydrogen into real-space density, recession velocity and a transmitted spectrum.

Neutral-hydrogen column $N_{\mathrm{HI}}=4.65\times10^{14}\,\mathrm{cm^{-2}}$

Mean transmitted fraction $\langle F\rangle=0.702$

Thermal Doppler width $b=12.8\,\mathrm{km\,s^{-1}}$

Selected light transmitted $F_{\mathrm{selected}}=0.159$

Move a beam through the gas

Gas temperature

10^4\,\mathrm K

T/\mathrm K

Photoionization rate

1.00

\Gamma_{\mathrm{photo}}/(10^{-12}\,\mathrm{s^{-1}})

Peculiar-velocity strength

1.00

s_v

Drag the bright source across the cube. Select a dip in the spectrum to follow that colour of light.

Preparing one complete sightline.

Sightline position and assumptions

Comoving transverse position

0.800

Comoving height

-0.400

A prescribed positive gas field in a finite slice at redshift three. Particle brightness shows density; the light pulses are a sped-up illustration.

Temperature changes neutral abundance and thermal width. It does not evolve or smooth the frozen gas field. Camera rotation changes only the view.

Pure hydrogen in uniform photoionization equilibrium; no helium, collisions, self-shielding calculation, gas dynamics or fitted cosmological parameters. The all-chord ionizing-depth bound applies only inside this finite cube. The thermal hydrogen mass is approximated by the proton mass.

This finite prescribed gas screen does not evolve cosmic structure. Its spectrum contains absorption inside the cube; a separate exercise uses an observed SDSS spectrum.

Start with the essentials

Focus question: Which gas makes the dip you selected?
One-sentence intuition: Several places can absorb at the same spectral velocity. Temperature spreads each contribution, and their optical depths add before the light is attenuated.

Core mathematical model

Neutral fraction in the declared hydrogen model

\Gamma_{\mathrm{photo}}n_{\mathrm{HI}}=\alpha(T)n_e n_p

Ionization removes neutral atoms while recombination restores them. This screen assumes pure hydrogen and a uniform radiation background.

Thermal width

b=\sqrt{\frac{2k_{\mathrm B}T}{m_{\mathrm H}}}

Hotter atoms have a wider spread of velocities. Their absorption spreads even when the gas positions stay fixed.

Positions become spectral velocities

u(x)=aH x+v_x(x)

Position is comoving; the scale factor converts its expansion contribution. Peculiar motion can crowd several locations into the same velocity. The display camera does not set this direction.

Add absorption along the ray

\tau(v)=\int n_{\mathrm{HI}}(x)\,\sigma_v[v-u(x)]\,a\,\mathrm dx,\qquad F(v)=e^{-\tau(v)}

The full Voigt cross section includes thermal and natural broadening. Forward integration stays finite when the velocity map folds; it does not invert that map.

Common difficulties

One dark line, one cloud?

Typical misconceptionA dip identifies one object at one known distance.

Better mental modelSeveral patches can share a recession velocity, and thermal wings overlap. The selected wavelength marks a combined contribution.

Temperature versus pressure history

Typical misconceptionTurning the temperature control also smooths away small gas structures.

Better mental modelHere it changes neutral abundance and line width only. Pressure smoothing requires an evolved thermal history, which this fixed field does not compute.

Run the experiment

01
Follow a dip
Select a dark part of the spectrum, then drag the source across the cube.
What to observe: The ray, density profile, velocity map and missing light change together.
02
Heat the same gas
Compare the cold and hot presets without changing the sightline.
What to observe: Lines broaden while hydrogen becomes less neutral. Both changes affect the transmitted light.
03
Crowd velocities
Compare zero peculiar velocity with the crowded preset.
What to observe: The spatial gas field stays put while the velocity map bends and can fold. A stronger dip need not mean an extra object.

Lyman-alpha Forest: Gas, Velocities and Absorption

Turn a patch of gas into a dark line

Core mathematical model

Neutral fraction in the declared hydrogen model

Thermal width

Positions become spectral velocities

Add absorption along the ray

Common difficulties

One dark line, one cloud?

Temperature versus pressure history

Run the experiment

Follow a dip

Heat the same gas

Crowd velocities

Related experiments and articles

From hydrogen to forest spectra