The Lyman-alpha forest
The Lyman-alpha forest
A quasar lights up the gas in front of it. Follow which hydrogen atoms absorb, how motion groups their contributions, and how a telescope spectrum becomes a conditional measurement.
L1
Why quasar light contains a forest of dark lines
Hydrogen along the light path absorbs one atomic transition. Expansion and motion place its marks at different wavelengths.
L1
Did the gas get hotter, or more strongly ionized?
Heating and stronger ionizing light can both weaken hydrogen absorption. Follow the atoms and their motions to see what line width adds to the picture.
L2
From a patch of hydrogen to an absorption spectrum
Calculate neutral abundance, define the line cross section and integrate a proper light path. Check the result against a uniform analytic limit.
L3
When different places share one spectral velocity
Build the position-to-velocity map and see how crowding, finite line width and saturation let one column produce different transmission spectra.
L3
Recompute transmission from one fixed SDSS sightline
Follow a fixed SDSS quasar coadd through masks, a continuum fit and conditional flux statistics, then measure how continuum assumptions move the answer.
L4
Read a thermal history in small-scale velocity gradients
Follow 2607.19938v1 from pressure history and velocity power to a flux template and observational fit, keeping scale conventions and inference limits explicit.
Independent calculations
Download the scientific ZIP · Read setup and scope
Python with NumPy and SciPy recalculates three synthetic spectra offline. The optional observed exercise also needs Astropy and the separately fetched, hash-pinned SDSS coadd. Instructions retain all pixels without clipping noisy ratios.
Scripts, file sizes and SHA-256
- README.md (5881 B)
0f1259a35614944edbc800caab26c9ddfda8efcbdcadb76a1c407b6ee41c21db - calculate.py (1960 B)
789206ae0a4100c1ad25437d59c64f4b55d8482d9d4a03dfde040e900b727b2b - expected-observed.json (10116 B)
469a2191d51bf9050e1800df9ebb5e5b9aa3083da81db313f3cea8b5f2f28c12 - expected-synthetic.json (51605 B)
1409ebb5261bcef0ab0871a40e48bdbce4a32404c08e9b6abe7a024ab7c56ade - fetch_sdss.py (1694 B)
23d8553b76c604c4e071411d845fe576f32471770313ae7e2e823c756c7ef32c - field-input.json (934 B)
1206529ed37acab5d72b1e83458c1db78f7a8cd579964ce01db4c02470c0dc43 - input-manifest.json (651 B)
692fce6cd598d3bc14288384381afd24f7432d4e8f054fb94609e1a469e8dcdb - lyman-alpha-science-v1.zip (29960 B)
0a169f89a41770dd33b6bbefa7cda8ccd1d8579d0c77013ea77e0ccaa6112ea3 - model.py (3656 B)
6a05678c4e50a5e4180aa8017633be68dcce3e7f16f55150df90edca9d465a22 - sdss.py (6728 B)
4c9e99d73bfee1f07c9069caf1442f77cdee2cfba51fd079c06732759b6055be
Sources and calculation scope
- Verner & Ferland, Atomic Data for Astrophysics: Radiative Recombination Rates, arXiv:astro-ph/9509083v1
Targeted reading of equation 4, the hydrogen row of the fitted-parameter table, and the rate definitions. Pure-hydrogen case-A radiative recombination is used over 5,000–30,000 K. No helium, collisional ionization, self-shielding or complete ion network is solved. This is not a full reading of every ion in the paper.
- Tepper García, Voigt profile fitting to quasar absorption lines, arXiv:astro-ph/0602124v1
Targeted equations 1–8 establish the complete Lorentz/Maxwell convolution and normalization. Our calculation uses the full Voigt function, not the paper’s small-damping approximation. The atomic scalars are explicitly rounded assumptions. Hydrogen mass is approximated by proton mass.
- Peeples et al., Pressure Support versus Thermal Broadening in the Lyman-alpha Forest, arXiv:0910.0256v3
Targeted abstract, sections 2–3 and equations 6–7: photoionization equilibrium, uniform Gunn–Peterson opacity, and distinctions between thermal broadening and pressure history. This reading does not reproduce the hydrodynamic runs or claim a full-paper review.
- Iršič et al., Ringing of the Reionization, arXiv:2607.19938v1
Complete fixed 15-page v1, Figures 1–11, both tables and appendices read; actual figures and tables inspected. July 2026 preprint, checked 5 November 2026. The empirical template, observational coverage, conditional errors and unresolved velocity-wavenumber/length convention remain explicit. Code/data offered on request were not acquired; simulations and Table 2 are not independently reproduced.
- Chen et al. (2017), published quasar target table: SDSS J030335.42−002001.1
Target-table entry used only to fix the published object name, position and approximate redshift 2.72 before flux analysis. The exact coadd instead supplies pipeline redshift 2.69456148147583. This was a targeted table reading, not a full-paper review.
- SDSS DR17: Spectroscopic Data Basics
Official interpretation of calibrated coadds, vacuum heliocentric wavelengths, flux units, inverse variance, logarithmic sampling and AND/OR masks. The fixed file has 3,812 coadded pixels; it is not raw exposure data or a measured unabsorbed continuum.
- Independent hydrogen and sightline calculation materials
Original prescribed periodic gas screen and linear-parent peculiar velocity; fixed redshift three, no hydrodynamic pressure evolution. Full Voigt integration is checked against independent SciPy and finite-grid refinements. The offline Python and own synthetic examples are separate from the protected browser Engine.
- Fixed SDSS continuum and flux-statistics exercise
Plate 2068/MJD 53386/fibre 316, run2d 26, SHA-256 83b81bfc16c91750030758d00646366ff2cada06b7f05a80ac97ad152fc387fa. Original FITS is fetched separately; derived ratios use stated continuum windows and masks. Noise correction is conditional on fixed continuum and diagonal noise, not a gas-temperature or cosmological inference.