Spectrum detective

A single dark line can mislead; a matching pattern is much stronger evidence. In this investigation, compare four hydrogen lines, predict how motion shifts them, and then find the pattern in measured light from Vega. The adjustable teaching model and the Hubble observations are separate: changing a slider never changes the data.

Helpful background. Reading starlight explains absorption lines and wavelength. You will read axes and compare ratios; the square-root formula is optional.

Spectral lines and a common shift

A spectrograph separates light by wavelength. Absorption lines are dips in the received light relative to the surrounding spectrum. They can reveal transitions between particular atomic energy levels, but identifying an element means checking a pattern, not just finding one convenient dip.

The four reference features below belong to neutral hydrogen’s Balmer series. For absorption, an electron goes from level 2 to level 3, 4, 5 or 6; emission reverses the transition. The familiar Hα, Hβ, Hγ and Hδ names label those four features. Individual features can contain unresolved fine structure; these beginner reference positions are not a catalog of its components. Compare the NIST Handbook, Hydrogen atomic-data notes.

We use vacuum wavelengths, the values light has in vacuum, in nanometres (nm). One nm is ten ångströms (Å). The reference values come from the SDSS 2005, DR4 vacuum spectral-line table. They should not be mixed with air-wavelength tables without conversion.

Before moving the controls, predict two things: will recession move every line toward longer wavelengths, and will the change in nanometres be the same for every line?

1. Match several lines

These four markers form a reference pattern for hydrogen's Balmer lines. The Greek letters identify different transitions. Compare their positions and unequal spacing; the equal marker heights carry no information about line strength.

Teaching template: reference wavelengths with equal-height markers, no physical intensity or line-width model. Hδ, Hγ, Hβ and Hα correspond to transitions between levels 2 and 6, 5, 4 and 3, respectively. Absorption goes upward in energy; emission reverses the transition.

Test an identification

Check the conclusion

Compare several features before identifying a pattern. A matching position alone does not measure how much of an element is present.

Explain the identification

A consistent multi-line pattern supports a hydrogen interpretation more strongly than one coincidence. Temperature, density, ionization, radiative transfer, blends and the instrument influence line strengths and shapes. This display has no abundance model.

2. Shift the whole pattern

Positive radial velocity means recession; negative means approach. Every wavelength changes by the same fraction. The close-up keeps fixed axes while the velocity changes. Choose another line to inspect its own wavelength window.

Change the teaching model

Radial velocity: 0 km/s

Recede at 1,500 km/sApproach at 1,500 km/sReset model

Position markers only. The display uses the exact special-relativistic formula for purely radial motion of an inertial source, bounded to ±3,000 km/s. It does not model cosmological or gravitational redshift, line broadening, or a temperature change.

At 0 km/s, all four wavelengths retain their reference values. Hβ remains at 486.268 nm: its shift is 0.000 nm.

All four lines share the same wavelength ratio

Line	Reference / nm	Shifted / nm
Hδ	410.289	410.289
Hγ	434.168	434.168
Hβ	486.268	486.268
Hα	656.461	656.461

Predict, then compare

Test at +1,500 km/s

A common fractional change need not be a common change in nanometres. Compare Hδ and Hα in the table.

Explain the wavelength comparison

At +1,500 km/s the fractional shift is about 0.5016%. Hδ moves by about 2.058 nm, while Hα moves by about 3.293 nm. Both shifts have the same ratio to their reference wavelength.

The diagrams, reference table and explanations work without JavaScript. If the controls do not activate, reload this laboratory or use the worked examples below.

3. Find the pattern in measured starlight

These are processed observations of Vega, measured by Hubble's Space Telescope Imaging Spectrograph in 2003 and calibrated in CALSPEC product version 012 (2026). Dots and small vertical statistical-error bars preserve the supplied samples. The model controls above never change these measurements.

Look for a broad dip near each reference wavelength. The four panels have different labeled vertical ranges; they are not normalized to a common continuum. Flux density is shown in units of 10⁻⁹ erg s⁻¹ cm⁻² Å⁻¹, even though the horizontal axis uses nanometres.

Hδ: 400–420 nm

73 samples; lowest sampled flux at 410.32 nm. This sampled minimum is not a fitted line centre or a radial-velocity measurement.

Hγ: 424–444 nm

73 samples; lowest sampled flux at 434.24 nm. This sampled minimum is not a fitted line centre or a radial-velocity measurement.

Hβ: 476–496 nm

73 samples; lowest sampled flux at 486.18 nm. This sampled minimum is not a fitted line centre or a radial-velocity measurement.

Hα: 644–669 nm

51 samples; lowest sampled flux at 656.32 nm. This sampled minimum is not a fitted line centre or a radial-velocity measurement.

Data credit: NASA/ESA Hubble Space Telescope, STIS, STScI/CALSPEC, and Bohlin and collaborators. Statistical error bars are mostly smaller than the dots. The separate systematic-error column is 1% of flux, with the source's warning that it may be larger. Broad stellar line profiles, blends and instrumental resolution all matter.

Source, processing and uncertainties

We retain all 270 source samples in four inclusive windows: 400–420, 424–444, 476–496 and 644–669 nm. The FITS file identifies these optical measurements as STIS data; its theoretical extensions outside 167.5–1020 nm are not used. Wavelengths are in the heliocentric vacuum frame, not the star's rest frame.

Only wavelength and spectral-resolution units change from Å to nm, dividing by ten. Downloaded fluxes retain their original per-Å units. No continuum normalization, interpolation, binning, smoothing, velocity correction or line fit is performed. All selected rows have CALSPEC DATAQUAL = 1, meaning good; none is replaced. Separate windows are never joined across gaps.

The reported spectral FWHM is about 0.55 nm in the three blue windows and 0.98 nm around Hα. Adjacent samples are therefore not independent resolution elements. The table preserves STATERROR and SYSERROR separately; it supplies no complete covariance matrix. Hubble is above Earth's atmosphere, so terrestrial absorption bands are absent, but stellar blends remain possible.

STScI 2026, CALSPEC Vega product alpha_lyr_stis_012.fits · STScI 2026, CALSPEC documentation, spectrum composition and wavelength frame · Bohlin and Gilliland 2004, §§ 2 and 4 · MAST, Data Use Policy.

Download the 270 measurements (CSV) · Download measurements and provenance (JSON) · Download the independent teaching model · Model assumptions and reproduction

Measured wavelengths in nm; flux and errors in 10⁻⁹ erg s⁻¹ cm⁻² Å⁻¹

Wavelength	Flux	Stat. error	Sys. error
400.1437	8.5247	0.0013	0.0852
400.4187	8.5961	0.0013	0.0860
400.6936	8.6543	0.0013	0.0865
400.9686	8.7089	0.0013	0.0871
401.2435	8.7254	0.0013	0.0873
401.5185	8.7211	0.0013	0.0872
401.7935	8.7700	0.0013	0.0877
402.0684	8.7653	0.0013	0.0877
402.3434	8.7418	0.0013	0.0874
402.6183	8.7180	0.0013	0.0872
402.8933	8.7016	0.0013	0.0870
403.1683	8.7198	0.0013	0.0872
403.4432	8.7293	0.0013	0.0873
403.7182	8.7491	0.0013	0.0875
403.9932	8.7134	0.0013	0.0871
404.2681	8.6512	0.0012	0.0865
404.5431	8.6038	0.0012	0.0860
404.8180	8.5891	0.0012	0.0859
405.0930	8.5834	0.0012	0.0858
405.3680	8.5441	0.0012	0.0854
405.6429	8.4912	0.0012	0.0849
405.9179	8.4197	0.0012	0.0842
406.1928	8.3301	0.0012	0.0833
406.4678	8.2897	0.0012	0.0829
406.7428	8.2451	0.0012	0.0825
407.0177	8.1310	0.0012	0.0813
407.2927	8.0264	0.0012	0.0803
407.5677	7.9163	0.0012	0.0792
407.8426	7.7553	0.0012	0.0776
408.1176	7.5554	0.0012	0.0756
408.3925	7.2628	0.0011	0.0726
408.6675	6.8658	0.0011	0.0687
408.9425	6.3749	0.0011	0.0637
409.2174	5.7630	0.0010	0.0576
409.4924	5.0435	0.0009	0.0504
409.7673	4.2180	0.0009	0.0422
410.0423	3.4804	0.0008	0.0348
410.3172	3.3068	0.0008	0.0331
410.5922	3.8354	0.0008	0.0384
410.8672	4.5760	0.0009	0.0458
411.1421	5.3052	0.0010	0.0531
411.4171	5.9305	0.0010	0.0593
411.6920	6.4327	0.0011	0.0643
411.9670	6.8365	0.0011	0.0684
412.2419	7.1557	0.0011	0.0716
412.5169	7.3825	0.0011	0.0738
412.7919	7.5127	0.0011	0.0751
413.0668	7.6415	0.0011	0.0764
413.3418	7.7686	0.0012	0.0777
413.6167	7.9043	0.0012	0.0790
413.8917	7.9682	0.0012	0.0797
414.1667	8.0208	0.0012	0.0802
414.4416	8.0167	0.0012	0.0802
414.7166	8.0547	0.0012	0.0805
414.9915	8.0603	0.0012	0.0806
415.2665	8.0677	0.0012	0.0807
415.5414	8.0654	0.0012	0.0807
415.8164	8.0932	0.0012	0.0809
416.0914	8.0825	0.0012	0.0808
416.3663	8.0238	0.0012	0.0802
416.6413	8.0313	0.0012	0.0803
416.9162	8.0265	0.0012	0.0803
417.1912	7.9807	0.0012	0.0798
417.4661	7.9313	0.0011	0.0793
417.7411	7.9210	0.0011	0.0792
418.0160	7.9361	0.0011	0.0794
418.2910	7.9560	0.0011	0.0796
418.5659	7.9746	0.0011	0.0797
418.8409	7.9721	0.0011	0.0797
419.1158	7.9582	0.0011	0.0796
419.3907	7.9410	0.0011	0.0794
419.6657	7.9109	0.0011	0.0791
419.9406	7.8912	0.0011	0.0789
424.0648	7.6871	0.0011	0.0769
424.3397	7.6521	0.0011	0.0765
424.6147	7.6182	0.0011	0.0762
424.8896	7.6034	0.0011	0.0760
425.1646	7.5747	0.0011	0.0757
425.4395	7.5715	0.0011	0.0757
425.7144	7.5749	0.0011	0.0757
425.9894	7.5609	0.0011	0.0756
426.2643	7.5365	0.0011	0.0754
426.5393	7.5155	0.0011	0.0752
426.8142	7.5029	0.0011	0.0750
427.0891	7.4520	0.0011	0.0745
427.3640	7.4230	0.0011	0.0742
427.6390	7.4190	0.0011	0.0742
427.9139	7.3794	0.0011	0.0738
428.1888	7.3640	0.0011	0.0736
428.4638	7.3527	0.0011	0.0735
428.7387	7.3357	0.0011	0.0734
429.0136	7.2619	0.0011	0.0726
429.2886	7.2107	0.0011	0.0721
429.5635	7.1599	0.0011	0.0716
429.8384	7.0883	0.0010	0.0709
430.1133	6.9745	0.0010	0.0697
430.3883	6.9459	0.0010	0.0695
430.6632	6.9158	0.0010	0.0692
430.9381	6.8436	0.0010	0.0684
431.2130	6.7580	0.0010	0.0676
431.4879	6.6123	0.0010	0.0661
431.7629	6.4831	0.0010	0.0648
432.0378	6.3024	0.0010	0.0630
432.3127	6.0627	0.0010	0.0606
432.5876	5.7190	0.0009	0.0572
432.8625	5.2574	0.0009	0.0526
433.1375	4.8406	0.0009	0.0484
433.4124	4.2906	0.0008	0.0429
433.6873	3.6327	0.0007	0.0363
433.9623	3.0465	0.0007	0.0305
434.2372	2.9520	0.0007	0.0295
434.5121	3.4189	0.0007	0.0342
434.7870	4.0376	0.0008	0.0404
435.0619	4.5876	0.0008	0.0459
435.3368	5.0736	0.0009	0.0507
435.6117	5.5029	0.0009	0.0550
435.8866	5.8484	0.0009	0.0585
436.1615	6.0997	0.0009	0.0610
436.4365	6.2622	0.0010	0.0626
436.7114	6.3995	0.0010	0.0640
436.9863	6.4970	0.0010	0.0650
437.2612	6.6108	0.0010	0.0661
437.5361	6.6743	0.0010	0.0667
437.8110	6.7273	0.0010	0.0673
438.0859	6.7617	0.0010	0.0676
438.3608	6.7072	0.0010	0.0671
438.6357	6.6974	0.0010	0.0670
438.9106	6.7516	0.0010	0.0675
439.1855	6.7830	0.0010	0.0678
439.4604	6.7750	0.0010	0.0678
439.7353	6.7807	0.0010	0.0678
440.0102	6.8047	0.0010	0.0680
440.2851	6.8152	0.0010	0.0682
440.5600	6.8243	0.0010	0.0682
440.8349	6.8545	0.0010	0.0685
441.1098	6.8536	0.0010	0.0685
441.3847	6.8332	0.0010	0.0683
441.6596	6.7947	0.0010	0.0679
441.9345	6.7838	0.0010	0.0678
442.2094	6.8207	0.0010	0.0682
442.4842	6.8386	0.0010	0.0684
442.7591	6.8238	0.0010	0.0682
443.0340	6.8069	0.0010	0.0681
443.3089	6.8131	0.0010	0.0681
443.5838	6.7860	0.0010	0.0679
443.8587	6.7663	0.0010	0.0677
476.0116	5.5126	0.0009	0.0551
476.2863	5.4995	0.0009	0.0550
476.5610	5.4651	0.0009	0.0547
476.8357	5.4639	0.0009	0.0546
477.1104	5.4582	0.0009	0.0546
477.3852	5.4487	0.0009	0.0545
477.6599	5.4385	0.0009	0.0544
477.9346	5.4268	0.0009	0.0543
478.2093	5.4273	0.0009	0.0543
478.4840	5.3910	0.0009	0.0539
478.7587	5.3617	0.0009	0.0536
479.0334	5.3400	0.0009	0.0534
479.3082	5.3207	0.0009	0.0532
479.5829	5.3148	0.0009	0.0531
479.8575	5.3069	0.0009	0.0531
480.1322	5.2790	0.0008	0.0528
480.4069	5.2494	0.0008	0.0525
480.6816	5.2350	0.0008	0.0523
480.9563	5.2033	0.0008	0.0520
481.2310	5.1810	0.0008	0.0518
481.5057	5.1458	0.0008	0.0515
481.7804	5.1159	0.0008	0.0512
482.0551	5.0878	0.0008	0.0509
482.3297	5.0486	0.0008	0.0505
482.6044	4.9902	0.0008	0.0499
482.8791	4.9583	0.0008	0.0496
483.1538	4.9187	0.0008	0.0492
483.4285	4.8445	0.0008	0.0484
483.7031	4.7729	0.0008	0.0477
483.9778	4.6212	0.0008	0.0462
484.2525	4.4778	0.0008	0.0448
484.5271	4.2920	0.0008	0.0429
484.8018	4.0384	0.0007	0.0404
485.0765	3.7614	0.0007	0.0376
485.3511	3.4344	0.0007	0.0343
485.6258	3.0499	0.0006	0.0305
485.9004	2.6294	0.0006	0.0263
486.1751	2.3438	0.0006	0.0234
486.4498	2.4943	0.0006	0.0249
486.7244	2.8767	0.0006	0.0288
486.9991	3.2565	0.0007	0.0326
487.2737	3.5686	0.0007	0.0357
487.5483	3.8458	0.0007	0.0385
487.8230	4.0820	0.0007	0.0408
488.0976	4.2861	0.0008	0.0429
488.3723	4.4393	0.0008	0.0444
488.6469	4.5517	0.0008	0.0455
488.9215	4.6219	0.0008	0.0462
489.1962	4.6826	0.0008	0.0468
489.4708	4.7488	0.0008	0.0475
489.7454	4.7962	0.0008	0.0480
490.0201	4.8323	0.0008	0.0483
490.2947	4.8594	0.0008	0.0486
490.5693	4.8832	0.0008	0.0488
490.8439	4.8726	0.0008	0.0487
491.1186	4.8880	0.0008	0.0489
491.3932	4.8923	0.0008	0.0489
491.6678	4.8996	0.0008	0.0490
491.9424	4.8754	0.0008	0.0488
492.2170	4.8640	0.0008	0.0486
492.4916	4.8491	0.0008	0.0485
492.7662	4.8940	0.0008	0.0489
493.0408	4.9121	0.0008	0.0491
493.3154	4.9091	0.0008	0.0491
493.5900	4.8935	0.0008	0.0489
493.8646	4.9061	0.0008	0.0491
494.1392	4.8892	0.0008	0.0489
494.4138	4.8887	0.0008	0.0489
494.6884	4.8972	0.0008	0.0490
494.9630	4.9014	0.0008	0.0490
495.2375	4.8811	0.0008	0.0488
495.5122	4.8627	0.0008	0.0486
495.7867	4.8667	0.0008	0.0487
644.1187	2.1991	0.0004	0.0220
644.6067	2.1941	0.0004	0.0219
645.0947	2.1886	0.0004	0.0219
645.5828	2.1764	0.0004	0.0218
646.0708	2.1733	0.0004	0.0217
646.5588	2.1721	0.0004	0.0217
647.0468	2.1654	0.0004	0.0217
647.5348	2.1642	0.0004	0.0216
648.0229	2.1513	0.0004	0.0215
648.5108	2.1414	0.0004	0.0214
648.9989	2.1382	0.0004	0.0214
649.4869	2.1296	0.0004	0.0213
649.9750	2.1233	0.0004	0.0212
650.4630	2.1161	0.0004	0.0212
650.9510	2.1006	0.0004	0.0210
651.4391	2.0840	0.0004	0.0208
651.9271	2.0633	0.0004	0.0206
652.4152	2.0458	0.0004	0.0205
652.9032	2.0215	0.0004	0.0202
653.3913	1.9881	0.0004	0.0199
653.8793	1.9383	0.0004	0.0194
654.3674	1.8680	0.0004	0.0187
654.8555	1.7713	0.0004	0.0177
655.3436	1.6405	0.0004	0.0164
655.8316	1.4913	0.0003	0.0149
656.3197	1.3760	0.0003	0.0138
656.8078	1.4292	0.0003	0.0143
657.2958	1.5748	0.0003	0.0157
657.7839	1.7060	0.0004	0.0171
658.2720	1.8038	0.0004	0.0180
658.7602	1.8687	0.0004	0.0187
659.2482	1.9132	0.0004	0.0191
659.7363	1.9430	0.0004	0.0194
660.2244	1.9674	0.0004	0.0197
660.7125	1.9806	0.0004	0.0198
661.2006	1.9876	0.0004	0.0199
661.6888	1.9900	0.0004	0.0199
662.1769	1.9958	0.0004	0.0200
662.6650	1.9967	0.0004	0.0200
663.1531	1.9958	0.0004	0.0200
663.6412	2.0006	0.0004	0.0200
664.1293	1.9957	0.0004	0.0200
664.6175	1.9858	0.0004	0.0199
665.1056	1.9849	0.0004	0.0198
665.5937	1.9832	0.0004	0.0198
666.0818	1.9848	0.0004	0.0198
666.5700	1.9796	0.0004	0.0198
667.0582	1.9758	0.0004	0.0198
667.5463	1.9725	0.0004	0.0197
668.0344	1.9707	0.0004	0.0197
668.5226	1.9601	0.0004	0.0196

What the observations establish

The four measured dips occur near the hydrogen reference pattern. Their finite widths and unequal depths do not contradict the equal-height teaching markers: those markers represent positions only. Real line profiles depend on the stellar atmosphere and the instrument. A missing or blended feature, wavelength-calibration error, or another candidate identification must be considered before making a stronger claim.

The measured excerpt comes from the 2026 version of Vega’s CALSPEC standard spectrum. All selected regions were observed with Hubble’s STIS instrument. The full source file also contains theoretical extensions at other wavelengths, which this excerpt excludes. The data are calibrated observations, with instrumental corrections and a flux scale tied to standard-star models; they are not untouched detector counts. Bohlin and Gilliland 2004, §§ 2 and 4; Bohlin, Hubeny and Rauch 2020, § 1; STScI 2026, CALSPEC, spectrum composition.

Do not estimate Vega’s radial velocity from the lowest dot in a panel. The displayed data have a finite spectral resolution and use heliocentric wavelengths; the four reference positions are rest wavelengths. A precision velocity measurement requires a consistent frame, profile model, calibration and uncertainty analysis. Here the data answer a simpler question: can you recognize several members of the same absorption pattern?

From a wavelength ratio to motion

In the teaching model, recession stretches each wavelength by the same ratio. Hα therefore shifts farther in nm than Hδ, because it starts with a longer wavelength. Their fractional shifts agree. Changing motion does not turn hydrogen into a different element, and this exercise says nothing about how hot the source becomes.

Show the math: why the change is a ratio

Preparation: ratios, square roots and the meaning of a speed relative to light.

Let $\lambda_0$ be a reference wavelength and let $v$ be the velocity of an inertial source directly away from the observer; $v\lt0$ means approach. Define $\beta=v/c$, with $c=299\,792.458\ \mathrm{km\,s^{-1}}$. The special-relativistic longitudinal Doppler relation is

$$\frac{\lambda_{\mathrm{obs}}}{\lambda_0} =\sqrt{\frac{1+\beta}{1-\beta}}, \qquad \frac{\Delta\lambda}{\lambda_0} =\sqrt{\frac{1+\beta}{1-\beta}}-1.$$

One way to derive it is to follow two successive wave crests. If their emission interval in the source frame is $T_0$, time dilation makes the interval $\gamma T_0$ in the observer’s inertial frame, where $\gamma=(1-\beta^2)^{-1/2}$. During that interval the receding source moves $v\gamma T_0$ farther away. The extra travel time gives an arrival interval $T_{\mathrm{obs}}=\gamma T_0(1+\beta)$. Since wavelength is $c$ times period, the ratio is $\gamma(1+\beta)$, equivalent to the square root above.

At $v=1500\ \mathrm{km\,s^{-1}}$, the ratio is approximately $1.005016$. Thus Hδ moves from $410.289$ to $412.347$ nm, while Hα moves from $656.461$ to $659.754$ nm. Their changes, $2.058$ and $3.293$ nm, differ; both fractional changes are about $0.5016\%$.

For $\lvert v\rvert\ll c$, the first-order approximation is $\Delta\lambda/\lambda_0\simeq v/c$. This model uses the exact expression within its ±3000 km/s bounds. The calculation is for radial motion in flat spacetime; it is not the relation between cosmic distance and cosmological redshift.

Investigate a competing explanation

Suppose four features all move to 1.005 times their reference wavelengths. A classmate instead proposes adding 2 nm to every reference value. Test the proposal using Hδ and Hα. What observation separates the explanations?

Explanation

A ratio of 1.005 shifts Hδ by about 2.051 nm and Hα by about 3.282 nm. Adding 2 nm nearly matches the first feature but misses the second by about 1.282 nm. If the measurement errors and resolution are small enough to distinguish that discrepancy, the multi-line comparison rejects the additive-shift explanation. The given common ratio corresponds to a radial-motion model; an actual astronomical interpretation still requires context.

For classrooms and clubs

Objective: distinguish one coincident feature from a pattern, and distinguish equal fractional shifts from equal additive shifts. Preparation is reading axes and using ratios; no logarithms or calculus are needed.

For a ten-minute demonstration, let learners predict the direction and relative sizes of the Hδ and Hα shifts before selecting the +1500 km/s preset. Ask each learner to complete: “The changes in nm differ because …; the fractional changes agree because ….”

For a twenty-minute investigation, use the four observed panels and the downloaded table. Mark approximate dip locations, list why the minima do not exactly equal the reference positions, and identify which parts of the display are measured and which are a teaching model. Timings are planning estimates.

Without a device, print the reference table, four observed panels and the competing-explanation task. A ruler and calculator suffice. The expected explanation is that a common multiplicative shift preserves wavelength ratios; real spectra also have finite resolution, broad profiles, blends and measurement uncertainty. Do not interpret marker heights as abundances or the activity as a measurement of Vega’s velocity.

Continue the investigation

Weighing stars uses repeated wavelength shifts to study orbital motion. The binary-star laboratory then shows which mass information a velocity curve can reveal—and which information the viewing angle can hide.

References

• Bohlin, R. C., and Gilliland, R. L. (2004). “Hubble Space Telescope Absolute Spectrophotometry of Vega from the Far-Ultraviolet to the Infrared.” The Astronomical Journal 127, 3508–3515. doi:10.1086/420715. Open PDF.
• Bohlin, R. C., Hubeny, I., and Rauch, T. (2020). “New Grids of Pure-hydrogen White-dwarf NLTE Model Atmospheres and the HST/STIS Flux Calibration.” The Astronomical Journal 160, 21. doi:10.3847/1538-3881/ab94b4. Open PDF.
• Mikulski Archive for Space Telescopes (n.d.). MAST Data Use Policy. Data-use and attribution terms. Accessed 28 September 2026.
• National Institute of Standards and Technology (n.d.). Handbook of Basic Atomic Spectroscopic Data: Atomic Data for Hydrogen. Hydrogen reference notes. Accessed 28 September 2026.
• Sloan Digital Sky Survey (2005). Data Release 4: Table of Spectral Lines Used in SDSS. Vacuum reference wavelengths.
• Space Telescope Science Institute (2026). CALSPEC: HST Flux Standards. Documentation; Vega spectrum, alpha_lyr_stis_012.fits, dated 16 March 2026, retrieved 28 September 2026. Local excerpt, transformations and provenance.