starburst episode. We conclude that our inferred stellar parameters are
accurate.

In the UV spectra we have measured a large number of photometric and kinematic
properties of the spectrally resolved Ly$\alpha$ emission line; we then use
the properties derived from the nebular lines and stellar modeling to
investigate how the Ly$\alpha$ output and spectral profile depend on physical
conditions and how they may be predicted from other data. We back up some of
these findings using estimates of the cool gas covering and kinematics, which
are also derived from the UV spectra.

Our main conclusions are:

  * •

Total Ly$\alpha$ output is strongest among young galaxies, when the most
massive stars remain on the main sequence. Evidence for this is mainly
provided by modeled age, and the equivalent width of Balmer lines. This is
natural since a young stellar population is necessary to produce the maximum
Ly$\alpha$ emission.

  * •

Stellar age cannot uniquely explain the Ly$\alpha$ output. Ly$\alpha$ EW
correlates most strongly with ionization parameter, as inferred from ratios of
strong forbidden lines [O iii]/[O ii] and [Ne iii]/[O ii], and higher nebular
EWs are also found among more highly ionized ISM conditions.

  * •

The effects of age and ionization conditions do not only influence the
Ly$\alpha$ production. Relations of equivalent amplitude and higher
significance are found when contrasting these quantities with the Ly$\alpha$
escape fraction, which traces only the output and transfer of Ly$\alpha$
photons. These properties have a significant impact on the large scale ISM.

  * •

Correlations with dust content are significant, but are insufficient to
explain the Ly$\alpha$ output. Since ionization parameter is the strongest
correlating variable, we expect that the main factor in influencing Ly$\alpha$
emission at early times, and therefore the observed EW, is the ionization
condition. The H i column density is reduced by the extreme ionizing
conditions and the Ly$\alpha$ transfer is eased.

  * •

This conclusion is further supported by the resolved Ly$\alpha$ line profile,
which shows more blueshifted emission at early times and with higher
ionization parameters. Most of the relations described above hold for the blue
and red components of the line, but relations for the blueshifted part alone
exhibit a larger dynamic range.

  * •

By stacking the ultraviolet continuum spectra and examining the low ionization
absorption lines, we see that all these phenomena are directly associated with
the column of absorbing gas. This decreases towards younger ages and higher
ionization parameters, reduces the Ly$\alpha$ scattering, and leads to higher
escape fractions. Moreover, the column of gas at zero velocity is lowest in
the galaxies with highest contributions of blueshifted Ly$\alpha$, indicating
that the removal of this gas by photoionization at early times is responsible
for the blueshifted emission.

  * •

Simple multi-parametric analysis can predict up to 80% of the variance in the
Ly$\alpha$ luminosity, performing equally well for the total and red peak.
Similar models can predict approximately 50% of the variance in the EWs.

  * •

We use variable selection methods to quantify which variables carry the most
weight in the relations. We find that the luminosity relations appear
dominated by ionization tracers such as [O iii] and [Ne iii] together with low
ionization lines like [O ii]. This is in line with the correlation analysis
presented earlier in this work. We also find that H$\beta$ provides a better
absolute value calibration than H$\alpha$ most likely due to the effect of the
bluer wavelength on the dust attenuation. In this multi-parametric experiment
we are unable to predict the $L_{\mathrm{B/R}}$ ratio.

  * •

The variable selection results for the EW relations is somewhat less clear cut
but does seem to give preference to dust tracers, in this case
H$\alpha$/H$\beta$ and to the H$\beta$ EW. Improving these multi-parametric
estimates will be the subject of future work.

  * •

We have no uniform estimates of the inclination nor morphology of our
galaxies, and neither can we estimate the influence of viewing angle on the
Ly$\alpha$ escape. These effects would cause our observations to miss
Ly$\alpha$ in some cases, and must certainly contribute scatter to some of the
relations, hiding some of the weaker trends.

## Acknowledgements

M.H. is Fellow of the Knut and Alice Wallenberg Foundation. M.G. thanks the
Max Planck Society for support through the Max Planck Research Group.

## Data Availability

All data are available in the Barbara A. Mikulski Archive for Space Telescopes
(MAST) at https://archive.stsci.edu/hst/search.php

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##  Appendix A Galaxy Coordinates and Redshifts

Table 1: Galaxy names and properties Name | Right Ascension | Declination | Redshift | $M_{\mathrm{UV}}$ | SFR(H$\alpha$) | $E_{B-V}$ | 12+log(O/H) | log($L_{\mathrm{Ly}\alpha}$)
---|---|---|---|---|---|---|---|---
| [∘] J2000 | [∘] J2000 |  |  | [M⊙ yr-1] | [mag] |  | erg s-1
SDSSJ0055-0021 | $13.86446$ | $-0.36349$ | $0.16743$ | $-20.33$ | $35.01$ | $0.227$ | $8.19$ | $41.45$
SDSSJ0150+1308 | $27.61838$ | $13.14956$ | $0.14674$ | $-20.54$ | $18.61$ | $0.188$ | $8.30$ | $41.37$
SDSSJ0213+1259 | $33.45221$ | $12.99761$ | $0.21897$ | $-20.36$ | $34.47$ | $1.024$ | $8.49$ | $41.70$
SDSSJ0808+3948 | $122.18450$ | $39.81459$ | $0.09125$ | $-19.97$ | $5.91$ | $0.326$ | $8.53$ | $42.01$
SDSSJ0921+4509 | $140.49746$ | $45.15344$ | $0.23500$ | $-21.02$ | $29.59$ | $0.416$ | $8.48$ | $41.49$
SDSSJ0926+4427 | $141.50183$ | $44.46015$ | $0.18068$ | $-20.84$ | $21.79$ | $0.096$ | $8.02$ | $42.78$
SDSSJ0938+5428 | $144.55621$ | $54.47364$ | $0.10207$ | $-20.43$ | $21.47$ | $0.174$ | $8.16$ | $41.34$
SDSSJ2103-0728 | $315.99475$ | $-7.46736$ | $0.13688$ | $-20.32$ | $16.69$ | $0.108$ | $8.49$ | $42.21$
SDSSJ0021+0052 | $5.25429$ | $0.88003$ | $0.09835$ | $-20.90$ | $20.11$ | $0.044$ | $8.12$ | $42.59$
SDSSJ1025+3622 | $156.45158$ | $36.38289$ | $0.12650$ | $-20.20$ | $16.07$ | $0.136$ | $8.09$ | $42.31$
SDSSJ1112+5503 | $168.18354$ | $55.06306$ | $0.13164$ | $-99.00$ | $27.33$ | $0.208$ | $8.37$ | $41.87$
SDSSJ1144+4012 | $176.09283$ | $40.20589$ | $0.12694$ | $-20.46$ | $11.52$ | $0.322$ | $8.30$ | $40.73$
SDSSJ1414+0540 | $213.72554$ | $5.67989$ | $0.08186$ | $-20.26$ | $10.02$ | $0.286$ | $8.21$ | $40.55$
SDSSJ1416+1223 | $214.05363$ | $12.39456$ | $0.12315$ | $-20.60$ | $24.02$ | $0.260$ | $8.34$ | $41.18$
SDSSJ1428+1653 | $217.23504$ | $16.89426$ | $0.18167$ | $-21.29$ | $27.71$ | $0.169$ | $8.24$ | $42.46$
SDSSJ1429+0643 | $217.44583$ | $6.72637$ | $0.17353$ | $-20.92$ | $42.88$ | $0.048$ | $8.08$ | $42.73$
SDSSJ1521+0759 | $230.42258$ | $7.98937$ | $0.09426$ | $-20.23$ | $8.53$ | $0.187$ | $8.20$ | $41.64$
SDSSJ1612+0817 | $243.18967$ | $8.28361$ | $0.14914$ | $-20.84$ | $38.59$ | $0.303$ | $8.35$ | $42.31$
GP0303-0759 | $45.83921$ | $-7.98978$ | $0.16485$ | $-20.56$ | $13.48$ | $-0.041$ | $8.02$ | $41.94$
GP0911+1831 | $137.80558$ | $18.51894$ | $0.26220$ | $-20.99$ | $32.52$ | $0.159$ | $8.20$ | $42.81$
GP1054+5238 | $163.37833$ | $52.63136$ | $0.25263$ | $-21.31$ | $38.74$ | $0.078$ | $8.12$ | $42.54$
GP1133+6514 | $173.26583$ | $65.22817$ | $0.24140$ | $-20.79$ | $8.72$ | $0.022$ | $8.06$ | $42.58$
GP1137+3524 | $174.34225$ | $35.40742$ | $0.19437$ | $-20.86$ | $27.82$ | $0.047$ | $8.10$ | $42.62$
GP1219+1526 | $184.76658$ | $15.43569$ | $0.19563$ | $-20.78$ | $19.65$ | $-0.029$ | $8.00$ | $43.19$
GP1244+0216 | $191.09737$ | $2.26122$ | $0.23943$ | $-20.66$ | $43.90$ | $0.066$ | $8.07$ | $42.56$
GP1249+1234 | $192.14429$ | $12.56747$ | $0.26339$ | $-20.91$ | $24.78$ | $0.080$ | $8.05$ | $43.07$
GP1424+4217 | $216.02383$ | $42.27953$ | $0.18477$ | $-20.79$ | $30.47$ | $0.064$ | $8.05$ | $42.94$
J0925+1403 | $141.38487$ | $14.05363$ | $0.30123$ | $-20.47$ | $26.92$ | $0.075$ | $8.01$ | $42.83$
J1152+3400 | $178.02033$ | $34.01386$ | $0.34193$ | $-20.77$ | $21.29$ | $0.001$ | $8.02$ | $43.00$
J1333+6246 | $203.26650$ | $62.76772$ | $0.31812$ | $-20.52$ | $-99.00$ | $-99.000$ | $8.09$ | $42.75$
J1442-0209 | $220.63079$ | $-2.16445$ | $0.29368$ | $-21.11$ | $29.37$ | $0.104$ | $7.93$ | $43.16$
J1503+3644 | $225.92846$ | $36.74743$ | $0.35569$ | $-20.43$ | $23.11$ | $0.068$ | $8.04$ | $42.86$
J0901+2119 | $135.44004$ | $21.32438$ | $0.29931$ | $-19.06$ | $15.92$ | $0.072$ | $7.99$ | $42.48$
J1011+1947 | $152.90950$ | $19.78915$ | $0.33217$ | $-19.33$ | $33.73$ | $0.302$ | $7.92$ | $42.64$
J1154+2443 | $178.70354$ | $24.72584$ | $0.36899$ | $-19.50$ | $12.74$ | $0.135$ | $7.92$ | $42.87$
J1243+4646 | $190.75262$ | $46.78067$ | $0.43171$ | $-20.67$ | $23.77$ | $0.098$ | $7.70$ | $43.08$
J1248+4259 | $192.04367$ | $42.99822$ | $0.36302$ | $-99.00$ | $25.27$ | $0.025$ | $7.93$ | $42.79$
J1256+4509 | $194.18396$ | $45.15472$ | $0.35320$ | $-19.85$ | $11.24$ | $0.076$ | $7.93$ | $42.54$
J0159+0751 | $29.96979$ | $7.86356$ | $0.06106$ | $-16.58$ | $1.99$ | $0.258$ | $7.79$ | $41.59$
J1205+4551 | $181.26479$ | $45.86415$ | $0.06539$ | $-16.41$ | $2.91$ | $0.131$ | $8.01$ | $41.65$
J1242+4851 | $190.61025$ | $48.86602$ | $0.06216$ | $-15.81$ | $0.70$ | $0.009$ | $7.69$ | $41.44$
SDSSJ0815+2156 | $123.96667$ | $21.93990$ | $0.14095$ | $-19.25$ | $7.04$ | $0.040$ | $7.96$ | $42.34$
J0240-0828 | $40.21746$ | $-8.47428$ | $0.08224$ | $-18.20$ | $8.63$ | $0.067$ | $7.99$ | $42.32$
J0851+5840 | $132.81521$ | $58.68194$ | $0.09190$ | $-18.35$ | $9.21$ | $0.108$ | $7.97$ | $41.64$
J1200+2719 | $180.06867$ | $27.33306$ | $0.08188$ | $-18.83$ | $8.01$ | $0.123$ | $7.95$ | $42.43$
J1226+0415 | $186.54954$ | $4.26002$ | $0.09422$ | $-18.06$ | $10.24$ | $0.168$ | $8.00$ | $42.02$
J1311-0038 | $197.88033$ | $-0.64566$ | $0.08106$ | $-18.08$ | $5.25$ | $0.184$ | $8.03$ | $42.03$
GP0822+2241 | $125.69859$ | $22.69558$ | $0.21622$ | $-20.12$ | $52.36$ | $0.198$ | $8.06$ | $42.35$
GP0917+3152 | $139.26052$ | $31.87238$ | $0.30038$ | $-20.96$ | $25.55$ | $0.176$ | $8.22$ | $42.59$
GP1009+2916 | $152.32914$ | $29.27264$ | $0.22192$ | $-19.75$ | $7.53$ | $0.069$ | $8.01$ | $42.34$
GP1122+6154 | $170.58222$ | $61.91263$ | $0.20456$ | $-19.24$ | $9.17$ | $0.150$ | $8.06$ | $42.26$
GP1440+4619 | $220.04142$ | $46.32693$ | $0.30078$ | $-21.43$ | $47.94$ | $0.137$ | $8.13$ | $42.81$
GP1454+4528 | $223.64825$ | $45.48231$ | $0.26852$ | $-20.31$ | $27.91$ | $0.181$ | $8.17$ | $42.27$
GP1514+3852 | $228.53598$ | $38.86871$ | $0.33263$ | $-20.68$ | $9.38$ | $-0.275$ | $8.14$ | $42.76$
GP1559+0841 | $239.85824$ | $8.68865$ | $0.29719$ | $-19.80$ | $-99.00$ | $-99.000$ | $8.18$ | $42.57$
GP2237+1336 | $339.39608$ | $13.61306$ | $0.29350$ | $-21.15$ | $41.17$ | $0.136$ | $8.10$ | $42.29$
GALEX1417+5228 | $214.43094$ | $52.46828$ | $0.20813$ | $-18.28$ | $1.77$ | $-0.083$ | $7.68$ | $42.06$
J0232-0426 | $38.06704$ | $-4.44076$ | $0.45237$ | $-99.00$ | $9.52$ | $0.101$ | $7.96$ | $42.58$
J0919+4906 | $139.98241$ | $49.10243$ | $0.40515$ | $-19.28$ | $6.24$ | $0.041$ | $7.99$ | $42.75$
J1046+5827 | $161.50825$ | $58.46582$ | $0.39675$ | $-20.40$ | $8.93$ | $-0.061$ | $7.93$ | $42.59$
J1121+3806 | $170.32591$ | $38.11189$ | $0.31787$ | $-99.00$ | $4.80$ | $-0.017$ | $7.96$ | $42.47$
J1127+4610 | $171.83750$ | $46.17847$ | $0.32221$ | $-99.00$ | $4.45$ | $-0.139$ | $7.88$ | $42.15$
J1233+4959 | $188.37825$ | $49.99707$ | $0.42199$ | $-99.00$ | $10.12$ | $-0.050$ | $8.03$ | $42.72$
J1349+5631 | $207.47958$ | $56.51969$ | $0.36361$ | $-99.00$ | $6.57$ | $0.157$ | $8.03$ | $42.32$
J1355+1457 | $208.97275$ | $14.95041$ | $0.36513$ | $-99.00$ | $11.92$ | $0.060$ | $7.92$ | $42.56$
J1455+6107 | $223.99820$ | $61.12214$ | $0.36786$ | $-20.05$ | $7.17$ | $-0.022$ | $7.99$ | $42.57$
J010534+234960 | $16.39057$ | $23.83325$ | $0.33807$ | $-19.71$ | $22.32$ | $0.121$ | $8.09$ | $42.69$
J015208-043117 | $28.03331$ | $-4.52145$ | $0.38359$ | $-20.23$ | $24.67$ | $0.168$ | $8.15$ | $42.79$
J020819-040136 | $32.07877$ | $-4.02679$ | $0.38445$ | $-20.56$ | $16.32$ | $-0.130$ | $8.02$ | $42.92$
J110359+483456 | $165.99582$ | $48.58219$ | $0.41795$ | $-20.25$ | $24.49$ | $0.177$ | $8.07$ | $42.64$
J110506+594741 | $166.27636$ | $59.79484$ | $0.40540$ | $-19.72$ | $17.02$ | $0.155$ | $8.06$ | $42.80$
J121948+481411 | $184.94943$ | $48.23625$ | $0.42022$ | $-20.42$ | $13.69$ | $0.055$ | $8.10$ | $42.63$
J124619+444902 | $191.58118$ | $44.81730$ | $0.32217$ | $-20.75$ | $40.72$ | $0.150$ | $8.07$ | $42.88$
J142535+524902 | $216.39628$ | $52.81728$ | $0.38695$ | $-19.74$ | $17.46$ | $0.156$ | $7.97$ | $42.49$
Names are according to MAST archive labeling.
$M_{\mathrm{UV}}$ is corrected for Milky Way extinction.
SFR(H$\alpha$) is corrected for internal attenuation and uses the Kennicutt &
Evans (2012) calibration
Oxygen abundance is derived from the O3N2 index using Marino et al. (2013).
$L_{\mathrm{Ly}\alpha}$ is derived from the _Lyman alpha Spectral Database_
(LASD Runnholm et al., 2021).