COMPUTING INTRINSIC LYα FLUXES OF F5 V TO M5 V STARS

The discovery of large numbers of extrasolar planets (exoplanets) has stimulated many observational and theoretical studies of their atmospheric chemical compositions. In particular, the habitability of an exoplanet at a given distance from its host star is generally thought to depend on the total flux received from the host star, the availability of greenhouse gases, and the presence of biomarkers such as O₂ and O₃ (but, see Feng et al. 2012). Estimates of the chemical composition of exoplanet atmospheres depend crucially on the near-ultraviolet (NUV, λ  = 1700–3200 Å), far-ultraviolet (FUV, λ = 1170–1700 Å), extreme ultraviolet (EUV, λ  = 300–911 Å), XUV (λ  = 100–300 Å), and X-ray (λ < 100 Å) radiation from the host star, which controls important molecular photodissociation and photoionization processes.

Early interest concerning the influence of a star on its substellar companions was focused on the erosion of volatile gases from the primordial atmospheres of the terrestrial planets of our solar system (especially Mars and Venus) by dissociative recombination powered by solar ultraviolet radiation and pickup-ion stripping by the solar wind. These processes would have been enormously enhanced when the Sun was young and more magnetically active than today (e.g., Zahnle & Walker 1982). Using a database of solar-type stars in young clusters of known age and extrapolating from solar fluxes over the sunspot cycle, Ayres (1997) showed that photoionization rates relevant to the Martian situation scale as power laws in time (as anticipated in the earlier Zahnle & Walker paper). Furthermore, the UV flux behavior could be reliably traced back to the epoch of the Late Heavy Bombardment (at solar age ∼800 Myr), because by then rotation rates of young G stars had funneled into a narrow distribution from an initially more diverse behavior (Delorme et al. 2011). It is the stellar spin that largely governs the degree of magnetic activity, and the decay of that spin by wind braking that causes the rapid decline of the UV and X-ray activity with increasing age.

More recently, the "Sun in Time" project (Ribas et al. 2005, 2010) and Sanz-Forcada et al. (2011) have extended the earlier work to a wider range of high energy measurements, especially including the important 912–1170 Å Far Ultraviolet Spectroscopic Explorer (FUSE) band, and to a broader range of spectral types (G0 to G5), utilizing field stars whose ages must be inferred indirectly, but are more accessible to observation than the mostly distant cluster members. These studies also showed that in different wavelength bands, power laws could be used to describe the decay of chromospheric and coronal radiation over time.

Ribas et al. (2005) called attention to the importance of the H i Lyα line (1215.67 Å), which is by far the brightest FUV emission line. They showed that for the Sun, the Lyα line flux is about 20% of the total flux between 1 and 1700 Å. The relative importance of the Lyα line is even more important for cooler stars as the photospheric emission at λ > 1700 Å decreases rapidly with decreasing effective temperature.

Since important molecules in planetary atmospheres, including H₂O, CO₂, and CH₄, have photodissociation cross sections that peak below 1700 Å,⁴ Lyα radiation can be the dominant cause of photodissociation for these and other molecules. For example, the solar Lyα line is responsible for 51% of the photodissociation rate of H₂O by solar UV radiation between 1148 and 1940 Å, and 71% of the total photodissociation rate of CH₄ by solar radiation between 56 and 1520 Å. However, recent models of exoplanet atmospheres that include photoionization, e.g., models for WASP-12b (Kopparapu et al. 2012), typically do not include realistic values for the stellar Lyα flux. In this recent model, the FUV fluxes were obtained from the compilation of Pickles (1998) that is based on International Ultraviolet Explorer (IUE) spectra without a large correction for interstellar absorption in the Lyα line or geocoronal Lyα emission. New ultraviolet spectra of six M-dwarf host stars observed with spectrographs on the Hubble Space Telescope (HST) by France et al. (2013) provide an observational basis for more realistic photochemical models of exoplanet atmospheres.

While exoplanet atmospheres absorb the Lyα flux from their host stars without attenuation, neutral hydrogen in the interstellar medium (ISM) scatters most of the Lyα flux out of the line of sight between the star and Earth. One must therefore correct for interstellar absorption by reconstructing the stellar Lyα profile and flux. For pre-main-sequence stars with disks, Herczeg et al. (2004) and Schindhelm et al. (2012) showed that the fluorescent H₂ emission lines pumped by Lyα provide a useful diagnostic for reconstructing the intrinsic Lyα emission line. For 62 main-sequence and giant stars without H₂ fluorescence, Wood et al. (2005) reconstructed Lyα fluxes using interstellar H i column densities and velocities inferred from the deuterium Lyα and metal lines. France et al. (2012) developed an alternative reconstruction technique in which the widths and strengths of one or two Gaussian emission lines representing Lyα and the velocities and column densities of interstellar absorption features are iteratively varied to obtain a solution that best fits the observed Lyα line wings. Both techniques require high-resolution spectra with good signal to noise and minimal contamination by geocorona Lyα emission. The only available spectrograph that can obtain such data is the Space Telescope Imaging Spectrograph (STIS) on HST. High instrumental sensitivity, especially important for faint M dwarfs, increasing interstellar hydrogen column densities with distance, and difficult-to-obtain HST observing time limit the number of stars for which Lyα fluxes can be reconstructed by these two techniques.

The objective of this study is to find different methods for inferring the Lyα flux incident on the atmospheres of exoplanets for stars when high-resolution Lyα spectra are not available. These methods should be applicable to a broad range of stars including M dwarfs, which are very numerous and could support habitable planets with short orbital periods. One proposed method is to use correlations of reconstructed Lyα line fluxes with other stellar features (lines of O i and C ii) formed in the same temperature range as Lyα, lines of Mg ii and Ca ii formed at slightly lower temperatures, and lines of C iv formed at somewhat higher temperatures. Our hypothesis is that ratios of the Lyα line flux to fluxes in these other lines should be similar for stars in limited ranges of spectral type with only a small dependence on stellar activity as indicated by the emission line fluxes. Empirical support for this hypothesis comes from the similar power-law slopes of UV emission lines (Ayres 1997; Ribas et al. 2005) and the correlation of Lyα and Mg ii fluxes (Wood et al. 2005). The similar shapes of the chromosphere and transition region thermal structures for regions on the Sun with very different heating rates (Fontenla et al. 2011) provide theoretical support for our hypothesis.

The paper is structured as follows. In Section 2 we describe our selection of targets that have reconstructed Lyα and other UV emission line fluxes. Section 3 describes our procedure for reconstructing the intrinsic Lyα flux using correlations with other UV emission lines and the errors and uncertainties of this method. Section 4 describes an extension of this procedure using correlations with ground-based Ca ii H and K line fluxes, and Section 5 describes how correlations with X-ray fluxes can be used to predict the intrinsic Lyα flux. Section 6 describes how the stellar effective temperature and rotation rate can provide rough estimates of the intrinsic Lyα flux when no emission line fluxes are available. The final section lists our conclusions. In a subsequent paper, we will apply the flux correlation technique to estimating stellar EUV radiation, which is responsible for photoionizing hydrogen and other species, heating outer atmospheres, and driving mass loss from exoplanets.

Our target list consists of all F5 to M5 main-sequence stars for which reconstructed Lyα fluxes are now available. Wood et al. (2005) reconstructed Lyα line profiles observed by STIS in its medium (spectral resolution ≈λ/45, 000) and high-resolution (≈λ/100, 000) echelle modes using interstellar deuterium Lyα and metal absorption lines to model the interstellar H i column density as a function of wavelength across the hydrogen Lyα line. They provided reconstructed Lyα line fluxes for 40 main-sequence stars with spectral types F5 to M5, together with Mg ii h and k line and X-ray fluxes for most of these stars. We also include five M-dwarf stars that are known to host exoplanets. The Lyα fluxes for these stars were reconstructed from STIS grating and echelle spectra using an iterative technique to measure the intrinsic Lyα profile and the interstellar absorption (France et al. 2012).

For most these stars, we have measured fluxes of the H i 1215.67 Å, O i 1304.86 Å + 1306.03 Å, C ii 1335.71 Å, and C iv 1548.19 Å + 1550.77 Å lines. In the semi-empirical solar chromosphere and transition region model computed by Avrett & Loeser (2008), the peak contributions to the line center emission for these lines are at temperatures near 40,000 K, 6700 K, 29,500 K, and 68,000 K, respectively. However, the wings of these lines are formed over a range of cooler temperatures. We did not use fluxes of the O i 1302.17 Å and C ii 1334.53 Å lines as these lines show strong interstellar absorption. We extracted the O i, C ii, and C iv line fluxes from Cosmic Origin Spectrograph (COS; Green et al. 2012) data with spectral resolution (≈λ/17, 000) available through the Mikulski Archive for Space Telescopes (MAST)⁵ and the well-calibrated STIS spectra from the StarCAT (Ayres 2010) Web site.⁶ In a few cases we used data obtained with the Goddard High Resolution Spectrograph (GHRS) instrument on HST. The O i data obtained with COS are not usable because of airglow contamination. We subtracted the underlying continuum from the emission line fluxes. Line fluxes for the solar-mass stars were measured by Linsky et al. (2012).

We also include solar spectral irradiance data observed with the Solar Radiation and Climate Experiment (SORCE) on the Solar-Stellar Irradiance Comparison Experiment II (SOLSTICE II; Woods et al. 2009; Snow et al. 2005). These are integrated sunlight spectra directly comparable with the stellar data. The 2008 April 10–16 data refer to the very quiet Sun, and the 2003 October 27 and November 10 data refer to the Sun when it was very active.

Table 1 summarizes the stellar and emission line fluxes f(line) in erg cm⁻² s⁻¹ at a distance of 1 AU for 45 stars, the quiet Sun, and the active Sun at two different times. Since most of the stars are variable, especially in the FUV, the fluxes refer to a single time and are not time averages. For most of the stars the STIS Lyα spectra and the COS spectra of the O i, C ii, and C iv were obtained at different times. Since stellar UV radiation varies with time especially for M dwarfs and active warmer stars, ratios of the Lyα flux to other emission lines will have systematic errors compared to the stars for which all of the emission lines were observed at nearly the same time.

Table 1. Stellar Line Fluxes (erg cm⁻² s⁻¹) at 1 AU

Stara	HD	[Fe/H]	Spec Typeb	d b (pc)	Lyαc	Mg ii h+kd	O i 130.4+130.6	C ii 133.6	C iv 154.8+150.1	X-Ray	Refe
Procyon	61421	−0.02	F5 IV–V	3.50	77.1	267	1.77	2.58	4.62	11.5	5
HR 4657	106516	−0.70	F5 V/L	22.6	27.8	62.6	0.418:	0.320:	0.493:	5.43	1
ζ Dor	33262	−0.15	F7 V	11.7	46.5	108	0.627	1.050	1.958	16.7	2
χ Her	142373	−0.50	F8 V/L	15.9	22.0	45.2	0.235	0.115	0.171	0.312	1
...	28033	+0.11	F8 V	46.4	24.7	50.4	...	...	...	19.2	...
χ1 Ori	39587	−0.09	G0 V	8.66	41.6	79.8	0.474	0.684	1.247	37.3	2
HR 4345	97334	−0.01	G0 V	21.93	42.8	108	0.569	1.016	1.631	39.9	2
SAO 136111	73350	+0.07	G0 V	23.98	32.8	65.8	0.296	0.429	0.737	19.3	2
V993 Tau	28205	+0.12	G0 V	47.01	55.5	140	0.901	1.286	2.46:	41.4	1
V376 Peg*	209458	−0.06	G0 V	49.63	15.7	...	...	...	...	...	...
Quiet Sun (4/2008)		+0.00	G2 V	...	5.95	18.2	0.0793	0.0862	0.129	0.224	3
Active Sun (11/2003)		+0.00	G2 V	...	7.04	...	0.0881	0.1041	0.152	1.99	3
Active Sun (10/2003)		+0.00	G2 V	...	9.15	...	0.1107	0.1497	0.212	2.85	3
α Cen A	128620	+0.25	G2 V	1.325	7.54	29.7	0.1032	0.1057	0.161	0.117	4, 13
HR 2882	59967	−0.19	G4 V	21.82	55.9	90.2	0.550	0.821	1.881	41.9	2
61 Vir*	115617	+0.00	G5 V	8.555	5.26	14.1	0.0488	0.0427	0.0603	0.265	1
κ1 Cet	20630	+0.09	G5 V	9.14	30.0	53.0	0.366	0.556	0.873	25.6	2
HR 2225	43162	+0.00	G5 V	16.72	41.0	...	0.396	0.479	0.835	48.1	1
HR 6748	165185	−0.06	G5 V	17.55	48.9	101.1	0.495	0.687	1.123	53.5	2
SAO 254993	203244	−0.21	G5 V	20.42	43.8	59.1	0.311	0.539	0.940	20.2	1
SAO 158720	128987	+0.01	G6 V	23.68	34.4	60.1	0.296	0.381	0.510	14.3	1
τ Cet	10700	−0.43	G8 V/L	3.65	5.66	7.93	0.0417	0.0229	0.0327	0.176	5
ξ Boo A	131156A	−0.13	G8 V	6.70	35.3	61.9	0.274	0.465	0.815	28.3	1
SAO 28753	116956	+0.03	G9 IV–V	21.9	33.0	57.5	0.336	0.504	0.781	24.7	1
α Cen B*	128621	+0.24	K0 V	1.255	10.1	19.1	0.0809	0.0925	0.132	0.533	5, 13
DX Leo	82443	−0.23	K0 V	17.8	31.1	79.1	...	...	...	59.7	...
70 Oph A	105341	−0.08	K0 V	5.09	23.6	30.6	0.222	0.296	0.431	6.62	5
HR 8	166	+0.15	K0 V	13.67	37.9	57.0	0.374	0.592	1.036	33.0	1
Eri*	22049	−0.08	K1 V	3.216	21.5	27.2	0.145	0.179	0.274	5.63	1, 9
40 Eri A	26965	−0.27	K1 V	4.985	7.33	12.3	...	...	...	1.15	...
36 Oph A	155886	−0.39	K1 V/L	5.464	18.0	14.0	0.0816	0.0873	...	3.72	...
HR 1925	37394	+0.14	K1 V	12.28	29.3	45.0	0.228	0.277	0.462	14.4	1
...*	189733	...	K1 V	19.25	11.8	...	0.202	0.274	...	5.34	5, 9
EP Eri	17925	+0.08	K2 V	10.35	27.6	61.1	...	...	0.917	32.9	5
LQ Hya	82558	...	K2 V	18.62	59.1	75.2	...	...	4.744	243.	5
V368 Cep	220140	...	K2 V	19.20	46.9	86.6	...	...	...	275.	...
PW And	1405	...	K2 V	21.9	47.1	51.8	...	...	3.154	187.	5
Speedy Mic	197890	−1.49	K2 V/L	52.2	214	190	...	...	...	4255.	...
61 Cyg A	201091	−0.35	K5 V/L	3.487	8.90	7.35	0.0353	0.0323	...	0.498	5, 13
Ind	209100	−0.20	K5 V	3.622	17.3	8.43	...	...	...	0.871	...
AU Mic	197481	...	M0 V	9.91	43.0	17.6	0.360	0.525	1.035	70.9	1, 8
AD Leo	GJ 388	+0.28	M3.5 V	4.695	9.33	2.19	0.0644	0.137	0.376	19.1	1, 10
EV Lac	GJ 873A	−0.01	M3.5 V	5.122	3.07	...	0.0163	0.0402	0.1094	19.5	1, 10
Proxima Cen	GJ 551C	...	M5.5 V	1.296	0.301	...	0.000408	0.00162	0.00719	0.142	1, 11
GJ 832*	204961	−0.12	M1.5 V	4.954	5.17	0.311	...	0.00278	0.00762	0.214	6, 9
GJ 667C*	...	...	M1.5 V	6.9	1.54	0.113	...	...	...	0.263	12
GJ 876*	...	+0.18	M5.0 V	4.689	0.409	0.0315	...	0.00874	0.0186	0.0574	7, 9
GJ 581*	...	−0.10	M2.5 V	6.3	0.513	0.0360	...	0.000820	0.00304	...	6
GJ 436*	...	+0.04	M3 V	10.3	1.571	0.1038	...	0.00182	0.00623	0.0334	6, 9

Notes. ^aExoplanet host stars listed in the http://exoplanets.org database are marked with an * symbol. ^bData from SIMBAD with M star metal abundances from the sources listed in Section 3.4. ^cReconstructed intrinsic Lyα line fluxes for most stars (Wood et al. 2005) and for the GJ stars (France et al. 2013). ^dMg ii h and k core emission corrected for interstellar absorption for most stars (Wood et al. 2005) and for GJ stars (this paper). ^eSources of the O i, C ii, and C iv data: (1) StarCAT (Ayres 2010); (2) Linsky et al. 2012; (3) M. Snow (2012, private communication); (4) Pagano et al. 2004; (5) This paper; (6) France et al. 2012; (7) France et al. 2013; (8) X-ray flux in Schneider & Schmitt 2010; (9) X-ray flux in Sanz-Forcada et al. 2011; (10) X-ray flux in Robrade & Schmitt 2005; (11) X-ray flux in Güdel et al. 2004; (12) X-ray flux from J. Schmitt (2012, private communication); (13) X-ray flux in Robrade et al. 2012.

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3.1. F5 V to G9 V Stars

Table 1 lists the measured fluxes for 21 F5–G9 stars and the Sun at three different times and activity levels. We plot in Figure 1 the flux ratio R(C iv) = f(Lyα)/f(C iv) versus f(C iv) with line fluxes measured in erg cm⁻² s⁻¹ at a distance of 1 AU. Figures 2–5 show similar plots of R(line) = f(Lyα)/f(line) versus f(line) using the previously described C ii, O i, and Mg ii lines. The R(line) ratios for the F5–G9 stars in Figures 1–4 follow tight trajectories of decreasing R(line) with increasing f(line). In Table 1 we list the iron abundances relative to hydrogen [Fe/H] listed in the SIMBAD⁷ database. Three of the F5–G9 stars (HR 4657, χ Her, and τ Cet) have large iron depletions (defined as [Fe/H] <0.3), and often have higher R(line) values than other stars with similar fluxes and [Fe/H] values close to the solar. This behavior is expected since R(line) should increase as the line's metal abundance decreases, but whether or not R(line) is inversely proportional to [Fe/H] will be considered in the next section. We therefore exclude the low [Fe/H] stars when computing least-squares fits for the remaining F5–G9 stars. The coefficients for these fits, log[R(line)] = A + B log[f(line)], are listed in Table 2. We note that the least-squares fits, which do not include the solar data, are close to the solar data. Also, the α Cen A ratios are similar to the quiet and active Sun ratios even though the solar and stellar data are measured by different instruments. Table 2 shows that the mean dispersions of the F5–G9 stars about the best-fit lines are 18%–24%.

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Table 2. Least-squares Fits to Line Flux Ratios

Star	Number	Spectral	Fluxa	Ab	Bb	Mean Dispersion	rms Dispersion
Group	Included	Line	Range			(%)	(%)
F5 V–G9 V	16	C iv	0.06–4.62	1.560	−0.353	18.4	22.2
K0 V–K5 V	8	C iv	0.13–4.74	1.508	−0.575	15.6	18.0
M0 V–M5 V	8	C iv	0.003–1.04	1.325	−0.355	118.5	159.3
F5 V–G9 V	16	C ii	0.043–2.58	1.723	−0.298	19.4	22.1
K0 V–K5 V	6	C ii	0.09–0.59	1.731	−0.314	25.0	35.6
M0 V–M5 V	8	C ii	0.0008–0.53	1.525	−0.404	113.2	156.4
F5 V–G9 V	16	O i	0.049–1.77	1.872	−0.198	22.5	27.2
K0 V–K5 V	6	O i	0.08–0.37	1.886	−0.198	22.3	32.8
M0 V–M5 V	4	O i	0.0004–0.36	1.871	−0.278	16.9	17.8
F5 V–G9 V	16	Mg ii	14.1–267	−0.291	−0.0208	24.2	31.2
K0 V–K5 V	12	Mg ii	8.4–86.6	0.338	−0.318	29.8	39.3
M0 V–M5 V	7	Mg ii	0.032–17.6	0.814	−0.296	27.8	33.8
F5 V–G9 V	13	Ca ii	11.4–149.	−0.223	0.080	42.2	49.6
K0 V–K5 V	10	Ca ii	5.9–39.4	0.605	−0.433	20.6	30.7
M0 V–M5 V	7	Ca ii	0.0076–6.53	1.028	−0.312	39.9	49.6
F5 V–G9 V	20	X-ray	0.12–52.5	1.156	−0.684	29.8	42.3
K0 V–K5 V	15	X-ray	0.50–3090	1.058	−0.707	22.2	27.4
M0 V–M5 V	8	X-ray	0.033–70.9	0.431	−0.573	122.	155.

Notes. ^aFlux range of the C iv, C ii, O i, and Mg ii lines and X-ray flux in erg cm⁻² s⁻¹ at a distance of 1 AU. ^bLeast-squares fit to log [f(Lyα)/f(line)] = A + Blog [f(line)], where the line is C iv, C ii, O i, or Mg ii.

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3.2. K0 V to K5 V Stars

3.3. M0 V to M5 V Stars

3.4. Errors and Uncertainties

The hydrogen Hα (6563 Å) and Ca ii H and K (3933 and 3968 Å) lines formed in the chromosphere are observable by ground-based telescopes. However, the Hα line is difficult to analyze since increasing heating first deepens the absorption line and then produces an emission feature. We consider instead the Ca ii lines because the emission in the centers of the broad photospheric absorption lines is a good indicator of the chromospheric heating rate. An important difficulty is distinguishing the chromospheric emission inside of the H1 and K1 features that define the emission core from the photospheric emission that would be present in the absence of a chromosphere. For active stars and especially M dwarfs, this is not a large uncertainty as the photospheric emission is faint compared to the bright chromospheric emission. For the less active G stars, the photospheric emission is comparable to or larger than the chromospheric emission. It is therefore essential to correct for the photospheric emission as we wish to correlate chromospheric Ca ii emission with the intrinsic Lyα flux.

Different authors have estimated the photospheric emission in and near the core of the Ca ii lines in different ways. Using high-resolution spectra, Linsky et al. (1979) and Pasquini et al. (1988) measured the flux in the Ca ii emission line cores between the H1 and K1 minima features and subtracted the small amount of flux in these wavelength intervals predicted by radiative equilibrium model photospheres. Robinson et al. (1990) and Browning et al. (2010) fitted the photospheric H and K absorption lines with Gaussians and then subtracted the flux interpolated in the line cores from the measured Ca ii emission. This approach somewhat overcorrects for the photospheric emission, but the error is small for the very cool stars that they observed. The resulting chromospheric Ca ii fluxes at 1 AU are listed in Columns 6 and 7 of Table 4.

Table 4. Ca ii H and K Line Fluxes (erg cm⁻² s⁻¹) at 1 AU

Stara	HD	[Fe/H]	Spec Typeb	Lyαc	Ca iid	Ca iie	Ca iif	Ca iig	Ca iih	Ca iii	Ca iij
Procyon	61421	−0.02	F5 IV–V	77.1				149.
HR 4657	106516	−0.70	F5 V/L	27.8			46.4	40.1
χ Her	142373	−0.50	F8 V/L	22.0			31.5	34.9		25.5
χ1 Ori	39587	−0.09	G0 V	41.6			48.3	53.0		52.7
HR 4345	97334	−0.01	G0 V	42.8			49.6	54.5		52.0
Mean Sun		+0.00	G2 V	6.5	10.8			16.1		17.2
α Cen A	128620	+0.25	G2 V	7.54	16.6					15.8	7.75
HR 2882	59967	−0.19	G4 V	55.9					44.7		27.4
61 Vir*	115617	+0.00	G5 V	5.26				11.3	11.6
κ1 Cet	20630	+0.09	G5 V	30.0	64.1		39.4	45.2		43.0
HR 6748	165185	−0.06	G5 V	48.9					45.6		21.8
SAO 254993	203244	−0.21	G5 V	43.8					33.0		23.8
τ Cet	10700	−0.43	G8 V/L	5.66			6.61	7.24	6.52	6.46	4.61
ξ Boo A	131156A	−0.13	G8 V	35.3	31.5		23.9	26.9	27.1	23.3
α Cen B*	128621	+0.24	K0 V	10.1	5.75				6.02		3.05
DX Leo	82443	−0.23	K0 V	31.1				39.4
70 Oph A	105341	−0.08	K0 V	23.6	23.1
Eri*	22049	−0.08	K1 V	21.5	19.7		15.9	16.8	14.8	15.9	9.37
40 Eri A	26965	−0.27	K1 V	7.33	7.99		7.42	8.08	6.41		3.70
36 Oph A	155886	−0.39	K1 V/L	18.0			10.4	10.5	9.39
HR 1925	37394	+0.14	K1 V	29.3				23.4
EP Eri	17925	+0.08	K2 V	27.6			34.2	34.1	32.9		22.2
61 Cyg A	201091	−0.35	K5 V/L	8.90	1.61		3.0	3.28	7.89	3.29
Ind	209100	−0.20	K5 V	17.3	3.29				8.13		2.92
AU Mic	197481	...	M0 V	43.0	8.60	4.46
AD Leo	GJ 388	+0.28	M3.5 V	9.33		0.264					0.958
EV Lac	GJ 873A	−0.01	M3.5 V	3.07		0.314
Proxima Cen	GJ 551C	...	M5.5 V	0.301							0.0067
GJ 667C*	...	...	M1.5 V	1.54		0.103
GJ 876*	...	+0.18	M5.0 V	0.409		0.00765
GJ 581*	...	−0.10	M2.5 V	0.513		0.00828
GJ 436*	...	+0.04	M3 V	1.571		0.0975

Notes. ^aExoplanet host stars listed in the http://exoplanets.org database are marked with an * symbol. ^bData from SIMBAD with M star metal abundances from the sources listed in Section 3.4. ^cReconstructed intrinsic Lyα line fluxes for most stars (Wood et al. 2005) and for the GJ stars (France et al. 2013). ^dCa ii H and K chromospheric flux at 1 AU (Linsky et al. 1979), Pasquini et al. (1988), and (Robinson et al. 1990). ^eCa ii H and K chromospheric flux at 1 AU (Browning et al. 2010). ^fCa ii H and K chromospheric flux at 1 AU (Noyes et al. 1984). ^gCa ii H and K chromospheric flux at 1 AU (Baliunas et al. 1995). ^hCa ii H and K chromospheric flux at 1 AU (Henry et al. 1996). ⁱCa ii H and K chromospheric flux at 1 AU (Hall et al. 2007, 2009; Lockwood et al. 2007). ^jCa ii H and K chromospheric flux at 1 AU (Cincunegui et al. 2007).

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Other observers have measured the S index, which is the flux in 1.09 Å bandpasses centered on the H and K line emission cores divided by the flux in continuum windows. Hartmann et al. (1984) provided a correction for the photospheric flux within the bandpass but outside of the H1 and K1 features using high-resolution spectra of stars with weak H and K emission. Columns 8 and 9 of Table 4 show the time-averaged Ca ii fluxes obtained at Mt. Wilson by Noyes et al. (1984) and Baliunas et al. (1995) after subtracting the photospheric flux following Hartmann et al. (1984). Columns 10 and 11 show Ca ii fluxes obtained by Henry et al. (1996), Hall et al. (2007, 2009), and Lockwood et al. (2007) using a similar approach. The last column in Table 4 lists the fluxes of Southern hemisphere stars obtained by Cincunegui et al. (2007). We plot in Figure 6 the ratio of Lyα–Ca ii flux, R(Ca ii), using the average of the Ca ii fluxes for all of the data in Table 3, except for the Cincunegui et al. (2007) fluxes which appear to be systematically smaller than the fluxes obtained from the other sources.

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The R(Ca ii) data in Figure 6 for each spectral-type bin show relatively small scatter about the least-squares fit lines. We find that the dispersion (see Table 2) is smallest for the K stars (only 20.6%), and larger for the variable M stars. The dispersion of 42% for the G stars likely results from uncertainty in the photospheric flux correction which is large for G stars. Thus, the Ca ii H and K line fluxes can be used to estimate the intrinsic Lyα flux from the fit lines, provided one can remove the photospheric component from the observed line core fluxes.

Except for the highly variable M dwarfs for which the Lyα and other emission lines were observed at different times, the correlations of reconstructed Lyα flux with emission lines formed at similar or somewhat higher temperatures in the chromosphere and transition region generally have small scatter about the least-squares fit lines. This behavior results from increasing mechanical heating shifting the chromospheric thermal structure to higher densities while keeping a similar shape (Fontenla et al. 2011). Thus, all of the emission lines brighten together roughly proportional to density squared. Ayres (1997), Ribas et al. (2005), and others have noted that slopes of power-law relations between X-ray and chromosphere line flux are generally near 2.0 rather than a linear relation. Also, soft X-ray emission as measured, for example, by ROSAT is highly sensitive to coronal temperature and is more time variable than chromospheric emission. For these reasons, we did not anticipate a tight correlation between reconstructed Lyα flux and X-ray flux. Wood et al. (2005) plotted X-ray flux versus reconstructed Lyα flux for F–M dwarfs and giants showing correlations, but with large scatter for each type of star.

We plot in Figure 7 the R(X) = f(Lyα)/f(X-ray) ratios versus X-ray flux at 1 AU for the stars in Table 1 using the ROSAT PSPC X-ray fluxes cited by Wood et al. (2005) or more recent X-ray flux measurements using Chandra and XMM-Newton (see the references cited in the footnotes of Table 1). The X-ray flux for GJ 667C, which was obtained with the HRI instrument on ROSAT rather than the PSPC, is uncertain due to the close proximetry of GJ 667A and GJ 667B.  Judge et al. (2003) estimated solar X-ray fluxes through the ROSAT PSPC bandpass from full disk solar observations by the SNOE-SXP instrument. For the quiet Sun, moderately active Sun, and active Sun, we use their X-ray luminosities, log L_X  = 26.8, 27.75, and 27.9, respectively.

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The Lyα/X-ray flux data show correlations with small scatter for the F5–G9 and K0–K5 dwarfs. The quiet and active solar data are consistent with the least-squares fit for the other F5–G9 stars. The mean dispersions listed in Table 2 are 29.8% for the F5–G9 dwarfs and 22.2% for the K0–K5 dwarfs, which are similar to the mean dispersions for the C iv, C ii, O i, Mg ii, and Ca ii lines. The mean dispersion for the M dwarfs is much larger than for the F5–K5 stars, although the slope of the fit line is similar to that of the warmer stars. X-ray time variability is the most likely cause of the large scatter of the M stars as the X-ray and Lyα data were obtained at different times. Despite the factor of 2–3 scatter about the M star fit line, the similar slope of the fit line to those for the warmer stars suggests that one can use the M-dwarf fit line to estimate the Lyα flux of an M dwarf at the time of an X-ray measurement with an uncertainty much smaller than the dispersion shown in Table 2. We note that GJ 832 is plotted very close to the quiet Sun in Figure 7, and that GJ 832 (M1.5 V) and AU Mic (M0 V) are consistent with the fit lines for the K0–K5 stars. This suggests that the R(X) versus X-ray flux correlation for K stars may also be useful for estimating the intrinsic Lyα flux of early M dwarfs.

We now consider whether the stellar Lyα flux of main-sequence stars can be estimated simply from the stellar effective temperature (T_eff). We plot in Figure 8 the Lyα flux for all of the stars in Table 1 versus T_eff. At each value of T_eff, there is a dispersion in the Lyα flux that increases from a factor of four near T_eff = 6000 K to a factor of 1000 for the M stars. The range in Lyα flux at a given T_eff is reduced significantly by grouping the stars according to their rotation period (P_rot), which is a rough measure of magnetic heating rates in the chromosphere and corona. We show least-squares fits, log f(Lyα) = A + B T_eff, for the stars in three groups: fast rotators (P_rot = 3–10 days), moderate rotators (10–25 days), and slow rotators (>25 days). The coefficients for these fits are listed in Table 5. Compared to the least-squares fits, the Lyα flux dispersion within each rotational period group is 32%–85% and largest for the M stars. Therefore, estimates of the Lyα flux based only on a star's T_eff and P_rot are reasonably accurate for G stars but not for the cooler stars.

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In Figure 9, we plot the Lyα flux in the habitable zone (HZ) of an exoplanet, where the distance from the star to the HZ is estimated approximately as proportional to the stellar luminosity, d_HZ = (R_⋆/R_☉)(T_⋆/T_☉)² AU. The location of the HZ, the region around a star where life forms are thought to be possible, involves many other considerations including greenhouse gases, orbital eccentricity and stability, and atmospheric chemical composition (Kasting & Catling 2003). In this HZ plot, the dispersion of the Lyα flux is reduced somewhat for the M stars (see Table 5). Lyα fluxes in the HZ trend significantly higher with decreasing T_eff, and the quiet Sun has nearly the smallest value of Lyα flux. Exoplanets of most of the stars discussed in this paper receive significantly larger Lyα fluxes and thus have higher molecular dissociation rates in their atmospheres. This is especially true for M dwarfs, which have smaller radii and lower effective temperatures than the Sun. Exoplanets in the HZs of the five M dwarfs in this study receive about 10 times the Lyα flux as the Earth receives from the quiet Sun. We therefore conclude that large FUV fluxes are received by exoplanets in their HZs from their M-dwarf host stars contrary to some previous assumptions. Also, the Lyα fluxes for stars with exoplanets do not appear to differ from stars without discovered exoplanets in these two plots.

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We have identified five methods for reconstructing or estimating the intrinsic Lyα stellar fluxes of main-sequence stars between spectral types F5 and M5. Whether a given method can be used and its accuracy depends on the quality of the available data. The first and most accurate method developed by Wood et al. (2005) requires high-resolution spectra of the Lyα line and knowledge of the interstellar velocity structure based on high-resolution spectra of the deuterium Lyα and metal lines. Wood et al. (2005) estimate typical errors of 20% in the reconstructed Lyα line fluxes using this method, but at present only the STIS instrument on HST can provide such data for nearby stars.

The second method developed by France et al. (2012) also requires high-resolution spectra of the hydrogen Lyα line, but does not require spectra of the deuterium Lyα line or any other interstellar absorption line. This technique solves for both the intrinsic Lyα line parameters and the interstellar absorption simultaneously. When the interstellar absorption has only one velocity component, the technique can be as accurate as the first, but it fails when the interstellar velocity structure has many components, which is not known in the absence of high-resolution interstellar absorption lines.

In this paper, we considered three additional methods that can be used with different accuracy when there is no available high-resolution spectrum of the Lyα line to serve as the basis for reconstruction. The third method described in Sections 3 and 4 requires flux measurements of the stellar C iv, C ii, O i, Mg ii, or Ca ii lines and the best-fit correlations of these lines with fluxes of the reconstructed Lyα lines in our data set. This method estimates Lyα fluxes with 18%–25% uncertainty for F5–K5 dwarf stars, provided one corrects high-resolution spectra of the Mg ii lines for interstellar absorption. This method is based on the hypothesis that the ratios of the Lyα line flux to C iv, C ii, O i, Mg ii, and Ca ii line fluxes, R(line), for stars of similar spectral type depend only gradually on line flux. We find that this hypothesis is valid for late-type dwarf stars with approximately solar abundances. Using this method for F5–K5 V stars, we find that the dispersions of R(C iv), R(C ii), R(O i), and R(Mg ii) about the least-squares fits are consistent with the likely errors in reconstructing the intrinsic Lyα fluxes. The dispersion of R(Ca ii) about the fit line for the F5–G9 stars is larger than for the other lines because of uncertain estimates of the photospheric flux.

Most dispersions for the M0–M5 V stars are significantly larger, probably due to stellar variability between the time the Lyα line was observed with the STIS instrument and the other lines were observed with COS or STIS with a different grating setting. Even with this time variability, the fit lines for the O i, C ii, and C iv lines should provide estimates of the intrinsic Lyα flux for a given star with an uncertainty less than a factor of two. We suggest that estimating the intrinsic Lyα flux from the Mg ii line flux and the least-squares fit will lead to smaller uncertainty provided that one has high-resolution Mg ii spectra with which to estimate interstellar absorption in these lines.

It is important, however, to recognize the limitations of this correlation method. The errors associated with measuring fluxes of the Mg ii, O i, C ii, and C iv lines are generally small at the time of these line flux measurements, although geocoronal emission through the large COS aperture can be important for the O i lines. Since the method does not use direct measurements of the Lyα line, there is no reconstruction error. In addition, there is no time variability error as the Lyα flux is the scaled value at the time the other emission lines are observed. The largest uncertainty is the stellar metal abundance. Stars known to have low metal abundances generally have R(line) ratios above the scaling relation predictions. Since the effect appears to be smallest for the Mg ii lines, correlations with the Mg ii line fluxes may provide more accurate intrinsic Lyα line fluxes. Observations of more stars, especially M stars, are needed to better understand the errors in R(line) associated with low metal abundances.

When no UV or Ca ii line fluxes are available but there are X-ray measurements with an energy range similar to that of the ROSAT PSPC, a fourth method can provide estimates of the intrinsic Lyα flux from least-squares fits to the intrinsic Lyα/X-ray flux ratio versus X-ray flux. The mean dispersions about the fit lines for F5–G9 dwarfs and K0–K5 dwarfs are 20%–30%, but the mean dispersion for the M dwarfs is much larger again due to the large time variability of X-ray emission and the comparison of X-ray and Lyα data obtained at different times. Since the slope of the Lyα/X-ray flux ratio versus X-ray flux for the M stars is similar to that obtained for the warmer stars, we suggest that one can obtain a factor of two estimate of the intrinsic Lyα line flux at the time of the X-ray measurement from the correlation fit line.

Even when no Lyα, UV emission lines, or X-ray data are available, one can use a fifth method to estimate the intrinsic Lyα flux for F5–M5 stars based only on the star's effective temperature and some measure of stellar activity. The plot of intrinsic Lyα flux versus stellar effective temperature shows more than an order of magnitude range in Lyα fluxes at a given effective temperature, but comparing data for stars of similar rotational period, a good measure of stellar activity, significantly reduces the range. Comparison of Lyα fluxes versus effective temperature for stars of similar rotational period as viewed from their HZs further reduces the mean dispersion about the fit lines to 30%–40%. Thus even in the absence of any spectroscopic data, this fifth method can provide useful estimates of the intrinsic Lyα flux of F5–M5 dwarf stars.

This work is supported by NASA through grants NNX08AC146, NAS5-98043, and HST-GO-11687.01-A to the University of Colorado at Boulder. We thank Martin Snow for providing the SORCE data, and Jurgen Schmitt for providing X-ray luminosities for M-dwarf stars. We thank the anonymous referee for a thorough critique of the initial manuscript. J.L.L. thanks the Kiepenheuer-Institut für Sonnenphysik in Freiburg Germany for hospitality while writing this paper. We thank Tom Woods for providing the SORCE data and Steven Osterman for information on the COS calibration.

Facilities: HST (COS) - Hubble Space Telescope satellite, HST (STIS) - Hubble Space Telescope satellite