The Relative Emission from Chromospheres and Coronae: Dependence on Spectral Type and Age^*

Essentially all stars with convective interiors from the A7 V star α Aql (Robrade & Schmitt 2009) to the late-M and perhaps L dwarfs (Hawley & Johns-Krull 2003; Berger et al. 2010; Stelzer et al. 2012) emit ultraviolet (UV; 91.2–300 nm) and X-ray (0.1–10 nm) photons from plasmas at temperatures ranging from roughly 5000 K to at least 10⁶ K. Since these plasmas are too hot to be explained by radiative/convective equilibrium in stellar photospheres, there must be an additional heat source to explain their elevated temperatures. This heat source is either the dissipation of MHD waves or direct magnetic field reconnection events called flaring; see review by Cranmer & Winebarger (2019). In analogy with the solar chromosphere and corona, stellar plasmas in the lower-temperature range are called chromospheres (see review by Linsky 2017), and plasmas in the higher-temperature range are called coronae (see review by Güdel 2004). Except for very faint stars where instrumental sensitivity limits detection, all dwarf stars with convective interiors show X-ray emission from coronae and emission lines of Mg ii, Ca ii, and H i Lyα indicating the presence of plasma at chromospheric temperatures.

There are many examples of correlations of chromospheric emission (e.g., Lyα, Ca ii H and K lines, Mg ii h and k lines, Hα) with such stellar activity indicators as age, rotation, and magnetic field strength and coverage (e.g., Wood et al. 2005; Guinan et al. 2016; Newton et al. 2017). There are also correlations of coronal properties such as X-ray emission with activity indicators (e.g., Güdel 2004; Wood et al. 2005). These correlations generally show saturation at high activity levels and linear regressions in log–log plots with decreasing activity indicators such as age and rotation. These correlations are usually described by power-law relations of the form $\mathrm{log}F$(corona) $=\,\alpha \mathrm{log}F$(chromo) $+\beta$, where F(corona) is a coronal flux or luminosity diagnostic, usually the broadband X-ray emission, and F(chromo) is the flux or luminosity of a chromospheric diagnostic, generally an emission line such as the Ca ii K line (393.3 nm), Mg ii k line (279.6 nm), or H i Lyα line (121.56 nm). An example of such power-law correlations between X-ray and Mg ii emission is $\alpha =2.20\pm 0.13$ for F and G dwarfs and $\alpha =2.90\pm 0.20$ for K dwarfs (Wood et al. 2005). Another example is the correlations of the chromospheric Ca ii K line with UV emission lines and extreme-UV (EUV; 10–91 nm) flux (Youngblood et al. 2017).

The correlations have steeper slopes for activity indicators formed at higher temperatures in the stellar atmosphere. For example, in a volume-limited sample of 159 M dwarfs located within 10 pc, Stelzer et al. (2013) found that the slope of X-ray luminosity with age is steeper than that for the luminosity in the Galaxy Evolution Explorer (GALEX) far-UV (FUV; 134–178 nm) emission formed in the upper chromosphere and the GALEX near-UV (NUV; 177–283 nm) emission formed in the lower chromosphere. Ribas et al. (2005) found a steeper decline of X-ray emission with age compared to chromospheric and transition region emission for solar analog stars, and Guinan et al. (2016) found a steeper decline of X-ray emission compared to Lyα emission for M0–M5 V stars. For M stars, Guinan et al. (2016) showed that the decay of X-ray emission with time is also faster than the decay of Lyα radiation. These pioneering studies point to a trend of decreasing stellar activity that results from the decay of magnetic fields with decreasing rotation rate. The age dependence of decreasing activity depends on stellar mass with a decay timescale of order 100 Myr for F–K dwarfs and increasing to several Gyr for late-M dwarfs (Reiners & Mohanty 2012).

Flux–flux diagrams, which plot one emission feature, such as X-rays, versus another emission feature, such as UV or Ca ii emission, are useful tools for studying the spectral energy distributions of radiation seen by exoplanets. Stelzer et al. (2013) found that in plots of X-ray luminosity versus luminosity in the GALEX FUV and NUV bands, M dwarfs with weak emission follow the same trend line as active M dwarfs over 3 orders of magnitude in X-ray luminosity. Walkowicz & Hawley (2009) showed that the X-ray flux and Ca ii emission follow a similar trend line for M3 V stars.

Oranje (1986), Schrijver & Rutten (1987), and Rutten et al. (1989) observed chromospheric emission in the Mg ii lines with the International Ultraviolet Explorer satellite and Ca ii emission from ground-based observatories together with X-ray emission observed by the European X-ray Observatory Satellite for main-sequence stars. They found that M dwarfs deviate from the chromosphere-coronal flux–flux correlation (here called trend lines) seen in the warmer stars in the sense that the chromospheric emission is systematically weak compared to coronal emission and that this weakness becomes more pronounced for the coolest and least active stars.

Increasing interest in the environment and habitability of exoplanets of M dwarfs (Shields et al. 2016; Kaltenegger 2017; Wandel 2018) and the availability of more sensitive UV spectra with the Hubble Space Telescope (HST) and X-ray fluxes with the ROSAT, Chandra, and XMM-Newton satellites encouraged us to reexamine the difference in the trend lines between M dwarfs and warmer stars. In particular, we explore whether there is a difference between the trend lines of warmer and cooler M dwarfs and whether stellar age and rotation set limits for these trend lines. Given that the emission from M dwarfs is variable at all wavelengths, our study benefits from the availability of near-simultaneous high-resolution UV spectra of M stars obtained for some of the stars in the HST Measurements of the Ultraviolet Spectral Characteristics of Low-mass Exoplanetary Systems (MUSCLES) Treasury Survey program (France et al. 2016). We will also use UV spectra obtained with other HST programs specifically aimed at M dwarfs.

This paper will explore the X-ray versus Lyα trend lines for M dwarfs separated into spectral type and age bins. The X-ray emission is the primary tool for measuring the heating rates in stellar coronae, although thermal conduction, winds, and radiation in the EUV are additional sinks for coronal heating. The Lyα emission line is by far the brightest feature emitted by chromospheres of G-type stars and represents at least half of the total emission in the UV spectra of M dwarfs (France et al. 2012). Claire et al. (2012) estimated that Lyα photons represented about 40% of all solar photons at $\lambda \lt 170\,\mathrm{nm}$ throughout the Sun's history. Compared to other chromospheric emission lines formed at temperatures less than 10,000 K, the power-law index a in the relation log F(Lyα) = a log F(line) + b is close to unity: $a=0.77\pm 0.11$ for the Mg ii k line (Youngblood et al. 2016) and $a=0.88\pm 0.11$ for the Ca ii K line (Youngblood et al. 2017). Thus, the flux in the Lyα line is a good but not perfect proxy for the total emission from a stellar chromosphere at temperatures less than about 15,000 K. In our comparison of coronal and chromospheric emission from stars between spectral types F and late M, we will use X-ray emission as a diagnostic of coronal emission and Lyα fluxes reconstructed to remove interstellar absorption as a diagnostic for chromospheric emission.

In Section 2, we list the available reconstructed Lyα and X-ray data and the origins of these data. Section 3 describes the different trend lines for the warmer stars compared to the M dwarfs, and in Section 4 we compare L(X)/L(bol) with L(Lyα)/L(bol) as functions of stellar effective temperature and age. We then consider possible explanations for the different trend-line slopes in Section 5 and summarize our conclusions in Section 6.

We include in this study all dwarf stars with spectral types later than mid-F for which there are both reconstructed Lyα and broadband X-ray fluxes. A major source of these data is the paper by Linsky et al. (2013) that gives Lyα and X-ray fluxes for 5 F stars, 18 G stars, 16 K stars, and 8 M stars. The coolest M dwarf in this list is Proxima Centauri (M5.5 V). The Lyα fluxes were reconstructed either by correcting for the observed interstellar H i Lyα absorption along the lines of sight to the stars (Wood et al. 2005) or by simultaneously solving for the intrinsic line profile and the interstellar absorption (France et al. 2012; Youngblood et al. 2016; Wilson et al. 2020). The observations and their data sources are listed in Table 1. The Lyα and X-ray fluxes (erg cm⁻² s⁻¹) are listed at a standard distance of 1 au. The stellar effective temperatures and ages are primarily from Schneider et al. (2019) and Melbourne et al. (2020). The bolometric luminosities are computed from the effective temperatures, stellar radii, and Gaia parallaxes cited in these papers. For many of the stars, these quantities are from A. Youngblood (2020, in preparation). In addition to the Lyα and X-ray fluxes cited in the Linsky et al. (2013) paper, we include new data from the following sources.

• MUSCLES Treasury Survey. The MUSCLES Treasury Survey (France et al. 2016; Loyd et al. 2016; Youngblood et al. 2016) observed seven low-activity M dwarfs and four K dwarfs together with coordinated X-ray and ground-based observations. We include in Table 1 the reconstructed Lyα fluxes (Youngblood et al. 2016) and coordinated X-ray fluxes corrected for interstellar absorption (Loyd et al. 2016). The MUSCLES fluxes for the stars GJ 667C, GJ 832, GJ 876, GJ 581, and GJ 436 are listed in Table 1 instead of the values listed in the previous Linsky et al. (2013) paper. Proxima Centauri was not part of the MUSCLES survey, but the fluxes for the 2017 HST and Chandra observations of the star are included on the MUSCLES team website.
• Mega-MUSCLES Program. Continuing from the MUSCLES program, the Mega-MUSCLES program (Froning et al. 2019; Wilson et al. 2020) observed 13 more active M dwarfs with HST (program GO-15071) with coordinated Chandra, XMM-Newton, and ground-based observations. A. Youngblood et al. (2020, in preparation) reconstructed the Lyα fluxes for these stars using the technique described in Youngblood et al. (2016). A. Brown et al. (2020, in preparation) analyzed the Chandra ACIS-S S3 CCD spectra of five of these stars: GJ 15A, GJ 163, GJ 849, LHS 2686, and GJ 699 (Barnard's star). The fluxes listed in Table 1 are mean values, except that a flare on GJ 799 was deleted to provide the quiescent emission level. The Chandra observation of GJ 15A was simultaneous with the HST observation.One of the Mega-MUSCLES targets, the M7.5 V star TRAPPIST-1, has a previously reconstructed Lyα flux (Bourrier et al. 2017) and X-ray flux (Wheatley et al. 2017). We use the new Mega-MUSCLES fluxes (Wilson et al. 2020) because the HST and XMM-Newton observations are nearly simultaneous and thus can be reliably compared. To obtain a rough estimate of the uncertainty in the Lyα flux of a late-M dwarf like TRAPPIST-1, one should consider both possible errors in the reconstruction technique and stellar variability. Bourrier et al. (2017) obtained a reconstructed Lyα flux of ${7.6}_{-3.0}^{+1.5}\times {10}^{-15}$ erg cm⁻² s⁻¹ from their 2016 Space Telescope Imaging Spectrograph (STIS) data, but, using a different reconstruction technique, Wilson et al. (2020) obtained $({1.09}_{-0.27}^{+0.40})\times {10}^{-14}$ when analyzing the same data. The analysis of the 2018 Lyα STIS spectra by Wilson et al. (2020) resulted in a reconstructed flux of $({1.40}_{-0.36}^{+0.60})\times {10}^{-14}$ in the same units. The uncertainty in the X-ray flux of TRAPPIST-1 is primarily due to stellar variability. Wheatley et al. (2017) obtained an X-ray flux of $(2.0\mbox{--}4.3)\times {10}^{-14}$ erg cm⁻² s⁻¹ from their 2014 XMM-Newton EPIC observation, while Wilson et al. (2020) obtained $2\times {10}^{-14}$ from their 2018 EPIC observation.
• High radial velocity stars program. We include the reconstructed Lyα line fluxes for Kapteyn's star (Guinan et al. 2016; Youngblood et al. 2016) and the reconstructed Lyα fluxes for two high radial velocity stars with spectral types G8 V to M4 V observed by A. Youngblood et al. (2020, in preparation) obtained with HST program GO-15190. We also include the high radial velocity stars Ross 825 and Ross 1044 analyzed by Schneider et al. (2019).
• Winds of M dwarf stars program. We include the reconstructed Lyα and X-ray fluxes of nine nearby M dwarf stars observed by B. E. Wood et al. (2020, in preparation) with HST program GO-15326. These stars were observed primarily to measure their winds using the Lyα line.
• FUMES targets. The Far-Ultraviolet M-dwarf Evolution Survey (FUMES; J. S. Pineda et al. 2020, in preparation) observed 10 M0 V to M5 V stars. We have included the two stars with STIS E-140M moderate-resolution spectra and three of the eight stars with STIS G-140L low-resolution spectra. A. Youngblood et al. (2020, in preparation) reconstructed the Lyα lines of these five stars with cited measurement uncertainties less than 25%.
• Individual targets. We also include in Table 1 the reconstructed Lyα line fluxes of the stars HD 28568 (Schneider et al. 2019), π Men (Garcia Munoz et al. 2020), Kepler-444 (Bourrier et al. 2017), Kapteyn's star (Guinan et al. 2016), GJ 3470 (Bourrier et al. 2018), GJ 821 and GJ 213 (Youngblood et al. 2017), GJ 1132 (Waalkes et al. 2019), and TRAPPIST-1 (Bourrier et al. 2017; Wheatley et al. 2017).

Table 1. Stellar Parameters, Fluxes (erg cm⁻² s⁻¹ at 1 au), and Luminosity Ratios

Star Names (Age Group)		Age (Gyr)	${T}_{\mathrm{eff}}$	Sp. Type	d(pc)	${L}_{\mathrm{bol}}$	f(Lyα)	f(X)	R(Ly $\alpha )$	R(X)	References
SAO 93981 (M)	HD 28568	1.16 ± 0.82 (S)	6567	F2 V	45.21	34.144	122.6	84.3	2.47	1.70	10, 23
SAO 76609 (M)	HD 28033	0.63 ± 0.05 (S)	6376	F8 V	48.38	33.983	24.7	19.2	0.722	0.561	1
χ Her (O)	HD 142373	${6.85}_{-0.52}^{+0.42}$ (S)	5890	F8 V	15.83	34.083	21.7	0.309	0.504	0.00717	1
V376 Peg (M)	HD 209458	${3.83}_{-0.70}^{+0.98}$ (S)	6071	F9 V	48.36	33.814	15.7	0.308	0.677	0.0133	1, 24
HR 4657 (M)	HD 106516	1.8 ± 0.5 (S)	6258	F9 V	22.35	33.802	27.8	5.43	1.23	0.241	1
ζ Dor (M)	HD 33262	0.68 ± 0.47 (S)	6147	F9 V	11.63	33.750	46.5	16.7	2.32	0.834	1
V993 Tau (M)	HD 28205	0.63 ± 0.05 (S)	6197	G0 V	47.78	33.913	55.5	41.4	1.91	1.42	1
${\chi }^{1}$ Ori (Y)	HD 39587	0.3 ± 0.1 (S)	5898	G0 V	8.840	33.602	41.6	37.3	2.92	2.62	1
HR 6748 (Y)	HD 165185	0.44 ± 0.19 (S)	5932	G0 V	17.20	33.612	48.9	53.5	3.36	3.67	1
π Men (M)	HD 39091	3 (Y)	5870	G0 V	18.28	33.695	5.39	0.952	0.306	0.048	6, 17
HR 4345 (Y)	HD 97334	0.45 ± 0.02 (S)	5906	G2 V	22.66	33.613	42.8	39.9	2.93	2.73	1
α Cen A (O)	HD 128620	5.3 ± 0.3 (S)	5793	G2 V	1.324	33.771	7.54	0.117	0.360	0.00557	1
Quiet sun (O)	⋯		5780	G2 V	⋯	33.586	5.95	0.224	0.436	0.0164	2
Active sun (O)	⋯		5780	G2 V	⋯	33.586	9.15	2.85	0.670	0.209	2
HR 2882 (Y)	HD 59967	0.35 ± 0.07 (S)	5830	G2 V	21.77	33.537	55.9	41.9	4.56	3.42	1
${\kappa }^{1}$ Cet (M)	HD 20630	0.6 ± 0.2 (S)	5723	G4 V	9.146	33.494	30.0	25.6	2.70	2.31	1
SAO 136111 (M)	HD 73350	0.51 ± 0.14 (S)	5836	G5 V	24.34	33.602	32.8	19.3	2.30	1.36	1
SAO 158720 (M)	HD 128987	0.62 ± 0.07 (S)	5574	G6 V	23.76	33.401	34.4	14.3	3.84	1.60	1
HR 2225 (Y)	HD 43162	0.32 ± 0.04 (S)	5651	G6.5 V	16.73	33.444	41.0	48.1	4.14	4.86	1
ξ Boo A (Y)	HD 131156A	0.2 ± 0.1 (S)	5483	G7 V	6.733	33.365	35.3	28.3	4.28	3.43	1
61 Vir (O)	HD 115617	${9.41}_{-3.15}^{+1.31}$ (S)	5538	G7 V	8.506	33.499	5.26	0.265	0.468	0.0236	1
SAO 254993 (Y)	HD 203244	0.33 ± 0.08 (S)	5480	G8 V	20.81	33.371	43.8	20.2	5.24	2.42	1
HR 8 (Y)	HD 166	0.3 ± 0.1 (S)	5327	G8 V	13.78	33.368	37.9	33.0	4.56	3.94	1
τ Cet (O)	HD 10700	5.6 ± 1.2 (S)	5290	G8.5 V	3.603	33.255	5.66	0.176	0.886	0.0276	1
SAO 28753 (Y)	HD 116956	0.33 ± 0.10 (S)	5308	G9 V	21.66	33.285	33.0	24.7	4.81	3.60	1
HR 1925 (M)	HD 37394	0.5 ± 0.1 (S)	5243	K0 V	12.28	33.274	29.3	14.4	4.38	2.15	1
40 Eri A (O)	HD 26965	${11.76}_{-5.19}^{+1.92}$ (S)	5147	K0.5 V	5.036	33.195	7.33	1.15	1.31	0.206	1
α Cen B (O)	HD 128621	5.3 ± 0.3 (S)	5232	K1 V	1.255	33.297	10.1	0.533	1.43	0.0756	1
DX Leo (Y)	HD 82443	0.25 ± 0.05 (S)	5315	K1 V	18.08	33.256	31.1	59.7	4.85	9.30	1
70 Oph A (M)	HD 165341	1.3 ± 0.3 (S)	5407	K1 V	5.122	33.308	23.6	6.62	3.26	0.915	1
GJ 3651 (O)	HD 97658	9.7 ± 2.8 (S)	5157	K1 V	21.57	33.101	18.01	0.321	4.01	0.0714	5, 24
Kepler-444 (O)	HIP 94931	${11.23}_{-0.99}^{+0.91}$ (S)	5053	K1 V	36.48	33.099	3.10	0.635	0.694	0.141	10, 24
EP Eri (Y)	HD 17925	0.2 ± 0.1 (S)	5167	K1.5 V	10.36	33.185	27.6	32.9	5.07	6.04	1
Eri (M)	HD 22049	0.5 ± 0.1 (S)	5077	K2 V	3.203	33.092	26.6	4.10	6.05	0.932	4, 5
36 Oph A (M)	HD 155886	1.7 ± 0.4 (S)	5103	K2 V	5.959	33.130	18.0	3.72	3.75	0.775	1
LQ Hya (Y)	HD 82558	${0.07}_{-0.02}^{+0.03}$ (S)	5376	K2 V	18.29	33.461	59.1	243.0	5.75	23.6	1
V368 Cep (Y)	HD 220140	${0.09}_{-0.04}^{+0.06}$ (S)	5075	K2 V	18.96	33.120	46.9	275.0	10.0	58.6	1
PW And (Y)	HD 1405	${0.15}_{-0.02}^{+0.05}$ (S)	4796	K2 V	28.34	32.976	47.1	187.0	14.0	55.7	1
GJ 4130 (O)	HD 189733	${6.4}_{-4.2}^{+4.8}$ (S)	5019	K2 V	19.77	33.102	11.8	5.34	2.63	1.19	2, 19
GJ 2046 (O)	HD 40307	6.9 ± 4.0 (S)	4925	K2.5 V	12.94	33.010	14.2	0.0712	3.91	0.0196	4, 5
V471 Tau (SB)	⋯	0.63 ± 0.05 (S)	5291	K2 V	47.71	33.270	277.9	1175.	42.0	178.	1, 23
Speedy Mic (Y)	HD 197890	0.03 ± 0.01 (S)	4609	K3 V	66.76	33.497	214.	702.	19.2	63.0,	1
Ind (M)	HD 209100	1.6 ± 0.2 (S)	4649	K4 V	3.639	32.936	17.3	0.871	5.63	0.284	1
61 Cyg A (O)	HD 201091	6.0 ± 1.0 (S)	4361	K5 V	3.497	32.742	8.90	0.498	4.54	0.254	1
GJ 370 (O)	HD 85512	5.61 ± 0.61 (S)	4455	K6 V	11.28	32.823	6.50	0.103	2.75	0.0435	4, 5
GJ 338A (O)	HD 79210J	5 (Y)	3940	M0 V	6.33	32.491	8.28	4.28	7.51	3.88	15
Ross 1044 (O)	GJ 1188	$\gt 10$ (S)	3754	M0 V	37.17	31.996	1.50	0.157	4.26	0.446	10
HIP 23309 (Y)	CD -57 1054	0.0244 (Y)	3500	M0 V	26.9	32.651	16.58	135.	10.40	84.7	16, 25
AU Mic (Y)	HD 197481	0.02 ± 0.01 (S)	3588	M1 V	9.725	32.445	43.0	70.9	43.5	71.7	2
Kapteyn's (O)	GJ 191	${11.5}_{-1.5}^{+0.5}$ (S)	3570	M1 VI	3.91	31.676	0.347	0.157	2.06	0.930	7, 11
GJ 410 (Y)	HD 95650	0.3 (M)	3775	M1 V	11.94	32.386	9.56	12.36	11.04	14.3	16, 25
GJ 49 (O)	HIP 4872	5 (M)	3175	M1.5 V	9.86	32.180	10.27	1.32	19.06	2.45	16, 24
GJ 667C (M)	HD 156384C	$\gt 2$ (S)	3472	M1.5 V	7.245	31.837	1.16	0.087	4.76	0.357	4, 22
GJ 205 (O)	HD 36395	5 (Y)	3719	M1.5 V	5.70	32.361	6.59	1.67	8.06	2.04	15
GJ 3470 (M)	LP 424-4	2 (Y)	3592	M2 V	29.45	32.235	3.64	0.82	5.95	1.34	18
GJ 15A (O)	HD 1326	5 (Y)	3470	M2 V	3.56	32.015	1.81	0.0458	4.91	0.124	14, 15, 20
GJ 887 (M)	HD 217987	2.9 (Y)	3720	M2 V	3.28	32.148	3.73	0.390	7.45	0.779	15
GJ 832 (O)	HD 204961	8.4 (S)	3522	M2 V	4.965	32.016	0.996	0.0650	2.70	0.176	4, 5
GJ 176 (O)	HD 285968	4.0 ± 0.3 (S)	3679	M2 V	9.473	32.113	1.49	0.183	3.24	0.397	4, 5
Ross 860 (O)	GJ 649	5 (Y)	3590	M2 V	10.38	32.231	5.49	6.28	9.06	10.36	14, 25
GJ 588 (O)	CD -40 9712	5 (M)	3490	M2.5 V	5.92	32.035	2.74	0.356	7.10	0.923	15
Ross 905 (O)	GJ 436	4.2 ± 0.3 (S)	3416	M3 V	9.756	31.978	0.850	0.0486	2.51	0.144	4, 5
GJ 860A a	HD 239960		3410	M3 V	4.01	31.782	0.750	0.935	3.48	4.34	15
GJ 581 (O)	HO Lib	4.1 ± 0.3 (S)	3415	M3 V	6.299	31.709	0.186	0.0304	1.02	0.167	4, 5
GJ 644B (SB) a	HD 152751	5 (M)	3450	M3.5 V	6.20	32.138	13.4	14.9	27.4	30.5	15
HIP 17695 (Y)	G80-21	0.1 (Y)	3400	M3 V	16.8	32.026	13.17	45.9	34.8	121.5	16, 25
GJ 674 (M)	CD -46 11540	0.5 (Y)	3260	M3 V	4.55	31.654	1.98	1.91	12.34	12.0	14, 24
GJ 729 (Y)	V1216 Sgr	0.5 (Y)	3240	M3.5 V	2.98	32.160	1.80	3.17	34.98	61.6	14, 24
Luyten's (O)	GJ 273	5 (M)	3290	M3.5 V	3.80	31.589	0.846	0.123	6.12	0.89	15
GJ 876 (O)	IL Aqr	9.51 ± 0.58 (S)	3129	M3.5 V	4.676	31.669	0.363	0.0846	2.19	0.509	4, 5
GJ 849 (O)	BD -05 5 (Y)	5 (Y)	3600	M3.5 V	8.80	32.107	1.43	0.156	3.14	0.34	14, 20
AD Leo (Y)	GJ 388	0.025–0.3 (S)	3308	M3 V	4.966	31.867	9.33	19.1	35.7	73.1	2
GJ 163 (O)	L229-91	5 (Y)	3225	M3.5 V	15.14	31.754	1.39	0.192	6.88	0.95	14, 20
Barnard's (O)	GJ 699	10 (Y)	3300	M4 V	1.83	31.123	0.14	0.00688	2.96	0.15	11, 14, 20, 22
YZ CMi (Y)	GJ 285	5 (M)	3200	M4 V	5.99	31.671	9.189	13.21	55.2	79.4	15
GJ 1132 (O)	L320-124	$\gt 5$ (S)	3216	M4 V	12.62	31.240	0.11	0.0363	1.92	0.588	12, 14, 24
GJ 1214 (O)	G139-21	5–10 (S)	3008	M4 V	14.65	31.065	0.119	0.0308	2.88	0.745	5, 24
EV Lac (Y)	GJ 873	0.025–0.3 (S)	3273	M5 V	5.050	31.663	3.07	19.5	18.7	119.0	1
LHS 2686 (O)	G177-25	5 (Y)	3220	M5 V	12.19	31.118	0.39	0.967	8.54	21.18	14, 20
Prox Cen (O)	GJ 551	5.3 ± 0.3 (S)	2840	M5.5	1.301	30.726	0.301	0.142	16.0	7.55	2
TRAPPIST-1 (O)	⋯	7.6 ± 2.2 (S)	2550	M7.5 V	12.43	30.301	0.092	0.131	13.0	18.5	8, 9, 14

Note.

^a The value of f(X) refers to half of the total X-ray flux from the binary system, as the X-ray observations could not resolve the emission from each star. R(Lyα) = 10⁵ L(Lyα)/L(bol). R(X) = 10⁵ L(X)/L(bol). Age group: Y = $\leqslant 450\,\mathrm{Myr}$, M = 0.5–3 Gyr, O = $\geqslant 4\,\mathrm{Gyr}$. SB = spectroscopic binary (treated as a young star). Age (Gyr): S = Schneider et al. (2019), Y = A. Youngblood (2020, in preparation), M = Melbourne et al. (2020). (1) Wood et al. (2005), (2) Linsky et al. (2013), (3) Youngblood et al. (2017), (4) Loyd et al. (2016), (5) Youngblood et al. (2016), (6) King et al. (2019), (7) Guinan et al. (2016), (8) Wheatley et al. (2017), (9) Bourrier et al. (2017), (10) Schneider et al. (2019), (11) Youngblood high RV program, (12) Waalkes et al. (2019), (13) Saur et al. (2018), (14) Mega-Muscles program, Wilson et al. (2020), (15) Wood et al. program GO-15326, (16) FUMES II paper, A. Youngblood et al. (2020, in preparation), (17) Garcia Munoz et al. (2020), (18) Bourrier et al. (2018), (19) Sans-Forcada et al. (2011), (20) A. Brown et al. (2020, in preparation), (21) Singh et al. (1999), (22) France et al. (2020), (23) ROSAT Hyades Catalog, (24) XMM Serendipitous Source Catalog, (25) XMM Slew Catalog, (26) Malo et al. (2014).

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2.1. X-Ray Fluxes

Figure 1 plots the reconstructed Lyα and X-ray fluxes listed in Table 1 for the F, G, and K stars. The X-ray and Lyα fluxes at the standard distance of 1 au are plotted with different symbols and colors for each spectral class. The least-squares linear fits to the data sets of the F, G, and K stars all have the same slopes, and the trend lines for the G and K stars overlap. We note that the most active single star, Speedy Mic (K3 V), lies at the top of the K-star trend line next to the spectroscopic binary V471 Tau (K2 V + WD), and that the least active K star as measured by the weakest X-ray flux, HD 40307 (K2.5 V), lies below the K-star trend line. In this and subsequent figures, we do not plot measurement errors, because a prime source of error is stellar activity, which is different for the UV and X-ray data typically obtained at different times, especially for cooler stars.

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Figure 2 shows the same data as Figure 1 but includes the M dwarfs divided into M0 V–M2.5 V and M3 V–M7.5 V groups. The early-M star with the weakest Lyα flux is the subdwarf Kapteyn's star (M1 VI). Its weak Lyα emission may result from the star's low metallicity and thus low electron density at chromospheric temperatures.

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We plot linear least-squares fits to the data for each spectral-type group. The fits to the F2–G9 and K stars are similar, with α equal to 2.32 ± 0.26 and 2.34 ± 0.31, respectively. These values are similar to the ones reported by Wood et al. (2005)—$\alpha =2.20\pm 0.13$ for the F–G dwarfs and $\alpha =2.90\pm 0.20$ for the K dwarfs—as would be expected, since there are many stars in common among the two data sets. A single least-squares fit with $\alpha \approx 2.3$ would fit all of the G and K stars, including the Sun, observed at low activity.

The M stars, however, show different trend lines than the F, G, and K stars. The M0 V–M2.5 V stars show a shallower slope ($\alpha =1.76\pm 0.24$). The two early-M dwarfs with X-ray and Lyα data obtained on the same day (GJ 644C and GJ 176) are on the trend line established by stars with mostly noncontemporaneous data. The most active of the early-M stars, the young stars AU Mic (M0 V) and HIP 23309 (M0 V), are at the top of the early-M dwarf and F–G star trend lines. The least active stars, GJ 667C (M1.5 V) and GJ 176 (M2.5 V), have Lyα fluxes a factor of 10 times weaker than the least active G and K stars with similar X-ray fluxes.

The M3–M7.5 group also shows a shallow slope ($\alpha =1.42\pm 0.17$), with the more active of these late-M stars having Lyα fluxes a factor of 4 times lower than the G and K stars with similar X-ray fluxes. The least active of the M3–M7.5 dwarf stars (GJ 581 and GJ 436) have a factor of 10 times weaker Lyα flux than the G and K stars with similar X-ray fluxes. The coolest M dwarf in our list, TRAPPIST-1 (M7.5 V), has a factor of 150 times lower Lyα flux than the G and K stars with similar X-ray fluxes. Figure 2 shows this pattern of decreasing chromospheric emission compared to coronal emission for the increasingly cool and less active M dwarf stars.

The most active stars lie near the top of each trend line, and the least active stars lie near the bottom. For example, the two young stars near the top of the G-star trend line, HR 6748 (age 440 ± 190 Myr) and V993 Tau (age 630 ± 50 Myr), have rotation periods of 5.9 and 4.65 days, respectively, whereas the old stars with the lowest X-ray fluxes at the bottom of the G-star trend line, α Cen A (age 5.3 ± 0.3 Gyr) and τ Cet (age $5.6\pm 1,2$ Gyr), have rotation periods of 28 and 34.5 days, respectively. Note that the quiet Sun (G2 V) lies near the bottom of the G-star trend line close to α Cen A and τ Cet. A star near the top of the K-star trend line is Speedy Mic, a young (30 ± 10 Myr) rapidly rotating star with a rotational period of 0.38 days. At the bottom end of the K-star trend line is the old (6.9 ± 0.4 Gyr) star HD 40307 with a rotation period of 48 days. For the M0 V–M2.5 V star group, AU Mic (age 20 ± 10 Myr) lies at the top of the trend line, and Kapteyn's star (age ${11.5}_{-1.5}^{+0.5}$ Gyr) lies at the bottom of the trend line. A similar trend is seen for the M3 V–M7.5 V star group, with the active and probably young stars AD Leo and EV Lac at the top of the trend line and the 4.2 ± 0.3 Gyr star Ross 905 (GJ 436) and the 7.6 ± 2.2 Gyr star TRAPPIST-1 near the bottom of the trend line. The stellar ages are from the compilation of Schneider et al. (2019).

As stars age on the main sequence, rotate more slowly, and generate less magnetic flux, they descend the trend line for their spectral type. However, the timescale for decreasing rotation depends on stellar mass, with the F–K dwarfs becoming slow rotators before the age of the Pleiades (125 Myr) and the M3–M7.5 stars remaining rapid rotators at the age of Praesepe (790 Myr; Rebull et al. 2017). Since X-ray and Lyα fluxes are usually not measured at the same time for a given star, part of the scatter about the trend lines is due to variable activity, which is larger for the M stars than for the warmer stars (Marino et al. 2002; Loyd & France 2014; Miles & Shkolnik 2017).

Figure 3 shows the decline of M dwarf chromospheres in a different way. The figure plots reconstructed Lyα flux divided by the Lyα flux ratio predicted if the M stars followed the trend line for the G stars at the same X-ray flux. The most important trend in this figure is the large decrease in Lyα flux toward the later spectral types.

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3.1. Error Analysis for the Regression Coefficients

We developed two methods for estimating the linear regression coefficients and their uncertainties for the plots of log F_x versus log ${F}_{{\rm{Ly}}\alpha }$ (Figure 2) and log ${L}_{x}/{L}_{\mathrm{bol}}$ versus log ${L}_{\mathrm{Ly}\alpha }/{L}_{\mathrm{bol}}$. The first method estimates the error of the regression fit by bootstrapping the residuals. For the observed data $({x}_{i},{y}_{i})$, we first estimate the regression coefficients of the linear fit and calculate the fitted values $\hat{y}$. The residuals of the fit are defined as ${e}_{i}={y}_{i}-\hat{y}$. We then built 10,000 bootstrap samples of the residuals $\widetilde{{e}_{i}}$. For each residual series, we computed the bootstrap $\widetilde{{y}_{i}}=\hat{y}+\widetilde{{e}_{i}}$ and then obtained the linear fit for each data set $({x}_{i},\widetilde{{y}_{i}})$. In this way, we obtained the mean and standard deviation of the regression coefficients. These results are shown in Table 2.

Table 2. Fit Parameters for Figures 2 and 4 and the Pearson Correlation Coefficients

Equation	Spectral Type	α	β	${r}_{\mathrm{Pearson}}$
$\mathrm{log}{F}_{x}=\alpha \mathrm{log}{F}_{{\rm{Ly}}\alpha }+\beta$	F2 V–G9 V	2.32 ± 0.26	−2.41 ± 0.38	0.842 ± 0.061
	K0 V–K7 V	2.34 ± 0.31	−2.34 ± 0.45	0.802 ± 0.08
	M0 V–M2.5 V	1.76 ± 0.24	−1.00 ± 0.18	0.815 ± 0.086
	M3 V–M7.5 V	1.42 ± 0.17	−0.25 ± 0.12	0.832 ± 0.072
$\mathrm{log}{L}_{X}/{L}_{\mathrm{bol}}=\alpha \mathrm{log}{L}_{{\rm{Ly}}\alpha }/{L}_{\mathrm{bol}}+\beta$	F2 V–G9 V	2.28 ± 0.20	−0.85 ± 0.09	0.888 ± 0.046
	K0 V–K7 V	2.27 ± 0.42	−1.36 ± 0.33	0.693 ± 0.114
	M0 V–M2.5 V	1.97 ± 0.44	−1.39 ± 0.39	0.655 ± 0.138
	M3 V–M7.5 V	1.89 ± 0.18	−1.06 ± 0.19	0.88 ± 0.052

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The second method, which is not a traditional bootstrap, involves allowing both x_i and y_i to vary within a wide range and then solving for the regression coefficients multiple times to determine their mean values and uncertainties. We allowed all values of ${F}_{\mathrm{Ly}\alpha }$ or ${L}_{\mathrm{Ly}\alpha }/{L}_{\mathrm{bol}}$ to vary randomly between 0.7 and 1.3 times the observed values and all values of F_x or ${L}_{x}/{L}_{\mathrm{bol}}$ to vary randomly between zero and twice the observed values. The results are very similar to those obtained by the first method.

Between the early-F and late-M dwarfs, stellar effective temperatures, radii, and bolometric luminosities change by large factors. Ratios of X-ray and Lyα luminosities to the stellar bolometric luminosities measure the relative amounts of radiated energy from the chromosphere and corona. Table 1 lists bolometric luminosities computed from the stellar radii, effective temperatures, and distances listed in Schneider et al. (2019), Melbourne et al. (2020), and A. Youngblood et al. (2020, in preparation). The ratios R(Lyα)=10⁵ L(Lyα)/L(bol) and R(X) = 10⁵ L(X)/L(bol) in Table 1 are computed from the fluxes and bolometric luminosities. The ages listed after the star names are in three categories: young stars (Y) 0–450 Myr, middle-aged stars (M) 0.5–3 Gyr, and old stars (O) $\gt 4\,\mathrm{Gyr}$. We group the stars into these three groups because many stellar ages are imprecise. Most of the ages are from the compilations of Schneider et al. (2019) and Melbourne et al. (2020).

In Figure 4, we plot L(X)/L(bol) versus L(Lyα)/L(bol) for the stars grouped by spectral type. Unlike Figure 2, the stars in Figure 4 are clumped together as the small bolometric luminosities of the M stars move their luminosity ratios to the upper right. The regression line slopes α in the luminosity ratio equation log L(X)/L(bol)=α log(L(Lyα)/L(bol)) + β are similar to the regression line slopes for the flux–flux equation as shown in Table 2. GJ 176 is on the trend line for early M stars, but GJ 667C is slightly off the trend line. The errors in the regression coefficients were computed as described in Section 3.1. We next consider how L(X)/L(bol) and L(Lyα)/L(bol) change with stellar effective temperature (${T}_{\mathrm{eff}}$) for stars with different ages.

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4.1. Young Stars

We have identified 21 young stars with reconstructed Lyα and X-ray fluxes. The range in ages for these young stars is 0.02 (AU Mic and HIP 23309) to 0.44 (HR 6748) Gyr. The boundary between young and middle-aged stars is arbitrary, but separating young from middle-aged stars at 0.45 Gyr reveals a clear pattern. We include two spectroscopic binaries (V471 Tau and GJ 644B) in the young star list, as tidally induced rapid rotation raises their activity levels to those of the rapidly rotating young stars (Wheatley 1998). The distribution of data points in Figure 5 and least-squares fits to the data show two interesting trends. The L(Lyα)/L(bol) data increase smoothly from ${T}_{\mathrm{eff}}=6000$ (near spectral type G0 V) to 3000 (near spectral type M5 V) K, implying that the fraction of the stellar bolometric luminosity that heats chromospheres increases steadily to cooler stars.

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The L(X)/L(bol) data behave differently than L(Lyα)/L(bol). At high temperatures, L(X)/L(bol) is roughly equal to L(Lyα)/L(bol), but beginning near 5400 K (about spectral type G8 V), L(X)/L(bol) rises steeply to near the saturation value of ${10}^{-3.1}$. The L(Lyα)/L(bol) does not reach saturation for young stars until ${T}_{\mathrm{eff}}\approx 3000$. This behavior may result from the different ages of stars in our young star sample. There are 12 stars in Figure 5 with ${T}_{\mathrm{eff}}$ in the range 5167–5932 K. Eleven of these stars have ages 200–450 Myr with a mean age of 310 Myr. All of these stars have L(X)/L(bol) below 10⁻⁴. The exception is LQ Hya, with an age of 70 Myr and ${T}_{\mathrm{eff}}=5376$ K, which has L(X)/L(bol) well above 10⁻⁴. Three other somewhat cooler stars with ages 30–150 Myr have L(X)/L(bol) close to ${10}^{-3.1}$, as shown in Figure 5. However, the L(Lyα)/L(bol) values for these four stars are close to the least-squares fit. We interpret these data in terms of coronal heating in G and K stars younger than about 150 Myr and cooler than about 5200 K being enhanced relative to chromospheric heating.

4.2. Middle-aged Stars

For the 17 stars with middle ages, which we consider here to be 0.5 ( Eri) to 3 (π Men) Gyr, the dependence on ${T}_{\mathrm{eff}}$ is somewhat different than that for the young stars. Like the young stars, the L(Lyα)/L(bol) in Figure 6 also increases smoothly to lower effective temperatures. On the other hand, the L(X)/L(bol) data points are widely scattered with no apparent pattern except that they are far below saturation and well below L(Lyα)/L(bol).

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4.3. Older Stars

In Figure 7, we show data for the group of 33 older stars between ages 4.0 (GJ 176) and 11.6 (Kapteyn's star) Gyr. The data for GJ 176 are on both trend lines. Similar to the young and middle-aged stars, L(Lyα)/L(bol) also increases smoothly to the coolest stars in our sample. Although the L(X)/L(bol) data are scattered, they show an increasing trend to lower ${T}_{\mathrm{eff}}$ with a steeper slope than L(Lyα)/L(bol). The mean ratio of L(Lyα)/L(bol) to L(X)/L(bol) decreases from a factor of about 100 near ${T}_{\mathrm{eff}}=6000$ K to a factor of about 3 near 3000 K. Here L(X)/L(bol) and L(Lyα)/L(bol) are nearly equal for some of the coolest stars. We find that for the older stars, with decreasing ${T}_{\mathrm{eff}}$, coronal emission and heating become increasingly important relative to chromospheric emission and heating.

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4.4. Comparison of L(Lyα)/L(bol) for Stars of Different Age Groups

Figure 8 compares the least-squares fits to the L(Lyα)/L(bol) data for the young, middle-aged, and older stars. These three plots are nearly parallel and show a decrease by an order of magnitude at all effective temperatures between the young and older stars. The black line in the figure is the least-squares plot of L(X)/L(bol) for the older stars showing an increased slope toward lower ${T}_{\mathrm{eff}}$ compared to L(Lyα)/L(bol).

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4.5. Comparison of L(Lyα)/L(bol) with L(X)/L(bol) for Stars with Saturated X-Ray Emission

Young F, G, and K stars are rapid rotators that generally show maximum X-ray emission with L(X)/L(bol) $\approx {10}^{-3.1}$ (Pizzolato et al. 2003). For early-F stars, however, the maximum value for L(X)/L(bol) is about ${10}^{-4.3}$ (Jackson et al. 2012). The decrease from saturated X-ray emission occurs with decreasing rotation rate after about age 100 Myr for F, G, and K stars but significantly later for M stars that have longer spin-down times (Newton et al. 2017). For F, G, and K stars, saturated emission occurs when the rotation period is less than 1.3–3.5 days, depending on stellar mass, but the maximum rotation period for saturation is greater than about 10.8 days for M stars (Pizzolato et al. 2003). As measured by the GALEX NUV and FUV fluxes corrected for photospheric emission, chromospheric emission is also saturated until approximately 100 Myr for F, G, and K stars but much later ages for late-M stars (Richey-Yowell et al. 2019; Schneider & Shkolnik 2019). A young star with L(X)/L(bol) exceeding 10⁻², GJ 871.1 (M4 IV) was not included in our analysis, as the observed L(X)/L(bol) ratio exceeded the saturation level by more than an order of magnitude, indicating that flares occurred during the observations.

Our data set provides an opportunity to explore the saturation behavior of X-ray and Lyα emission as a function of ${T}_{\mathrm{eff}}$ in the same stars. We first select stars with ages less than 100 Myr. As shown in Figure 9, there are eight stars that meet this criterion. For stars cooler than 5075 K (V368 Cep), the values of L(X)/L(bol) are close to ${10}^{-3.1}$ with little dispersion, but the corresponding L(Lyα)/L(bol) values are much lower than L(X)/L(bol). This shows that when the coronal emission is saturated (or nearly so), the saturated emission level for chromospheric emission is an order of magnitude lower for early-K stars (${T}_{\mathrm{eff}}\approx 5000\,{\rm{K}}$) but only a factor of 3 lower for late-M dwarfs.

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To check on the broader applicability of these trends, we include older stars with large L(X)/L(bol). These are shown as colored letters in Figure 9. The K2 V star PW And is in the AB Dor moving group with an age of ${149}_{-19}^{+51}$ Myr. The values of both L(X)/L(bol) and L(Lyα)/L(bol) are consistent with the younger stars at similar ${T}_{\mathrm{eff}}$. The M4 V star YZ CMi also fits these trends despite its field star age (about 5 Gy), indicating that late-M stars can also have saturated emission like the young stars. Another group of stars that could have saturated X-ray and Lyα emission are short-period spectroscopic binaries that have been spun up due to tidal interactions. There are two spectroscopic binaries in Table 1: the ${P}_{\mathrm{orb}}=0.521$ day period V471 Tau (K2 V + DA) binary (Hussain et al. 2006) and the ${P}_{\mathrm{orb}}=2.9655$ day period GJ 644B (M3.5V + SB) multiple system (Mazeh et al. 2001). The two systems are only partially consistent with the trends shown by the younger stars. For V471 Tau, L(X)/L(bol) is slightly above ${10}^{-3.1}$, perhaps due to X-ray emission from the hot white dwarf star, but L(Lyα)/L(bol) is far above the trend line. For GJ 644B, L(X)/L(bol) is well below ${10}^{-3.1}$, but L(Lyα)/L(bol) is on the trend line. A much larger sample of spectroscopic binaries is needed to test whether their saturation properties are similar to the $\lt 100\,\mathrm{Myr}$ stars.

5.1. Trends with Spectral Type and Effective Temperature

5.2. Possible Explanations for the Different Emissions from Coronae and Chromospheres

5.3. Search for Observational Evidence of Changes When Stars Become Fully Convective

This paper seeks to answer two questions that were not usually asked in previous studies of dwarf stars with convective interiors. First, what is the relative amount of UV flux from stellar chromospheres and X-ray flux from stellar coronae emitted by F, G, K, and M dwarf stars? These emissions as measured by the stellar Lyα flux and X-ray flux, respectively, are critically important for understanding the rate of mass loss and photochemical reactions occurring in exoplanet atmospheres. Are there patterns in the relative behavior of these two types of emission for different types of stars?

Second, we ask whether the relative amount of heating in stellar chromospheres and coronae depends upon stellar effective temperature and age. The answer to this question is important for determining which types of heating processes operate in stars. Our analysis of 79 stars observed in recent observing programs with HST and several X-ray observatories has led to the following conclusions.

• 1.  
  For stars with similar spectral types and effective temperatures, the trend lines between chromospheric and coronal emission are described by power laws. As stars become less active with increasing age, slower rotation, and weaker magnetic fields, the relative fluxes of the chromospheric and coronal emissions both decrease following the trend line for their spectral type. We show that the trend lines for F, G, and K dwarfs are nearly identical, but the trend lines for M stars differ significantly from those of the warmer stars. In particular, the trend-line slopes (α) for the M0–M2.5 ($\alpha =1.76\pm 0.24$) and M3–M7.5 ($\alpha \,=1.42\pm 0.17$) stars are smaller than for the F2–G9 V ($\alpha =2.32\pm 0.26$) and K0–K7 V ($\alpha =2.34\pm 0.31$) stars.
• 2.  
  At the same X-ray flux level (normalized to a distance of 1 au), the more active M3–M7.5 stars show Lyα emission a factor of 4 smaller than corresponding F–K stars, and for the least active late-M stars, the Lyα emission is a factor of 10 lower. The coolest star in the sample, TRAPPIST-1 (M7.5 V), emits a factor of 150 times less Lyα flux than do the least active F–K stars with similar X-ray fluxes. The relative amounts of chromospheric and coronal emission in M stars are thus qualitatively different from the warmer stars. This difference is most extreme for the coolest star in the sample.
• 3.  
  We call attention to a possible fundamental link between atmospheric structure and the trend lines relating heating of coronae and chromospheres. With their higher gravities and lower photospheric temperatures, M dwarf atmospheres are denser and less ionized and have smaller pressure scale heights than warmer stars. The precise nature of the link is uncertain, but one underlying cause could be that higher photospheric gas pressures increase the equipartition magnetic field strengths (${P}_{\mathrm{gas}}={B}^{2}/8\pi$), and M dwarfs usually have significantly higher magnetic field strengths than solar-type stars. The relative heating rates in chromospheres and coronae should be related to the strength and scale height of the magnetic fields in stratified atmospheres with different pressure scale heights.
• 4.  
  The M stars show different trend lines and wider scatter about the trend lines than the warmer stars. Increased scatter is expected, as even low-activity M dwarfs flare more often than warmer stars and show larger UV and X-ray variability. The different trend lines for the M stars compared to the warmer stars suggest that different heating mechanisms may operate in the M stars compared to the warmer stars that distribute heat differently between their chromospheres and coronae.
• 5.  
  We find that the fraction of a star's bolometric luminosity that heats its chromosphere increases smoothly with decreasing ${T}_{\mathrm{eff}}$ for dwarf stars of all ages, but this fraction decreases by a factor of 10 from the group of young stars (age $\lt 450$ Myr) to the older stars (age $\gt 4$ Gyr) at all effective temperatures.
• 6.  
  The dependence of L(X)/L(bol) on ${T}_{\mathrm{eff}}$ is very different for the young and older stars. For G and K stars younger than about 150 Myr, saturated coronal heating as measured by L(X)/L(bol) is significantly larger than saturated chromospheric heating as measured by L(Lyα)/L(bol). As stars age, both L(X)/L(bol) and L(Lyα)/L(bol) decrease from their saturation levels, and L(Lyα)/L(bol) becomes larger than L(X)/L(bol). For the older stars, L(X)/L(bol) increases far more steeply with decreasing ${T}_{\mathrm{eff}}$ than does L(Lyα)/L(bol). We conclude that, at least for the older stars, coronal heating becomes much more important compared to chromospheric heating with decreasing ${T}_{\mathrm{eff}}$.
• 7.  
  We asked whether the decreasing ratio of Lyα to X-ray emission in the cooler M dwarfs results from chromospheres becoming weaker or coronae becoming stronger. Plots of L(X)/L(bol) and L(Lyα)/L(bol) with respect to stellar effective temperature show that for the younger stars, chromospheric emission increases gradually with decreasing effective temperature, but coronal emission increases dramatically to saturation levels for stars with ${T}_{\mathrm{eff}}\lt 5300$ K (spectral type K2 V). The likely explanation for this effect is that for stars younger than about 150 Myr, coronal heating is an order of magnitude larger than chromospheric heating, but this difference decays with age. For the older stars, L(X)/L(bol) increases much faster to lower ${T}_{\mathrm{eff}}$ than does L(Lyα)/L(bol). We have described several possible explanations for coronal heating increasing much faster than chromospheric heating with decreasing ${T}_{\mathrm{eff}}$. We conclude that the decreasing ratio of Lyα to X-ray emission in the cooler M dwarfs results from coronal emission becoming stronger rather than chromospheric emission becoming weaker with decreasing ${T}_{\mathrm{eff}}$.
• 8.  
  We searched for observational evidence for an abrupt change in Lyα or X-ray flux near spectral type M3.5 V (${T}_{\mathrm{eff}}\approx 3300$ K), where dwarf stars become fully convective. We found gradual changes in Lyα and X-ray fluxes and luminosities divided by bolometric luminosity but no abrupt changes at or near the boundary.
• 9.  
  Photochemistry and mass loss in exoplanet atmospheres are driven by the spectral energy distribution of the host star's radiation. Very different evolutions of exoplanet atmospheres can result from whether the host star is an M dwarf or a warmer star. The different trend lines of M stars compared to warmer stars mean that the spectral energy distributions of M stars will evolve in different ways than warmer stars as stars age on the main sequence. This difference in the host star's evolution will be important in assessing whether exoplanets of M stars can retain their atmospheres.

J.L.L. acknowledges support from STScI for programs HST-AR-15038, HST-GO-15071, HST-GO-15190, and HST-GO-15326. B.W. acknowledges support from STScI and NASA through program HST-GO-15326. A.Y. thanks STScI and NASA for funding program HST-GO-15190. A.B. acknowledges support for processing the X-ray observations used in this paper from Chandra Guest Observer grants GO4-15014X, GO5-16155X, and GO8-19017X. K.F. acknowledges support through HST-GO-15071. S.P. thanks STScI and NASA for support of program HST-GO-14640. S.R. thanks the Glasstone Foundation and Jesus College for her research funding and support. P.W. acknowledges support from STFC through consolidated grants ST/P000495/1 and ST/T000406/1.

Facilities: HST(STIS) - Hubble Space Telescope satellite, HST(COS) - , XMM-Newton - , Chandra X-ray Observatory - , ROSAT. -