LIVING WITH A RED DWARF: ROTATION AND X-RAY AND ULTRAVIOLET PROPERTIES OF THE HALO POPULATION KAPTEYN'S STAR^*

Kapteyn's Star (GJ 191; HD 33793) attained notoriety over a century ago when the star's discovery was reported by Kapteyn (1897), who co-discovered the star with Robert Innes and the help of photographic plates obtained by David Gill (Croswell 2006). The star was found to have a very high proper motion (recently determined to be μ_α = +6505.08 mas yr⁻¹; μ_β = 5730.84 mas yr⁻¹ by van Leeuwen 2007). Curtis (1909) measured its space motions and, until 1916 (when displaced by Barnard's Star), it had the highest known space velocity relative to the Sun (see Kotoneva et al. 2005). This high relative velocity indicated that it was a Halo (Pop II) star, and subsequent studies have shown that Kapteyn's Star is indeed metal-poor, with [Fe/H] = −0.86 ± 0.05 (Woolf & Wallerstein 2005, and references therein). Modern measures of its proper motions from Hipparcos (van Leeuwen 2007) and a radial velocity of RV = +245.2 km s⁻¹ (from Nidever et al. 2002) yield very high (U, V, W) space motions of +21.1 ± 0.3, −287.8 ± 0.3, −52.6 ± 0.3 km s⁻¹ (Kotoneva et al. 2005). Eggen (1996) identified a number of other stars with similar space motions to Kapteyn's Star. He proposed these stars as members of the Kapteyn Moving Group (Star Stream). These motions place Kapteyn's Star in an eccentric, retrograde galactic orbit. Subsequent studies of its space motions and low metal abundance indicate that Kapteyn's Star (and other possible moving group stars) may have originated from the old globular cluster ω Cen (Wylie-de Boer et al. 2010). But the association of the Kapteyn Moving Group (though not Kapteyn's Star itself) with ω Cen has been recently questioned by Navarrete et al. (2015) on chemical abundance grounds. It is believed that ω Cen may be the remnant of an old dwarf spheroidal galaxy that interacted with our Galaxy (Bekki & Freeman 2003). For the purposes of this study, we adopt an age of ${11.5}_{-1.5}^{+0.5}$ Gyr, which is near the estimated mean age determinations of the ω Cen cluster (Kotoneva et al. 2005). This age is also consistent with Kapteyn's Star's combination of high space motions and low metallicity , placing it within the Halo population of the Milky Way, which has a recent age determination of 11.4 ± 0.7 Gyr (Kalirai 2012). We note that low metallicity on its own would not be hard evidence of Halo membership, but combined with the space motions, it offers further support. The star's primary properties are summarized in Table 1.

Until recently, the "claim to fame" of Kapteyn's Star was being one of the brightest and fastest moving red dwarfs, and the closest bona fide Pop II dM stars. Recently, though, Anglada-Escudé et al. (2014a) reported that Kapteyn's Star may host two super-Earth planets. These planets were discovered via spectroscopic radial velocities. The measured RV amplitudes are K_b,c = 2.25 ± 0.31 m s⁻¹ and 2.27 ± 0.28 m s⁻¹, respectively, for Kapteyn b and c. Kapteyn b has a minimum mass of M_p sin i = 4.8 ± 0.9 M_⊕, an orbital period of P_orb = 48.6 days and a semimajor axis of a = 0.168 au. Kapteyn c has a minimum mass of M_p sin i ≥ 7.0 ± 1.1 M_⊕, orbits with a period of P_orb = 121.5 days and a semimajor axis of a = 0.31 au. From Anglada-Escudé et al. (2014a) the habitable zone of Kapteyn's Star is HZ ≈ 0.126–0.23 au. Thus, as pointed out by Anglada-Escudé et al. (2014a), Kapteyn b orbits within the star's HZ and receives a mean instellation of S/S(Earth) ≈ 40% of the insolation the Earth receives from the Sun. This is similar to the insolation received by Mars and thus this planet is potentially habitable if it has Greenhouse gas temperature enhancements similar to (or somewhat higher than) Earth (∼30 K). On the other hand, Kapteyn c receives only 12% of the insolation that the Earth receives and is thus likely too cold for life to evolve, unless its atmosphere supports a large Greenhouse temperature enhancement. Kapteyn b is one of the oldest known (probable) rocky Earth-size exoplanets that is potentially habitable. Moreover, if this discovery is confirmed, the existence of rocky planets hosted by the old, metal-poor Kapteyn's Star demonstrates that terrestrial planets form in the metal-poor environments of other Halo/Pop II stars over 10 Gyr ago.

However, the results of Anglada-Escudé et al. (2014a) have been questioned by Robertson et al. (2015) who argue against the existence of Kapteyn b. Their analysis of the spectroscopic data indicates possible correlations between stellar rotation and measured radial velocities. They conclude that Kapteyn b is not a planet but an artifact of stellar rotation. More recently, however, Anglada-Escudé et al. (2015) defended their results and reasserted the existence of this planet.

Recently, Campante et al. (2015) reported the discovery of the Kepler-444 exoplanet system that consists of five transiting Earth and sub-Earth size planets hosted by an old, high velocity, metal deficient dwarf K0 star (HIP 94931; LHS 3450). An astereoseismic analysis of the Kepler photometry was carried out, yielding an age of 11.2 ± 1.0 Gyr, indicating an Old Disk/Population II host star. Thus, this system and Kapteyn's Star system (if confirmed) demonstrate that planet formation in our Galaxy may date back to the earliest eras of star formation—at times when metal abundances were significantly lower than now. Furthermore, the existence of old exoplanet systems could portent the possibility of complex (and possibly very advanced, even intelligent) life in the solar neighborhood around commonplace stars much older than our Sun. As noted in Section 5, these planets, their atmospheres, and possible primordial life, all must survive the expected high levels of XUV radiation when the host stars were young, rotating fast, and thus very active.

Kapteyn Star is designated as VZ Pic in the General Catalog of Variable Stars¹ where it is classified as a BY Dra-type variable star, whose light variations typically arise from small, rotational brightness variations due to starspots. However, for a star as old (and presumably inactive) as Kapteyn's Star, only very small light variations are expected.

In 2009 (January through May) we secured high precision time-series CCD photometry of Kapteyn's Star using the 41 cm Panchromatic Robotic Optical Monitoring and Polarimetry Telescope Number 4 (PROMPT4; Reichart et al. 2005). This telescope is equipped with a 1k × 1k Apogee CCD camera (Nysewander et al. 2009), resulting in 059 per pixel, for a 10' field of view (Reichart et al. 2005). The star was observed with standard BVR filters on ∼50 nights over an interval of ∼120 days. Each night of observation usually consisted of 4 × 20 s B-band, 6 × 8 V-band and 9 × 5 R-band exposures. Images were reduced in the usual fashion and differential photometry was carried out with Maxim DL using four nearby reference stars. The V-band photometry revealed small, periodic light variations attributed to star spots rotating in and out of view. Thus, this apparently confirms the BY Dra variable star designation. Period searches of these data were conducted using the Peranso software's analysis of variance (ANOVA—Schwarzenberg-Czerny 1996) statistics algorithm. A quasi-sinusoidal light variation was found with a period of P_rot = 82.2 ± 11 days from the V-band data and a light amplitude of V_amp ≈ 15 ± 4 mmag. As discussed next in Section 3.2, a very similar but better defined rotation period of P_rot = 83.7 ± 0.3 days is returned from a study of the Ca ii HK emissions. The V-band data are plotted in Figure 1(a). While Figure 1(b) shows the resulting period analysis. This photometric period is assumed to be the rotation period of the star. Because of the small light variations and the lack of reliable light curves at different wavelengths, only a rough estimate of the star spot coverage of the star can be made. Additional spectroscopy and high precision multi-wavelength photometry are needed to secure more precise spot properties. Estimates of the star spot coverage were made using the relations given by Dorren (1987). Adopting a two spot model, stellar inclination i > 60°and spot to star temperature ratio of T_spot/T_star ≈ 0.8–0.9, the minimal star spot areal coverage of ∼1.1%–3.0% was estimated. For comparison, the total fractional spot areas on the Sun are typically 0.1%–0.2% of the photosphere (Cox 2000).

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It is noteworthy that most of the red dwarf stars in our program (as well as those observed by the Kepler mission) show small, quasi-sinusoidal and periodic light variations presumable also arising from the presence of star spots on their rotating surfaces. Thus, they are also BY Dra variables (e.g., see Engle & Guinan 2011). In the case of Kapteyn's Star, the inferred starspots cover more surface area than sunspots do on our Sun, even during solar maxima. Additional high precision, time-series photometry of Kapteyn's Star is needed to confirm this tentative period, and is currently underway. One problem that can limit photometric precision for Kapteyn's Star is its large proper motions that cause the star to undergo ∼8'' yr⁻¹ motions relative to fainter background stars. This can cause photometric measurement errors as the star moves across individual pixels on the CCD. Additionally, there is the possibility of varying fainter background stars being included/excluded in the brightness measures over time.

We also searched for evidence of quasi-periodic light variations in the available online all-sky photometry data sets that include Hipparcos (ESA 1997), and the Warsaw University All-Sky Automated Survey (ASAS). Because of both the temporal coverage and relatively low photometric precision (±0.015 mag) of these data, no compelling evidence of significant systematic light variations was found. More recent analysis of additional all-sky photometry from the Kilo-degree Extremely Little Telescope (KELT) also revealed no coherent, periodic light variations (J. Pepper 2016, private communication) to the level of typical photometric sensitivity (±0.014 mag). This was not unexpected, given the large proper motion of Kapteyn's Star, potential source contaminations and the large pixel scale of the instrument.

Ca ii HK (3968.5 and 3933.7 Å) chromospheric emission line measures from Anglada-Escudé et al. (2014a), obtained with data from the HARPS spectrograph, were also searched for variability. These observations were carried out to secure high precision radial velocities of the star to reveal any hosted planets. Ca ii HK emissions (commonly given as the S-index) have long been recognized as tracers of magnetic activity in cool stars (Wilson 1978; Vaughan et al. 1981). If active, magnetic (chromospheric) features are asymmetrically distributed over the stellar surface, then periodic variability in the Ca ii emission strength can be used to determine stellar rotation. The S-index has been used for decades to study magnetic cycles and rotation rates for cool stars. Studies have shown Caii HK emission to be a less ambiguous indicator of magnetic activity and variability, displaying a more linear emission response to varying levels of magnetic activity (see Gomes da Silva et al. 2014; Mullan et al. 2015). The Hα (6562.81 Å) feature, on the other hand, is more complicated to interpret since, as magnetic activity increases, the feature goes from being in absorption to eventually emerging into emission above a certain activity threshold (Mullan et al. 2015, and references therein). In cool stars, the presence of strong photospheric continuum flux in the Hα spectral region adds to the ambiguity in interpreting this feature. As such, we concentrated on analyzing the Ca ii S-index for rotation-induced variability, to support the photometric findings, since photometric and S-index variations should both arise from differences in stellar active region (starspot, plage) coverage.

Planet hosting stars, in particular, offer excellent opportunities for such studies since they normally possess a wealth of high-quality spectroscopic measures (e.g., Forveille et al. 2009, where rotation of the planet-hosting M2V star GJ 176 was also observed in both photometric and Ca ii measures). Anglada-Escudé et al. (2014b) published 95 measures of the Ca ii S-index of Kapteyn's Star taken over the course of a decade, from 2003 December to 2014 January. These data were analyzed for periodicities, and the results are given in Figure 2. For analysis, three potential flare points were excluded (discussed below), nightly means were determined, and as with the photometry, examined with the ANOVA algorithm. A well-defined, periodic variation of P_rot = 83.7 ± 0.3 days was found, in good agreement with the photometric rotation period. Because of the very strong detection, this is the final adopted rotation period. The resulting light curve and power spectrum are given in Figure 2. Also, this rotation period agrees with the 71.4 day rotation period we find for GJ 478 from ASAS-3 data. GJ 478 is an Old Disk/Halo K7V–M0V star (Leggett 1992) and therefore similar in age and mass to Kapteyn's Star.

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If a rotation period of P_rot = 83.7 days is adopted, then v sin i ≈ 0.2 km s⁻¹, when a stellar radius R = 0.291 ± 0.025 R_⊙ (derived via interferometry by Ségransan et al. 2003; see Table 1) and i > 60° are assumed. At present, this rotation velocity is too small to be measured spectroscopically. The current practical precision limit to secure the rotation line broadening is ≳0.5 km s⁻¹. For Kapteyn's Star, only an upper limit of v sin i < 3 km s⁻¹ is available (see Anglada-Escudé et al. 2014a).

As shown in Figure 2(a), three possible flare events may have occurred: 2009 February 17 (S = 0.487), 2013 May 11 (S = 0.436), and 2013 May 15 (S = 0.420). These values are ∼1.6–1.8× the data set's mean Ca ii S-index ($\langle S\rangle \approx 0.25$) for the star. Very rough estimates of flare probability can be made: using the fact that 3 spectra indicated a potential flare, out of the 95 reported, this gives a flare probability of ∼3.2%; using exposure times for the spectra, a flare was observed for 2009 s out of the total 60759, thus giving a flare probability of ∼3.3%. At face value, this translates to approximately 3–4 similar-size flares per day. More intensive observations are needed to confirm flare activity in Kapteyn's Star. If confirmed, it could indicate that even very old dM stars can continue to generate flares. The flare activity indicated by the Ca ii (S-index) data for Kapteyn's Star appears to be similar to the flares reported by Kowalski et al. (2009) and Hilton et al. (2010) for older population red dwarfs. Additional Ca ii HK or Hα spectroscopy and time-series UBV photometry (especially U-band photometry) are needed to better define the flare activity of Kapteyn's Star. In the limited data sets, no super-flares (i.e., flares with total energies E > 10³³ erg) have been observed.

A third HST orbit on Kapteyn's Star was employed to observe the Lyα region with the COS G130M spectral element. This observation gives the resolution necessary to perform a detailed study of the Lyα feature, comparing it to the reconstructed Lyα fluxes modeled by (Wood et al. 2005; France et al. 2013 and references therein) and to test acoustic heating models for stars with very slow rotations. This observation provides the first "clean" integrated Lyα flux for a star (other than the Sun).

The chromospheric H i Lyα emission line is by far the strongest emission feature in the solar EUV/FUV spectrum (see Tian 2013, and references therein). This line is also dominant in the EUV/FUV of cool (G, K, M) main-sequence stars (see Linsky et al. 2014). Because of its importance to solar-chromospheric physics and also for heating and ionizing effects on Earth's upper atmosphere and ionosphere, the solar Lyα emission has been studied for over 60 years with rockets, satellites, and solar missions (e.g., Tian 2013, and references therein). As such, Lyα emission is the most important contributor to the heating, ionization, and photochemistry of the upper atmospheres of planets. In particular the Lyα flux plays a major role in the photodissociation of important molecules such as H₂O, CO₂, and CH₄. For the Sun, the Lyα emission line contributes the overwhelming majority of the EUV/FUV 100–1250 Å flux. Though the H i Lyβ (1028 Å) is strong in the Sun, and it can easily be measured without interference from H i ISM absorption, it is still significantly weaker than Lyα (solar Lyα/Lyβ ratio ≈212–230 from SOHO-SUMER—Tian 2013). However, due to the very strong H i local ISM absorption and possible contamination from geo-coronal emission, the Lyα line is very difficult to measure even for nearby stars. Nonetheless, over the last decade, measures of Lyα emission fluxes have been obtained with HST (e.g., Wood et al. 2005; France et al. 2013; Linsky et al. 2014). These stellar Lyα integrated fluxes have been reconstructed from HST STIS and COS spectra for a small sample of mainly main-sequence G, K, & M stars. The stellar Lyα emission is calculated by taking into account the ISM absorption and removing the sharp geo-coronal emission contributions. For the cases in which the stellar Lyα emission is weak (e.g., older, inactive stars), the corrections to the observed Lyα profile can be very large. The model-reconstructed stellar fluxes can be more than 10–20× the observed, uncorrected profile. The applied corrections lead to uncertainties of 10%–30% in the resulting, integrated Lyα emission fluxes.

Because of the high RV of Kapteyn's Star (RV = +245.19 km s⁻¹—Nidever et al. 2002), the stellar Lyα emission feature is redshifted by ∼1 Å. This redshift displaces the stellar emission feature from both the ISM absorption and geo-coronal emission features (see Figure 7), allowing a much more "clean" determination of the stellar activity. Kapteyn's Star was observed with COS (G130M) to produce a spectrum of sufficient resolution to model the Lyα feature. Still, care had to be taken with the modeling, since there is overlap between the red wing of the geo-coronal feature and the blue wing of the stellar feature (Figure 7). To account for this overlap, a multi-component Gaussian fit was run to both features simultaneously. This permitted accurate fitting of the non-Gaussian shape of the geo-coronal feature, in addition to the broad peak and wings of the stellar feature.

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Kapteyn's Star is ∼2.5× the age of the Sun and rotates more than 3× slower. Nonetheless, its coronal X-ray and chromospheric FUV Lyα surface fluxes are comparable to the Sun near its activity minimum. The ratios of the X-ray and Lyα surface fluxes of Kapteyn's Star relative to the mean Sun are F_KS/F_Sun = 4.33 and 0.59, respectively. In spite of its slow rotation, this magnetic-related activity most likely arises from the star's deeper convective zone and more efficient dynamo.

The (liquid water) habitable zone for Kapteyn's Star is HZ ≈ 0.13–0.24 au (Anglada-Escudé et al. 2014a). For purposes of comparison, we adopt the near mid-HZ of 0.17 au, chosen to also be close to the semimajor axis (a = 0.168 au) of the exoplanet candidate Kapteyn b. The mean X-ray (0.3–2.5 keV) irradiance at 0.17 au is f_X (0.17 au) = 5.41 erg s⁻¹ cm⁻², while the mean X-ray irradiance of the Earth from the Sun is 0.271 erg s⁻¹ cm⁻². Thus, even at the very old age of Kapteyn's Star, a planet near the mid-HZ receives, on average, an X-ray flux ∼20× greater than the mean level that the Earth receives from the Sun. The FUV irradiance, defined by the dominant Lyα feature, near the mid-HZ (0.17 au) of Kapteyn's Star is f_Lyα (0.17 au) = 12.0 erg s⁻¹ cm⁻²; for the Sun–Earth, the mean Lyα irradiance is ∼7.00 erg s⁻¹ cm⁻². Thus, a planet near the mid-HZ (e.g., Kapteyn b) receives (on average) ∼1.7× more Lyα FUV radiation than the corresponding average solar Lyα irradiance of the Earth.

The XUV irradiance near the mid-HZ of Kapteyn's Star is higher on average than that the Earth receives from the present Sun, but not extreme. Thus, these X-ray and Lyα irradiances do not appear to be limiting factors for the survival of planetary atmospheres (or life) on a magnetically protected planet like the Earth, located near the mid-HZ of Kapteyn's Star at its present (old) age. But this was not always the case. Kapteyn's Star, when young (age < 0.5 Gyr) is expected to have rotated fast (P_rot < 10 days) and correspondingly to have been more magnetically active than today (see Figures 4 and 8). The X-ray and FUV Lyα fluxes of the young Kapteyn's Star can be estimated from other young (∼0.1 Gyr < ages < 0.5 Gyr) red dwarfs—such as AD Leo and EV Lac. The mean values of f_X (1.0 au) = 19.3 erg s⁻¹ cm⁻² and f_Lyα (1.0 au) = 6.2 erg s⁻¹ cm⁻², respectively, are obtained for AD Leo and EV Lac from Linsky et al. (2014). Using these stars as young proxies, the corresponding mean X-ray and FUV irradiances at ∼0.17 au (the location of Kapteyn b) are estimated to be ∼123× and ∼18× higher, respectively, in the past when Kapteyn's Star was ∼11 Gyr younger.

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These high XUV HZ irradiances inferred for Kapteyn's Star during its youth, as well as for other young red dwarfs, appear to be unfavorable for the development of life on a hosted, inner-HZ planet unless the planet is protected by a significant geo-magnetosphere. Such high stellar XUV fluxes (in addition to the possible large, frequent flares) ionize and possibly erode a HZ planet's atmosphere even before life has time to develop (e.g., Lammer et al. 2008; Engle & Guinan 2011, and references therein).

From a number of studies of flare characteristics for young stars, based primarily on Kepler Mission data, it appears that young G, K, M stars show frequent, energetic flares (e.g., see Walkowicz et al. 2011; Shibayama et al. 2013; Candelaresi et al. 2014; Guinan et al. 2015; Maehara et al. 2015 and references therein). Moreover, the flare rates of red dwarfs indicate that flares persist to older ages, when compared to G-type stars. Flares—and the resulting strong XUV radiation, plasma (proton) ejection events, and possible associated coronal mass ejections (CMEs)—could have deleterious effects on the atmospheres and even the ground-level environments of close-in HZ planets. The possible long-term persistence of strong flaring and associated CME events for dM stars and their effects on hosted HZ planets are the main concerns regarding the development and evolution of life on such worlds.

On the other hand, Segura et al. (2010) studied the effects of a strong stellar flare on the atmosphere of an Earth-like planet orbiting within the HZ of a young, very active dM3 star. They used a well observed, large flare on AD Leo (one of the most active dM (flare) stars) to study the XUV effects of the flare, including its high energy protons, on the atmosphere and atmospheric chemistry of the impacted planet. They conclude that such flares would not significantly affect the potential habitability of the planet or be a direct hazard to life on the surface. They carried out the modeling on a planet identical to Earth, but without a magnetic field. Although such flares can affect a HZ planet's atmosphere and ozone temporarily, these effects appear to be short-lived and not harmful to most surface life.

Historically, older red dwarfs have not yet been extensively studied for flare activity, primarily because they appear "dull" with rather weak emission lines and also their ages are difficult to determine reliably. A notable exception is the thorough analysis of Sloan Digital Sky Survey photometry by Kowalski et al. (2009), where flare rates for M dwarfs were found to decrease by an order of magnitude or more as distance from the galactic plane (taken as a proxy for stellar age) increased. Additionally, the solar-age red dwarf Proxima Centauri (age ∼5.1 ± 0.5 Gyr—from membership in the α Cen system) has been extensively studied for flares in the X-ray–UV regions (Fuhrmeister et al. 2011, and references therein). These analyses indicate a significant X-ray–UV flare rate (Walker 1981; Haisch et al. 1983, and references therein). The examination of the available VR photometry of Kapteyn's Star shows no significant flares in the optical region. But the overall on-star sample-time is relatively small, and no high-precision, time-series flare searches have been carried out in either the U or B bands where flares are easier to detect since they emit a higher flux at these wavelengths, while the stellar continuum is much weaker. However, there is some evidence for possible "chromosphere flares" from the Ca ii spectroscopic observations discussed earlier.

However, on a positive note for potential habitability, these inferred high XUV HZ irradiances for the young Kapteyn's Star (and for similar young red dwarfs) are about the same as endured by the Earth some ∼4.0–4.5 Gyr ago when the Sun was young and very magnetically active. As shown from Ribas et al. (2005), the inferred X-ray and FUV irradiances received by the young Earth were ∼200–300× and ∼10–20× higher, respectively, than now (Guinan et al. 2003; Ribas et al. 2005). On the other hand, young dM stars such as AD Leo and EV Lac have frequent large flares (AD Leo: Osten & Bastian 2008; Hunt-Walker et al. 2012—for EV Lac: Osten et al. 2005, 2010) that can cause considerable damage and loss to the atmospheres (and life) on close-in HZ planets such as Kapteyn b when its host was young. But young solar-type stars (age < 300 Myr) also appear to have large (super)flares. By extension, the young Sun is expected to have also generated superflares with total energies of E_total > 10³³ erg (see Notsu et al. 2013; Ayres 2015, and references therein). In all cases it appears necessary that the HZ planet sustain a strong geomagnetic field and thick atmosphere. This will help shield it from the deleterious effects of the host star's high XUV radiation, strong stellar winds, and frequent flares/coronal mass ejections, which are especially strong when the host star is young and very active. This is an even more important factor for planets hosted by dM stars, since their HZs are close (<0.2 au) and their periods of strong stellar activity may persist for longer times.

The observed variations of the star in coronal X-ray emission (from L_X = 2.4–6.0 × 10²⁶ erg s⁻¹) and the possible flare-like variations in the Ca ii HK emission (from an average value of $\langle S\rangle =0.25$ up to $\langle S\rangle$ ≈ 0.43–0.48 on three individual observations) indicate that the star is still active. To search for corroborative evidence of variability, we compared our chromospheric Mg ii hk emission fluxes with a recently available HST-STIS spectrum containing this feature. A high resolution spectrum of Kapteyn's Star was secured with the STIS E230H element on 2014 August 18—nearly a year after our COS observations. This snapshot spectrum (PI: Redfield; Program ID: 13332) is centered on the Mg ii hk emission feature. We measured an integrated emission flux (the sum of both lines) of f_{Mg ii} = 7.55 × 10⁻¹⁴ erg s⁻¹ cm⁻² Å⁻¹ from this STIS spectrum. Surprisingly, this flux is over twice the Mg ii flux (=3.07 × 10⁻¹⁴ erg s⁻¹ cm⁻² Å⁻¹) returned from our COS G230L spectrum on 2013 September 22. This relatively large variation could arise from a flare or may be part of a long-term activity cycle. The relative observed change in the Mg ii fluxes are similar in magnitude to the three possible flare events seen in the Ca ii lines.

We analyzed the FUV Lyα emission flux levels (versus stellar age) for dM stars. Including Kapteyn's Star, only 10 dM stars have Lyα flux measures. We used the measures of the Lyα flux at 1 au given by Linsky et al. (2014), and combined these with our determination of the Lyα flux for Kapteyn's Star. We did not include au Mic in this study because it is a very young, probable pre-main-sequence, member of the β Pic moving group (Barrado y Navascués et al. 1999) with an estimated age of ∼23 ± 3 Myr (Mamajek & Bell 2014). We estimated the ages for the other stars using various criteria such as membership in Moving Groups along with rapid rotation (AD Leo & EV Lac), membership in a wide multiple star system of known age (Proxima Cen), and large space motions/low metals (Kapteyn's Star). The ages of the other stars were inferred from rotation–age relations or (less certain) activity–age relations. The results are given in Table 4. The Mg ii hk fluxes are also given, as they are the most prominent emission feature in the NUV. The integrated flux measures are computed for 1 au (as a reference distance) and also for 0.17 au, near the mid-HZ of Kapteyn's Star and close to the mean distance of Kapteyn b (see previous section). We have included Proxima Cen in the table even though it is a M5.5 V star (R = 0.145 R_⊙ from interferometry—Ségransan et al. 2003), and much smaller than the other stars. It is included since it has well determined properties—especially radius (determined via interferometry by Ségransan et al. 2003), age, and rotation.

Table 4.  The Integrated Fluxes of Red Dwarfs Possessing Lyα Measures

Star	Sp.	fLyα	fLyα	fMg ii	Age	Rotation	Age
	Type	(1 au)	(0.17 au)	(1 au)	(Gyr)	(days)	Ref.
AD Leo	M3.5 V	9.33	322.8	2.19	∼0.2 ± 0.1	2.23 ± 0.006	f
EV Lac	M3.5 V	3.07	106.2	0.637a	∼0.4 ± 0.1	4.35 ± 0.001b	g
GJ 436	M3.0 V	1.571	54.36	0.104	3.6 ± 0.8	⋯	h
Proxima	M5.5 V	0.301	10.42	0.045a	5.1 ± 0.5	82.9 ± 0.6	i
GJ 832	M1.5 V	5.17	178.89	0.311	6 ± 1.5	⋯	h
GJ 667C	M1.5 V	1.54	53.29	0.113	6.5 ± 1.4	103 ± 2c	j
GJ 876	M4 V	0.409	14.15	0.032	7.9 ± 1.2	116.4 ± 2.5d	j
GJ 581	M2.5 V	0.513	17.75	0.036	9 ± 2	157.6 ± 2.5d	k
Kapteyn	M1.5 V	0.347	11.99	0.018	${11.5}_{-1.5}^{+0.5}$	83.7 ± 0.3e	l

Notes.

^aDoyle et al. (1990). ^bDal & Evren (2011). ^cAnalysis of HARPS Ca ii HK data from Anglada-Escudé et al. (2014a). ^dGround-based photometry carried out by us. ^eThis paper. ^fCastor Moving Group, from Klutsch et al. (2014). ^gPossible UMa Moving Group, from Klutsch et al. (2014). ^hAge determined from our X-ray activity–age relationship. ⁱα Cen ABC triple system, see Reipurth & Mikkola (2012) and references therein. ^jAge determined from our rotation–age and X-ray activity–age relationships. ^kAge determined from our rotation–age and X-ray activity–age relationships, considering that the star's metallicity and space motions are inconsistent with the Halo population, putting an upper limit on the final age. ^lAge determined from our rotation–age and X-ray activity–age relationships, along with metallicity and space motions indicative of a Halo population star.

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The integrated Lyα emission fluxes (at a reference stellar distance of 1 au) for this small sample of red dwarfs are plotted against age in Figure 8, illustrating the decline in FUV activity with age. To better account for the range of spectral types (and hence Lyα emitting areas) in our sample, each star's flux has been adjusted to the radius of a M3 V star—0.39 R_⊙ Rugheimer et al. (2015). For the dM stars in the plot, radii were determined based on spectral type (Rugheimer et al. 2015), except for Proxima Cen and Kapteyn's Star, whose interferometric radii were used instead. Lyα is used as a proxy for FUV emissions as a whole. This is because, as discussed earlier, the Lyα flux makes up over 80%–90% of the total FUV flux for dM stars. This estimate of Lyα flux contribution to the total EUV–FUV region is scaled from solar measures (see France et al. 2013; Linsky et al. 2014). The Sun is the only cool star with complete X-ray–EUV–FUV–NUV spectral coverage, due to nearly total H i absorption at ∼500–900 Å.

As shown in Figure 8, the decay in the Lyα flux with age is less rapid than found for the coronal X-ray fluxes. Using the relation of log f_Lyα (at 1 au) = 0.475–0.647(log Age [Gyr]) given in the figure, the decline in the Lyα flux from young stars (reference age = 0.5 Gyr) to old disk/Pop II stars (reference age ∼ 10 Gyr) is ∼7/1. But it should be noted that the relation between Lyα flux and age is defined by only nine stars. In Figure 8, the high Lyα flux for the assumed age of GJ 832 could arise from uncertainties in the reconstructed Lyα profile, or from its age estimate. This star is plotted, but not used in the activity–age relations. Additional Lyα emission measures with HST-COS are sorely needed for stars with reliable ages. A similar decline in chromospheric Ca ii HK emission for red dwarfs has been found by Eggen (1990). Using our previous reference ages of ∼0.5 Gyr and 10 Gyr for young and old stars, respectively, a decrease in Ca ii HK emission flux is ∼15/1. Mamajek & Hillenbrand (2008) find a decrease in Ca ii HK flux over the same age range for K stars is about 25/1, whereas a smaller decline of Hα emission has been recently reported by West et al. (2015) for M dwarfs.