INTERESTING FEATURES IN THE COMBINED GALEX AND SLOAN COLOR DIAGRAMS OF SOLAR-LIKE GALACTIC POPULATIONS

Our analysis depends on the calibration of SDSS and GALEX colors with T_eff, and our calibration is based on stars in the SDSS/GALEX sky. Their temperatures have rms errors of ±100–125 K and are on average −90 K below the Pinsonneault et al. (2012) recalibration and about 125 K higher than the original KIC calibration for cool (T_eff ⩽ 6.5 kK) stars. In their photometric analysis of cool stars, An et al. (2013) adopted a T_eff scale that is similarly 100 K higher than the SDSS pipeline scale. The Kepler Working Group on Stellar Properties (WGSP) has likewise recommended that a T_eff scale close to the Pinsonneault one be used for the interim (Huber et al. 2014).

Another parameter relevant to an understanding of anomalous color populations is the surface gravity. At best, we can hope for no more than a clean separation between "giants" (luminosity classes I–III) and dwarfs. As we will see, the separation of these classes from high-gravity objects (WDs, sdBs) can be confirmed by differences in red fluxes of the high-gravity stars in various color–color diagrams. Primarily, the dwarf/giant separation can be accomplished by: (1) evaluating the distributions of the two groups' apparent magnitudes (distances from Sun); (2) determining log g from photometry or spectrophotometry, e.g., by trusting values given in the KIC or (for non-FOV sky regions) the SDSS pipeline and rough determinations of log g; and (3) relying on photometric measurements of the size of the Balmer jump, at least for the hot end (AF types) of our sample. In our study we make use of all these diagnostics. Most F-K stars in the four associations in the FOV (NGC 6866, NGC 6811, NGC 6819, and NGC 6791) are dwarfs and in principle would be counted as such. Yet, the first three clusters were not included in the GALEX surveys, and only one GALEX tile even brushed the edge of the NGC 6791 field. Therefore, we could not make any luminosity class reassignments for these stars. This is unfortunate as it would be helpful to include clusters of stars of known ages.

Histograms of log g values from our separate KIC (FOV) and SDSS/GALEX populations exhibit similar bimodal distributions. A primary peak is centered at log g = 4.0, and a secondary one at 3.2, with an interpeak midway in between. Ciardi et al. (2011) classify as giants those F and earlier-type stars with log g ⩽ 3.5, G-type stars with log g < 3.7, and K-M-type stars with log g < 4.0. These criteria are consistent with the study of Galactic thick-disk (r < 4 kpc) stars using SDSS spectra (Carollo et al. 2010). For those KIC stars examined by the Kepler WGSP and brighter than K_p = 14, the distribution of log g values suggests that the percentage of giants and supergiants among AF stars is about 35% and includes most horizontal branch and RR Lyrae stars. The percentage of giants to dwarfs levels off at ≈40% for G stars (Batalha et al. 2010) and rises again to about 50% among K and early M stars when the red giant branch is included (e.g., Mann et al. 2012). The general conclusion is that the number of dwarfs exceeds that of giants but by less than a factor of two. Aside from our exclusion, otherwise important, of faint (K_p > 16.0) and thus most mid- to late M-type stars, we found no reason to believe that our sample is different from the full KIC population.

Our provisional strategy was to use the simple Kepler magnitude for the GALEX–SDSS star populations. We note here that the K_p and r_kis magnitudes are generally within ±0.15 mag of one another. We used the criterion described by Ciardi et al. (2011) as the demarcation between the space distribution of giants (K_p ⩽ 14.0) and dwarfs (K_p > 14.0). Of course, this rough criterion admits some spillover from one group to the other. Mann et al. (2013) found that ∼7 ± 4% of K_p < 14.0) dwarfs fall into the so-defined giant domain. A somewhat smaller percentage of apparently faint giants, perhaps 4 ± 1%, fall into the dwarf pool. Therefore, as a secondary criterion, we required that the published KIC log g must be less than 4.0–3.5 dex, according to the Ciardi et al. demarcations. In the occasional conflict between these two criteria or if the KIC listed no log g value, we classified the star as a dwarf. This agrees with the findings of the Huber et al. (2014) catalog, which used spectroscopy and asteroseismology to estimate log g values. Given their study, 23% of "unclassified stars" (those 7% of KIC stars with K_p ⩾ 14 and without listed log g values) are giants. In terms of "UV-excess stars" described below, 98% of this group that we classify as dwarf stars are dwarfs (log g ⩽ 4.0) in the Huber et al. catalog. Conversely, 96% of the UV-excess stars we call giant stars are giants in this catalog. Although the dwarf/giant dichotomy enters into our discussion below, our conclusions are not sensitive to the sizes of the two populations.

The study of stellar ages for solar-like stars in the thin Galactic disk has meanwhile proceeded apace. The derived ages support the general mix of giants and dwarfs in the KIC. Although nucleocosmochronological techniques applied to the oldest stars in the thin disk suggest that some of them formed 8 Gyr ago (del Peloso et al. 2005), recent studies of the various stellar populations of the Galaxy (e.g., Soderblom et al. 1991; Carollo et al. 2010) generally find a typical age of 3–4 Gyr for stars in the solar neighborhood. In terms of stellar subpopulations, this range includes F-K main-sequence stars, type BAF horizontal branch stars (including RR Lyrae and δ Sct variables), and GK giants. It is chiefly to these groups that we now confine our attention.

Bianchi et al. (2007, 2011) used the (g − r), (FUV − NUV) color diagram with model spectral energy distributions (SEDs) to differentiate stars from extragalactic objects, and to establish a stellar T_eff relation with (FUV − NUV). These authors pointed out that this color is nearly independent of reddening for a normal Galactic ISM color law (see Table 2 of Bianchi 2011). We plotted T_eff values determined from the SDSS spectroscopic pipeline for the stars that SDSS and GALEX observed spectroscopically. The first result of this exercise is a diagonal sequence in Figure 3 that reflects the relationship between SDSS T_eff and (FUV − NUV).

We identified a group of stars within ±250 K of a smoothed quadratic fit of the diagonal distribution (solid symbols). These were mapped to the (g − i), (FUV − NUV) plane, and a quadratic fit was then computed to define a calibration sequence for UV-normal stars. We next transformed this sequence by adding 0.47 mag to the (g − i)_kic values to obtain the equivalent in the KIS (Vega) system. Note here that many faint K and M stars with normal, weak UV fluxes are not captured in this sample.

Figure 4 exhibits these stars plotted in the (FUV − NUV) (g − i)_kis plane and the UV-normal sequence curve. Note that by definition our sample of stars has (FUV − NUV) colors and thus is magnitude limited. This means that some mid-K and nearly all M stars with red UV colors are excluded.

Zoom In Zoom Out Reset image size

Figures 3 and 4 exhibit a secondary scatter in their respective lower left regions, that is, points falling below the dot-dashed line. The shifted colors of this population are mainly due to a blueing of the (FUV − NUV) color of typically 3–4 mag and occasionally ≳5 mag and a much smaller amount of reddening in the color (g − i)_kis. The displacements from the primary sequence are less on average for the hotter stars and greatest for the cooler ones. We refer below to these objects as UV-excess ("UVe") stars. We also note that when plotted on the sky plane the UVe stars exhibit no tendency to cluster, e.g., from membership in associations.

All but two stars represented in the lower left region of Figure 3 have K_p > 14.0, and all but eight have log g_kic ⩾ 3.5. This suggests that the great majority of them are dwarfs. As for the stars of Figure 4 occupying the same region of the diagram, only about 15% (79/506) are giants, according to our brightness and KIC log g criteria. Also, one finds there that the ratio of UVe giants to dwarfs increases as one proceeds to the cooler K stars. In short, 22% ± 1% of stars represented in this sample fall in the UVe zone to the lower left. (The ±1% error is derived by comparing the statistics in two halves of the FOV covered by the two KIS surveys.) This fraction is similar to the 17% figure we found in Figure 3. Thus, we see that the statistics of the UVe stars are similar for populations observed using KIS photometry in the FOV and the high Galactic latitude portion of the sky covered by SDSS.

From the annotations in Figure 1 we can also see the effect of the differing degrees of scatter in the (FUV − NUV) color for stars in various T_eff bins. Figure 1 shows that the stars with the greatest UV blueing are the coolest ones. Also, the incidence of UVe is smallest among hot stars. Interestingly, when the giants are split out from the dwarfs, we see that the 5 kK dwarf group has a much bluer 〈FUV-NUV〉 than the 5 kK giants. To a smaller extent this is true for the 4 kK (early M-type) stars as well. This is another way of demonstrating that the late-G/early-K dwarfs are subject to greater UV excesses than the giants. When arriving at our few M stars, the (FUV − NUV) colors of UVe giants exhibit decreases by similar amounts as dwarfs.

Our sample of GALEX-observed stars in the FOV imposes two countervailing biases. The first bias depends on the ratio of sky areas observed in the NUV and FUV bands, and the second on the loss of detections of FUV-normal ("red") stars. The area ratio is 1.15 and is magnitude independent. The second effect increases the number of faint UVe stars relative to UV normal ones. At K_p = 14.0 we find that this bias in our reddest sample ((g − i)_kis ≲ 1.0) is a 15% effect. As one goes to K_p = 17.0, the bias increases to 40%. Even though our study limit was K_p = 16.0, we use the K_p = 17 limit figure. Then the ratio of these two values, 1.15/1.40 = 0.82, will be used as a rough estimate of the incompleteness of the (FUV − NUV) colors and the fraction of faint UV-normal stars that could be missed by the GALEX surveys. Thus, we expect that their UVe numbers are overrepresented and should be corrected by this factor.

Do the UVe stars stand out among known binaries? To pursue the possibility that the UVe stars are in binary systems, we consulted the Kepler Eclipsing Binary Catalog (EBC), version 3,⁷ (Matijevic et al. 2012) and asked whether the stars listed there and also observed by GALEX show similar UV excesses. We found 116 such stars. The KIC log g values for these stars range from 3.4 to 4.7. Even given the uncertainties in these photometrically derived values, few members of this sample are likely to have optical primary giants or supergiants, and probably none are WDs. Figure 5 depicts the relation between (FUV − NUV) and the KIC effective temperatures. One can see immediately that the distribution is much the same as in Figure 3. In particular, the number of UVe stars in the lower left of the figure is 20, corresponding to a fraction of 17% ± 4%, i.e., within the 17%–22% range found for the GALEX–SDSS and Kepler FOV samples. In addition, the hotter main-sequence stars are again relatively rare, and the (FUV − NUV) blueshifts are the largest for the coolest EBC primary stars. We also find that the distribution of orbital periods of the UVe stars is consistent with the UV-normal star population. For example, if we take those few stars with P_orb < (1/3) days, a value chosen to mitigate effects in synchronous or mass-transferring binary systems, we still find no real difference between the UVe and UV-normal subsamples.

Zoom In Zoom Out Reset image size

We have also examined 12 members of the Kepler Objects of Interest (KOIs), as listed (as of 2013 July) in the MAST archives, that have available (FUV − NUV) and (g − i)_kis colors and T_eff or log g values from the EBC. All 12 have F-G spectral types, and all but one are dwarfs. We find their distribution in the (FUV − NUV), T_eff diagram to be similar to those shown in the other figures. Only 2 of the 12 KOI members, K03868.01 and K01345.01, fall in the UVe region of this and the (FUV − NUV), (g − i)_kis diagrams. This is consistent with the ∼20% fractions found for our two larger populations.

We see from this study that the UVe population has a similar presence in EB systems and the general Galactic disk. This does not mean that binarity is a necessary condition for the UV excesses. In fact, as a counterexample to a binary scenario we can point out that one short-period Algol system in the Kepler FOV, WX Dra (KIC 10581918), fits the physical description of what a UVe system might look like. The KIC (photometric) T_eff is 7252 K for this system. Spectral types for the two components have been estimated as A8 and KO (Budding et al. 2004). However, the colors of this system fall on the normal side of the UV-normal/UVe demarcation in Figures 3 and 4. Clearly, binaries with cool and warm components are not necessarily UVe objects.

In one of the few papers devoted to the characteristics of GALEX spectra of normal stars, Bertone & Chavez (2011) have demonstrated the common-sense expectation that the flux gradients of spectra obtained with the NUV camera correlate well with spectral types, at least for Henry Draper stars in the range A0-K0. Surprisingly, no corresponding demonstration has been published to date for FUV spectra.

To rule out that the UVe stars' small and negative (FUV − NUV) colors can arise from noise sources in the FUV filter, and recalling that there is almost no overlap of objects observed in the SDSS grism program in the Kepler FOV, we searched through the entire SDSS spectroscopic catalog for objects observed in the common GALEX–SDSS sky. Examples of these matches are shown in Figure 6 and are ordered in the panels by increasing (FUV − NUV) from lower left to upper right. This figure also annotates the SDSS T_eff values and GALEX (FUV − NUV) colors. Also, following Bianchi (2011), we list computed GALEX colors that we computed by running spectral fluxes through GALEX filter transmission curves. These track both the catalog colors and the continua slopes.

Zoom In Zoom Out Reset image size

The solid line in Figure 6(a) depicts a GALEX spectrum of a G star with a modest positive slope increasing with wavelength. However, this UV continuum slope is inconsistent with the star having a T_eff = 5325 K, according to its SDSS optical spectrum. This example is tagged as the point marked with an arrow in Figure 3—it is a mild member of the UVe population. Indeed, the decrease in this star's flux from 2700 Å to 1900 Å is only a factor of two or so, whereas according to Bertone & Chavez the flux reduction across this range should be 10 times steeper for G stars of this effective temperature, 5325 K (see Figure 7).

Zoom In Zoom Out Reset image size

T_eff values of six F-G star examples in Figure 6 lie in the range 5230–7363 K, and their (FUV − NUV) catalog colors range from +4.59 to −0.30. Two of the three spectra represented in the left panel have T_eff values consistent with their being late G stars, from the SDSS pipeline, whereas two of the examples in the right panel, associated with negative (FUV − NUV) colors, have T_eff values corresponding to F types. This is consistent with the smaller blue displacements in UV color in Figure 3 for warmer members of the UVe population and suggests once again that UV excesses are smaller for warm stars. Note also that the spectra do not show even a hint of emission in the C iv or Mg ii h/k doublets.

Figure 7 assembles FUV/NUV-merged spectra for four HD stars with types A7-K0 represented in Bertone & Chavez (2011). Annotations show the GALEX catalog UV color. The montage also compares these spectra with a UVe spectrum (shown in bold) displayed also in Figure 6. The UVe star represented has an SDSS (optical) spectrum consistent with a mid-F star; the UV continuum slope is indicative of an A star.

In assembling UV colors of these standards, we note a curiosity that is confirmed in the catalog and simulated GALEX colors: the change in advancing color with spectral type ultimately decreases among the mid-G and K stars. In our G8 and K0 examples the UV color can overlap. The spectra show that this is because, although the FUV continuum decreases with late types, the strengthening of the NUV lines increases as well; the two effects nearly cancel. We speculate that this is because by ∼G5 the NUV lines are still saturating, whereas the lines in the FUV have already fully depressed the spectrum.

In any case, the key point from the spectrum figures is that since the continuum slopes track the (FUV − NUV) colors of these stars, there is no reason to doubt the GALEX colors. Instead, we must look to explanations involving stellar classes for the existence of UVe stars.

To complement the GALEX UV spectra, we checked the SDSS archives with the online Spectroscopic Query Form to examine the appearance of optical spectra. We have used this tool to compare a number of spectra on either side of the UVe/UV-normal demarcation (dot-dashed) line in Figure 3. For brevity we display in Figure 8 the first and second spectra in Figure 6, i.e., the near-UV normal spectrum of GLX J172312.5+593928, as well as examples of spectra of two UVe stars, GLX J122321.1+155205 and GLX J121309.5+504539. The SDSS F9 template spectrum is also shown for reference.⁸ These examples summarize most but not all of the differences we find in these objects. In the great majority of cases, and allowing for equal effective temperatures, we find that blue fluxes are greater in the UVe stars.

Zoom In Zoom Out Reset image size

Our SDSS spectra show similarities with those given by Yanny et al. (2009). In particular, their spectra of "F/G" and "G giant" stars (their Figure 9) are similar to our reference standard. However, our UVe star spectra exhibit somewhat a weakened Ca ii K and infrared triplet lines and G band with respect to the F9 template. According to Figure 8, the line weakening extends to the Ca ii triplet in the IR as well. This indicates that the line weakening is not necessarily entirely limited to short wavelengths. Indeed, we would expect that the cores of all these Ca ii lines would be sensitive to the raising of the atmospheric temperature minimum associated with a strong chromosphere. All told, there is good evidence for a mild flux enhancement in at least the blue region of these optical spectra, from either a secondary star or a strong chromosphere.

Zoom In Zoom Out Reset image size

After defining the loci of the main stellar populations in GALEX–SDSS color–color diagrams, Bianchi et al. (2007) showed that hot and warm (≳18 kK) WDs can be separated from other stellar populations according to their UV colors. One then asks, could WD single or binary systems be the cause of the UV excesses of the UVe stars? The predicted WD locus in their (g − i), (FUV − NUV) plot suggests that a simple extrapolation of the colors of the WD sequence might overlap the UVe class.

Yet, closer examination of extant WD star lists establishes that this explanation is not promising. An unpublished list by R. Ostensen (2013, private communication) of 24 warm to cool WDs classified from stellar spectra shows that the stars are too faint (K_p > 18) and/or fall in the wrong section of the (FUV − NUV), (g − i) diagram to be considered as UVe members. Only three of the Ostensen objects fall within the upper left edge of the observed distribution, and all of them are fainter than the K_p = 16 mag limit we considered for our investigations. Cooler WDs do not continue this trend because their red and near-IR colors do not continue to increase. In addition, we find that the computed WD sequences in the (g − r), (U − r) diagram follow a redder sequence in (g − r) than do the main-sequence and fainter stars (e.g., Verbeek et al. 2012b). A similar mismatch is depicted by the WD locus computed by Groot et al. (2009) in Figure 10 (dotted line). For cool WDs the computed locus lies well to the red of most of the observed colors of our sample.

The Girven et al. (2012a) catalog of single DA WDs verifies this conclusion with a much larger sample. The subset of this catalog population with GALEX and SDSS colors totals 12,149 stars. Only 0.18% of the members of this population fill the upper left edge of the UVe region in our (FUV − NUV), (g − i)_kis diagram ((g − i)_kis ⩽ 0.7). Nearly all DAs from Girven et al. fall in the upper left region of Figure 4, where the Bianchi et al. (2007, 2009) diagram predicts they should be. A handful of cooler stars (T_eff = 6.5–9 kK) fall to the upper left (defined again as (g − i)_kis ⩽ 0.7), but none of these spill into the UVe zone. In a similar (r − K), (NUV−r) diagram, Girven et al. show that the DA stars have (NUV−r) colors that are 1–5 mag bluer than all objects in our KIS sample, including our UVe population.

This discussion assumes that catalog objects are either single stars or binary systems in which the late-type secondary companions contribute substantially to the optical/near-IR colors. Indeed, the fact that we find that the DA stars are restricted to a blue region, (g − i)_kis ⩽ 0.7, in Figure 4 would be consistent only with secondaries having early K0 spectral types or earlier.

Other instructive resources are the Rebassa-Mansergas et al. (2010, 2012) catalogs of WDMS systems. These binaries consist of visible wavelength primaries and dM secondaries. These authors' (g − i), (FUV − NUV) figures of WDMS systems in the SDSS–GALEX sky show almost no overlap with our UVe zone. Rather, the UV excesses are significantly larger than our group, the only stellar class in our GALEX–SDSS survey for which this is true. Moreover, their WDMS systems have magnitudes of K_p = 19–20.

In addition, the space density of all WDs in the solar vicinity is estimated to be 3.2 × 10⁻³ M_☉ pc⁻³ (Holberg et al. 2008), or only about 10% of the local density of lower main-sequence stars (Gilmore & Zeilik 2000).

In sum, neither single WDs nor WDs in binaries with late-type secondaries are bright and numerous enough to contribute much to the UVe population.

Another interesting population to compare to our UVe population is the class of subdwarf B (sdB) stars. These core He-burning stars are found on the extreme blue end of the horizontal branch (eHB) and are thought to reside there for ∼160 Myr. Thus, they form a rarer, though more luminous, population than the hot DA or DB stars.

Evolutionary models suggest a few possible routes to the formation of sdB stars, usually in close binaries (e.g., Han et al. 2003). However, it is unclear from observations that the observed frequency (40%–70%) of short-period sdB binaries is as high as the models predict (Barlow et al. 2012). Some studies have reported that a substantial fraction of sdB binaries have F-K main-sequence secondaries. For example, decompositions of binary sdB spectra suggest typical crossovers for the fluxes of the two component stars in the blue–yellow wavelength range (Aznar Cuadrado & Jeffery 2001; Németh et al. 2012). Even though they emit primarily in the UV, the sdB components of such systems are so bright that usually they are the visible band primaries.

There are problems matching the detailed color anomalies of sdB binaries beyond those we have reported. The simulated sdB-dwarf binary zone in model binary SEDs by Girven et al. (2012b) is shown in our Figure 9. One can see here that the distribution of our UVe population stars falls to the lower right of where these models indicate they would be. One can imagine a better agreement if the secondaries of sdB systems were late-type giants because this would redden the colors, moving the model locus to the right in the figure. However, we have seen that the fraction of giants among UVe stars is at most 22%. From Girven et al.'s models best agreement with our colorimetric results is met when the UV excesses are smaller and hence the radii of the contaminating hot secondaries are smaller. According to their work, the best match in color–color diagrams for hot degenerate-main-sequence binaries occurs for small radii, corresponding to the requirement log g ≳ 7. But such high log g values obtain only for WDs, not sdBs, and we all but ruled these out because of their faintness and low space densities.

The space density of sdB objects is only ∼10⁻⁶ M_☉ pc⁻³ (Nelemans 2010). Then the sdB population fails by two orders of magnitude to explain the UVe stars.

Considering the presence of excess blue flux (Figure 8), our focus on the cause of the UV color excesses should be directed toward populations that are almost comparable to the full UV-normal population itself. We have mentioned two such explanations. The first is that the chromospheres are strong (e.g., stellar youth). The second is subgiant–main-sequence binaries with the components having only slightly unequal masses (e.g., blue stragglers). Such systems would have hot secondaries on the main sequence that dominate the UV and evolved primaries, possibly aged main-sequence stars, subgiants, or just evolved giants. The systems favor primaries being cool giants, for which temperature differences are greatest. However, the contribution from the hot dwarf secondaries would then be less because of their smaller radii. We consider here whether a viable parameter space exists for the nondegenerate binary scenario.

To address this question, we tested whether fluxes of less evolved, hot secondaries dominate the GALEX UV colors of binary systems. We did this by folding the GALEX and SDSS filter transmission curves with fluxes of each star, in the matter described by Bianchi (2009), and evaluating the summed fluxes in each filter. To carry out these tests, we took atmospheric flux models for standard main-sequence T_eff, log g, and radii from Astrophysical Quantities (Drilling & Landolt 2000). We repeated the exercise for various ranges of temperatures and secondary radii.

Our computed colors show that for late/early-type binary configurations, we could not explain the positions of the UVe stars in an (FUV − NUV), (g − i)_kis diagram. In Figure 4 we indicate the sequences for G0, F0, and A0 optical primaries by colored crosses. Our computations show that temperature differences between the component binary stars carry the (FUV − NUV) and (g − i)_kis colors along the main sequence for single stars—but this is not what is required. As one moves to models with B-type secondaries, the (FUV − NUV) color indeed becomes much bluer, but the effect on the (g − i) color is also to make it too blue for a given shift in (FUV − NUV). As a result, the vector extends approximately along the main-sequence locus for single stars. For no combination of star component temperatures do we find that the color vectors move to the lower left (or even horizontally) and into the UVe zone. Moreover, if the hot primary is a late-type giant instead of a main-sequence star, the shifts toward bluer colors quickly become small or insignificant. These and all other trials from our models demonstrated conclusively that the colors of binary stars are not moved to the UVe zone. Accordingly, we must reject a cool-primary, hot-primary binary scenario.

Stellar ages and activity considerations. In active G- and K-type stars the atmospheric temperature minimum occurs at large depths, causing higher temperatures to prevail above this point. If a chromospheric temperature rise is strong, it can influence the formation of strong UV/optical lines. The effects are greatest for the principal resonance lines such as Mg ii (h/k) and Ca ii (H/K), and therefore they are the first spectral features to be driven into emission. Also, enhanced emission of continuum flux first shows its presence in FUV spectra of young stars.

Several authors have found that the mean FUV emission decreases with age but levels off by about 1.5 Gyr (e.g., Pace & Pasquini 2004; Pace 2013). The mean NUV decay rate is less certain for older stars. Another consideration is that for a given age the enhanced flux from UV lines and continuum tends to be weaker as one proceeds along the main sequence to M stars (Guinan et al. 2009). Although the general dependences of these diagnostics on age have long been known broadly, recent work indicates that critical details of the age–activity relation are still not understood. Contrary to earlier discussions, it is no longer clear that magnetic activity, whether measured by optical or X-ray flares, or strong chromospheric emission in the UV, is necessarily a reliable indicator of age or vice versa (Soderblom 2010). Indeed, similar chromospheric strengths can be found in stars that are either very young or as old as the Hyades.

Despite these ambiguities, ages of stars in the KIC can be estimated from asteroseismology and from matching the colors and magnitudes to up-to-date stellar isochrones. Mathur et al. (2012) studied the pulsational mode structure of 22 bright solar-type stars using different asteroseismological tools and found a uniform distribution of ages in the range 3–11 Gyr. More comprehensively, preliminary results based on model fittings to isochrones computed from the Dartmouth Stellar Evolution Database (Dotter et al. 2008) have been constructed by the Kepler WGSP (Huber et al. 2014). This work finds a flat distribution out to 5 Gyr, as well as a secondary flat distribution of older stars out to 15 Gyr with an incidence of 40% as great as the incidence of the <∼5 Gyr stars. A caveat to this description is that below 0.5 Gyr there is a relative dearth, and then a significant increase, of stars with ages of 0.5–1 Gyr. This estimate suggests that the incidence of young (⩽0.5 Gyr) stars is 4%. This is about the same as the 3% fraction of a total of 700 solar-type stars that exhibit so-called very active levels of K line emission (Bastien et al. 2013; F. A. Bastien 2013, private communication). These estimates, albeit preliminary, suggest that the active chromospheres hypothesis cannot be dismissed.

Light curves and rotational periods. Another clue to a G/K star's age is its rotational period or, if no spot-induced modulation is observable, the presence of a "flat-lined" light curve. To investigate this property, we examined Kepler light curves of 55 "extreme UVe" stars for which (FUV − NUV) and (g − i)_kis colors are ⩽ −2.9 and ⩾0.4 mag, respectively, from those indicated by the dot-dashed demarcation line in Figure 4 and also have Kepler light curves in the MAST archives. Twenty-nine dwarfs satisfied this criterion. Typical parameters for these are T_eff ≈ 5000 K and log g ≈ 4.4. Contrary to the young active star hypothesis, a substantial fraction of these stars exhibit intermediate to long (7–23 day) rotational periods. Seven have light curves that can be described as "flat" or imperceptibly weak rotational signals. These are arguably old stars still on the main sequence. Light curves of the remaining extreme UVe stars are chaotic, possibly late-type γ Dor variables or eclipsing binaries. About half of these have been studied in detail (Basri et al. 2010; Walkowicz et al. 2011; Howard et al. 2012), but none have been called out as especially young stars. According to our search, most of the UVe stars are not very young.

Any results to be drawn from the statistics of binary and chromospherically active stars are far from final. Indeed, if we take a control sample of UV-normal Kepler-observed dwarfs, we find that their light curves are not all flat or dominated by long rotational periods; many of these stars are pulsators or eclipsing binaries. UV-normal G stars with flat curves also exist (e.g., KIC 11606351), but so do stars with short rotational periods (e.g., KIC 11658452; P_rot ≈ 6 days). These are counterexamples to the proposition that moderately rotating G stars must show UV excesses. In all, the light curves provide neither refutation nor support for the idea that a young population with active chromospheres is responsible for the UVe class.

Enhanced UV flux and X-ray activity. Examples of UV color blueing of spectra of young solar-type stars have been documented (Ribas et al. 2005; Guinan & Engle 2009; Linsky et al. 2012). These examples show that the FUV continua of young G-M dwarfs can be over 3 mag brighter relative to the continua of their oldest stars. This is in agreement with the photometric results of Findeisen et al. (2011). In addition, in Figure 12 we exhibit four merged IUE spectra for fluxes for four solar-type standards (all near G1 V) and for which ages have been estimated by Ribas et al. Here have we scaled the spectra to fluxes of unity at 3000 Å. These spectra clearly show a spread of fluxes below ∼2200 Å such that the younger stars have the greatest FUV fluxes. Differences can be discerned even between the youngest two stars, EK Dra (0.1 Gyr) and π¹ UMa (0.3 Gyr). Our computed (FUV − NUV) colors from their spectra are 4.93, 4.70, 6.44, and 6.19. The color span is only about 1.5 mag. This is less than the ⩾2 mag range in the FUV region alone. Inspection of the spectra suggests that this difference is due to a confluence of Fe emission lines at 2000–2100 Å and is stronger, e.g., for π¹ UMa than for the very youngest star, EK Dra. Similarly, enhanced Fe lines are responsible for an (FUV − NUV) color inversion of the two older stars, although both FUV and NUV continuum levels maintain a monotonic sequence with age.

Zoom In Zoom Out Reset image size

To examine the rotational/UV activity arguments further, we have cross-correlated the positions of the UVe stars in the Kepler field with HEASARC's bright and faint ROSAT All Sky Survey catalogs. Young stars with active chromospheres can be expected to exhibit strong soft X-ray flux. However, among our UVe sample we find only one solar-type star, KIC 10730406, that has even barely significant (>3σ) X-ray fluxes detected by the ROSAT surveys. (None of our stars were detected in the Chandra or RXTE imaging catalogs either, but their coverages of the Kepler fields are very small.) For a reddening-corrected distance of 700 pc for KIC 10730406, the implied L_x in the band 0.5–2 keV is ∼3 × 10³⁰ erg s⁻¹. This is consistent with a very young (∼30 Myr) star with a strong corona, but not with an older star. Yet many of our stars are more distant than this one, so it is possible that we might miss several X-ray active stars.

It may be a problem to suppose that young stars (e.g., <500–600 Gyr old) are even numerous enough to explain the observed population of UVe stars. The mean age of 3–4 Gyr quoted earlier for solar-type stars implies a more or less uniform distribution of ages. This argument carries even more weight for the UVe stars in our high-latitude GALEX–SDSS sample. Similarly, the EBC suffers no known bias toward young stars (A. Prsa 2013, private communication). To the contrary, any biases in this catalog should be toward underrepresentation of large (evolved) stars in close binaries, not small ones on the zero-age main sequence. Finally, those UV excesses that are observed in GK giants cannot generally be expected to arise from strong chromospheres. All this said, we would not be surprised if strong chromospheres of some late-type dwarfs, whether strong from their youth or association in close binaries, are the cause behind many or most of the UVe stars.