The UV Emission of Stars in the LAMOST Survey. I. Catalogs

The design of LAMOST enables it to take 4000 spectra in a single exposure to a limiting magnitude as faint as r = 19 at resolution R = 1800. In 2015 May 30, LAMOST finished its third-year survey (the third data release; DR3) and the all-sky coverage is ∼35%. DR3 of the LAMOST general catalog contains objects from the LAMOST pilot survey and the three-year regular survey, totaling 5,755,216 objects that were observed multiple times. Objects with a unique designation in the catalog are selected as unique objects. The stars of our sample are extracted from the catalog with the following criteria: class = STAR and subclass = from O to M (Luo et al. 2015); this yields 4,010,635 stars.

The stellar parameters of T_eff, log g, and [Fe/H] are extracted from the A, F, G, and K type star catalog, which was produced by the LAMOST stellar parameter pipeline (LASP, Wu et al. 2014). The molecular indices are selected from the M star catalog.

We cross-match the stars with the ALLWISE catalog (Cutri et al. 2013) in order to estimate the extinction with the RJCE method. We apply the following criteria to retrieve photometry in the bands of W2 and H: the match radius is set to 5''; the extended source flat (ext_flg) is set to 0; the contamination and confusion flags (cc_flags) are set to 0; and the photometric quality flag (ph_qual) is set to A (Wang et al. 2016b). Every star in our sample has an infrared counterpart in the ALLWISE catalog, but 23,388 stars do not have magnitudes in the H-band. We reject these stars, and there are 3,987,247 stars left.

We cross-match the stars to GALEX Releases 6 and 7 (GR6/GR7) in order to obtain their photometry in the FUV and NUV. With the help of the Catalog Archive Server Jobs (CasJobs),⁷ nearby matching is made to the table of PhotoObjAll using the following criteria: the match radius ≤5'' (Gezari et al. 2013); nuv_artifact and fuv_artifact ≤1; the distance from the center of view ≤055 (Jones & West 2016); and signal-to-noise ratio (S/N) of the magnitude ≥2, which yields 1,805,254 stars detected in the co-added exposures.

In order to obtain magnitudes from the visit exposures, the nearby matching is made to the table of VisitPhotoObjAll with the match radius ≤5'' and the distance from the center of view ≤055. The criterion of uv_artifact is not used here, since we want to select as many time-domain observations as possible. We flag the detections with uv_artifact >1 in our catalog. The result includes 2,202,116 stars detected in the co-added and/or the visit exposures. The nearest counterpart is selected for the stars with more than one counterpart within 5'' in the same exposure, and they are marked in the catalog. There are 87,178 and 1,498,103 stars detected more than once in the visit exposures in the FUV and NUV, respectively.

The observed but undetected stars are extracted from the tables of PhotoExtract and VisitPhotoExtract, with the match radius ≤5'' and the distance from the center of view ≤055. This results in an additional 889,235 stars. The density map of all 3,091,351 stars is shown in Figure 2.

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Gezari et al. (2013) defined the upper limit magnitude determined as a function of exposure times, and the brightness of the sky background. In their calculation, the background is a constant. However, the UV background emission, which is dominated by zodiacal light and diffuse galactic light, significantly depends on Galactic position (Murthy 2014).

In order to calculate the position and exposure-time-dependent background, we extract sources from the table of VisitPhotoObjAll with the following criteria: distance from the center of view ≤055; S/N ≲ 1.8 and ≲1.2 in the FUV and NUV. This method is similar to that used in Ansdell et al. (2015).

We average the magnitudes of these sources in the three-dimensional bins: the Galactic coordinates l, b and the exposure times. The step size of each bin is 2° and 1° for l and b, respectively, and 10 s for exposure times. The magnitudes in each bin of the Galactic coordinate are then fitted with a function similar to that in Gezari et al. (2013):

$$\begin{eqnarray}&&{m}_{\mathrm{lim}}=-2.5\,\mathrm{log}(5\sqrt{\mathrm{Sky}/{T}_{\exp }})+{zp},\end{eqnarray} \tag{ 1 }$$

where Sky is the fitted background in counts s⁻¹ and zp values are 18.08 and 20.08 in the FUV and NUV, respectively (Morrissey et al. 2007). Nearest-neighbor interpolation is used to estimate the magnitudes that are not valid in some bins of the Galactic coordinates. We present the distributions of the upper limit magnitudes on the Galactic coordinate in Figure 3. We plot the magnitudes with exposure times from 100 to 120 s in the map of the detector coordinate in Figure 4, and there is no obvious correlation between the upper limit magnitudes and the distances to the detector center.

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The stars with low S/Ns are near the detection limit of GALEX, and they have been used as proxies for the upper limit magnitudes. Ansdell et al. (2015) adopted an S/N of 2. We extend the S/Ns to lower values in order to come closer to the detection limit of GALEX, and use these stars to trace the upper limit magnitudes rather than fitting the dim bound of the UV magnitudes. We visually compare the count rate of some randomly selected sources to that of their background, and find that they are similar. The magnitudes fitted from Equation (1) are adopted as the upper limit magnitudes for stars in the visit and the co-added exposures.

A novel Bayesian method developed by Burnett & Binney (2010) and Binney et al. (2014) has been used for stars in the RAVE survey, which has demonstrated the ability to obtain accurate distance and extinction. Wang et al. (2016b) measured extinction and distances using this for stars with valid stellar parameters in the first data release of RAVE, and in the second data release of the LAMOST survey (J. L. Wang 2018, private communication). They used the spectroscopic parameters T_eff, [Fe/H] and log g, and 2MASS photometry to compute the posterior probability with the Bayesian method. They adopted a three-component prior model of the Galaxy for the distribution functions of metallicity, density, and age, in order to construct the prior probability. They then derived the probability distribution functions of parallaxes and extinctions. An introduction to this technique is given in the appendixes of Wang et al. (2016a, 2016b).

For stars without valid extinction measured with the Bayesian method, we use the RJCE method to estimate their extinction. This method has shown that the extinctions are reliable for most stars. The RJCE method derives the extinction by combining both the near and mid infrared. We calculate ${A}_{{K}_{s}}$ from the equation:

$$\begin{eqnarray}&&{A}_{{K}_{s}}=0.918(H-[4.5\,\mu {\rm{m}}]-{(H-[4.5\mu {\rm{m}}])}_{0}),\end{eqnarray} \tag{ 2 }$$

where the [4.5 μm] data are the photometry of W2 from the ALLWISE catalog (Majewski et al. 2011; Cutri et al. 2013).

Here, (H − [4.5 μm])₀ is the zero-point that depends on spectral types (Majewski et al. 2011). We use the BT-Cond grid (Baraffe et al. 2003; Barber et al. 2006; Allard & Freytag 2010)⁸ of the PHOENIX photospheric model (Hauschildt et al. 1999) in Theoretical Model Services (TMS)⁹ to calculate the the effective-temperature-dependent zero-points. Based on the calibration provided by Gray & Corbally (2009), the subclass in the LAMOST catalog is used to estimate their effective temperature for stars without valid effective temperatures. The extinction provided by Schlegel et al. (1998) is adopted, if the extinction estimated from the RJCE is larger than that of the Milky Way.

Figure 5 shows the comparison between the extinction derived from the Bayesian and RJCE methods. There is no systematic deviation between the two methods statistically, but about five percent of the stars have A_V differences larger than one. For A and K stars, extinction from the Bayesian method is higher than that from the RJCE within a discrepancy of ΔA_V ≲ 0.7 mag, which is consistent with the result of Wang et al. (2016b). Extinction values from the Bayesian method suffer uncertainty in the stellar parameters, if they are not well constrained in the LAMOST pipeline (Wu et al. 2011, Section 4.4 of Luo et al. 2015). However, the Bayesian methodology offers several advantages compared to RJCE, as discussed in Sale (2012). The RJCE could overestimate the extinction for stars with small A_V (Rodrigues et al. 2014), which can be seen in the upper panel of Figure 5.

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We present the FUV and NUV counterparts from both the co-added and the visit exposures in Table 1. For stars observed but undetected by GALEX, we give their upper limits in the FUV and NUV. Since the co-added exposures are combined from some but not all the visit exposures, we flag the visit exposures that are combined to the listed co-added exposures.

All the magnitudes in Table 1 do not reach the limits of saturation¹⁰ before the extinction correction. The saturation effect is insignificant in our sample, since about 0.3% and 0.1% of the stars in the FUV and NUV reach the more conservative limits of m_FUV < 12.6 and m_NUV < 13.9 (Morrissey et al. 2007; Findeisen et al. 2011).

We check the distributions of exposure time in our sample. The bimodal distributions are dominated by images from the all-sky imaging survey and the medium imaging survey.

We calculate the mean magnitudes from the average fluxes of the visit exposures, and present the colors' distributions in Figure 6. The (FUV − NUV) is not only very sensitive to the young massive stars (Kang et al. 2009), but also a useful indicator of stellar activities for low-mass stars (Welsh et al. 2006; France et al. 2016). Both K giants and dwarfs have blue (FUV − NUV), probably due to the strong FUV line emission from upper atmosphere layers primarily in emission lines of C ii, Si iv, and C iv (Jones & West 2016). The stars of T_eff ∼ 6000 K are redder than others, forming a red valley in the HR-like diagram. On one hand, their colors are redder than earlier-type stars due to the lower effective temperatures. On the other hand, their FUV emission from upper regions of their atmosphere is weaker than that of later-type stars, probably due to their weaker upper atmosphere emission.

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The infrared bands, which are dominated by flux from the photosphere, are insensitive to upper atmosphere emission. The very blue (FUV − J) colors for K dwarfs are due to emission from upper atmosphere layers. The (NUV − J) colors for the K dwarfs are not very blue because the NUV emission is mostly photospheric. The colors of (FUV − J) and (NUV − J) decline with increasing T_eff, and dwarfs are bluer than giants. We find that the K stars with T_eff ∼ 4500 K, log g ∼ 4 (the gray circles in Figure 6), are bluer than other K stars. The bluer (UV − IR) colors and smaller gravities might be due to their rapid rotations (Stelzer et al. 2013) or the interactions with spectrally unresolved companions (Ansdell et al. 2015).

The UV excess (Equation (3)) and the normalized UV excess (Equation (4)) describe the distributions of UV flux with respect to a basal value:

$$\begin{eqnarray}&&{E}_{\mathrm{UV}}={m}_{\mathrm{UV},\mathrm{obs}}-{m}_{\mathrm{UV},\mathrm{ph}},\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{R}_{\mathrm{UV}}^{{\prime} }=\displaystyle \frac{{f}_{\mathrm{UV},\mathrm{obs}}-{f}_{\mathrm{UV},\mathrm{ph}}}{{f}_{\mathrm{bol}}},\end{eqnarray} \tag{ 4 }$$

where f_UV,obs (m_UV,obs) and f_UV,ph (m_UV,ph) are the observed UV flux (magnitude) and the photospheric flux (magnitude) in the same UV band. The f_bol is the bolometric flux calculated from the effective temperature (Findeisen et al. 2011; Stelzer et al. 2013).

We estimate the photospheric flux in the FUV and NUV with the BT-Cond grid. All synthetic magnitudes in the FUV, NUV, and J bands are extracted with the help of TMS. We construct a theoretical grid for interpolation, and the dimensions are effective temperatures, surface gravities, and metallicities. The scaling factor ${\left(\tfrac{{R}_{* }}{d}\right)}^{2}$, the squared ratio between the stellar radius and the distance, is calculated from the (UV − J) color predicted from the synthetic model. The scaling factor is used to convert the observed UV flux to that from the stellar surface (Stelzer et al. 2013). We only compute the E_UV and ${R}_{\mathrm{UV}}^{{\prime} }$ for stars with valid stellar parameters, and estimate their corresponding uncertainties from the errors in magnitudes, T_eff, log g, and [Fe/H].

About 11% and 22% of the ${R}_{\mathrm{UV}}^{{\prime} }$ are below zero in the FUV and NUV, respectively. In these cases, the normalized UV excesses are insignificant and probably dominated by uncertainties in the extinction and the model interpolation. The uncertainties of the extinction are from the errors in the stellar parameters, when the extinction is given with the Bayesian method. We present stars with ${R}_{\mathrm{UV}}^{{\prime} }\gt 0$ in Table 2.

Table 2.  UV Parameters in Our Catalog

LID	EFUV	eEFUV	ENUV	eENUV	log ${R}_{\mathrm{FUV}}^{{\prime} }$	$\mathrm{log}\,{{eR}}_{\mathrm{FUV}}^{{\prime} }$	log ${R}_{\mathrm{NUV}}^{{\prime} }$	$\mathrm{log}\,{{eR}}_{\mathrm{NUV}}^{{\prime} }$	σint,FUV	σint,NUV	Sd,FUV	Sd,NUV
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
101077	−2.65	1.51	1.25	0.61	−5.37	−5.72	⋯	⋯	⋯	⋯	⋯	0.34
101150	−8.80	0.91	−0.54	0.49	−5.08	−5.46	−5.74	−5.86	⋯	0.52		1.54
103032	−0.29	0.76	−0.44	0.23	−8.07	−7.89	−5.51	−5.86	0.41	0.03	⋯	⋯
104056	−0.47	0.35	−0.35	0.16	−7.19	−7.39	−5.20	−5.60	0.69	0.02	0.11	0.01
106049	−5.74	1.16	−0.11	0.29	−5.49	−6.37	−6.11	−5.47	0.33	0.04	0.93	0.12

Note. Column (1): Object IDs in the LAMOST catalog. Column (2): excesses in the FUV. Column (3): errors of E_FUV. Column (4): excesses in the NUV. Column (5): errors of E_NUV. Column (6): normalized FUV excesses. Column (7): errors of ${R}_{\mathrm{FUV}}^{{\prime} }$. Column (8): normalized NUV excesses. Column (9): errors of ${R}_{\mathrm{NUV}}^{{\prime} }$. Column (10): intrinsic variabilities in the FUV. Column (11): intrinsic variabilities in the NUV. Column (12): structure functions on timescales of days in the FUV. Column (13): structure functions on timescales of days in the NUV.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

The color excess (FUV − NUV) suffers from less uncertainties than the UV excesses, and could shed light on the stellar activity (Shkolnik 2013; Smith et al. 2014). The normalized FUV excess as a function of (FUV − NUV) is shown in Figure 7, in which the anti-correlation can be fitted with a linear relation,

$$\begin{eqnarray}\mathrm{Log}({R}_{\mathrm{FUV}}^{{\prime} }) & = & (-0.380\pm 0.001)\times (\mathrm{FUV}-\mathrm{NUV})\\ & & -(4.85\pm 0.01).\end{eqnarray} \tag{ 5 }$$

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It is suggested that the (FUV − NUV) could trace the ${R}_{\mathrm{FUV}}^{{\prime} }$. The stars with stronger upper atmosphere emission have larger ${R}_{\mathrm{FUV}}^{{\prime} }$. These stars are mostly K stars with (FUV − NUV) near zero. The correlation implies that such emission is more obvious in the FUV than in the NUV. Therefore, the ${R}_{\mathrm{NUV}}^{{\prime} }$ shows no obvious correlation with the (FUV − NUV) in Figure 7. There is an effective temperature dependence in the ${R}_{\mathrm{FUV}}^{{\prime} }$ plot. The dependence may be due to the different FUV origination. The FUV of the early-type stars is mainly from the photospheres, while that of the late-type stars is mainly from the upper atmospheres.

We present the color-coded distributions of the UV and the normalized UV excesses in Figure 8, in which the excesses depend on T_eff and log g. The E_FUV increases with increasing T_eff. The E_NUV has a similar distribution but with a smaller increasing level. This indicates that low-mass stars have strong UV excesses, especially in the FUV.

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The ${R}_{\mathrm{FUV}}^{{\prime} }$ is higher than the ${R}_{\mathrm{NUV}}^{{\prime} }$ for stars with T_eff ≲ 6000 K, since their stellar activities might be more efficient at powering the line emission in the FUV than the continuum in the NUV (Jones & West 2016). The ${R}_{\mathrm{UV}}^{{\prime} }$ of giants is lower than those of dwarfs, because the upper atmosphere emission of giants is buried beneath their atmospheres (Holzwarth & Schüssler 2001; Nucci & Busso 2014). There are some bins with average ${R}_{\mathrm{UV}}^{{\prime} }$ below zero in Figure 8, which results in the empty areas of early-type stars.

The rms scatter has been used to describe the intrinsic variability in optical and UV bands (Sesar et al. 2007; Gezari et al. 2013),

$$\begin{eqnarray}&&{\sigma }_{\mathrm{int}}=\sqrt{{{\rm{\Sigma }}}^{2}-\langle \xi {\rangle }^{2}},\,\mathrm{where}\,{\rm{\Sigma }}=\sqrt{\displaystyle \frac{1}{n-1}\displaystyle \sum _{i=1}^{n}{({m}_{i}-\langle m\rangle )}^{2}}.\end{eqnarray} \tag{ 6 }$$

In order to estimate the mean photometric error $\langle \xi \rangle$, we extract over six million objects in the FUV and NUV bands. The mean photometric error depends on both the magnitude and the exposure time in Figure 9. We construct a two-dimensional grid with a bin size of Δm = 0.5 mag and Δlog(ExpT) = 0.1 s.

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We then obtain mean photometric error with the interpolation, and calculate the rms scatter σ_int of the stars detected in at least two visit exposures. This yields 46,022 and 700,039 stars with available σ_int in the FUV and NUV, respectively. The distributions of σ_int are presented in the left panels of Figure 10. The intrinsic variability declines with the increase of T_eff, implying that late-type stars tend to have strong variabilities. The σ_int values in the FUV are generally larger than those in the NUV, probably due to the higher amplitudes of light curves at shorter wavelengths (Wheatley et al. 2012).

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Another parameter to characterize the variability is the structure function (see di Clemente et al. 1996 for details)

$$\begin{eqnarray}&&V({\rm{\Delta }}t)=\sqrt{\displaystyle \frac{\pi }{2}\langle | {\rm{\Delta }}{m}_{{ij}}| {\rangle }_{{\rm{\Delta }}t}^{2}-\langle {\sigma }_{i}^{2}+{\sigma }_{j}^{2}\rangle },\end{eqnarray} \tag{ 7 }$$

where brackets stand for averages for all pairs of points on the light curve of an individual source with i < j, Δm_ij = m(t + Δt) − m(t) and t_j − t_i = Δt. We calculate the structure functions on the timescale of days, S_d, from the characteristic time bins of V(Δt). The S_d is defined as the maximum value of the structure function evaluated for Δt_2d = 2 ± 0.5 day, Δt_4d = 4 ± 0.5 day, Δt_6d = 6 ± 0.5 day, and Δt_8d = 8 ± 0.5 day (Gezari et al. 2013). This value is also presented in Table 2. The distributions of S_d are shown in the right panels of Figure 10. The distributions of σ_int and S_d are similar. The stars with lower T_eff have higher variabilities, which might be naturally explained by the strong upper atmosphere emission of late-type stars.

The stars can appear UV-luminous for reasons unrelated to their upper atmosphere emission or photospheric radiation. These cases are so-called false positives, which are falsely matched background active galactic nuclei (AGNs) within ∼5''. Another kind of possible false positive is binaries composed of non-degenerate stars and white dwarfs. These binaries are unresolved by spectra from the LAMOST facility. The wrongly selected UV counterpart should also be considered a false positive, when there is more than one counterpart within 5'' in the same exposure.

We estimate the probability of false positives from background AGNs by matching false-star positions within a random arcminute of their true positions with the GALEX archive data (Jones & West 2016). This yields about a 0.14% chance of matching for given a random position, and about 0.25% for our sample, given that over 55% of the LAMOST stars are detected in GALEX.

The catalog of Rebassa-Mansergas et al. (2013) is used to select the potential white dwarf main-sequence (WDMS) binaries in our sample. We follow the same procedure described in Section 2 to find the UV counterparts of these WDMS binaries. We find that the combination of UV and IR could separate WDMS binaries, since they cluster at FUV − NUV ∼ 0 and W1 − W2 ∼ 0.14, as seen in Figure 11. There are 17,428 stars in our sample, ∼0.56% of the sample overall, located inside the density contour of two per bin, which are potential WDMS-binary candidates unresolved by LAMOST (Table 3).

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There are 13,845 stars with more than one counterpart within 5'' in the same co-added or visit exposures. If they are all wrongly selected as UV counterparts, the occurrence of false positives is 0.45%. The overall occurrence of these false positives is below 1.3% in our sample.

We present color distributions in Figure 12. The (FUV − NUV) declines with increasing effective temperature for stars with T_eff > 7000 K, because their UV fluxes are dominated by radiation from stellar photospheres. This trend disappears and the UV color distribution becomes dispersive for stars with T_eff ∼ 6000 K, since their UV colors from upper atmosphere emission probably became comparable to photospheric UV colors. Some inactive G stars follow the colors predicted by the model, while other active stars have blue excesses. These active G stars might either be in active close binaries or young single stars (Smith et al. 2014).

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For stars later than G, the color distributions exhibit remarkably blue excesses because of the additional bluer UV emission from the upper regions of atmosphere. The UV colors of these stars are (FUV − NUV) ∼ 1, similar to the blue peak in Smith et al. (2014), which might indicate the general colors of the stellar active regions.

When integrating the distributions of all stars with different types, we also detect the bimodal distribution of (FUV − NUV) in our sample, similar to Smith & Shiao (2011). The bimodal distribution is perhaps due to the two sub-populations, the UV red stars having weak activities and mid effective temperatures, and the UV blue stars having strong activities or high effective temperatures (Smith et al. 2014).

The peaks of the distributions are anti-correlated with effective temperatures in the figures of (FUV − J) and (NUV − J), but we can see obvious blue excesses for the stars with T_eff ≲ 6000 K and T_eff ≲ 5500 K in the two figures, respectively. This implies when the radiation from upper regions of the atmosphere begins to dominate the UV flux. For stars with higher effective temperatures, the UV fluxes are mainly from stellar photospheres, where the UV-IR colors depend on the effective temperatures rather than the upper atmosphere emission.

There are some late A stars redder than the colors predicted by theoretical models in the distribution of (NUV − J). The nature of the bias is still unclear, which might indicate some deviation between observation and theoretical templates for the radiation from stellar photospheres, or amount to potential spectrally unresolved companion stars with slightly lower effective temperature than primary stars.

We cross-match the stars with valid stellar parameters in our catalog with the SDSS stars processed through the SEGUE Stellar Parameter Pipeline (SSPP, Lee et al. 2008a, 2008b), in order to check the difference in the effective temperatures derived from two independent pipelines. In Figure 12, there is no obvious systematical deviation in the color distributions. We can conclude that the distributions of the colors associated with UV are independent in the stellar parameter pipelines, and indicate the intrinsic properties of our sample. Here, we do not cross-identify with APOGEE stars, since they are mainly giants with effective temperatures in the range from 4000 to 5500 K.¹¹

Because of its large size and homogeneous nature, this catalog not only provides a wealth of information for the study of upper atmosphere emission, but also enables a time-domain exploration in the UV. In this section, we would like to discuss some scientific applications of the catalog.

4.2.1. A Possible UV Reference Frame

The MK spectral classification sets the general reference frame for stars on physical parameters, and further plays a critical role in identifying the truly peculiar stars that do not fit comfortably into the frame (Gray & Corbally 2009, 2014). However, the reference frame is poorly constrained in the UV band due to small samples of stellar emission from upper regions of atmospheres. Using this large catalog, we could present a possible UV reference frame based on radiation from all regions of stellar photospheres.

We calculate the absolute magnitudes for stars with valid parallaxes (Wang et al. 2016b), and average the fluxes in each bin of T_eff and log g (left panels of Figure 13). The UV absolute magnitude declines with the increase of the effective temperature, which is similar to the results of Shkolnik (2013), while the standard deviation is larger in the FUV than in the NUV for stars with T_eff ≲ 6000 K. Such standard deviation is probably due to their strong intrinsic variability, as shown in the upper two panels in Figure 10. Because of the small standard deviation and homogeneity in the stellar parameters, the NUV absolute magnitudes could be used as a possible reference frame to calibrate the stellar NUV emission. Such NUV emission includes the stellar radiation not only from the photosphere but also the upper regions of the atmosphere.

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4.2.2. Colors of Giant and Dwarf Stars

Giant stars, owing to their high luminosities, are popular tracers of substructures in the Milky Way, and help us address important questions such as the size of our Galaxy (Bochanski et al. 2014), the shape of the dark matter halo (Piffl et al. 2014), substructures in the outer Galactic halo (Sheffield et al. 2014), the metallicity distribution (Hayden et al. 2015), etc.

We use the criterion provided by Ciardi et al. (2011) to separate giants from dwarfs. Neither the UV-involved colors (Figure 14) nor the UV excesses can provide a good separation between giants and dwarfs in our sample. The distribution of dwarfs exhibits a clear "Λ" shape. The stars in the right branch are mainly K dwarfs, which overlap with the giants. The UV-involved colors could separate the stars with T_eff ∼ 6000 K, located in the red valley in Figure 6, from other stars with higher temperatures or stronger upper atmosphere emission. UV and IR photometry-based methods cannot provide a good separation, but some spectra-related methods could distinguish giants, such as spectral line features (Liu et al. 2014).

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However, the color of (NUV − J) can separate M giants from M dwarfs in Figure 15. Here, we use a robust linear separation, the lowest density of the stars in the diagram of molecular-band indices in Figure 16 (Zhong et al. 2015). The upper atmosphere emissions of giant star are weaker than those of dwarfs, and the colors constructed by both UV and IR bands could provide a good statistical separation.

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4.2.3. RR Lyrae Stars

RR Lyrae (RR Lyr) stars are pulsating periodic horizontal-branch variables with great variation in the UV in the range of 2–5 mag (Wheatley et al. 2012), making them more likely to be detected in the UV. They are thus popular tracers of Galactic structures, the halo (Sesar et al. 2010b), and streams (Drake et al. 2013).

We cross-match the RR Lyr stars in Drake et al. (2013) and Abbas et al. (2014) with our sample, and plot them over the A and F stars in Figure 17. The UV counterparts of RR Lyr stars are concentrated in the region of high S_d and σ_int,NUV, and have a bluer color of (FUV − J) than other A and F stars. In Figure 18, we plot the light curve of an RR Lyr star with LID = 254809148 as an example. The amplitude of the UV light curve is higher than that in the optical band by a factor of 2 (Sesar et al. 2010a).

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