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A&A
Volume 694, February 2025
Article Number A131
Number of page(s) 9
Section Stellar atmospheres
DOI https://doi.org/10.1051/0004-6361/202452792
Published online 06 February 2025

© The Authors 2025

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1 Introduction

The line emission, which is the primary defining characteristic of classical Be stars, can be intermittent and arises from variable amounts of circumstellar gas configured in an equatorial Keplerian disk (Collins 1987; Rivinius et al. 2013). The currently favored physical concept for the formation of Be-star disks has been worked out as the viscous decretion disk (VDD) model (Lee et al. 1991; Rivinius et al. 2013). However, the key driving mechanism for intermittent outflow events (outbursts) probably feeding the disk remains unclear. Several possible scenarios have been proposed to explain the frequently observed optical brightenings and enhancements of Balmer emission lines. These are (1) rapid rotation plays a role in feeding disks (e.g. Cranmer 2005; Delaa et al. 2011; Meilland et al. 2012; de Almeida et al. 2020), but rotation alone is insufficient to cause mass transfer to the disk as the rotation rates are significantly subcritical (Collins 1987; Rivinius et al. 2013); (2) multi-mode non-radial pulsation could trigger the mass ejection (e.g. Baade et al. 2016, 2018a,b; Baade & Rivinius 2020); (3) stellar activity coupled with rapid rotation may induce mass loss (Wright et al. 2011; Smith & Bohlender 2007). Up to now, none of these concepts, in their most basic form, appears to provide sufficient energy and/or angular momentum for the star-to-disk mass transfer.

A recent systematic color-absolute magnitude study of variable stars by the Gaia Collaboration (2019) based on the Gaia time-domain photometric survey (Gaia Collaboration 2016) revealed that most Be stars turn redder when they brighten, in contrast to virtually all other intrinsically variable stars. This is qualitatively explained by the circumstellar disk adding a pseudophotosphere (Vieira et al. 2015) and quantitatively described by the VDD model (Lee et al. 1991; Carciofi & Bjorkman 2006, 2008). The variations are due to variable amounts of circumstellar matter. The larger the star+disk system is, the brighter and redder it appears. The variability is drastically different if the line of sight toward the central star passes through the circumstellar disk. The ability of the VVD model to reproduce this elementary dichotomy (Haubois et al. 2012) demonstrates the fundamental validity of the VDD concept. With the emergence and continuous gathering of high-precision photometric monitoring and multi-epoch spectroscopic data of millions of stars, thanks to the Kepler (Borucki et al. 2010) and Transiting Exoplanet Survey Satellite (TESS) (Ricker et al. 2015) space photometers and, for example, the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) multi-object spectroscopy (Ren et al. 2016), many Be stars have been extensively studied, revealing new observational characteristics, which may shed light on the mechanism(s) driving the Be-star mass ejection.

Despite the relative faintness of KIC 9715425 at V ~ 13 mag, a similarly rich and diverse set of observations is available for few other Be stars. For instance, the original Kepler field was selected so that a large number of solar-type stars could be monitored for planetary transits. Therefore, it contains a relatively low fraction of early-type stars, and Kepler data of only three of them have been studied as Be stars before (Kurtz et al. 2015; Balona et al. 2015; Rivinius et al. 2016; Pápics et al. 2017).

KIC 9715425 was identified as a candidate Be star by Gao et al. (2018), unpublished). In the Kepler database, they found 152 objects with Teff > 10 000 K and observations from at least 15 quarters. Guided by the outbursting exhibited by many Be stars, they searched this sample for long-term (>100 d), large-amplitude variations. Among the four best candidates are KIC 9715425 (this paper) and KIC 6954726 (StHA 166; Rivinius et al. 2016). Along with HD 186567 (Kurtz et al. 2015), these two stars are among the first to be spectroscopically confirmed as Be stars on account of their photometric variability only (for major photometric searches see also Mennickent et al. 2002; Sabogal et al. 2005; Jian et al. 2024). The detection of Hα line emission in KIC 9715425 followed only later (this paper; Škoda et al. 2020).

KIC 9715425 is, therefore, a non-supergiant B-type star that has exhibited (transient) Balmer emission lines, thus, a Be star according to the least stringent definition (Rivinius et al. 2013). On four additional accounts, the classification can be streamlined to that of a classical Be star, these are as follows. (i) Among the B-type stars, only classical Be stars (Labadie-Bartz et al. 2022) and slowly pulsating B-type (SPB) stars (Van Beeck et al. 2021) show photometric variability with a huge number of frequencies arranged in distinct groups. For KIC 9715425, this emerges from the Kepler and TESS photometry analyzed here and in a companion paper (Wang et al. 2025, hereafter Paper II). (ii) Only from Be stars outbursts are known with an amplitude of several 0.1 mag as in KIC 9715425 (Labadie-Bartz et al. 2022). (iii) The Kepler lightcurve (LC) of the major outburst (MAB) and the light profiles of the pre-MAB minor outburst (MIBs) have the shape of typical Be-star outbursts (Paper II). (iv) KIC 9715425 provides another example (analyzed in Paper II) of contemporaneous changes in pulsation amplitudes and mean brightness (Huat et al. 2009; Baade et al. 2018b), which may hold the key to the Be phenomenon (Baade & Rivinius 2020). To squeeze KIC 9715425 out of the classical-Be-star territory would require more than imagining it as an SPB star in a mass-exchanging binary.

The firm classification of KIC 9715425 as a classical Be star is important because, not considering the presumable exception of the bluing during the MAB (Sect. 4), all observations available support it. Therefore, all new insights gained for KIC 9715425 represent candidates for a generalization to Be stars at large.

For the time of the MAB captured by Kepler, the VDD model delivers an acceptable simultaneous fit to a blue optical spectrum, the transient Hα line emission, and the broad-band SED. However, before and near the maximum of the MAB, the Galaxy Evolution Explorer (GALEX) observed the star in the near-ultraviolet (NUV). During the MAB, KIC 9715425 was bluer than before, in strong contrast to the redder-when-brighter norm of the Be-star population. The VDD model cannot reproduce this discrepant behavior of a low-inclination star without the inclusion of additional components or processes. Therefore, during the MAB of this Be system, something else must have played a role, which is still unknown and to be explored.

This paper is organized as follows: the observations and the data processing are the subject of Sect. 2. Section 3 presents the stellar parameters we derived from low- and intermediateresolution optical spectra and the spectral energy distribution (SED). In Sect. 4, we explain the conflicts between these observations and models for their explanation and discuss ways to resolve them. A summary and our conclusions follow in Sect. 5.

2 Observations and data processing

Multi-epoch photometric and spectroscopic data from various telescopes are combined in this study. Details are introduced below and summarized in Table 1.

KIC 9715425 was monitored by Kepler almost continuously for ~1500 days (Quarters Q0 – Q17), starting from May 2, 2009. Simple Aperture Photometry (SAP) data (Van Cleve & et al. 2016) were retrieved from Kepler DR 251 (Thompson et al. 2016) and detrended manually following Revalski et al. (2014). We visually inspected the target pixel files, confirming no contaminating sources within 12″ (Gao et al. 2016; Shibayama et al. 2013) that could mimic an outburst2. Nearby stars showed no similar flux variations, confirming that the event originated from KIC 9715425. Gaps between quarters were removed following the method described in Bányai et al. (2013). A linear long-term trend was also removed from Quarter 1. The resulting stitched light curve (LC) is displayed in Fig. 1. The Kepler magnitude was derived from the SAP flux using the following formula: Kmag = 13.065–2.5 × log10(fluxSAP), where 13.065 is the Kepler magnitude given in the Kepler Input Catalog (KIC).

For comparison, the photometric measurements in the other bands at different epochs were converted to the Kepler magnitudes and overplotted in Fig. 1. These include: the Isaac Newton Telescope (INT) multi-band observation on July 10, 2012 (red circle), the Xinglong 1.26-m gri photometry on December 15, 2015 (filled blue circle), the Gaia archive data around 2015.5 (green circle), and the All-Sky Automated Survey for SuperNovae (ASAS-SN) (Shappee et al. 2014; Jayasinghe et al. 2019) data (black dots with error bars). Among them, the INT and Xinglong gri-band photometric measurements were converted to the Kepler band magnitudes via direct interpolation of the g and r magnitudes. The ASAS-SN g-band LC was scaled to match the Xinglong 1.26 m g-band magnitude in December 2015. The dotted orange line is extrapolated from the last 100-d Kepler data, which matches well with the ASAS-SN LC.

Relative to the MAB as the pivotal part of the LC (Fig. 1), we distinguish two more phases. Up to day ~600, there was some slow, low-amplitude undulation of the LC with a few narrow spikes superimposed. We call this the precursor phase (PP). Starting slightly before day 2000, the stellar activity nearly completely subsided, marking the quiescent state (QS). In our analysis described below, we assume that the QS is representative of the central B star with negligible contributions from the circumstellar disk. One may be wondering whether the star was in another QS at the beginning of the Kepler observations. The variability of the 0.964 d−1 frequency proves that it was not (Paper II).

About 6.2 years after the Kepler mission, during its return to quiescence, KIC 9715425 began being monitored by the TESS mission (Ricker et al. 2015) for ~27.4 d each in Sectors 14, 15, 40, 54, 55, 74, and 75 (Table 1) with a band-pass from 6000 to 10 000 Å. The TESS data were retrieved using the Python packages: Lightkurve, Astropy, and tesscut (Lightkurve Collaboration 2018; Astropy Collaboration 2013, 2018, 2022; Ginsburg et al. 2019; Brasseur et al. 2019).

The GALEX archive (Martin et al. 2003) contains two NUV (1750–2800 Å) observations of KIC 9715425. One was taken from 30 June 2010 to 1 July 2010 through a guest investigator (GI) program (218, PI: Geraldine Peters). A total of 17 exposures were obtained for the first observation. The ten exposures far from a detector edge were averaged to determine the NUV magnitude for the PP.

The other GALEX observation was obtained on September 10, 2011, nearly at the MAB peak, through the All-Sky Survey (AIS) program. The flux collected in the second observation is ~36% larger than that in the first one. A visual investigation of the GALEX image found no hint of a close prominent contaminator. In addition, other sources in the GALEX field are mostly quiet and do not show a similar brightening. A literature survey and archive search revealed that no far-ultraviolet (FUV) observation of KIC 9715425 has ever been performed. The first NUV magnitude was scaled to match the PP magnitude of 13.065, and the same scale factor was applied to the second NUV magnitude.

The LAMOST-Kepler project (Ren et al. 2016) provided seven spectra as part of Data Release 5 (DR5). Six of them have signal-to-noise ratios (S/N) ≳50 and were utilized for detailed analysis. Two spectra were obtained during the decline of the MAB, while the other four were acquired in the QS after the MAB. The observing dates of the six spectra are denoted by vertical lines in Fig. 1.

The default relative flux calibration of LAMOST DR5 spectra can be imperfect, as the LAMOST pipeline chooses spectrophotometric standard stars automatically. Sometimes, the chosen standard star has a rather late spectral type, or suffers temporal variations, or different standard stars are used for the same target observed at different epochs. Therefore, we performed an independent flux calibration using the same A-type standard star (KIC 9835837) located in the same field, which is not variable according to its Kepler LC. This standard star provides the best relative flux calibration for KIC 9715425.

Finally, we examined an optical spectrum obtained with the Kitt Peak National Observatory (KPNO) 4-m telescope on May 9, 2014. It covers the 3950–4710 Å range at a resolving power of R ~ 72003. Further technical details can be found in Hanes et al. (2019). The spectrum is free of any line emission, including Hγ and Hδ. From the large depth and relatively low width of the spectral lines, it is immediately clear that KIC 9715425 is not a classical Be star viewed equator-on.

Table 1

Summary of all observations considered in this paper.

thumbnail Fig. 1

Summary of the KIC 9715425 data and power spectra. Bottom: overview of data for KIC 9715425. The LCs obtained by the Kepler and ASAS-SN missions are shown as blue lines and black dots with 1σ error bars, respectively. The NUV magnitudes from GALEX and the optical ones from the Isaac Newton Telescope (INT), Gaia, and the Xinglong 2.16 m telescope are converted or re-scaled to Kmag (see details in Sect. 2) and overplotted as filled circles. The ordinate values of the seven spectra are arbitrarily set to match the Kmag values at the times of the spectroscopy. The Gaia data are based on multiple visits, but only an epoch of 2015.5 is given in the Gaia archive. The five MIBs before the MAB are indicated by the black arrows. The MAB reached a maximum flux increase of ~25% (~0.24 mag) on day 970 and lasted for ≥1000 d. Informative texts (telescope names and observing dates) for other data are inserted along the vertical lines at the corresponding times. Top: power spectra map showing frequencies with highest amplitudes at different stages. Left panel: Kepler observations. Right panel: ASAS-SN observations. We note that only one frequency was detected in the ASAS-SN LC due to the latter’s lower data quality. The PP ended around day 600, the MAB lasted from ~day 600 until presumably day 2000, when the QS began. The first TESS observations were obtained after day 3800 (Table 1) and are not plotted.
thumbnail Fig. 2

Continuum-normalized Hα, Hβ, and Hγ line profiles observed by LAMOST (red), compared to a Lorentz profile (gray) fit to the respective latest spectrum. All spectra are shifted to the rest frame of the respective latest observation. From top to bottom, the observing dates are 22 May 2013, 04 September 2013, 13 September 2014, 1 October 2015, 15 May 2017 and 14 June 2017, respectively.

3 Spectral modeling

3.1 Stellar parameters

Previous analyses on this target yielded inconsistent stellar parameters. The KIC catalog4 gives a log g=3.636−0.1080.459$\[g=3.636_{-0.108}^{0.459}\]$ and Teff =11360−1462+587 K$\[T_{\text {eff }}=11360_{-1462}^{+587} \mathrm{~K}\]$, respectively. Hanes et al. (2019) derived the following parameter values: Teff = 15750 ± 1500 K, log g = 3.52 ± 0.27, and v sin i = 122 ± 12 km s−1 from the KPNO spectrum. More recently, Pedersen (2022) derived a log g=3.86−0.040.08$\[g=3.86_{-0.04}^{0.08}\]$ and Teff =16218−730+1160$\[T_{\text {eff }}=16218_{-730}^{+1160}\]$, respectively. Frasca et al. (2016) determined an effective temperature of 18 190 and 17 635 K, and spectral types of B2.5IV and B2.5V, respectively, from the two LAMOST spectra taken on 2013-09-14 and 2014-09-13. These two spectra possess notable disk emission (Fig. 2), possibly leading to an overestimation of stellar effective temperature and spectral type. In the calibration by Harmanec (1988), even these higher temperatures only correspond to a spectral type of B4, which is later than B2.5 published by Frasca et al. (2016).

Employing the Universite de Lyon Spectroscopic analysis Software (ULySS) package (Koleva et al. 2009; Wu et al. 2011) and the non-LTE Tlusty BSTAR2006 model (Lanz & Hubeny 2007), our spectroscopic analysis of the three QS-phase LAMOST spectra revealed an effective temperature of ~15,500K and a log g ~3.5, which are similar to the values given by Hanes et al. (2019), but with the log g value being significantly lower than that from Pedersen (2022) and the Teff value being higher than that of the KIC catalog. With the spectral-classification scheme for B-type stars published by Ramírez-Preciado et al. (2020) with LAMOST template spectra, we obtained B3-B5.

However, all the above spectral analyses did not consider the fact that KIC 9715425 is a classical Be star (see introduction). Be stars typically rotate at ~80% of the critical rate and are elliptically distorted so that the large equator-to-pole variation in gravity leads to substantial temperature gradients with stellar latitude (Rivinius et al. 2013). The resulting so-called gravity darkening implies that a single value for Teff is only a crude approximation. Therefore, we repeated the analysis of the spectrum studied by Hanes et al. with BRUCE04, which can incorporate stellar oblateness and non-radial pulsations when constructing time-resolved synthetic spectra of early-type stars (Townsend 1997).

The BRUCE04 code determines four key parameters: stellar mass M, polar radius Rp, luminosity L, and the ratio of angular-to-critical velocity Ω/Ωc, where Ωc is the angular velocity at which the centrifugal force equals the gravitational force at the equator. We note that the photogeometric distance of KIC 9715425 estimated by Bailer-Jones et al. (2018) based on Gaia DR2 and adopted by Hanes et al. (2019) is 6059−1101+1547$\[6059_{-1101}^{+1547}\]$ pc. However, we used the updated distance of 10 301−1238+2074$\[10~301_{-1238}^{+2074}\]$ pc from Gaia DR3 so that our values derived for stellar mass, radius, and luminosity differ from those of earlier works based on the older Gaia DR2 distance. The inclination angle i was constrained by the projected rotational velocity of 110±10 km s−1, which we derived from the He I line at 4388 Å in the KPNO spectrum, using the Fourier transform method of Jankov (1995).

We applied Markov chain Monte Carlo (MCMC) fitting (Foreman-Mackey et al. 2013) to find the BRUCE04 parameters simultaneously matching the observed Xinglong/GALEX (1750–2800 Å; Martin et al. 2003) SED and the KPNO spectrum. We included the total extinction E(B − V) as an additional free parameter. The literature values for interstellar E(B − V) range from 0.097 ± 0.018 mag from 3D dust mapping by Green et al. (2019) to 0.1655 ± 0.0065 mag obtained by Schlegel et al. (1998). Moreover, the KPNO stellar spectrum indicates a stellar temperature ~15 000 K while the reddening-corrected SED yields temperatures below 13 000 K. This inconsistency suggests non-negligible local extinction in addition to the large-scale interstellar extinction. We therefore set E(B − V) as a free parameter in the modeling.

However, in the initial MCMC fitting attempts, severe parameter degeneracy prevented convergence when the rotational parameters Ω/Ωc and E(B − V) were kept free. The posterior distribution of Ω/Ωc is nearly uniform, indicating the fitting is insensitive to Ω/Ωc. Pedersen (2022) estimated for this target that Ω/Ωc = 94.37−4.97+0.71%$\[94.37_{-4.97}^{+0.71}\%\]$. We therefore fixed Ω/Ωc to 0.89, the lower limit. The extinction E(B − V) was later fixed to 0.23 mag, which best fit the SED in the first-round MCMC runs. The remaining parameters including M, Rp, and L were kept as free parameters.

Convergence was achieved after the first 100 steps. The final MCMC run adopted 30 walkers for 1600 steps. We discarded the initial 100 steps and thinned the chain with a factor of 15. The resulting posterior distributions of the parameters are displayed in Fig A.1. The median values and the 16 and 84% levels of the posterior distribution of each stellar parameter of interest are listed in Table 2.

Table 2

The best-fit stellar parameters and the best-fit chi-square values in the quiescent phase assuming Ω/Ωc = 0.9 (cf. details in Sect. 3.1).

3.2 Circumstellar Balmer line emission

Two of the six LAMOST spectra were obtained during the descent from the maximum of the MAB, while the other four in the QS. They are marked by vertical lines in Fig. 1. As shown in Fig. 2, an Hα emission component clearly presents in the stellar Hα absorption cores of the four spectra taken before 2016, and disappears in the last two spectra from 2017. Weak Hβ emission is also visible in the first two spectra taken in 2013, i.e., during the decline from the MAB. The emission-line nature of KIC 9715425 was first published by Škoda et al. (2020) following a deep-learning-powered survey of the LAMOST database.

Because of the combination of low stellar inclination and low spectral resolution, the Be-star typical double-peaked and rotationally broadened emission profiles cannot be detected even if present. Nevertheless, there is no doubt that KIC 9715425 is a classical Be star (see introduction).

4 Non-negligible challenges

4.1 Blue or red

In theory, a Be star should turn redder in the MAB phase considering the emergence of a VDD that is heated and illuminated by the central star, and thus it should be cooler than the central star. Such a change is evidently seen in the non-equator-on Be stars covered by the Gaia multi-epoch CMD (Gaia Collaboration 2019), as mentioned in the introduction. However, the low-inclination Be star KIC 9715425 was bluer than the central star during the MAB phase. This follows from the comparison of the two GALEX (Martin et al. 2003) NUV 1750–2800 Å and the gri-band observations. Coincidentally, the first NUV observation was taken just before the MAB, and the second one was near the maximum of the MAB. Intriguingly, the NUV magnitude measured during the MAB is 13.862±0.008 mag, ~36% larger than the 14.196 ± 0.006 mag obtained during the PP. The NUV flux increase is notably higher than the 25% rise in the Kepler band, as illustrated by the filled purple circles in Fig. 1, suggesting the total luminosity of KIC 9715425 increased substantially more in the NUV than in the optical during the MAB phase. Therefore, whatever turned bright during the MAB must be bluer than the star itself.

It is also evident from Fig. 3 that the g-band MAB/PP flux ratio is significantly larger than the ri-band ratios from a direct comparison between the multiband (Ugri) photometric measurements with the INT on July 10, 2012 (Greiss et al. 2012) and those taken by the Xing-long 1.26-m telescope gri photometry on December 15, 2015. Their corresponding fluxes were converted to the Kepler band and are shown as red and blue circles, respectively, in Fig. 1. The MAB/PP ratios in the gri-bands are represented in Fig. 3 by the green square, the yellow circle and the red diamond, respectively, where the g-band flux ratio is similar to that in the NUV (purple triangle) and obviously larger than those in r (yellow circle) and i (red diamond). This reaffirms that the brightened component should be bluish.

The FWHMs of GALEX and Kepler are 5.6″ and 3.1–7.5″, respectively. The nearest source is ~20″ away and >5 mag fainter in the Gaia G band as we determined by checking all public photometric survey data releases and images, particularly Gaia DR3 and the GALEX image. The sub-arcsecond spatial resolution of Gaia ensures that there should be no relevant external contaminating source around our target, down to 0.2″ angular separation.

Apart from the observed discrepancies of the MAB/PP flux ratios between the blue (the NUV and g bands) and red wavelengths (the Kepler and ri bands), the photometric outburst profile is prototypical of mass-loss events in Be stars as shown in Labadie-Bartz et al. (2022) and Richardson et al. (2021). This suggests that the anomalous bluish flux increase may stem from processes external to the standard Be phenomenon.

thumbnail Fig. 3

Triangle, square, circle, diamond, and asterisk mark the observed MAB/PP SED ratios in the NUV band; INT/Xinglong g, r and i bands; and the Kepler band, respectively. Dashed lines with different colors represent SED ratios predicted by HDUST models with various parameters (as labeled) during the MAB and PP phases.

4.2 Dense or tenuous?

Disk continuum flux and line profiles can be predicted by HDUST, a 3D non-LTE Monte Carlo radiation-transfer code (Carciofi & Bjorkman 2006, 2008), designed to study highly asymmetric circumstellar environments such as Be disks. We ran a series of HDUST models to reproduce the disk spectra, which are combined with stellar spectra generated by BRUCE04 using the best-fit stellar parameters as listed in Table 2, to simulate (1) MAB/PP flux ratios at given epochs and wavelengths or bands; and (2) line profiles and equivalent widths (EWs) of given lines at given epochs. We compared them with the available photometric and spectroscopic data. However, we failed to fit the flux ratios and Hα emission simultaneously, simply because weak Hα emission and large flux ratios require contradictory parameters, particularly in the MAB phase, as described below.

The predicted light increases due to the emergence of a VDD in the Kepler band are tabulated in Fig. 4 for different ρ0 and n combinations using the central-star parameters from the BRUCE04 model, where ρ0 is the disk base density at the central star’s equator (r = R_eq, z = 0) and the exponent n describes the radial density profile (cf. Equation (9) in Carciofi & Bjorkman 2006). It is clear from this compilation that a relatively dense and flat VDD is required to reproduce the ~25% Kepler band light increase. For example, a VDD with log ρ0 = −10.0 [cgs] and n = 3.5, or log ρ0 = −9.5 [cgs] and n = 4.5, both yield ~25% growth in the Kepler-band flux. However, such models do not reproduce two other observations.

Firstly, as shown in Fig. 3, the model-predicted MAB/PP flux ratios (open symbols and broken lines) deviate substantially from the observations (filled circles with error bars) in all non-Kepler bands. The five VDD parameter sets used for Fig. 3 are the best fits to the Kepler-band light increase. All of them yield a very low NUV MAB/PP flux ratio of ~3%, which is much lower than the observed value of 36%. This is a natural consequence of our assumption in HDUST that the temperature of a VDD is ~60% of that of the central star. Therefore, adding a VDD will only make the system redder, while the observed SED becomes bluer in the MAB phase.

Secondly, the LAMOST spectrum taken during the decline phase of the MAB shows obvious emission at the Hα absorption core. We find that to reproduce the Hα emission component, the VDD should be tenuous, faint, and dissipating with a low surface density of logρ0 = −12.5[cgs] and a shallow radial profile with n = 2.5 (Fig. 5). In addition, the INT narrow-band photometric observation from 2012 suggests potentially stronger Hα emission with EW ~ −2 Å, which is consistent with a low-density disk with logρ0 = −11.6 [cgs], n = 3.3. However, such disks can only account for roughly a 0.2 and 2% Kepler band flux increase, more than one order of magnitude smaller than the observed increase by 8 and 20% on the dates of the first LAMOST spectrum and the INT data, respectively.

thumbnail Fig. 4

Fractional contribution by disk predicted by HDUST in Kepler band with respect to stellar flux for various combinations of disk’s base density ρ0 and power-law index n. The color-coding follows the scheme from Vieira et al. (2017): forming disks (n > 3.5, blue), steady-state disks (3 ≤ n ≤ 3.5, green), dissipating disks (n < 3, red), forbidden zone (upper left region, n − logρ0 ≤ 12.5, black), and detection limit (bottom gray region where flux enhancements become negligible).
thumbnail Fig. 5

HDUST fit to LAMOST spectrum from 22 May, 2013. The observed spectrum is plotted in black with 1σ error bars, while the model spectrum for logρ0 = −12.5 [cgs], n=2.5 and convolved to the LAMOST resolution appears in red.

5 Summary, extended discussion, and conclusions

The multi-epoch multi-wavelength data available for KIC 9715425 cannot be simultaneously explained with only a single standard VDD. Two discrepancies exist (Sect. 4): (1) the NUV and Kepler-band MAB/PP flux ratios require a dense and luminous disk, while the Hα emission EWs imply a dissipating, low-density disk, which can only yield a close-to-unity MAB/PP flux ratio; (2) the MAB/PP colors suggest that the disk must be hotter than the star, while in theory the disk should be cooler. To resolve these two discrepancies, an unknown component (in addition to the B star and the VDD) that turns bright and hot needs to be invoked, or the disk is heated by a bluer component and, therefore, hotter than in typical VDD models. When searching for an explanation, it should be kept in mind that the VDD model does not describe how matter is tossed up above the photosphere. It only takes over after this has happened and does not conserve a memory of how matter got there.

One possible way to solve the riddle is that the central star, or part of it, heated up during the MAB. For example, if the B star’s polar temperature increased to as much as ≳18 000 K, the combination with a low-density disk can roughly resolve the two above-mentioned discrepancies.

Because of the accompanying strong changes in the pulsation spectrum and the resulting elevated mass loss (Paper II), an immediate thought is that they are the reason for the discrepancies. However, the GALEX observation with the high NUV flux was obtained close to the maximum of the MAB, nearly 300 d after the decay of the 0.1d−1 variability that lasted ~100 d and probably triggered the event (Paper II). For any causal connection between synchronized pulsations, increased mass loss, and UV excess, continued mass loss beyond the initial ~100 d quasi-resonant time interval is required. In fact, a small number of weak MIBs are seen during this period (Fig. 1) so an elevated star-to-disk mass-transfer rate could play a role in the bluing.

The observations of KIC 9715425 do not invalidate the VDD model. Not considering the bluing, the description delivered by the VDD model of the variability is quite satisfactory. Therefore, one may ask what property of a VDD does not enter into the observables that the model delivers. One such detail is that, in order to build a Keplerian disk from mass packets almost all of which do not have the necessary angular momentum, approximately 99% of the initially uplifted matter must fall back to the star. Matter impacting denser regions of the atmosphere and collisions between outward- and inward-moving matter may lead to shock heating. If outbursts of Be stars release excess surface angular momentum with a minimum of mass loss (Krtička et al. 2011), this will reduce the fall-back fraction albeit presumably not by much. Therefore, an increased star-to-disk mass-transfer rate may lead to local heating.

A closely related and more general possibility along the MAB line of thought is that with the expulsion of matter due to rapid rotation, pulsation velocity, and heating, the release of excess angular momentum, radiative forces, and so on can be easily imagined as a violent process. This may be a mechanical source of heat in the disk.

Another approach to understanding the bluing in the context of the MAB would be to look into the central B star. Perhaps by a change in the mix of modes with and without a spherical cap in their geometrical patterns, the polar and therefore hottest region of this nearly pole-on star gained in mean brightness. However, without the detailed identification and modeling of the NRP modes at different times, it is impossible to conclude whether this is true. In a nonrotating star, the effect should be negligible, but Be stars rotate ultra-rapidly.

A different source of blue photons could be a compact companion orbiting the B-type star. Such companions are being found in an increasing number of Be stars (Wang et al. 2023). If material ejected from the latter during the MAB is transferred to the companion, accretion events may release significant amounts of radiation at short wavelengths. We measured the radial velocities (RVs) in the six LAMOST spectra and found them in the range of ~−8 to −20 km s−1 with a mean value of −14.5 ± 4.2 km s−15. A Lomb-Scargle power spectrum analysis of the RVs reveals that the probability of a periodic variation is <10−4. The largest velocity difference ΔRVmax is 11.3 km s−1, and the shortest time separation is about 28 d. Under the assumption that ΔRVmax is the velocity amplitude and that the orbital period is 28 d, the companion mass is ~0.008 M⊙. Therefore, the presence of a stellar-mass companion to KIC 9715426 is not favored by the current spectroscopic dataset, unless the system happens to be viewed nearly face-on.

Despite their physical validity, all of the above attempts to understand the bluing of KIC 9715425 during the MAB suffer from the lack of properties that would distinguish the star from the bulk of the Be-star population. The processes considered should, if relevant, be activated in any Be star experiencing an MAB. However, the bluing of KIC 9715425 seems to be a rare – if not unique – case within the voluminous literature on Be stars. Therefore, the best way to uncover the underlying explanation is to obtain multi-epoch NUV and FUV observations of a Be star with cyclically repeating outbursts (as listed in Paper II). If these observations do not yield an equivalent of the GALEX observations of KIC 9715425, an explanation specific to this star may have to be sought. This would include identifying properties of KIC 9715425 that differentiate it from the bulk of B stars. Currently available data, aside from the NUV observations, do not suggest such distinguishing features.

Acknowledgements

We would like to express our heartfelt thanks to R.G. Vieira, S.B. Howell and P. Nemeth for their invaluable contributions. We are grateful to Richard Hanes for providing the reduced KPNO spectrum. This work is supported by the National Natural Science Foundation of China (NSFC, grants Nos. 11988101, 42075123 and 62127901). W.W. thanks for the support from the China Manned Space Project with NO. CMS-CSST-2021-A11 and the Pre-research project on Civil Aerospace Technologies No. D010301 funded by China National Space Administration (CNSA). C.A. and M.C. thank the support from Fondecyt project № 1230131. E.S.G. de Almeida has been financially supported by ANID Fondecyt postdoctoral grant №3220776. The Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope LAMOST) is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences. This paper includes data collected by the Kepler and TESS mission and obtained from the MAST data archive at the Space Telescope Science Institute (STScI). Funding for the Kepler and TESS mission is provided by the NASA Science Mission Directorate, and Explorer Program, respectively. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5–26555.

Appendix A Additional figures

thumbnail Fig. A.1

The posterior distributions of the physical parameters of KIC 9715425 from modeling with BRUCE04. The mean and 16th and 84th percentile values are shown in Table 2.

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2

The SIMBAD database (Wenger et al. 2000) does not include any source within 30″.

3

The reduced spectrum was kindly made available by Dr. R. Hanes.

5

That is, we do not confirm the RVs of −84.6 and −96.9 km s−1 published by Frasca et al. (2016). The large discrepancy cannot be explained by measuring errors. Since the differences in these authors’ determinations of the spectral type (Sect. 3.1) and effective temperature (Sect. 3.1) compared to ours are also striking, the star may have been misidentified in the catalog of Frasca et al. (2016).

All Tables

Table 1

Summary of all observations considered in this paper.

In the text
Table 2

The best-fit stellar parameters and the best-fit chi-square values in the quiescent phase assuming Ω/Ωc = 0.9 (cf. details in Sect. 3.1).

In the text

All Figures

thumbnail Fig. 1

Summary of the KIC 9715425 data and power spectra. Bottom: overview of data for KIC 9715425. The LCs obtained by the Kepler and ASAS-SN missions are shown as blue lines and black dots with 1σ error bars, respectively. The NUV magnitudes from GALEX and the optical ones from the Isaac Newton Telescope (INT), Gaia, and the Xinglong 2.16 m telescope are converted or re-scaled to Kmag (see details in Sect. 2) and overplotted as filled circles. The ordinate values of the seven spectra are arbitrarily set to match the Kmag values at the times of the spectroscopy. The Gaia data are based on multiple visits, but only an epoch of 2015.5 is given in the Gaia archive. The five MIBs before the MAB are indicated by the black arrows. The MAB reached a maximum flux increase of ~25% (~0.24 mag) on day 970 and lasted for ≥1000 d. Informative texts (telescope names and observing dates) for other data are inserted along the vertical lines at the corresponding times. Top: power spectra map showing frequencies with highest amplitudes at different stages. Left panel: Kepler observations. Right panel: ASAS-SN observations. We note that only one frequency was detected in the ASAS-SN LC due to the latter’s lower data quality. The PP ended around day 600, the MAB lasted from ~day 600 until presumably day 2000, when the QS began. The first TESS observations were obtained after day 3800 (Table 1) and are not plotted.
In the text
thumbnail Fig. 2

Continuum-normalized Hα, Hβ, and Hγ line profiles observed by LAMOST (red), compared to a Lorentz profile (gray) fit to the respective latest spectrum. All spectra are shifted to the rest frame of the respective latest observation. From top to bottom, the observing dates are 22 May 2013, 04 September 2013, 13 September 2014, 1 October 2015, 15 May 2017 and 14 June 2017, respectively.
In the text
thumbnail Fig. 3

Triangle, square, circle, diamond, and asterisk mark the observed MAB/PP SED ratios in the NUV band; INT/Xinglong g, r and i bands; and the Kepler band, respectively. Dashed lines with different colors represent SED ratios predicted by HDUST models with various parameters (as labeled) during the MAB and PP phases.
In the text
thumbnail Fig. 4

Fractional contribution by disk predicted by HDUST in Kepler band with respect to stellar flux for various combinations of disk’s base density ρ0 and power-law index n. The color-coding follows the scheme from Vieira et al. (2017): forming disks (n > 3.5, blue), steady-state disks (3 ≤ n ≤ 3.5, green), dissipating disks (n < 3, red), forbidden zone (upper left region, n − logρ0 ≤ 12.5, black), and detection limit (bottom gray region where flux enhancements become negligible).
In the text
thumbnail Fig. 5

HDUST fit to LAMOST spectrum from 22 May, 2013. The observed spectrum is plotted in black with 1σ error bars, while the model spectrum for logρ0 = −12.5 [cgs], n=2.5 and convolved to the LAMOST resolution appears in red.
In the text
thumbnail Fig. A.1

The posterior distributions of the physical parameters of KIC 9715425 from modeling with BRUCE04. The mean and 16th and 84th percentile values are shown in Table 2.
In the text

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