Long-term Near-infrared Brightening of Nonvariable OH/IR Stars

The asymptotic giant branch (AGB) phase is a late evolutionary phase of low- and intermediate-mass stars with main-sequence masses of ∼1–10 M_⊙ (Habing 1996; Herwig 2005; Karakas & Lattanzio 2014). The stars in this phase show significant variability caused by stellar pulsation and mass ejection. Dust grains are created in mass-loss winds, and consequently, the circumstellar dust shell is developed around the central AGB stars. Among AGB stars, more massive and more evolved AGB stars are thought to experience stronger mass loss, resulting in the optically thicker dust shell causing greater obscuration of the central star (Vassiliadis & Wood 1993; Blöcker 1995a; Ferrarotti & Gail 2006).

OH/IR stars are believed to be such objects undergoing the heaviest mass loss. The name OH/IR indicates that this kind of objects shows OH maser emission at 1612 MHz and are bright in the infrared rather than the optical (Habing 1996). These characteristics arise from a thick circumstellar shell created by massive mass-loss winds. In addition, these objects show long-period variability with periods from several hundred to over a thousand days (Engels et al. 1983; Herman & Habing 1985; Habing 1996). Such a long-period variability is also expected for the evolved stars, which are larger but less massive (Vassiliadis & Wood 1993). These pieces of evidence support the hypothesis that OH/IR stars are evolved AGB stars.

On the other hand, some OH/IR stars are known to have no or little variability, and they are called nonvariable OH/IR stars. The variability of OH/IR stars is often investigated through OH maser emission, because their variability is difficult to monitor in the optical. Such nonvariable OH/IR stars were discovered by Herman & Habing (1985). They monitored the OH maser emissions of bright OH/IR stars selected from Baud's catalog (Baud et al. 1981) to evaluate their variability and found that 25% of their targets showed no or little variability.

Such a nonvariability is expected to occur after the end of AGB mass loss. In the transition from the AGB phase to the following post-AGB phase, the significant pulsational variability and heavy mass ejection of the central star are thought to cease, because these characteristics are not observed from post-AGB stars (e.g., Vassiliadis & Wood 1994; Blöcker 1995b). As a result, the circumstellar dust shell starts to dissipate, and the central star obscured in the AGB phase gradually brightens in the optical and near-infrared (NIR). This reappearance of the stellar emission in the NIR has been suggested from spectral energy distribution (SED) analyses. Engels (2007) found that some nonvariable OH/IR stars showed NIR excess while normal OH/IR stars did not show such an NIR excess. This NIR excess was interpreted as the emission from the star that was reemerging from the optically thick dust shell. This result suggests that the nonvariable OH/IR stars are in transition from the AGB phase to the post-AGB phase. Bedijn (1987) also supported this picture from mid- to far-infrared SED modeling. He reported that nonvariable OH/IR stars dominated a region in the IRAS two-color diagram ($\mathrm{log}\left[\lambda {F}_{\lambda }(25)/\lambda {F}_{\lambda }(12)\right]\,\gtrsim 0.2,\mathrm{log}\left[\lambda {F}_{\lambda }(60)/\lambda {F}_{\lambda }(25)\right]$ ∼ −0.6–0.1) and their colors could be reproduced by models with a dispersing dust shell after the cessation of AGB mass loss.

These studies were based on one-epoch observations, but now, we can investigate the long-term brightness evolution of these objects by using infrared archival data. In this paper, we investigate the long-term NIR (the J-, H-, and K-band) brightness evolution of nonvariable OH/IR stars to reveal their real-time evolution. Data in wavelength regions longer than the K band are also useful especially to investigate the evolution of the thermal emission from the circumstellar dust shell. However, the treatment of the thermal emission from the dust shell requires the detailed modeling of radiative-transfer processes, which is beyond our scope. Therefore, we focus on only the NIR evolution in this paper. Below, in Section 2, we describe the target identification by searching for infrared counterparts of nonvariable OH/IR stars. The search method for the long-term brightness evolution using NIR archival data is described in Section 3. Section 4 shows the results, and we discuss the origin of the observed brightness evolution in Section 5. Section 6 summarizes this study.

The targets are selected from the list of OH/IR stars monitored by Herman & Habing (1985). They measured the variability amplitude of OH maser emission in radio magnitude, which is defined as the logarithm of the peak maser flux density. We select 16 OH/IR stars with variability amplitudes less than 0.3 as nonvariable OH/IR stars. They are listed in Table 1.

Table 1.  Names and Positions of the Target Nonvariable OH/IR Stars

Object	2MASS	SSTGLMC	R.A.	Decl.	Position
Namea	Name	Name	(deg; J2000)	(deg; J2000)	Source
OH 0.3−0.2		G000.3335−00.1805	266.778946	−28.744976	GLIMPSE
OH 1.5−0.0b		G001.4837−00.0612	267.337090	−27.698449	GLIMPSE
OH 11.5+0.1	J18103867−1852583	G011.5599+00.0873	272.661187	−18.882896	GLIMPSE
OH 15.7+0.8		G015.7010+00.7705	274.107406	−14.920483	GLIMPSE
OH 17.7−2.0	J18303070−1428570		277.627928	−14.482512	2MASS
OH 18.3+0.4		G018.2956+00.4291	275.679577	−12.794966	GLIMPSE
OH 18.5+1.4	J18193549−1208081	G018.5182+01.4129	274.897885	−12.135602	GLIMPSE
OH 18.8+0.3		G018.7687+00.3016	276.022247	−12.436756	GLIMPSE
OH 25.1−0.3	J18381546−0709543	G025.0568−00.3505	279.564387	−07.165077	GLIMPSE
OH 31.0+0.0		G030.9439+00.0351	281.921407	−01.753168	GLIMPSE
OH 31.0−0.2		G031.0123−00.2193	282.179217	−01.808404	GLIMPSE
OH 37.1−0.8		G037.1184−00.8473	285.526137	+03.337738	GLIMPSE
OH 51.8−0.2	J19274203+1637239	G051.8038−00.2248	291.925188	+16.623349	GLIMPSE
OH 53.6−0.2	J19312537+1813103	G053.6303−00.2392	292.855788	+18.219504	GLIMPSE
OH 77.9+0.2	J20283067+3907009		307.127821	+39.116924	2MASS
OH 359.4−1.3c		G359.3798−01.2008	267.216181	−30.088645	GLIMPSE

Notes.

^aNames used by Herman & Habing (1985). ^bOH 001.484−00.061 is regarded as OH 1.5−0.0 (see text for details). ^cMore precisely, 07 northwest from the GLIMPSE position (see text for details).

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At first, we determine their precise coordinates by finding bright infrared objects in images taken with the Spitzer Space Telescope (SST; Werner et al. 2004). OH/IR stars are sometimes invisible even in the NIR because of heavy obscuration by the circumstellar dust but are very bright in the thermal infrared (TIR) beyond the NIR. Therefore, high-resolution TIR images are useful to determine the precise coordinates of OH/IR stars (e.g., Deguchi et al. 2007; Engels 2007). We use TIR images of the target nonvariable OH/IR stars taken with the Infrared Array Camera (IRAC; Fazio et al. 2004) on board the SST. The SST data are now easily retrievable from the Spitzer Enhanced Imaging Products (SEIP) database on the NASA/IPAC Infrared Science Archive (IRSA).⁸ As all of the targets are found near the galactic plane, the IRAC images and source list made available by the Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE) project are useful for the target identification. We look for infrared-bright objects in the IRAC images in the SEIP Cryogenic Release v3.0 (CR3) and the GLIMPSE catalog (Spitzer Science 2009) using the IRSA viewer service⁹ on the IRSA website.

The target positions are initially obtained from the SIMBAD service (Wenger et al. 2000)¹⁰ by querying with the object names used by Herman & Habing (1985). Then, we look for a source around the SIMBAD position of the target nonvariable OH/IR stars in IRAC images by using the IRSA viewer. At the same time, the 2MASS images (Skrutskie et al. 2006), 2MASS point-source catalog (PSC; Cutri et al. 2003), and GLIMPSE catalog (Spitzer Science 2009) are also examined in the IRSA viewer. Infrared counterparts are identified by finding red bright objects in these data.

The results are shown in Table 1 and Figure 1. Except for the following three objects, OH 1.5−0.0, OH 15.7+0.8, and OH 31.0−0.2, infrared counterparts are found close to the positions given by SIMBAD. The results are summarized as follows.

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OH 0.3−0.2: A bright object is clearly found in the IRAC band 4 image (8.0 μm) at the SIMBAD position, while in the other images, another object is found in the northeast direction from the SIMBAD position. The previous object becomes fainter in shorter wavelengths, and the latter object gets brighter than the previous object in shorter wavelengths. We identify the previous object, SSTGLMC G000.3335−00.1805 in the GLIMPSE catalog, as OH 0.3−0.2 because of the redness and brightness in the TIR and the positional agreement with SIMBAD.

OH 0.3−0.2 is also listed as OH 0.335−0.180 in the SIMBAD database. The NIR spectrum of OH 0.335–0.180 is reported by Vanhollebeke et al. (2006). However, according to the observed position in their log (Table A.3 in Vanhollebeke et al. 2006), the reported object seems to be a different object, 2MASS J17470734−2844282, brightly seen at the north edge of the 2MASS H-band image in Figure 1.

OH 1.5−0.0 (OH 001.484−00.061): Because this object is recorded without coordinates in the SIMBAD database, we searched for an OH/IR star around (l, b) = (15, −00) in the OH maser source catalog created by Sevenster et al. (1997) and found OH 001.484−00.061 as the only object around the position. Therefore, we regard OH 001.484−00.061 as OH 1.5−0.0 and adopt the position of OH 001.484−00.061 as the initial position for OH 1.5−0.0. A bright infrared object, SSTGLMC G001.4837−00.0612, is found at this position, while the 2MASS images only show another object named 2MASS J17492131−2741555 in the east direction. This suggests that SSTGLMC G001.4837−00.0612 has very red color in the NIR. Based on the positional agreement, red color, and TIR brightness, we identify SSTGLMC G001.4837−00.0612 as OH 1.5−0.0.

OH 11.5+0.1: A very bright infrared object is found in both 2MASS and IRAC images at the SIMBAD position. It is 2MASS J18103867−1852583 and SSTGLMC G011.5599+00.0873 in the 2MASS PSC and the GLIMPSE catalog, respectively. We identify this object as OH 11.5+0.1.

OH 15.7+0.8: There is an object at the SIMBAD position clearly seen in the 2MASS images. However, there are much brighter objects in the vicinity of the SIMBAD position in the IRAC images. This object at the SIMBAD position of OH 15.7+0.8 is therefore rather blue, and hence, is unlikely to be an OH/IR star.

The reddest object in the vicinity of the SIMBAD position is thus the object at 6'' east of the SIMBAD position, which we consider to be OH 15.7+0.8. This object is cataloged as SSTGLMC G015.7010+00.7705 in the GLIMPSE catalog.

IRAS 18135−1456 is listed as an alternative name of OH 15.7+0.8 in SIMBAD. Its NIR spectrum is reported by Oudmaijer et al. (1995). However, the target coordinate listed in their Table 1 corresponds to the position of a different object, 2MASS J18162412−1455138, seen 18'' west from the SIMBAD position (out of the image in Figure 1). Therefore, the spectrum reported by Oudmaijer et al. (1995) is probably not of OH 15.7+0.8.

OH 17.7−2.0: A pair of bright objects is seen in the 2MASS images at the position of OH 17.7−2.0 given by SIMBAD. SIMBAD suggests that OH 17.7−2.0 is the southeast object of the pair, which corresponds to 2MASS J18303070−1428570. A bright object is found at the same position in the IRAC images retrieved from SEIP, and not listed in the GLIMPSE catalog. Therefore, we identify 2MASS J18303070−1428570 as OH 17.7−2.0 and use the 2MASS position as the target position.

OH 18.3+0.4: At the SIMBAD position, a bright object is seen only in the IRAC images. This is SSTGLMC G018.2956+00.4291 in the GLIMPSE catalog. Based on the absence of the object in the 2MASS images, this object is very red, which is a usual characteristic of OH/IR stars. Therefore, we identify this object as OH 18.3+0.4.

OH 18.5+1.4: One bright object is seen in both 2MASS and IRAC images. This is listed as 2MASS J18193549−1208081 and SSTGLMC G018.5182+01.4129 in the 2MASS PSC and the GLIMPSE catalog, respectively. We identify this object as OH 18.5+1.4.

OH 18.8+0.3: In the IRAC images, a bright red object is found at the SIMBAD position, while no object is seen in the 2MASS images. We identify this red object, SSTGLMC G018.7687+00.3016 in the GLIMPSE catalog, as OH 18.8+0.3.

OH 25.1−0.3: A bright red object is found in both the 2MASS and IRAC images at the SIMBAD position. This object is 2MASS J18381546−0709543 and SSTGLMC G025.0568−00.3505 in the 2MASS PSC and the GLIMPSE catalog, respectively. This object is thought to be OH 25.1−0.3.

OH 31.0+0.0: A bright red object is found at the SIMBAD position in the IRAC images, while no object is found in the 2MASS images. The object is cataloged as SSTGLMC G030.9439+00.0351 in the GLIMPSE catalog. We identify this object as OH 31.0+0.0.

OH 31.0−0.2: No object is found at the SIMBAD position of OH 31.0−0.2 in both 2MASS and IRAC images. However, we find a bright red object 10'' northeast of the SIMBAD position in the IRAC images. We identify this object, listed as SSTGLMC G031.0123−00.2193 in the GLIMPSE catalog, as OH 31.0−0.2.

OH 37.1−0.8: A bright red TIR object is seen in the IRAC images at the SIMBAD position. This object is listed as SSTGLMC G037.1184−00.8473 in the GLIMPSE catalog. We identify this object as OH 37.1−0.8 based on the redness and brightness in the TIR. In the 2MASS images, this object is not seen, while a different object is seen in the west. This is 2MASS J19020603+0320170. We note that this 2MASS object is not OH 37.1−0.8.

OH 51.8−0.2: A bright red TIR object is found in the IRAC images. This is SSTGLMC G051.8038−00.2248 in the GLIMPSE catalog. This object is faintly seen in the 2MASS K_S-band image and listed as 2MASS J19274203+1637239 in the 2MASS PSC. We identify this object as OH 51.8−0.2.

OH 53.6−0.2: One bright object is seen in all the 2MASS and IRAC images. This is 2MASS J19312537+1813103 and SSTGLMC G053.6303−00.2392 in the 2MASS PSC and the GLIMPSE catalog, respectively. We identify this object as OH 53.6−0.2.

OH 77.9+0.2: One bright red object is seen in all the 2MASS and IRAC images. This object is listed in the 2MASS catalog as 2MASS J20283067+3907009 but not listed in the GLIMPSE catalog. Therefore, we use the position of 2MASS J20283067+3907009 as the target position.

OH 359.4−1.3: A bright TIR source is found in the IRAC band 4 image 07 northwest of the GLIMPSE catalog position of SSTGLMC G359.3798−01.2008 (Table 1, Figure 1). This TIR source coincides well with OH 359.380−01.201, the only OH maser source in the vicinity (Sevenster et al. 1997). The positional offset between this TIR source and the OH maser source is 03, within the positional accuracy of the respective data (03; Spitzer Science 2013: 05; Sevenster et al. 1997). Hence, we regard this TIR object as the OH maser source. The UKIDSS K-band image at a higher spatial resolution shows two marginally resolved objects, the brighter one 06 east and the fainter one ∼06 northwest of the SSTGLMC G359.3798−01.2008 catalog position (Figure 2; also see the next section). Therefore, we consider the fainter of the two NIR objects in the UKIDSS K-band image as the TIR/OH maser source, i.e., OH 359.4−1.3.

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The long-term brightness evolution of the nonvariable OH/IR stars is examined with the 2MASS PSC, UKIRT Infrared Deep Sky Survey (UKIDSS) data, and data taken with the Okayama Astrophysical Observatory Wide Field Camera (OAOWFC; Yanagisawa et al. 2019). Three stars in our sample, OH 0.3−0.2, OH 1.5−0.0, and OH 359.4−1.3, are included in the observation area of the Vista Variables in the Vía Láctea (VVV) survey (Minniti et al. 2010). However, we do not find their photometric data in the VVV Data Release 4 (DR4). Therefore, we use only 2MASS, UKIDSS, and OAOWFC data in this study.

As shown in Table 1, seven objects are listed in the 2MASS catalog. Their NIR magnitudes from 1997 to 2001 can be investigated by using the 2MASS catalog. However, the J-, H-, and K_S-band magnitudes of OH 17.7−2.0 are not reliable because they have a quality flag of U or E. OH 51.8−0.2 has a reliable K_S-band magnitude with a quality flag of B, while its J- and H-band magnitudes have a quality flag of U and are unreliable. Other objects have reliable J-, H-, and K_S-band magnitudes with a quality flag of A or B. The 2MASS catalog gives the total photometric error including not only measurement errors but also systematic errors such as calibration and flat errors as [jhk]_msigcom (Cutri et al. 2006). We employ [jhk]_msigcom as the photometric error. We can also get precise observation dates from the catalog.

The UKIDSS project is described by Lawrence et al. (2007). UKIDSS uses the UKIRT Wide Field Camera (WFCAM; Casali et al. 2007) and a photometric system described by Hewett et al. (2006). The pipeline processing and science archive are described by Irwin et al. (2004) and Hambly et al. (2008). In the UKIDSS data, the target objects are observed in the Galactic Plane Survey (GPS; Lucas et al. 2008). In the GPS program, the north galactic plane ($| b| \lt 5^\circ$ in l = 15°–107°, 142°–230°; $| b| \lt 2^\circ$ in l = −2° to +15°) was surveyed by the UKIRT 3.8 m telescope once in the J and H bands and twice in the K band from 2005 to 2012. We use the source catalog and images opened in the 11th data release (DR11PLUS), which is available from the WFCAM Science Archive (WSA; Hambly et al. 2008) website.¹¹

Figure 2 shows the UKIDSS images. Among the 16 targets, 13 objects except for OH 0.3−0.2, OH 1.5−0.0, and OH 18.3+0.4 are found in the UKIDSS images. OH 18.8+0.3 and OH 359.4−1.3 are detected in the UKIDSS images but are not listed in the GPS catalog. Therefore, only 11 objects have photometric data in the GPS catalog. Three of 11 objects, OH 11.5+0.1, OH 17.7−2.0, and OH 18.5+1.4, have unreliable magnitudes because of saturation. The other eight objects have reliable magnitudes with error bits, ppErrBits, less than 256, which is a criteria to select good-quality data, the same as used by Hambly et al. (2008). Various photometric magnitudes measured with different sizes of aperture photometry are listed in the database. Among the magnitudes, AperMag3, the photometric magnitude measured with an aperture diameter of 2'', is the default magnitude in the catalog (Lucas et al. 2008). We adopt this AperMag3 magnitude in this study. Uncertainties are also available in the database as AperMag3Err. However, according to Lucas et al. (2008), this error is usually underestimated because it does not take into account systematic calibration errors. Such systematic errors were evaluated by Hodgkin et al. (2009). They evaluated the repeatability of photometric measurements and concluded that an accuracy of 1%–3% could be achieved by applying appropriate corrections even under thin clouds. Therefore, in this study, we estimate the total photometric error by calculating the square root of the sum of squares (SRSS) of the measurement error (AperMag3Err) and 0.03 mag calibration error. The observation dates are obtained from the header of the FITS data for each target retrieved from the WSA website.

The OAOWFC is an NIR camera developed by modifying the 0.91 m telescope at the Okayama Astrophysical Observatory (OAO). The OAOWFC has been dedicated to a galactic plane monitoring survey in the K_S band since 2015. The survey region is $| b| \lt 1^\circ$ in l = 21°–36° and 75°–85°. Two of the 16 targets, OH 25.1−0.3 and OH 77.9+0.2, are found in the survey data. After basic reduction steps such as dark subtraction, flat correction, and World Coordinate System (WCS) matching, instrumental magnitudes are measured by the Source Extractor (SExtractor; Bertin & Arnouts 1996) and calibrated by comparing the 2MASS K_S-band magnitudes.

In order to compare the magnitudes obtained by different instruments, a system-conversion process must be applied. For the UKIDSS-GPS data, the system conversion was discussed by Hodgkin et al. (2009). However, they investigated the system-conversion equation only in a blue region, where the 2MASS (J − K_S) color, (J − K_S)_2MASS, is 0–1 mag. To deal with our red targets with (J − K_S)_2MASS = 1.1–4.2 mag, we define our own system-conversion relation appropriate for red objects by using 2MASS and UKIDSS-GPS data. We cross-match objects in the Galactic center region ($| l| \lt 1^\circ$ and $| b| \lt 1^\circ$) listed in the 2MASS PSC (with quality flags of A, B, and C) and UKIDSS-GPS catalog (with magnitudes greater than 10 mag to avoid saturation) by using the CDS X-Match service¹² with a search radius of 01.

The results of the cross-matching are shown in Figure 3 as plots of the difference of the JHK magnitude between the two systems as a function of the corresponding 2MASS color. The gray dots are the data taken from the UKIDSS-GPS and 2MASS catalogs, and the black points and bars show the averages and standard deviations calculated in each 0.2 mag color bin with 3σ clipping. The results are converged within 10 iterations of the sigma clipping calculations. The averaged values are used to convert the 2MASS magnitudes to the WFCAM magnitudes.

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As for the OAOWFC data, Yanagisawa et al. (2019) give a system-conversion equation between the OAOWFC and 2MASS systems. However, the two objects observed by OAOWFC have redder colors, (H − K_S)_2MASS ∼ 1.7 mag, than the objects used for the derivation of their system-conversion equation, typically (H − K_S)_2MASS ≲ 1.2 mag. Therefore, we derive a new system-conversion relation that covers redder color regions. To cover redder regions, data taken in three fields in the galactic plane are used, because red objects obscured by interstellar dust exist in the galactic plane. After the basic calibrations, the systematic K_S-band magnitude difference against (H − K_S)_2MASS is examined. In this process, data with large photometric error (>0.05 mag) are removed. Data that have significant magnitude differences between 2MASS and OAOWFC data (larger than five times the photometric error) are also removed as unreliable data. The result is shown in Figure 4. The derived relation shows that the difference between 2MASS and OAOWFC systems is very small as shown by Yanagisawa et al. (2019). The OAOWFC magnitudes are corrected to WFCAM magnitudes by using both this relation and the relation between the WFCAM and 2MASS systems derived above.

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NIR multiepoch data are established for seven objects, OH 15.7+0.8, OH 25.1−0.3, OH 31.0−0.2, OH 37.1−0.8, OH 51.8−0.2, OH 53.6−0.2, and OH 77.9+0.2. They are summarized in Table 2. The table shows the object names; J-, H-, and K-band magnitudes (where appropriate); observation dates; and data sources. All of the magnitudes except for the K-band magnitude of OH 51.8−0.2 observed by 2MASS are converted to those of the WFCAM system. The K-band magnitude of OH 51.8−0.2 cannot be converted to WFCAM magnitude, because it does not have the (H − K_S)_2MASS data required for the system conversion. Therefore, we can correctly examine NIR variability only for six objects except for OH 51.8−0.2.

Table 2 also shows the rate of change of the magnitude in the last column. The rate of change for the UKIDSS observations are derived by dividing the magnitude difference with the time interval between the first-epoch 2MASS or UKIDSS observation and the second-epoch UKIDSS observation. The first finding is that the six objects all show negative rates of change, i.e., brightening over a few thousand days. The brightening of these six objects is also clearly seen in Figure 5, which shows the time evolution of the magnitude over multiepoch observations. In the J band, the apparent brightening is found in OH 25.1−0.3, OH 53.6−0.2, and OH 77.9+0.3 with significances of 1σ–2σ. In the H band, the apparent brightening is detected for OH 25.1−0.3, OH 53.6−0.2, and OH 77.9+0.3 at the 1σ, 3σ, and 5σ levels, respectively. The K-band brightening observed between 2MASS and UKIDSS observations is of >3σ significance. OH 25.1−0.3, OH 53.6−0.2, and OH 77.9+0.2 are observed three times in 2MASS and UKIDSS observations, and the apparent brightening found in each of the two consecutive intervals is consistent within the uncertainties.

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As for OH 51.8−0.2, the difference of the K-band magnitude is +0.139 (i.e., darkening) between the first-epoch 2MASS observation and the second-epoch UKIDSS observation without the system conversion. As shown in Figure 3, the differences between the K-band magnitudes of the 2MASS and UKIDSS observations are small, −0.037 to +0.030 mag in the whole (H − K_S)_2MASS range. If we evaluate the total uncertainty on the magnitude change as the SRSS of this system-conversion uncertainty and the photometric uncertainties of the 2MASS and UKIDSS observations, it is calculated to be 0.138–0.140 mag. Therefore, it is difficult to conclude if OH 51.8−0.2 is darkening with a reasonable amount of certainty.

For OAOWFC data, the rate of change in Table 2 is derived by linear fitting of the OAOWFC monitoring data shown in Figure 6. Figure 6 shows the long-term variations of the K-band magnitude for the two nonvariable OH/IR stars, OH 25.1−0.3 and OH 77.9+0.2 (black plots), together with nearby reference stars (gray plots). Some OAOWFC data whose measured magnitudes sensitively change depending on the photometric aperture size are removed as unreliable data. The reference stars are selected with the criterion that the star is seen in the proximity of the target with a K-band magnitude close to that of the target. For OH 25.1−0.3, 2MASS J18381571−0710026 is selected as the reference star. This reference star is 9'' north from OH 25.1−0.3 and has a K-band magnitude of ∼11.1 mag, which is close to the K-band magnitude of OH 25.1−0.3 (11.2–11.6 mag). The reference star for OH 77.9+0.2 is 2MASS J20282996+3907096, which exists 12'' northwest from OH 77.9+0.2. The K-band magnitude (∼11.8 mag) is close to that of OH 77.9+0.2 (11.6–11.9 mag).

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For OH 25.1−0.3, a slight periodic variability with an amplitude of ∼0.1 mag and a period of ∼50 days may be seen in the OAOWFC light curve. Even if we take into account this possible variability by setting the magnitude errors to be 0.2 mag, a linear fitting of all 2MASS, UKIDSS, and OAOWFC data gives a significant negative rate of change of −0.008 ± 0.003 mag yr⁻¹. Therefore, we conclude that OH 25.1−0.3 brightened since the 2MASS era even with the possible periodic variability. This brightening is also supported by the comparison of light curves of the target and the reference star, which shows that such a brightening is only seen in the target light curve. In the target light curve, only the data around MJD = 57,100–57,350 are relatively faint compared to the trend seen in the 2MASS and UKIDSS data, while the data around MJD = 56,000 seem to be on that trend. The discrepancy between the data around MJD = 57,100–57,350 and those around MJD = 56,000 is the cause of the large rate of change shown for the OAOWFC data in Table 2. If we assume that the faint magnitudes around MJD = 57,100–57,350 are caused by calibration problems and evaluate the rate of change since the second UKIDSS observation without these faint data, the rate of change is derived to be −0.021 ± 0.007 mag yr⁻¹. This is consistent with the values derived from 2MASS and UKIDSS observations.

As for OH 77.9+0.2, any periodic variability like OH 25.1−0.3 is not seen in the OAOWFC light curve. Although the overall magnitudes observed by OAOWFC are slightly fainter than those expected from the 2MASS–UKIDSS trend, the OAOWFC magnitudes are significantly brighter than the 2MASS magnitudes. Because the brightening trend is seen only in the target light curve, it can be concluded that OH 77.9+0.2 has also brightened since the 2MASS era. The rate of change derived from the OAOWFC light curve is consistent with those derived from the 2MASS and UKIDSS observations as in Table 2. Therefore, the magnitude offset between the 2MASS–UKIDSS trend and OAOWFC light curve may be caused by systematic error (see Appendix A.4).

As shown in Table 2, we have multicolor, multiepoch data for three objects, OH 25.1−0.3, OH 53.6−0.2, and OH 77.9+0.2, enabling us to study their color changes. Figure 7 shows the time variations of the (H − K) and (J − K) colors between the 2MASS and UKIDSS observations. The rates of the color change are summarized in Table 3. Conventionally, we have expected that a nonvariable OH/IR star becomes brighter and bluer as its mass-loss rate drops at the end of the AGB evolution. However, contrary to this picture, we find that the three nonvariable OH/IR stars kept their colors constant or became redder over a few thousand days. This is the second finding of this study. OH 25.1−0.3 and OH 77.9+0.2 do not show significant color change in both (H − K) and (J − K). On the other hand, the color of OH 53.6−0.2 in the UKIDSS observation is redder than that in the 2MASS data. The significance levels of the color changes are 1.4σ and 2.2σ in (H − K) and (J − K), respectively.

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To investigate the origin of the observed long-term brightness evolution, we make a simple model based on the conventional picture and compare it with the observed rates of brightening and color change.

5.1. A Simple Model

In the conventional picture, it is thought that nonvariable OH/IR stars have ceased the dust supply to the circumstellar dust shell, and the dust shell is expected to expand its inner cavity. Therefore, we assume a spherical dust shell created by a stellar wind with a constant expansion velocity, v_exp, and a constant dust mass-loss rate, ${\dot{M}}_{{\rm{d}}}$, and that its inner radius, r_in, is increasing with time, t, after the cessation of dust production.

At a wavelength λ, the apparent magnitude of a star with an intrinsic apparent magnitude m_λ,i is written as

$$\begin{eqnarray}&&{m}_{\lambda }={m}_{\lambda ,{\rm{i}}}+{A}_{\lambda ,{\rm{c}}}+{A}_{\lambda ,{\rm{i}}},\end{eqnarray} \tag{ 1 }$$

where A_λ,c and A_λ,i are the extinction caused by the circumstellar dust and interstellar dust, respectively. Here, we omit the thermal emission from the circumstellar dust shell, because it is difficult to model without mid- to far-infrared data simultaneously taken with the NIR data. This assumption is thought to be reasonable for a situation where enough time elapsed since the cessation of the dust supply and hot dust grains (≳700 K) disappeared (e.g., t ≳ 10 yr for a star with L = 10⁴ L_⊙ and v_exp = 10 km s⁻¹). If such hot dust grains exist in the dust shell, their thermal emission can contribute to the NIR brightness especially at longer wavelengths. Such a possible contribution of the dust emission will be addressed in Section 5.4.

A_λ,c is described as

$$\begin{eqnarray}&&{A}_{\lambda ,{\rm{c}}}=-2.5\mathrm{log}[\exp (-{\sigma }_{\lambda }N)]\approx 1.09{\sigma }_{\lambda }N,\end{eqnarray} \tag{ 2 }$$

where σ_λ and N are the absorption cross-section and the column density of dust grains in the dust shell.

$\dot{{M}_{{\rm{d}}}}$ is related to the number density of dust grains, n_d, as

$$\begin{eqnarray}&&\dot{{M}_{{\rm{d}}}}=4\pi {r}^{2}{v}_{\exp }{m}_{{\rm{d}}}{n}_{{\rm{d}}},\end{eqnarray} \tag{ 3 }$$

where r is the distance from the star, and m_d is the mass of a single dust particle. Because we assume a constant v_exp and a constant ${\dot{M}}_{{\rm{d}}}$, n_dr² becomes a constant, $C=\dot{{M}_{{\rm{d}}}}{(4\pi {v}_{\exp }{m}_{{\rm{d}}})}^{-1}$.

Then, N is written as

$$\begin{eqnarray}&&N={\int }_{{r}_{\mathrm{in}}}^{{r}_{\mathrm{out}}}{n}_{{\rm{d}}}(r){dr}=C\left(\displaystyle \frac{1}{{r}_{\mathrm{in}}}-\displaystyle \frac{1}{{r}_{\mathrm{out}}}\right),\end{eqnarray} \tag{ 4 }$$

where r_in and r_out are the inner and outer radii of the dust shell. If we assume that r_out is sufficiently larger than r_in, N is approximated to be

$$\begin{eqnarray}&&N\approx \displaystyle \frac{C}{{r}_{\mathrm{in}}}=\displaystyle \frac{C}{{r}_{\mathrm{in},0}+{v}_{\exp }t},\end{eqnarray} \tag{ 5 }$$

where ${r}_{\mathrm{in},0}$ is the inner radius of the dust shell at t = 0.

By substituting Equation (5) into Equation (2) and introducing a crossing-time parameter, t_cross = r_in,0/v_exp, we get an expression of A_λ,c as

$$\begin{eqnarray}&&{A}_{\lambda ,{\rm{c}}}(t)=\displaystyle \frac{{A}_{\lambda ,{\rm{c}}}(0)}{1+t/{t}_{\mathrm{cross}}}.\end{eqnarray} \tag{ 6 }$$

If we assume that the properties of the central star and interstellar extinction (i.e., m_λ,i and A_λ,i) are constant, the rate of change of the apparent magnitude is described as

$$\begin{eqnarray}&&\displaystyle \frac{{{dm}}_{\lambda }}{{dt}}\left(t\right)=\displaystyle \frac{{{dA}}_{\lambda ,{\rm{c}}}}{{dt}}=-\displaystyle \frac{{A}_{\lambda ,{\rm{c}}}(0)}{{t}_{\mathrm{cross}}{\left(1+t/{t}_{\mathrm{cross}}\right)}^{2}}.\end{eqnarray} \tag{ 7 }$$

Another important observable is the rates of color change. In the model, the color in the wavelength range of λ–$\lambda ^{\prime}$ is

$$\begin{eqnarray}&&{C}_{\lambda \lambda ^{\prime} }={C}_{\lambda \lambda ^{\prime} ,{\rm{i}}}+{E}_{\lambda \lambda ^{\prime} ,{\rm{c}}}+{E}_{\lambda \lambda ^{\prime} ,{\rm{i}}},\end{eqnarray} \tag{ 8 }$$

where ${C}_{\lambda \lambda ^{\prime} ,{\rm{i}}}$ is the intrinsic color of the central star. ${E}_{\lambda \lambda ^{\prime} ,{\rm{c}}}$ and ${E}_{\lambda \lambda ^{\prime} ,{\rm{i}}}$ are the color excess in λ–$\lambda ^{\prime}$ caused by the circumstellar and interstellar dust, respectively. If we assume that the stellar properties and interstellar extinction (i.e., ${C}_{\lambda \lambda ^{\prime} ,{\rm{i}}}$ and ${E}_{\lambda \lambda ^{\prime} ,{\rm{i}}}$) are constant, the rate of color change is described by using Equations (2) and (8) as

$$\begin{eqnarray}&&\displaystyle \frac{{{dC}}_{\lambda \lambda ^{\prime} }}{{dt}}\left(t\right)=\left(\displaystyle \frac{{\sigma }_{\lambda }}{{\sigma }_{\lambda ^{\prime} }}-1\right)\displaystyle \frac{{{dA}}_{\lambda ^{\prime} ,{\rm{c}}}}{{dt}}.\end{eqnarray} \tag{ 9 }$$

The wavelength dependence of the absorption cross-section is often expressed as a power-law function. If the power-law index is written as p $({\sigma }_{\lambda }\propto {\lambda }^{p})$, the rate of color change is written as

$$\begin{eqnarray}&&\displaystyle \frac{{{dC}}_{\lambda \lambda ^{\prime} }}{{dt}}\left(t\right)=\left[{\left(\displaystyle \frac{\lambda }{\lambda ^{\prime} }\right)}^{p}-1\right]\displaystyle \frac{{{dA}}_{\lambda ^{\prime} ,{\rm{c}}}}{{dt}}.\end{eqnarray} \tag{ 10 }$$

We compare the observed results with this model in the following sections.

5.2. K-band Brightening Rate

The K-band brightening rate can be calculated based on Equation (7) by substituting appropriate values of the crossing time and initial K-band circumstellar extinction, A_K,c(0), to t_cross and A_λ,c(0), respectively.

According to the SED analysis by Justtanont & Tielens (1992), the inner radii of OH/IR stars are 1.3–15 × 10¹² m, and the expansion velocities are in the range of 2.3–24.2 km s⁻¹. The combinations of these values lead to the crossing times of 2.8–24 yr. The actual expansion velocities of the six objects can be estimated from the velocity differences of the OH maser emission peaks. Based on the observations by Herman & Habing (1985), their expansion velocities are estimated to be 11.0–14.7 km s⁻¹ and are actually in the parameter range above. The optical depth at 9.7 μm, τ_9.7, the peak of the silicate feature, is also given by Justtanont & Tielens (1992) and ranges from 0.03 to 19.6. The extinction in the K band can be estimated from this 9.7 μm optical depth to be ≲10 mag by assuming the silicate opacity proposed for OH/IR stars by Suh (1999).

If we assume A_K,c(0) = 10 mag as an example of the optically thickest dust shell of OH/IR stars and t_cross = 2.8–24 yr, the time evolution of the K-band brightening rate is calculated as shown in Figure 8. In Figure 8, the thin solid and dashed lines show the calculated results. Based on Equation (7), the maximum value of the absolute brightening rate at each time t is found to be A_K,c(0)/4t, which occurs in the model with t_cross = t. This is shown with the thick solid line in Figure 8. The expected range is the region enclosed by these lines and indicated with the shaded region.

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The K-band brightening rates observed between 2MASS and UKIDSS observations are shown with the horizontal dotted lines in Figure 8. The K-band brightening rates are ≲0.1 mag yr⁻¹ except for OH 31.0−0.2. These values are found in t = 10–90 yr in the model. It means that their brightening rates can be explained as the dispersal effect of the dust shell at such times after the cessation of dust production. However, the large brightening rate of OH 31.0−0.2, 0.331 ± 0.063 mag yr⁻¹, is difficult to explain with this interpretation. Such a value is attained only at t ≲ 8 yr as indicated by the thick line in Figure 8, which appears inconsistent given that this object was recognized as a nonvariable OH/IR star by Herman & Habing (1985), which is more than 10 yr earlier than 2MASS observations.

One possible cause of this large brightening rate is a large A_K,c(0) (i.e., very optically thick dust shell). As shown in Equation (7), the absolute value of the brightening rate is proportional to A_K,c(0). Therefore, a very optically thick dust shell with a large A_K,c(0) shows a large brightening rate in each elapsed time, and the time range showing a brightening rate can be delayed. To obtain the elapsed time showing the large brightening rate of OH 31.0−0.2 (3–8 yr with A_K,c(0) = 10 mag) to >10 yr, we have to assume an extremely high A_K,c(0) of ∼20 mag. Such a high A_K,c(0) corresponds to a very large τ_9.7 of ∼40, and this scenario does not seem to be plausible. Therefore, the large brightening rate of OH 31.0−0.2 implies other mechanisms, rather than the dispersal of the dust shell.

5.3. Rate of Color Change

Based on Equations (7) and (10), we can calculate the rate of color change by additionally assuming the wavelength power-law index p. The index p depends on the dust model, and various dust models are proposed for oxygen-rich AGB stars (Draine & Lee 1984; David & Papoular 1990; Ossenkopf et al. 1992; Suh 1999). They are well summarized in Figure 1 in the paper presented by Suh (1999). Their power-law indices in the NIR are −0.7 to −1.5, and if we assume p = −0.7, the rate of color change is calculated as shown with the solid and dashed lines in Figure 9.

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Based on Figure 8, the elapsed time since the cessation of dust production for the three targets whose NIR colors were observed is 40–90 yr depending on the assumption of t_cross. In this range, the NIR color becomes slightly bluer, according to Figure 9, as the dust shell continues to disperse. The expected rates of color change can be calculated from the observed K-band brightening rates based on Equation (10) independently from the assumption of A_K,c(0) and t_cross. If we assume p = −0.7, the rates of change in the (H − K) and (J − K) colors for the three objects are calculated to be −0.0036 to −0.0038 and −0.0086 to −0.0088 mag yr⁻¹, respectively. These values are shown by the gray regions in Figure 9. We can see that the observed values are greater than expected, indicating that these OH/IR stars did not become bluer as expected.

The difference between the observed and expected values of the rate of change in (J − K) color corresponds to the difference of the observed J-band brightening rate and the K-band brightening rate scaled by (λ_J/λ_K)^p, where λ_J and λ_K are the wavelengths of the J and K bands, respectively. Therefore, we evaluate the deviation of the rates of color change by calculating the significance of the difference between the J-band brightening rate and the scaled K-band brightening rate (for (H − K) color, use H instead of J).

OH 25.1−0.3 shows a positive rate of change in (H − K) color, which deviates from the expected value with 1.1σ, while in (J − K), it does not show a significant deviation. OH 77.9+0.2 shows a positive rate of (J − K) color change which deviates from the expectation with 1.9σ significance, while it shows no significant deviation in the rate of (H − K) color change. The rates of change of OH 53.6−0.2 are greater than the expected value with significances of 1.9σ and 2.9σ in the (H − K) and (J − K) colors, respectively. This means that OH 53.6−0.2 significantly became redder than expected.

Based on these results, nonvariable OH/IR stars do not seem to have become bluer as expected: some of them seem to have become redder even. At least, OH 53.6−0.2 clearly shows positive rates, and the observed reddening is difficult to explain with the dispersing dust shell model. These results depend on the assumption of p. However, even if we decrease p to −1.5, to the end of the p range, the discrepancy between the observations and the model becomes more pronounced. Therefore, we need to consider other mechanisms rather than the dispersing of the circumstellar dust shell.

5.4. Possibilities beyond the Simple Model

5.5. Relation with the Stellar Evolution

5.6. Future Investigations

We investigated the long-term brightness evolution of 16 nonvariable OH/IR stars (Herman & Habing 1985). Based on the infrared images taken with 2MASS and SST/IRAC, their precise positions on the sky were determined. Their recent NIR magnitudes were looked up in the UKIDSS-GPS and OAOWFC data. As a result, multiepoch data were established for seven objects. However, for one object (OH 51.8−0.2), we were unable to determine the time evolution of its brightness.

All of the remaining six objects appeared to have brightened in a few thousand days. Their K-band brightening rate ranges from 0.010 to 0.331 mag yr⁻¹. The observed K-band brightening is basically explained with a simple model of a dispersing dust shell with typical parameters of OH/IR stars. However, the largest brightening rate, 0.331 mag yr⁻¹, is difficult to explain with this model. This large brightening rate implies the presence of other mechanisms.

For three of the six objects, OH 25.1−0.3, OH 53.6−0.2, and OH 77.9+0.2, we examined the long-term brightness evolution for more than one band. None of these three objects appeared to have become bluer, and among the three objects, OH 53.6−0.2 was significantly confirmed to have been reddened. This color change is contrary to the expectation from the dispersal of the dust shell and requires to consider other mechanisms.

An increase of the dust emission could explain both observed phenomena simultaneously. One possible mechanism is an increase of the stellar temperature, which is expected to occur in the transition from the AGB phase to the post-AGB phase. Another possibility is an increase of the stellar luminosity or new dust production which can happen with the fast stellar expansion in the thermal pulse cycles during the AGB phase. To explain the observed reddening, a reduction of the stellar temperature was also proposed.

To understand the cause of the observed variabilities, further investigations in theoretical calculations and observations are needed. Such studies will lead to a better understanding of the evolutionary states of nonvariable OH/IR stars and the evolution of AGB stars.

This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. This research has made use of the NASA/IPAC Infrared Science Archive, which is funded by the National Aeronautics and Space Administration and operated by the California Institute of Technology. This research made use of the SIMBAD database, operated at CDS, Strasbourg, France. This research made use of the cross-match service provided by CDS, Strasbourg.

Facilities: IRSA - , Spitzer - , CTIO:2MASS - , FLWO:2MASS - , UKIRT - , OAO:0.91 m. -

Software: SExtractor (Bertin & Arnouts 1996), IRSA, IRSA viewer, SIMBAD (Wenger et al. 2000), VizieR, CDS X-match.

To further validate the time evolution of the NIR magnitudes of several OH/IR stars found in Section 4, we examine the systematic errors in the various methods of photometry employed and residual calibration errors.

A.1. 2MASS Data

A.2. UKIDSS Data

The UKIDSS magnitudes are measured based on the aperture photometry with various aperture radii. The aperture-photometry-based magnitudes are given as AperMag[1–13] measured with aperture diameters of 1'', $\sqrt{2}$'', 2'', $2\sqrt{2}$'', 4'', $4\sqrt{2}$'', 8''... (Irwin et al. 2004; Lucas et al. 2008). The default magnitude, AperMag3, is measured with a 2'' diameter aperture. To check the validity of AperMag3, we examine the aperture-diameter dependence of the measured magnitudes.

Figure A1 shows the aperture-size dependence of the measured magnitudes. A smaller aperture setting can give more reliable magnitudes of sources in crowded regions. However, if the source has a radial profile thicker than a PSF because of some causes such as seeing and intrinsic diffuse emissions, a small aperture setting can result in underestimating the source brightness. In such a case, the aperture-size dependence will show an increasing trend. On the other hand, a large aperture setting can lead to unstable measurement of the source brightness, because it is easily affected by contamination from surrounding stars and the poorly estimated sky background. Therefore, reliable magnitudes are thought to be in between these two cases, and such a region will appear as a plateau region in Figure A1.

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In the case of OH 25.1−0.3, the default magnitude is on the plateau in all bands and seems to be reliable as the source brightness. However, for OH 53.6−0.2 and OH 77.9+0.2, the default magnitude is not on the plateau, and the magnitudes measured with larger apertures may be better for the total source brightness. If we employ the magnitudes measured with larger apertures, the source brightness increases by 0.1–0.3 mag, and the brightening since the 2MASS era will be more significant. In the case of OH 15.7+0.8, the default magnitude for the first UKIDSS observation is on the plateau. As for the second observation, the magnitudes measured with apertures larger than the default are unstable. Therefore, the default magnitude seems to be good as the source magnitude. OH 31.0−0.2 shows decreasing trends with increasing aperture diameter in both data, and magnitudes measured with smaller apertures seem to be reliable. If we use the magnitudes measured with aperture diameters of 1'' and $\sqrt{2}^{\prime\prime}$, the source will get brighter by 0.6–0.7 and 0.06–0.07 mag in the first and second data, respectively. In the case of OH 37.1−0.8, the default magnitude is at the plateau in the second data, but in the first data, it is at the edge of the plateau. The magnitudes measured with aperture diameters larger than 4'' are unstable. Therefore, the magnitude measured with an aperture diameter of $2\sqrt{2}^{\prime\prime}$ seems to be most reliable, but it is consistent with the default magnitude within the error.

The magnitude differences between two UKIDSS K-band observations are almost independent of the aperture settings. However, as for the case of OH 31.0−0.2, the magnitude difference between the two UKIDSS observations may be overestimated when using the default magnitudes. If we employ the magnitudes measured with smaller apertures, the magnitude difference between the two UKIDSS observations decreases by ∼0.6 mag, but the difference (brightening) is still significant. This correction also decreases the brightening rate of OH 31.0−0.2 to 0.23 mag yr⁻¹. This value still requires a short elapsed time of ≲11 yr since the cessation of dust production, which is difficult to explain with the dispersal of the dust shell as discussed in Section 5.2. Therefore, this correction does not change the conclusion that OH 31.0−0.2 is showing a very fast brightening, which cannot be explained with the dispersal of the dust shell.

The magnitude differences between two UKIDSS K-band observations of the surrounding objects are shown in Figure A2 to examine the systematic errors between the magnitude difference and object brightness. To examine the local systematic errors, we select objects within 3' from the target OH/IR stars and compute the average and standard deviation of the magnitude difference for each 1 mag bin (Figure A2). The data for the nonvariable OH/IR stars are also shown by black diamonds, and we find that the observed magnitude differences of our targets significantly deviate from the average. Therefore, we conclude that the brightening observed between two UKIDSS observations is real even if the systematic errors are considered.

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A.3. 2MASS–UKIDSS Difference

The systematic difference between the 2MASS and WFCAM systems is corrected by the system conversion as described in Section 3. However, there can be a residual systematic difference that cannot be corrected with the system conversion. To assess such a residual systematic error, we examine the magnitude differences between the 2MASS and UKIDSS observations.

Figures A3 and A4 show the magnitude difference plotted against 2MASS magnitudes and 2MASS colors, respectively. Gray dots represent the data corresponding to objects within 3' from the target. To reduce the degree of data scatter, data with 2MASS photometric errors of >0.2 mag are removed. In Figure A4, only bright objects are plotted: the magnitude threshold is set to 14, 15, and 15 mag for OH 25.1−0.3, OH 53.6−0.2, and OH 77.9+0.2, respectively. The difference is calculated after converting the 2MASS magnitudes to the WFCAM photometric system. The average and standard deviation are calculated in each 1 mag bin in the horizontal direction, and the 1σ, 2σ, and 3σ regions are indicated by the solid, dotted, and dashed–dotted lines in each panel. In the K-band plot for OH 77.9+0.2 in Figure A4, the average and standard deviation of the magnitude difference are calculated in a 2 mag color bin because of the small number of samples.

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For OH 25.1−0.3, systematic trends with a positive slope are seen in all bands in Figure A3. The magnitude difference in the K band slightly deviates from the systematic trend, while those in the J and H bands are not significant. The average magnitude differences in the bins containing the target are −0.039, −0.043, and 0.028 mag in the J, H, and K bands, respectively. These are within the systematic calibration error expected from the systematic uncertainties of 2MASS and UKIDSS observations. The color dependence of the magnitude difference is not significant. If we correct the measured systematic errors, the brightening in the J and H bands becomes insignificant, while that in the K band increases by ∼20%. The color changes also get more significant.

In the plots for OH 53.6−0.2, the data show flat patterns in the range around the target position in both Figures A3 and A4. OH 53.6−0.2 shows deviation from the trend in all bands, especially in the K band. The absolute values of the mean magnitude differences in the bins where the target is contained are 0.004–0.039 and are in the range expected from calibration errors. Because this kind of error is already taken into account, we do not need extra correction for these offsets.

The plots for OH 77.9+0.2 also show flat patterns around the target position in both Figures A3 and A4, and the data of OH 77.9+0.2 significantly deviate from the trends seen in the surrounding stars. However, in Figure A3, faint stars show slightly large offsets in the J band. In the bin containing the target, the average magnitude difference is 0.072 mag in the J band. This is a large value to explain with the systematic uncertainties of the 2MASS and UKIDSS observations, while other bands show only small differences. By correcting the large offset in the J band, the brightening of OH 77.9+0.2 in the J band increases by a factor of 1.7, and the rate of change in the (J − K) color changes to −0.001 ± 0.007 mag yr⁻¹. Even if this correction is applied, the result that OH 77.9+0.2 does not show a significant color change is not affected.

Based on the discussion above, the findings of this work, the K-band brightening and the absence of the expected bluing, are not affected by the possible residual systematic errors.

A.4. OAOWFC Data

To assess the systematic errors of the OAOWFC data, we examine the light curve of the reference stars in detail. Figure A5 shows the close-up plots of the light curves. The dashed lines are the average magnitudes calculated from the 2MASS and UKIDSS observations.

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The standard deviations of the OAOWFC data are 2%–3% and consistent with the measurement errors shown with the error bars in the bottom panels of Figure A5. It means that the photometric measurements and error evaluation of the OAOWFC data are properly performed.

The 2MASS and UKIDSS data are distributed within ±3%–4% around the average magnitudes. This is reasonable based on the systematic uncertainties of 2MASS and UKIDSS data of 2%–3%. The typical deviations of the OAOWFC data from the average magnitudes are ∼3% as seen in Figure A5. In addition, the OAOWFC data seem to show slightly fainter magnitudes than the average. This tendency can be the reason for the magnitude difference between the OAOWFC observations and the 2MASS–UKIDSS trend seen in Figure 6. We do not further investigate the cause of this systematic error because it is out of the scope of this study, but if we correct this systematic error, the brightening of the target objects becomes more significant.

Finally, the light curve of the reference star for OH 25.1−0.3 does not show periodic variabilities unlike OH 25.1−0.3. This means that the periodic variability seen in the light curve of OH 25.1−0.3 can be a real variability. Because the number of observations is small, continuous and dense monitoring observations are required to validate the variability.