Long-term 4.6$\mu$m Variability in Brown Dwarfs and a New Technique for Identifying Brown Dwarf Binary Candidates

The photometry used in this work is derived from the Spitzer observations (IRSA 2022) used to compute the trigonometric parallaxes of 361 L, T, and Y dwarfs in Kirkpatrick et al. (2021), covering a long time baseline (Figure 1). This long time baseline, spanning upwards of seventeen years, provides an excellent dataset with which to study brown dwarfs at their peak wavelengths over a timescale that has never been explored before. The photometry comes from Spitzer’s Infrared Array Camera (hereafter, Spitzer/IRAC; Fazio et al. 2004), which, during the cryogenic mission, was capable of observing at ch1 ($\sim$3.6$\mu$m), ch2 ($\sim$4.6$\mu$m), ch3 ($\sim$5.8$\mu$m), and ch4 ($\sim$8.0$\mu$m) bands (Werner et al. 2004). Of these four, the one that was used is Spitzer ch2, as this is the band in which brown dwarfs are brightest (Mainzer et al. 2011).

Spitzer’s cryogenic mission observed only 14 of the 361 objects in our sample. However, every object includes Spitzer warm mission ch2 data, and most have a time baseline of >10 years.

The spectral type distribution for these 361 brown dwarfs is seen in Figure 2. These spectral types come from Kirkpatrick et al. (2021) where objects that have optical and infrared spectra are marked as “SpecO/SpecIR” and objects that have spectral classifications based on colors are marked with “SpecAd”.

Most objects are at distances <20pc, which makes them the brightest members of their class. Hence, the photometric uncertainties will be as low as possible, allowing us the best chance to detect variability for these classes. Moreover, the majority of these objects were observed for several years and multiple times a year, meaning that each object will have an abundance of data points.

Figure 3a shows the number of Astronomical Observation Requests (hereafter, AOR), N_spitzer, for all 361 objects. Most objects have 6-16 AORs. However, many objects have >16 AORs and these will have the most data-rich light curves.

To provide additional 4.6$\mu$m data, NASA’s Wide-field Infrared Survey Explorer (hereafter, WISE; Wright et al. 2010) and Near-Earth Object WISE (hereafter, NEOWISE; Mainzer et al. 2011) W2 photometry was considered. As Figure 15 of Kirkpatrick et al. (2021) shows, Spitzer ch2 and WISE W2 filter bandpasses for brown dwarfs can be interchanged. WISE data were obtained by cross-matching our objects with the unTimely Catalog (Meisner et al. 2022), which contains detections from WISE/NEOWISE W2 coadds. The unTimely Catalog contains time-series W1 and W2 photometry from the beginning of the WISE mission to the most current publicly released NEOWISE data. The WISE and NEOWISE timescales can be seen at the top of Figure 1. The unTimely Catalog also contains W1 photometry over multiple epochs; this photometry could be explored for variability in future research.

Figure 3a shows the distribution of the number of unTimely detections, N_WISE, per object. There is much less variation compared to N_spitzer as a result of WISE/NEOWISE covering the whole sky every six months. Theoretically, every object should have 16 unTimely detections for each of the 16 sky passes made from classic WISE up through NEOWISE year 7. However, some objects have N_WISE values of <16 because of background contamination problems. Due to the fact that the WISE spacecraft precesses, some objects will have N_WISE values of 17 because in NEOWISE year 7 a portion of the sky already has its 17th coverage. The distribution of the number of points per object, combining N_spitzer and N_WISE, can be seen in Figure 3b. Figure 4 displays the distribution for each photometry measurement per magnitude interval. Lastly, Figure 5 shows the distribution of Spitzer and unTimely points per MJD interval. We can see that the number of points per unit time increases with time.

For some of the 361 objects, a trend is seen when comparing ch2_aperture to ch2_PRF. Specifically, all the PRF points are dimmer than the aperture measurements. Of 361 objects, 126 (35$\%$) show this effect. A possibility is that a blended secondary component, which is being appropriately measured in the aperture’s radius, causes a poor PRF fit measuring only the primary component. (The unTimely data were not used in this test because there is only a PSF fit with no corresponding aperture measurement.)

The 126 objects showing this trend have been divided into four different classes:

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  Class 0: Includes only those objects for which passive deblending in the Spitzer PRF-fit photometry was triggered 100$\%$ of the time and N_spitzer is >5 (for statistical robustness). This class includes 16 objects.

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  Class 1: Includes objects for which $\tilde{ch2}_{aperture}+\sigma_{\tilde{ch2}_{aperture}}$ < $\tilde{ch2}_{PRF}-\sigma_{\tilde{ch2}_{PRF}}$ and the three rules below apply. This class includes 11 objects.

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  Class 2: Includes objects for which $\tilde{ch2}_{aperture}$ < $\tilde{ch2}_{PRF}-\sigma_{\tilde{ch2}_{PRF}}$ and the three rules below apply. This class includes 35 objects.

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  Class 3: Includes objects for which the Class 1 and 2 restriction on $\tilde{ch2}_{aperture}$ do not apply, but the three rules below are still met. This class includes 64 objects.

For an object to fall in Class 1-3, it must have the following three characteristics:

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  Spitzer aperture magnitude brighter than its PRF-fit magnitude at every epoch.

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  N_spitzer >5 (again for statistical robustness)

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  Passive deblending must have been triggered less than 100$\%$ of the time.

The subplots in Figure 8 show examples of Classes 1, 2, and 3.

These four classes were considered for binary candidacy because a possible secondary could be affecting the flux measurements. This method has the potential to discover physical brown dwarf binaries with the components having the same distance, metallicity, and age. Figure 9 shows various imaging of WISE J022623.98$-$021142.8 (Kirkpatrick et al. 2011), which is known to have a secondary component. We see that the binary is clearly separated in $Keck$/NIRC2 $J$ (top panel; Gelino 2012), while in Spitzer/IRAC ch2 (middle panel; Kirkpatrick et al. 2021) and WISE/unTimely W2 (bottom panel; Meisner et al. 2022) it is blended. Note that the secondary is significantly redder in $J-$ch2 than the primary. Kirkpatrick et al. (2021) shows that for objects later than T5, the J$-$ch2 color quickly changes towards very large values. Figure 14d of the same paper shows that the decrease of M_ch2 with spectral type is less drastic. One can imagine a system like WISE J022623.98$-$021142.8 for which the secondary is even colder. In this case, the ground-based $J-$band image might not have the sensitivity to detect the companion, but at the 4.6$\mu$m wavelength of Spitzer, the presence of the companion could be detected. Thus, this technique has the potential to identify new binaries in which the companion objects are too low in temperature to be found in ground-based, $J-$band follow-up. Additionally, it also provides a priority target list of nearby brown dwarfs that may not yet have seen any high-resolution imaging follow-up. For example, if a late-T or early-Y dwarf has a secondary candidate around it, there is a possibility it would be the first ever mid-late Y dwarf found.

For Figure 6, which compares ch2_PRF and W2_PSF, we find that all the outliers were marked as Class 0. As illustrated in Figure 9, the poorer resolution of the WISE data blends the secondary more thoroughly with the primary, meaning that the WISE PSF fit is more successful at capturing the light of both components. In Figure 7, all but one outlier (mentioned in the caption) are identified as Class 1. This is because Class 1 objects are blended enough that a single PRF fit, though still poor, is not bad enough to trigger passive deblending, which would have made them Class 0 objects. Note that Classes 1-3 are numbered this way in order of the severity of the difference between the aperture and PRF-fit measurements. Class 0’s name results from its being a unique class compared to the rest.

The spectral energy distributions of subdwarfs show drastic differences compared to normal dwarfs within the wavelength ranges where they have been observed (Lodieu et al. 2019). Subdwarfs are the metal-poor counterparts to normal metallicity brown dwarfs (Lépine et al. 2003). This could affect how the point source looks on the detector. If there are large absorption bands in ch2/W2 that are drastically altering the effective wavelength through this bandpass, it would, because of the wavelength dependence of the MOPEX FWHM, change the full width half maximum value of the PRF. This difference between the expected PRF fit and the true PRF fit of a subdwarf would result in a high $\chi^{2}$ value. This is partly supported by the fact that one object in Class 3, 2MASS J06453153$-$6646120 (Kirkpatrick et al. 2010), is an L subdwarf. We have compared a “LOWZ”³³3https://doi.org/10.7910/DVN/SJRXUO (Meisner et al. 2021) spectral model of Z=$-$1.5 and T_eff=1300K to a solar-metallicity model at the same temperature. For the low-metallicity model, there is relatively more flux in the blue half of the W2 band compared to the solar-metallicity model. Based on this effect, we would expect a small change in the PRF width for the low-metallicity object, likely not large enough to support the hypothesis above. However, the models at these low-metallicities are completely untested in this wavelength regime. This effect can not be currently quantified because of the lack of observational spectra for subdwarfs at 4.6$\mu$m. Further data, particularly from JWST (Gardner et al. 2006), will be needed to test this hypothesis. Nonetheless, as subdwarfs are rare in a volume-limited census, it is unlikely that this effect is the cause for any other aperture/PRF discrepancies within our sample.

To better understand Classes 0, 1, 2, and 3, we made finder charts for each object that include images from the Digitized Sky Survey 1 and 2 $B$, $R$, and $IR$; the Pan-STARRS1 survey $g$, $r$, $i$, $z$, $y$; the UKIRT Infrared Deep Sky Survey $J$, $H$, and $K$ (Lawrence et al. 2007); the UKIRT Hemisphere Survey $J$ (Dye et al. 2018); the VISTA Hemisphere Survey $J$ and $K_{s}$ (McMahon et al. 2021); the Two Micron All Sky Survey $J$, $H$, and $K_{s}$ (Skrutskie et al. 2006); and WISE W1, W2, W3, and W4. These finder charts span a long time baseline and show the background sky at different epochs to see if our target was contaminated by a distant source at the Spitzer epochs. We also did a literature search for each object to check for binaries or subdwarfs. This led to the creation of 4 different subclasses: contaminated objects (C), potential binaries (P), known binaries (K), and subdwarfs (S).

Once the finder charts were made, it was then possible to search for an estimate of a true and false positive rate for the binary candidates. Although the finder charts provide a starting point for accessing false positives, high-resolution imaging is needed for more fully computing both the true and false positive rates.

To estimate a true positive rate, we searched two high-resolution archives and the literature for known binaries in classes 0 through 3. We searched papers in SIMBAD (Wenger et al., 2000) to find published binary systems. The two high-resolution archives we selected are the Keck Observatory Archive (hereafter, KOA; https://koa.ipac.caltech.edu) and the Hubble Space Telescope/NICMOS image archive studied in Factor & Kraus (2022). The known binary systems found, 12 in total, are listed in Table 5. Comparing this to our K+P+S lists of 72 objects we find an estimated true positive rate of $\sim$17$\%$. The true positive rate is likely higher because there are other high-resolution archives that could be searched, and there are some objects that have yet to be observed at high-resolution. This exercise is left for a future paper.

For some of our objects, a real false positive rate is impossible without high-resolution images at the same wavelengths as our Spitzer observations, 4.6$\mu$m. Consider a binary T8 (the most abundant spectral type in our sample) and Y1 at a distance of 10pc. Using Figures 16(a) and 16(d) from Kirkpatrick et al. (2021), we find apparent J magnitudes of $\sim$18 mag for the T8 and $\sim$24 mag for the Y1, and apparent ch2 magnitudes of $\sim$13.5 mag for the T8 and $\sim$16 mag for the Y1. These values of $\Delta$J$\approx$6 mag and J$\approx$24 mag would make the secondary difficult/impossible to image, even with adaptive-optics imaging from the ground (Davies & Kasper 2012 and Zhang et al. 2021). However, values of $\Delta$ch2$\approx$2.5 mag and ch2$\approx$16 mag are much easier with Spitzer or JWST.

For earlier type primaries however, a false positive rate can be attempted because observations at $\sim$1$\mu$m can provide a $\Delta$ magnitude sufficient to rule out most secondaries detectable with our technique. Figure 4 of Gelino et al. (2011) shows the contrast ratios achievable for typical high-resolution observations for brown dwarf binary pairs. These ratios depend on the separation between the two objects, the primary’s brightness, and the dynamic range available for secondary detection. The contrast ratios start to plateau at binary separations of >$0\farcs 2$. Since our ability to detect binaries is limited by the Spitzer/IRAC ch2 FWHM of $1\farcs 72$, we can assume this plateau value. It is typical for ground based and NASA/ESA Hubble Space Telescope observations to have a depth of $\sim$22mag (Lowrance et al. 2005, Burgasser et al. 2006, and the Keck NIRC2 exposure time calculator⁴⁴4https://www2.keck.hawaii.edu/inst/nirc2/nirc2_snr_eff.html). A typical contrast ratio at wide separations is $\Delta$H$\approx$4mag (Gelino et al., 2011). At our average distance of 15.9pc, an apparent magnitude of H=22mag would correspond to an absolute H magnitude of 21mag, or a spectral type of Y0 (Figure 16(b) of Kirkpatrick et al. 2021). A Y0 detection with $\Delta$H=4 mag is just achievable if the primary has a spectral type of T7.5. At primary spectral types earlier than this, a companion detectable via our Spitzer technique would likely also be detectable via ground based or Hubble Space Telescope observations.

In Table 4 the final column, labeled “High-Resolution Imaging”, indicates whether our candidate binary has high-resolution imaging observations in KOA or in Factor & Kraus (2022). There are 25 objects earlier than spectral type T7.5 with high-resolution imaging from these 2 archives. Using these data it is possible to estimate a false-positive rate. We will do this as follows. First, we compare our 25 false binaries to the total number of objects earlier than T7.5 in sub-classes K, P, and S (59) to provide a false positive rate of $\frac{25}{59}$ = 42$\%$. However, there are still 25 objects earlier than T7.5 not in Table 5 and lacking high-resolution imaging in Table 4, so this value is actually a (loose) lower bound for the false-positive rate. Second, we instead compare the same 25 false binaries to the subset of objects earlier than T7.5 with high-resolution imaging observations in Tables 4 and 5. This gives a new false-positive rate of $\frac{25}{34}$ = 74$\%$. However, this is likely an upper bound because the faintest companions to our 25 “false” binaries may not be detectable by our ground-based observations. In reality, we must wait for JWST 4.6$\mu$m imaging to calculate a real false-positive rate, as an object lacking a companion detection at J-band might yet be harboring a cold companion seen only at longer wavelengths.

Figure 10 shows the median of the standard deviation as a function of ch2/W2 magnitude in 0.5-mag intervals. If an object has variability above the line, our analysis would have detected it. For example, if an object has a magnitude of 14.2, no variability can be detected below $\sim$12mmag (1$\sigma$) for the Spitzer photometry or $\sim$60mmag (1$\sigma$) for WISE photometry. Points 1 and 2 are known variable objects 2MASS J21392676+0220226 and 2MASS J22282889$-$4310262 (Yang et al. 2016), respectively (not included in this study). Number 1 and 2 can be seen to be well above all three lines, which indicates that variability could be found in the unTimely photometry and easily detected in our Spitzer photometry. Specifically, for 2MASS J21392676+0220226 we were able to find 14.5$\%$ variations in the unTimely W2 photometry, which is different from what is seen in Yang et al. (2016) which found Spitzer ch2 peak-to-peak variations of 26$\%$. Furthermore, this plot indicates that the unTimely data will only detect variability if it has relatively large amplitude, while the Spitzer data should be able to detect much smaller variations. If we instead looked at the magnitude percentage variations, we are sensitive to variability of >4$\%$ at 11.5 mag and >13$\%$ at 16 mag, for the unTimely photometry.

This study has shown no variability in brown dwarfs at $\sim$4.6$\mu$m over a time period of >10 years to the sensitivity limits shown in Figure 10. The large-scale variability to which our survey is sensitive has only been seen in a small number of published objects. This illustrates that large-amplitude variability is rare among brown dwarfs. At smaller amplitudes, however, Yang et al. (2016)) found an increase in the percentage of objects with variability near the L/T transition compared to those in the T/Y transition. Figure 2 shows that we have excellent statistics at the T/Y transition, yet we find no large-amplitude variability there.

Brown dwarf binaries are rare and hard to find. Two common ways to find brown dwarf binaries are obtaining a spectrum of a clear spectral composite object (Bardalez Gagliuffi et al. 2014) or visually separating the components via imaging. Our Aperture-PRF technique provides a new way of finding these binaries, in much the same way that the PRF technique alone, through passive deblending, has previously been used to find secondary components (e.g., in circumstellar disks; Martinez & Kraus 2019).

We now compare the MOPEX FWHM of Spitzer to the average separation of known nearby brown dwarf binaries, to test our binary hypothesis. The MOPEX FWHM of Spitzer is $1\farcs 72$ at ch2 (4.6$\mu$m). Figure 2 of Burgasser et al. (2007) shows that the average brown dwarf binary has a physical separation between $\sim$3 $-$ 10 AU. When considering the average distance for our 361 objects is 15.9pc, this leads to an expected separation between $0\farcs 19$ $-$ $0\farcs 63$. The distribution of the 361 objects angular separation based on distance assuming 3 and 10AU binary separation can be seen in Figure 11. We see that the objects clump around the predicted separations. However, there are a few objects that are outside of this separation, indicating that they could be angularly separated in the Spitzer photometry. Objects of Class 0 must have separation >$1\farcs 72$ in order for the code to passively deblend the object into two different PRF fits. This separation means that Class 0 is very unlikely to have physical binaries. Objects of Class 1, 2, and 3 are only marginally resolved or are within the MOPEX FWHM, meaning that Class 1-3 are the ones most likely to have hidden, faint secondaries.

In Table LABEL:table_2 we show how many objects fall in each class and subclass as defined in §6.1 and §6.3. Details of all 126 objects can be found in Tables 3, 4, and 5. There was only one subdwarf found in this process, 2MASS J06453153$-$6646120, listed in Table 5 with the known binaries.

We compare known binary/contaminated statistics below for each class:

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  Class 0: Only 1 known binary was found. Most known brown dwarf binaries have separation smaller than the separations at which passive deblending ($1\farcs 33$ to $7\farcs 67$) would take place. Contamination by background objects is the highest among all four classes ($\frac{10}{16}$ = 63$\%$).

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  Class 1: This is the highest percentage of known binaries of all four groups ($\frac{3}{11}$ = 27$\%$). The true binaries in this class are likely to have the smallest $\Delta$mag and/or largest separations, because they have the most discrepant aperture and PRF-fit measurements. Class 1 also has a significant percentage of background contamination ($\frac{3}{11}$ = 27$\%$).

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  Class 2: This class has a much smaller percentage of known binaries ($\frac{3}{35}$ = 9$\%$). True binaries here will likely have slightly larger $\Delta$mag and smaller separations. Contamination by background objects is high ($\frac{18}{35}$ = 51$\%$).

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  Class 3: This class has the smallest percentage of known binaries ($\frac{5}{64}$ = 8$\%$) and sizable percentage of background contamination ($\frac{23}{64}$ = 36$\%$). Given the smaller difference between aperture and PRF-fit measures, this group is likely to have more spurious binaries than the other classes, but could also have binaries with the tightest separation and/or largest $\Delta$mags.