A SEARCH FOR A DISTANT COMPANION TO THE SUN WITH THE WIDE-FIELD INFRARED SURVEY EXPLORER^*

Beyond the orbit of Neptune, the solar system is known to contain multiple populations of small, icy bodies that extend out to ∼100, 000 AU (Edgeworth 1949; Oort 1950; Kuiper 1951; Jewitt & Luu 1993). It has been speculated that a gas giant planet or a brown dwarf might also reside in the outer solar system. A variety of observations have been cited over the past century as indirect evidence for such an object. For instance, a possible periodicity in mass extinctions has been interpreted as the orbital period of a distant companion that perturbs comets in the Oort cloud during perihelion (a ∼ 100, 000 AU, Davis et al. 1984; Whitmire & Jackson 1984). More recently, an anomaly in the orbits of outer Oort cloud comets has been attributed to a 1–4 M_Jup object in a somewhat smaller orbit (a ∼ 10, 000–30,000 AU, Matese et al. 1999; Matese & Whitmire 2011). Some aspects of these scenarios have been questioned, such as the stability of very wide orbits (Torbett & Smoluchowski 1984) and the evidence of an extinction periodicity (Feng & Bailer-Jones 2013). Nevertheless, given that substellar companions have been found at separations of >1000 AU from a few nearby stars (Burgasser et al. 2000; Scholz et al. 2003; Luhman et al. 2011), the presence of a similar body in the outer solar system is plausible.

To search for a new member of the solar system, one can seek a detection in either reflected sunlight at optical wavelengths or thermal radiation at infrared (IR) wavelengths. The former has a steeper dependence on distance from the Sun (r⁻⁴) but a shallower dependence on mass. As a result, reflected light is generally easier to detect in the inner solar system, unless a body has a low albedo or a large mass (and hence a high temperature). At greater distances from the Sun, thermal radiation dominates for an increasing range of masses until eventually becoming the only option for detection. Jupiter and the largest trans-Neptunian objects (TNOs) span ∼10 mag in the brightness of their reflected light at a given distance, which corresponds to a range of only a factor of ∼10 in the distance limits. For instance, recent reflected light surveys have reached 100–200 AU for TNOs and 1000–2000 AU for gas giants (Trujillo & Brown 2003; Elliot et al. 2005; Larsen et al. 2007; Schwamb et al. 2010; Sheppard et al. 2011). At the outer limit of 2000 AU for those surveys, the Infrared Astronomical Satellite (IRAS) and the Two Micron All-Sky Survey (2MASS; Skrutskie et al. 2006) were capable of detecting the thermal emission of brown dwarfs with masses as low as ∼3 and 6 M_Jup, respectively (Burrows et al. 1997). It is likely that the IRAS and 2MASS databases have been thoroughly searched for a distant companion to the Sun, although detailed descriptions of such analysis have not been published.

Because of the combination of its mid-IR sensitivity and all-sky coverage, the Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) offers the best available constraints on the presence of a large body in the outer solar system, reaching masses that are an order of magnitude lower than the limits from 2MASS and IRAS. In addition, the multiple epochs of images collected by WISE are perfectly timed for the detection of parallactic motion, providing a discriminating means of identifying a solar companion. This paper presents the results of a search of the WISE database for objects exhibiting this signature. It begins with descriptions of the WISE mission (Section 2) and my search strategy and data processing (Sections 3 and 4). I then evaluate candidate moving objects (Sections 5 and 6) and characterize the resulting constraints on the presence of a distant companion to the Sun (Section 7).

A full description of WISE has been provided by Wright et al. (2010). I summarize the aspects of the mission that are relevant to this study.

WISE collected images in four bands that were centered at 3.4, 4.6, 12, and 22 μm, which are denoted as W1, W2, W3, and W4. The angular resolution was ∼6'' in the first three bands and ∼12'' in W4. The satellite was stationed in a Sun synchronous orbit with a period of 95 minutes. The telescope was pointed at 90° solar elongation, scanning great circles centered on the Sun during its orbit. A 47' × 47' field was observed simultaneously in all operable bands. At intervals of 11 s, one 8.8 s exposure was obtained in each band at a fixed position on the sky. Adjacent images during an orbit overlapped by 10%. The scans from adjacent orbits overlapped by 90%–100% at ecliptic latitudes of 0°–90°, respectively. As a result, the number of images at a given position and band ranged from 12 near the ecliptic plane to hundreds near the ecliptic poles, and consecutive images of most positions were separated by the 95 minute orbital period. The sky was fully mapped after 6 months of observations. WISE operated from 2010 January 7 to 2011 February 1, completing two maps of the sky and beginning a third one. Images were obtained through all four bands during the first 7 months of the mission, which is known as the 4-Band Cryo phase. Because of the successive exhaustion of its outer and inner cryogen tanks, observations were performed through W1, W2, and W3 from 2010 August 6 to 2010 September 29 (3-Band Cryo) and through W1 and W2 for the remaining 4 months of the mission (NEOWISE Post-Cryo; Mainzer et al. 2011).

WISE has produced images and source catalogs as its data products (Cutri et al. 2012a, 2012b). The images consist of the single exposures from each of the three phases and coadditions of the single exposures from the 4-Band Cryo and 3-Band Cryo phases, which are known as the Atlas images. Sources detected in the Atlas images are tabulated in the All-Sky Source Catalog and the 3-Band Cryo Source Working Database, respectively. Sources from the single exposures are provided in the All-Sky Single Exposure (L1b) Source Table, the 3-Band Cryo Single Exposure (L1b) Source Table, and the Post-Cryo Single Exposure (L1b) Source Table. In areas of sky that are unconfused and near the ecliptic plane, the images from WISE typically achieved a signal-to-noise ratio (S/N) of 5 at W1 = 16.8, W2 = 15.6, W3 = 11.3, and W4 = 8.0. The sensitivity was better at higher ecliptic latitudes because of the larger number of exposures. The typical astrometric precision was 04 at S/N = 20.

If the Sun has a distant companion, it probably has a spectral type of late T or later given the detection limits from previous all-sky surveys (Section 7). If such an object has been detected by WISE, it is likely that it would be found during the photometric searches for T and Y dwarfs in the solar neighborhood (Cushing et al. 2011; Kirkpatrick et al. 2011, 2012). However, it could be missed by those surveys if it has unusual colors. In addition, if a solar companion is in the portion of sky that was mapped twice during the 4-Band Cryo phase, it could have a large enough parallactic motion that it appears elongated or has a degraded S/N in the 4-Band Cryo Atlas images, which are the source of the All-Sky Source Catalog that has been used in the photometric surveys. To avoid these possible obstacles, I have performed a search that is based on parallactic motion instead of colors. This analysis also is capable of uncovering a companion that has been detected in previous all-sky surveys like 2MASS but has been overlooked.

WISE mapped each position in the sky 2–3 times at intervals of ∼6 months. Because of the timing of those observations, they capture nearly the full amplitude of parallactic motion. For distances of 1000–100,000 AU, a solar companion should move 20''–002 from orbital motion and 400''–4'' from parallactic motion during a 6 month period between WISE observations. Thus, the motion of a companion should be dominated by parallax, and it should be easily detected given the astrometric precision of WISE data. Although the goal of this study is the measurement of such parallactic motion, my analysis is also capable of detecting the large proper motions of members of the solar neighborhood, as demonstrated by the discovery of the nearby binary brown dwarf WISE J104915.57−531906.1 (hereafter WISE 1049−5319, Luhman 2013).

4.1. Catalog of Single- and Multi-epoch Objects

4.2. Comparison to WISE All-Sky Catalog

The analysis in the previous section produced a catalog that contains the mean coordinates and proper motions computed from groups of WISE single-exposure sources that are near each other on the sky. Some of these entries are based on groups of detections from multiple epochs, which typically span ∼6 or 12 months, while others are based on groups of detections at single ∼1 day epochs for which a matching group at another epoch was not present within 15. In this section, I search for high proper motion objects among the former, which should have motions of ≲ 3'' yr⁻¹.

For the initial sample of high proper motion candidates, I selected multi-epoch objects that exhibit μ/σ_μ > 5, have counterparts within 15 in the All-Sky Source Catalog, and are brighter than the threshold of W2 = 14.5 that was adopted in the previous section for this survey. To assess the completeness of this sample, I identified the counterparts of previously known high proper motion stars and brown dwarfs (e.g., Subasavage et al. 2005; Lépine & Shara 2005; Faherty et al. 2009) among the multi-epoch objects. This was also done for the sample of single-epoch objects described in the next section, which encompasses stars with μ ≳ 3'' yr⁻¹. These two samples recovered 90% of previously known objects with μ > 1'' yr⁻¹ and W2 < 14.5. Most of the 10% of stars that were not recovered (6.5%) had large astrometric errors due to saturation. The remaining stars were blended with a binary companion or a field star, rejected during construction of the catalog (e.g., cc_flag), or had uncertain proper motions (μ/σ_μ < 5).

After removing known high proper motion stars from the sample, I searched for matches within 3'' in the 2MASS Point Source Catalog for the remaining candidates. If a match was not present, the 2MASS images were inspected for a detection at either the WISE position or a location that would be consistent with the proper motion derived from the WISE astrometry. A detection in 2MASS at <3'' from the WISE coordinates implies a proper motion of ≲ 03 yr⁻¹; I rejected most of these candidates since I wish to search for objects with higher proper motions. Because a distant solar companion would have a negligible proper motion, it could appear in 2MASS near the location of the WISE detection. Therefore, when rejecting the candidates with <3'' counterparts from 2MASS, I required that μ + σ_μ < 4'' yr⁻¹, which corresponds to π ≳ 1'' for a solar companion. For the remaining unrejected candidates, I inspected the WISE Atlas images to remove extended objects, spurious detections, and blends of multiple objects, which can produce false indications of motion between epochs. The sample contained ∼1500 viable candidates at this stage. For 761 of these objects, I found detections in 2MASS that confirmed their high proper motions.

The WISE colors of the high proper motion candidates provide constraints on their nature. Spurious detections are fairly common at W3 and W4 in the WISE catalogs, which can lead to misclassifications during an analysis of the colors. Therefore, I inspected the WISE Atlas images of the candidates and removed photometric measurements for which detections were not visually apparent. In Figure 1, I plot W2 − W3 versus W1 − W2 and W2 − W3 versus W2 − W4 for the candidates that have photometry in these bands. In each diagram, the candidates form two distinct populations, one with neutral and moderately red colors and the other with much redder colors. These groups also correspond to candidates with and without 2MASS counterparts, respectively. The colors in the first group are consistent with those of main-sequence stars and brown dwarfs. Most of the candidates in the second group are probably evolved stars that are projected against extended emission or galaxies, although a few could be very cool brown dwarfs, as illustrated in Figure 1, which shows the boundary below which Kirkpatrick et al. (2011) selected candidate T and Y dwarfs. If a candidate appears above that boundary or resides in the red group of candidates in W2 − W3 versus W2 − W4, I treat it as having non-stellar colors. All of the candidates that are absent from Figure 1 (no W3 or W4) are consistent with stellar colors since W1 − W2 spans a wide range of values among stars and brown dwarfs.

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For the small number of candidates that have stellar colors and lack confirmation of their motions via 2MASS detections, I inspected images from public data archives of various observatories and wide-field surveys. All of these candidates showed evidence of extended emission or blended stars, leading to their rejection from the sample. The remaining viable candidates consist of the 761 objects with motions confirmed by 2MASS. This final sample is presented in Table 1, which contains their designations and photometry from 2MASS and WISE and proper motions measured from the combined astrometry in those surveys. In Luhman (2013), I reported the discovery of one member of this sample, WISE 1049−5319, which is a binary system whose components are near the L/T transition.

To illustrate how the candidates are distributed in magnitude and proper motion, I have plotted them in diagrams of W2 versus proper motion in Figure 2. These proper motions are based on the WISE data alone. The left panel of Figure 2 shows the sample of candidates prior to the analysis of the color–color diagrams, and the right panel shows the final sample of 761 objects. In addition to those multi-epoch candidates, a high proper motion object found through inspection of the single-epoch objects in Section 6 is also included in Figure 2 and Table 1. It is the candidate with the largest proper motion (μ ∼ 5'' yr⁻¹). The parallactic motion of a solar companion within 1 pc would appear as a motion of ≳ 4'' yr⁻¹ in these data. None of the multi-epoch candidates in Figure 2 exhibit a motion of this size, which was expected given the matching threshold of 15 for those candidates. The object from the single-epoch analysis does exceed 4'' yr⁻¹; the question of whether it could be a solar companion is discussed in Section 6.

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One of the brightest candidates in Figure 2 is WISE 1049−5319 (W2 = 7.3). It is plotted in Figure 2 with a motion of 13 yr⁻¹, which was computed from two epochs of astrometry. However, its parallactic and proper motions partially canceled each other between those epochs, and its true proper motion is larger than that value (28 yr⁻¹, Luhman 2013). A third epoch of data is available for WISE 1049−5319, but it was not matched to the other pair because the separation was greater than 15, and hence it appears as a single-epoch object in my catalog.

The single-epoch objects should contain stars with motions of μ ≳ 3'' yr⁻¹, which corresponds to parallactic motions at distances of ≲ 1.3 pc. Thus, a solar companion should appear in this sample if it was detected by WISE. As in the analysis of the multi-epoch objects, I adopted a limit of W2 ⩽ 14.5 for the single-epoch sample, which was satisfied by 4.4 million objects. Many of these sources are either spurious detections or stars that appeared at the same position in the images from different epochs but that have only one epoch in the catalog. The latter typically consist of blends of multiple sources (e.g., binary stars) and stars near the faint limit of the sample. In an attempt to remove these contaminants, I rejected single-epoch objects that have counterparts within 3'' in 2MASS. If a substellar companion to the Sun was detected by 2MASS, it could have been overlooked by surveys for nearby brown dwarfs with 2MASS photometry if its S/N was low. Therefore, I have retained single-epoch objects with 2MASS counterparts if they have S/N < 10 in all 2MASS bands. As an additional filter against stationary stars that are missing epochs in the catalog, I rejected single-epoch objects that had more than one counterpart within 1'' at a different epoch in the single-exposure catalogs. In other words, a stationary star may have single-exposure detections at all epochs, but in some epochs the number of detections is too low to result in an entry in my catalog (see Section 4.1), which can occur for components of blended stars. A single-epoch object was rejected in this way only if no other single-epoch objects were within 5'' since such a source could be responsible for a matching single-exposure detection at the other epoch. Meanwhile, I also removed single-epoch objects with <1'' single-exposure matches at a different epoch if multi-epoch objects were present within 5'' and at the same epoch as the former, which is indicative of a pair of blended stars. The sample contained ∼228,000 objects after these criteria were applied. If a solar companion or other rapidly moving source is in the initial sample of single-epoch objects, then there is a ∼1.6% probability that it would be rejected through these criteria based on their application to a sample of random positions across the sky that are not within 15 from an All-Sky source (i.e., positions that do not coincide with multi-epoch objects).

Because the entire sky was mapped during the 4-Band Cryo phase, a solar companion should appear in the data from that period if it exists and is detectable by WISE. My sample contains ∼61,000 single-epoch objects from that phase. The size of this sample could have been reduced by a factor of >100 by excluding objects that are not sufficiently red in the WISE bands to be brown dwarfs, but that was not done here so that the survey is unbiased in terms of colors. To check whether each candidate is a high proper motion object, I visually inspected all epochs of WISE images at its location. For epochs during the 4-Band Cryo phase, I used the Atlas images if a candidate's position was observed only once. If it was observed at two epochs spanning ∼6 months, the single-exposure images at each epoch were coadded separately. I employed the Atlas images for the 3-Band Cryo phase and the coadded single-exposure images for the Post-Cryo phase.

In Section 4.1, I described two scenarios in which only a subset of epochs of a moving star might be matched to form a multi-epoch object. In one case, two epochs of a solar companion that span a year are matched, but the intervening epoch is not. It is also possible that only 2/3 epochs are matched for high proper motion stars, although the two epochs must be consecutive. To search for these kinds of objects, I identified matches between single- and multi-epoch objects that had complimentary, non-overlapping epochs and had ΔW2 < 1 mag. Their images were inspected in the same manner as for the larger sample of singe-epoch objects.

Most of the single-epoch objects in the inspected sample are spurious detections, blends of neighboring stars, and objects that appear in the images at all epochs but have detections in the catalog at only one epoch (some of which are variable sources). The spurious detections are heavily concentrated in areas with high densities of stars or extended emission like the galactic plane and nearby galaxies. I recovered more than 100 previously known high proper motion stars and found two new objects with large motions, WISE 1049−5319 and WISE J085510.83−071442.5. The first epoch of WISE 1049−5319 is a single-epoch object because it was not matched to its other two epochs during construction of the multi-epoch objects, as mentioned in the previous section. WISE J085510.83−071442.5 consists of two single-epoch objects that are separated by 25 and six months. The direction of its motion is inconsistent with purely parallactic motion, and hence it cannot be a solar companion. The proper motion and W2 measurement for WISE J085510.83−071442.5 are included in Figure 2. The characteristics of this object will be discussed in more detail in a separate study.

Among the WISE bands, W2 provides the best constraints on the presence of a companion to the Sun. Given the typical sensitivities achieved by WISE (Section 2), W2 is capable of detecting objects at larger distances than W1, W3, and W4 for W1 − W2 > 1.2, W2 − W3 < 4.3, and W2 − W4 < 7.6, respectively. Although W1 offers higher S/N at W1 − W2 < 1.2, any brown dwarf with that color (≲T2) would be easily detected at W2 if it is within the range of plausible distances for a solar companion (<1 pc) based on the absolute magnitudes of L and T dwarfs (Dupuy & Liu 2012). The temperatures and absolute magnitudes corresponding to W2 − W3 ∼ 4.3 and W2 − W4 ∼ 7.6 have not been empirically determined for brown dwarfs because sufficiently cold objects have not been found, but models of brown dwarfs and giant planets can provide some guidance. The models of brown dwarfs from Burrows et al. (1997, 2003) extend down to 1 M_Jup for an age of 5 Gyr (T ≳ 100 K). The predicted spectra from those models do not exceed W2 − W3 ∼ 4.4 and W2 − W4 ∼ 7.6, which would suggest that W2 is the most sensitive band for that range of masses. However, models of Jupiter and Saturn from Fortney et al. (2011) computed for no solar irradiation (J. Fortney 2013, private communication) do exhibit colors that are redder than those values. As a result, the W3 and W4 bands may reach a solar companion at ≲ 1–2 M_Jup out to greater distances than W2, although only ∼20% of the sky was mapped twice in those bands at their full sensitivity, which is necessary for a survey based on parallactic motion.

In Figure 3, I show the masses as a function of distance that correspond to my survey limit of W2 = 14.5 based on the theoretical spectra from Burrows et al. (1997, 2003) and Fortney et al. (2011). The 1 M_Jup brown dwarf at 5 Gyr from Burrows et al. (1997) (M_W2 = 24.0) is fainter than the unirradiated analog of Jupiter from Fortney et al. (2011) (M_W2 = 21.5), resulting in different distance limits at that mass from the two models. I have also included constraints from 2MASS, IRAS, and reflected light surveys in Figure 3. The limits for 2MASS and IRAS are derived with J = 16.6 and F_ν(12 μm) = 0.4 mJy (S/N ≳ 5) and the brown dwarf models from Burrows et al. (2003). For reflected light, I show the typical limit for current surveys (R = 21; e.g., Sheppard et al. 2011) and the magnitude that should be reached by future facilities like the Large Synoptic Survey Telescope (R = 26). For the reflected light limits, I adopted the average V magnitudes of Jupiter, Saturn (ringless), and Neptune and assumed that each planet has V − R = 0. Because brown dwarfs and gas giants are expected to have similar radii at masses above ∼1 M_Jup, the reflected light limits for Jupiter have been adopted for all higher masses in Figure 3.

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My analysis of the multi-epoch astrometry from WISE has uncovered several hundred new high proper motion objects, including the third-closest known system to the Sun (Luhman 2013). However, none of these sources exhibit a motion that is consistent with a distant companion to the Sun (d ≲ 1 pc). The limit of W2 = 14.5 for this survey corresponds to analogs of Saturn and Jupiter at 28,000 and 82,000 AU, respectively, based on the fluxes predicted by models of these planets in the absence of irradiation (Fortney et al. 2011). In their model of a 1 M_Jup brown dwarf at an age of 5 Gyr, Burrows et al. (1997) predict fainter mid-IR fluxes than the model of Jupiter, resulting in a closer distance limit of 26,000 AU for that mass. These constraints on the mass of a solar companion at a given distance are an order of magnitude lower than those available from previous IR all-sky surveys, and they indicate that the outer solar system probably does not contain a brown dwarf or a large gas giant planet.

I thank Adam Burrows, Jonathan Fortney, and Caroline Morley for providing their model spectra. I acknowledge support from grant NNX12AI47G from the NASA Astrophysics Data Analysis Program. WISE is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory (JPL)/California Institute of Technology (Caltech), funded by NASA. 2MASS is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center (IPAC) at Caltech, funded by NASA and the NSF. The images of these surveys are based on photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope. The plates were processed into the present compressed digital form with the permission of these institutions. This work used data from the NASA/IPAC Infrared Science Archive (operated by JPL under contract with NASA). The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium.