The Faintest WISE Debris Disks: Enhanced Methods for Detection and Verification
Rahul I. Patel, Stanimir Metchev, Aren Heinze, Joseph Trollo
aa r X i v : . [ a s t r o - ph . S R ] D ec Draft version April 5, 2018
Preprint typeset using L A TEX style AASTeX6 v. 1.0
THE FAINTEST
WISE
DEBRIS DISKS:ENHANCED METHODS FOR DETECTION AND VERIFICATION
Rahul I. Patel , Stanimir A. Metchev , Aren Heinze and Joseph Trollo (Accepted to Astronomical Journal on December 2, 2016) Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125 Department of Physics & Astronomy, Centre for Planetary Science and Exploration, The University of Western Ontario, 1151 RichmondStreet, London, Ontario, N6A 3K7, Canada Department of Physics & Astronomy, Stony Brook University, 100 Nicolls Rd, Stony Brook, NY 11794–3800 Institute for Astronomy, 2680 Woodlawn Dr., Honolulu, HI 96822–1839
ABSTRACTIn an earlier study we reported nearly 100 previously unknown dusty debris disks around
Hipparcos main sequence stars within 75 pc by selecting stars with excesses in individual
WISE colors. Here, wefurther scrutinize the
Hipparcos
75 pc sample to (1) gain sensitivity to previously undetected, faintermid-IR excesses and (2) to remove spurious excesses contaminated by previously unidentified blendedsources. We improve upon our previous method by adopting a more accurate measure of the confidencethreshold for excess detection, and by adding an optimally-weighted color average that incorporatesall shorter-wavelength
WISE photometry, rather than using only individual
WISE colors. The latteris equivalent to spectral energy distribution fitting, but only over
WISE band passes. In addition,we leverage the higher resolution
WISE images available through the unWISE.me image service toidentify contaminated
WISE excesses based on photocenter offsets among the W
3- and W new debris disks around 75 pc Hipparcos main sequence stars using precisely calibrated
WISE photometry. This expands the 75 pc debrisdisk sample by 22% around
Hipparcos main-sequence stars and by 20% overall (including non-mainsequence and non-
Hipparcos stars). INTRODUCTIONDebris disks around main sequence stars are typically discovered by their characteristic infrared (IR) excesses. Theirfluxes at λ & µ m are significantly higher than would be expected from stellar photospheric emission alone. A debrisdisk can be detected by fitting a photospheric model to the shorter-wavelength (visible and near-IR) photometry, andby subtracting the fitted photosphere to check for a & µ m excess. A large number of debris disk-host stars havebeen found this way, using data from IRAS (e.g., Mo´or et al. 2006; Rhee et al. 2007; Zuckerman 2001, and referencestherein),
Spitzer (e.g., Su et al. 2006; Bryden et al. 2006; Trilling et al. 2008; Carpenter et al. 2009),
AKARI (e.g.,Fujiwara et al. 2013), and
WISE (e.g., Cruz-Saenz de Miera et al. 2014; Vican & Schneider 2014).A limitation of this approach is the accuracy of the determination of the underlying stellar photosphere. Fluxcomparisons across wide wavelength ranges—optical/near-IR for the photosphere and mid-IR for the excess—can beuncertain by several per cent. The combination of photometric data from different surveys (e.g., Tycho–2, SDSS, , WISE , IRAS ) incorporates often unknown systematic uncertainties in the photometric calibration among thesurvey filters. Any stellar variability between the observation epochs also adds an unknown contribution. Thus, whilethe systematic color uncertainties of photospheric models are generally well below a per cent, the determination ofthe photospheric emission in the mid-IR is uncertain by a few per cent (1 σ ). Adding to these limitations are otherdata systematics, most common of which can be uncertainties in the mid-IR filter profiles and the corresponding colorcorrections (e.g., Wright et al. 2010). As a result a number of previous searches for WISE excesses through SED fittinghave resulted in high fractions of spurious excess detections, up to 50% (see discussion in Patel et al. 2014a, henceforthPMH14).Notable exceptions are the surveys of Carpenter et al. (2009), Lawler et al. (2009), and Dodson-Robinson et al.(2011), who demonstrate that the Infrared Spectrograph (IRS; Houck et al. 2004) on Spitzer was the most sensitive
Patel, Metchev, Heinze, Trollo instrument ever for detecting 10–40 µ m photometric excesses from debris disks, with nearly twice as many detectionsas MIPS at 24 µ m. The advantage of IRS was in the ability to locally calibrate the stellar photospheric model overa spectral range that is close to the excess wavelengths, and in the fact that the entire 5–40 µ m spectrum could beobtained nearly simultaneously.With its better sensitivity than IRAS , a wavelength range that—similarly to
Spitzer /IRS—samples both the 3–5 µ mstellar photosphere and potential 10–30 µ m excesses simultaneously, and with the advantage of full-sky coverage over Spitzer , WISE (Wright et al. 2010) presents an opportunity to find unprecedentedly faint mid-IR excesses over theentire sky. In particular, the greatest sensitivity to faint mid-IR excesses can be obtained by analyzing the distributionsof stellar colors formed from combinations of short- (3.4 µ m and 4.5 µ m; W W
2, respectively) and long-wavelength(12 µ m and 22 µ m; W W
4, respectively)
WISE bands: e.g., W − W W − W WISE data. Rizzuto et al. (2012) used it to search forexcesses around Sco-Cen stars based on their W − W W − W WISE
Preliminary ReleaseData Release . Theissen & West (2014) applied a similar approach to search for excesses around M dwarfs using theSloan Digital Sky Survey Data Release 7 and the AllWISE Data Release .In PMH14 we implemented a color-excess search on the cross-section of the entire WISE
All-Sky Survey DataRelease and the Hipparcos catalog (Perryman et al. 1997), with the goal to determine the frequency of warm debrisdisk-host stars within 75 pc. We identified stars with infrared excesses in the W W WISE colors ( W − W , W − W , W − W W − W
4, or W − W WISE colors independently.This had the advantage of not excluding stars without valid measurements in some of the
WISE bands: for example,if W W − W W − W WISE bands—the majority of cases—an optimally weightedcombination of colors should have lower noise and potentially deliver greater sensitivity to faint excesses.We implement such an optimally weighted-color excess search on the same 75 pc
Hipparcos sample in the presentstudy. We further refine our threshold determination for what constitutes a
WISE color excess: by employing anempirically-motivated functional assumption about the behavior of
WISE photometric errors. Finally, we implementan automated method of rejecting stars with IR photometry contaminated by nearby point-like or extended objects.We summarize the selection of our sample of stars in Section 2. In Section 3 we describe the improved accuracy withwhich we set the confidence threshold when seeking
WISE excesses, and detail our weighting scheme when employingall available
WISE photometry to calibrate the stellar photosphere. In Section 4 we describe our automated methodfor identifying contaminated sources from their photocenter offsets between W W
4. We use these techniques toconfirm or reject previously discovered
WISE excesses and to find new ones; we summarize the results in Section 5. InSection 6 we discuss the differences in the results between the single- and the weighted-color excesses search approaches,and find that while the latter produces higher-fidelity IR excess detections, it is likely to miss a small fraction of bonafide excesses. SAMPLE DEFINITIONThe sample for the present study comprises the majority of the
Hipparcos main sequence stars selected in PMH14,with the added constraint that they should have reliable
WISE
All-Sky Catalog photometry in at least W W
2, or W
3. Although we identify and report excesses associated with stars within 75 pc, we use a larger volume of stars outto 120 pc for the entire analysis, as this larger population better samples the random noise and the photospheric
WISE colors discussed in Section 3.1. The 120 pc “parent sample” of stars resides in the Local Bubble (Lallement et al.2003), and so have little line-of-sight interstellar extinction. Hence, these stars are suitable for correlating optical andinfrared colors. The 75 pc “science sample” of stars is a subset of the parent sample, chosen to take advantage of moreaccurate parallaxes, and so giving a clear volume limit to our study.Stars were also selected if they were outside the galactic plane ( | b | > ◦ ) and constrained to the − .
17 mag
Debris Disks Figure 1 . Distributions of the weighted-color excess metrics, Σ E [ W (left) and Σ E [ W (right) for all stars in our 120 pc parentsample. We have assumed that the negative portion of each Σ E distribution is representative of the intrinsic random andsystematic noise in the data (Section 3.1). The mode of the full distribution is shown by a vertical black dashed-dot line. Areflection (dashed histogram) of the negative portion of the Σ E histogram around the mode is thus representative of the falsepositive excess expectation. We define the FDR at a given Σ E as the ratio of the cumulative numbers of > Σ E excesses in thepositive tails of the dashed and solid histograms. The vertical dotted lines indicate the FDR thresholds for each weighted W j excess: 2% for W W
4. We identify all stars with FDR values below these thresholds (correspondingly higher Σ E values) as candidate debris disk hosts. Each inset shows a log-log fit of a line to the last ten points in the reverse cumulativedistribution function (CDF) of the uncertainties (see Section 3.1). Assuming exponential behavior in the tail of the uncertaintydistribution, this fit smoothes over the stochasticity in this sparsely populated region of the uncertainty distribution to attaina more accurate estimate of the FDR threshold. now add a search for weighted W W W W W W
3, while for the weighted W SINGLE-COLOR AND WEIGHTED-COLOR EXCESSESWe define as single-color excesses those that are identified in individual
WISE colors (Section 3.1). Weighted-color excesses are those that are identified from the weighted combination of
WISE colors. Thus, a star can haveboth W − W W − W W Improved Identification of Single-color Excesses
We identify single-color
WISE excesses from the significance of their color excess as defined in Equation 2 of PMH14:Σ E [ W i − W j ] = W i − W j − W ij ( B T − V T ) σ ij . (1)The numerator determines the color excess E [ W i − W j ] by subtracting the mean photospheric color W ij ( B T − V T )from the observed W i − W j color. We used the calibrations of
WISE photospheric colors of main sequence stars fromPMH14 (see also Patel et al. 2014b). The significance of the excess Σ E [ W i − W j ] is obtained by normalizing by the totaluncertainty σ ij , which is a quadrature sum of the WISE
All-Sky Catalog photometric uncertainties, uncertainties inthe saturation correction applied to bright stars, and uncertainties in the photospheric color estimation (PMH14).Throughout the rest of this paper, the significance of a single-color excess is denoted with Σ E .The single-color WISE excesses are selected by seeking stars with Σ E values above a pre-determined confidence level(CL) threshold: CL=98% at W W
4. The CL can be expressed in terms of the false-discovery rate(FDR): FDR = 1 − CL. We denote the Σ E value at CL as Σ E CL . As in PMH14, we determine the Σ E CL values forthe different colors from the Σ E distributions themselves. Thus, the Σ E CL values for our respective 98% and 99.5%CL thresholds in W W W W E excess distributions. To estimate the distributions of un-certainties, we assume that the effect of random errors on Σ E is symmetric with respect to Σ E = 0. This would be In PMH14 we incorrectly called the FDR the false-positive rate (FPR). See Figure 4 in Wahhaj et al. (2015) for an illustration of thedifference between the two terms.
Patel, Metchev, Heinze, Trollo −3 −2 −1 0 1 2 3 4 𝘌[𝘞𝟣−𝘞𝟦] R e v e r s e CD F 𝘌[𝘞𝟣−𝘞𝟦] 𝘭𝘰𝘨(𝘊𝘋𝘍( 𝘌 ))= +𝟧.𝟢𝟣𝟫−𝟣.𝟦𝟫𝟤 𝘌 New CLOld CL
Figure 2 . A reverse cumulative distribution function (rCDF, Section 3.1) of the uncertainty (black) and excess (red) distributionsof Σ E [ W − W . We use the rCDF to estimate the FDR at any Σ E , with FDR being the ratio of the black and red rCDFs. Thevertical dash-dotted line shows the more conservative Σ E . estimate of the confidence threshold from PMH14, set half-waybetween the last two points. The vertical dashed line shows the present Σ E . estimate, based on a fit (solid green line) tothe last ten data points in the tail of the rCDF (magenta squares). The left panel shows the full rCDFs, while the right panelzooms in near the Σ E CL threshold. generally true if, as is our supposition, photometric errors are symmetrically distributed around zero.The Σ E distributions of the various colors do indeed peak close to zero (PMH14), which supports this assumption.Hence, we assume that the negative halves of the Σ E distributions are representative of the negative sides of theuncertainty distributions. We then mirror the negative Σ E values to obtain the full distributions of uncertainties. Weillustrate this method for determining the FDR in Figure 1, albeit not for the single-color excess Σ E metrics discussedhere and in PMH14, but for the weighted-color excess Σ E metrics introduced in Section 3.2.This empirical estimate of the FDR offers a straightforward method to assess the reliability of candidate excesses.However, the exact value of the Σ E CL threshold tends to rely only on the one or two most-outlying stars in the (negativewing of the) Σ E distribution (Figure 1), and so is uncertain. In PMH14 we purposefully overestimated Σ E CL by thehalf distance to the star prior to the one that satisfied the FDR threshold. Our estimate of the Σ E CL was conservative,not very accurate, and may have excluded potentially significant excesses.Here we iterate on this approach by taking advantage of the near-Gaussian behavior of each uncertainty distribution.To circumvent the small-number sampling in the tail, we average the functional behavior by fitting an exponentialcurve to the last ten points in the reverse cumulative distribution function (rCDF) of the uncertainty distribution(Figure 2). This continuous form of the tail of the uncertainty distribution enables a more accurate estimate of theFDR. aint WISE
Debris Disks Table 1 . Single- and Weighted-Color Excess Selection Summary
Color Σ E CL a
Stars in Stars in Excesses in Debris Disk Newor Σ E CL Parent Sample ( <
120 pc) Science sample ( <
75 pc) Science Sample Candidates Excesses W − W W − W W − W W − W W − W W W · · · Note — Summary of the results from our
WISE single-color and weighted W W ECL outlined in Section 3.1. Σ
ECL is the threshold Σ E above which we select an excess at a confidence level higher than CL . CL = 99 .
5% for W W W , W
2, and W W WISE bands (for W a Excess significance threshold for single-color excesses (Σ
ECL ) or weighted-color excesses (Σ E CL ). We used the improved confidence threshold determination procedure to search for additional single-color excesses inthe same sets of stars and colors ( W − W W − W W − W W − W W − W
3) as in PMH14. We found29 additional single-color excess candidates. We rejected HIP 104969, and HIP 111136 after visual and automatedinspections (Section 4) for line-of-sight contamination, and we rejected HIP 910 on suspicion of it being a spuriousdetection (see Section 5.1.1). We are thus left with 26 single-color excess candidates, 18 of which do not have IRexcess detections reported in the literature. Of these 18, 17 are newly detected single-color excesses at W W
3, with a marginal excess at W E significances arelisted individually in Table 2. The 3 rejected single-color excess candidates are included in a list of rejected candidatesin Table 3. Patel, Metchev, Heinze, Trollo
Table 2 . IR Excess Information for 75 pc Debris Disk Candidates not Identified in PMH14 Σ E Σ E HIP Single Color Weighted New? W − W W − W W − W W − W W − W | µ m) W W · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · Note —The second column indicates the combination of detections from individual colors. Each flag is a five character string that identifies whether thestar has a statistically probable (Y) or insignificant (N) single-color excess in the following order: W − W W − W W − W W − W W − W
3. Any star can have an unlisted (U) value, indicating that the star was rejected by the selection criteria for that particular color (Section2.2 in PMH14). “U” entries correspond to null entries in the corresponding Wi − Wj Σ E column. Column 3 shows a two-character flag to indicatewhether the star has a significant weighted-color excess in the following order: weighted W W W W µ m), or not. Dashed entries (“-”) indicate no detected excess in that band.The last seven columns list the significance of the excess for each color or weighted metric. Defining a New Weighted-Color Excess Metric
In PMH14 and Section 3.1 we identified debris disk-host candidates by selecting stars with individual anomalouslyred
WISE
W i − W j colors, where i = 1 , , j = 3 ,
4, and i < j . However, it may be possible to attain more reliableexcess detections at
W j by combining all relevant
W i − W j colors. Herein we define this new “weighted-color excess”metric.As in Equation 1, we first remove the contribution from the photospheric emission. Thus the single-color excess is: aint
WISE
Debris Disks Table 3 . Rejected
WISE
Excesses
HIP WISE ID RejectionID Reason
New Single-Color and Weighted-Color Excesses
HIP910 J001115.82-152807.2 2HIP13631 J025532.50+184624.2 1HIP27114 J054500.36-023534.3 1HIP60689 J122617.82-512146.6 1,3HIP79741 J161628.20-364453.2 1HIP79969 J161922.47-254538.9 1,3HIP81181 J163453.29-253445.3 1HIP82384 J165003.66-152534.0 1HIP83221 J170028.63+150935.1 1,3HIP83251 J170055.98-314640.2 1HIP99542 J201205.89+461804.8 1,3HIP104969 J211542.61+682107.2 1,3HIP111136 J223049.77+404319.8 1
Previously Identified Single-Color Excesses from PMH14 a HIP19796 b J041434.42+104205.1 3HIP20998 J043011.60-675234.8 3HIP28498 J060055.38-545704.7 3HIP35198 J071625.22+350102.8 4HIP60074 b J121906.38+163252.4 4HIP63973 J130634.58-494111.0 3,4HIP68593 b J140231.57+313939.3 3HIP78010 J155546.22-150933.9 4HIP79881 J161817.88-283651.5 3HIP95793 b J192900.97+015701.3 3
Note —Rejection reasons:1. Contamination by nearby infrared source based on visual “by-eye” in-spection.2. Spurious excess. See Section 5.1.1.3. Contaminated by extraneous extended emission based on a significantdifference between the W W W W a These rejected excesses were also recovered using our improved single-colordetection techniques. b These rejected excesses have been confirmed as debris disk hosts by higherangular resolution
Spitzer observations. See Section 4.3. E [ W i − W j ] =
W i − W j − W ij ( B T − V T ) . (2)Since we want to use the strength of all possible WISE color combinations for band
W j , we constructed the weightedaverage of the color excesses as E [ W j ] = 1 A j − X i =1 E [ W i − W j ] σ W i , (3)where σ W i is the photometric uncertainity of
W i and j = 3 ,
4. Here, A = j − P i =1 1 σ i is a normalization constant. Our Patel, Metchev, Heinze, Trollo Single-Color W3 Excesses Weighted W3 Excesses a)
10 1165
Single-Color W4 Excesses Weighted W4 Excesses b) Figure 3 . Venn diagrams comparing the candidate excesses from the single-color excess selection (left circles; Section 3.1) andthe weighted-color excess selection (right circles; Section 3.3). For the W W W W W WISE bands. definition for the significance (cid:16) Σ E [ W j ] (cid:17) of the weighted-color excess at W j is the ratio of the weighted average of allcolor excesses (Equation 3) to the uncertainty in the weighted average ( σ E [ W j ] ):Σ E [ W j ] = E [ W j ] /σ E [ W j ] (4)= A j − P i =1 E [ W i − W j ] σ i q σ j + 1 /A . (5)The full derivation of this metric can be found in Appendix A. We use Σ E throughout the rest of the paper as shorthandfor the significance of the weighted-color excess for either W W
4, as appropriate, and Σ E as shorthand for thesignificance of the single-color excess when the discussion does not refer to any specific color.3.3. Weighted-Color Excesses
We extend the same procedure used to identify stars with single-color excesses in Section 3.1 to search for optimallyweighted-color excesses in W W E CL . We plot the Σ E distributions as solid red histograms for both W W E CL threshold is shown as the vertical dotted green line. We claim that astar has a significant weighted-color excess if its Σ E ≥ Σ E CL .We identify 6 stars with 98% significant weighted W × .
12 to be false positives. We identify 187 stars with 99.5% significant weighted W . ×
187 = 0 .
94 to be false positives. These FDRs only take into account theprobability of detecting an excess due to random noise, and do not filter out real excesses that may be caused by otherastrophysical contaminants (e.g., IR cirrus or unresolved projected companions).As with the single-color excess candidates (Section 3.1), we performed visual and automated inspection of the
WISE images to determine contamination. None of the six weighted W W W W W W W AUTOMATED REJECTION OF CONTAMINATED STARS USING REPROCESSED WISE IMAGES
WISE offers higher angular resolution than
IRAS . However, source photometry is still prone to contamination byunrelated astrophysical sources seen in projection. Possible contaminants may include nearby point sources at angular aint
WISE
Debris Disks
WISE W W W W W WISE
All-Sky Survey Catalog nor the AllWISE Catalog list astrometric positions in each of the separatebands. Therefore, we downloaded the co-added W W WISE angular resolution ratherthan the smoothed, √ × broader images accessible from the WISE
All-Sky Survey or AllWISE data releases.4.1.
Using unWISE
Images to Identify Contaminants
Instead of using the co-added and mosaicked ‘Atlas’ images from the
WISE
All-Sky Survey, we used the higherangular resolution unWISE images, which can be retrieved from the unWISE image service (Lang 2014). In theofficial All-Sky Survey and AllWISE data releases, the final images were created by stacking individual exposures andthen convolving each stack with a model of the detector’s PSF. In contrast, the unWISE images were created byeliminating the final convolution step, thus preserving the original WISE resolution (Lang 2014). Hence, the unWISE
PSF is a factor of √ ∼ ′′ vs. ∼ ′′ at W W W ∼ ′′ vs. ∼ ′′ at W ′′ × ′′ postage-stamp W W unWISE website for all of our excesscandidates, each centered on the stellar coordinates at the mean WISE observational epoch. We also downloadedimages for the 16960 PMH14 parent sample stars:
Hipparcos main sequence stars within 120 pc. This sample isthe union of all the stars that comprised the parent samples for the five different color excess searches in PMH14: W − W W − W W − W W − W
4, and W − W
4. We use this amalgamated parent sample as a basis fordetermining which candidate excess stars have statistically significant positional discrepancies.We explored two independent ways to automatically detect unrelated contamination: one primarily for point sourcesand one for extended sources. We hypothesized that unrelated point-source contaminants can be identified throughsignificant positional offsets between the centroids of the W W unWISE images. These would represent caseswhere the catalogued W W − W W W W W unWISE postage stamps. We denote these as ~r W and ~r W , respectively. The centroid positionswere obtained from 2D Gaussian fits to the pixel values in a 3.06 pixel (8.42 ′′ ) radius aperture, with a Gaussian of σ = 1 .
02 pixels. The σ value was chosen to yield a full width at half maximum (FWHM) of 2.40 pixels (6.60 ′′ ), slightlylarger than the FWHM of the W unWISE PSF.We also hypothesized that extended-source contaminants could be identified by comparing the W r = 3 .
06 pixel (8.42 ′′ ) aperture to a W r = 10 . ′′ ) aperture (extendingout to the second Airy minimum). These would correspond to cases where a star is projected on a background ofinterstellar cirrus. The smaller-aperture centroid would be dominated by the stellar PSF, while the wider-aperturecentroid would be weighted more strongly by the spatial distribution of the cirrus. If the cirrus surface brightnessdistribution is uneven, that would generally result in a systematic offset between the narrow- and wide-aperturecentroids. As before, we extracted W unWISE postagestamps. We denote the W ~r W , wide .Altogether, we aim to automatically identify contaminants based on large offsets between the W W ~r W ,W = ~r W − ~r W ), or between the W ~r W ,W = ~r W − ~r W , wide ). We can set the threshold for contamination in our science sample by studying the distributionof positional offsets for the parent sample. We can then mark as contaminated all science sample stars with offsetslarger than the chosen threshold for either of the methods.4.2. Rejecting Astrometric Contaminants
The automated contamination checking approach outlined in the preceding Section 4.1 needs to take into account twoconsiderations. First, the positional uncertainty of an object depends on its signal-to-noise ratio (SNR). Consequently, http://unwise.me P a t e l , M e tc h e v , H e i n z e , T r o ll o T r an s f o r m ed c en t r o i d o f s e t s : ⁄ [ (cid:0) ∆ ◌ ⃑ − ◌ ⃑ ) Σ / ] Transformed centroid of sets: ⁄ [( ∆ ◌⃑ − ◌⃑ ) Σ / ] We divide the data into bins along W4 SNR such that all binscontain equal numbers of stars. We use the largest number ofbins such that the sequence of red points (calculated in panel b)has a monotonically increasing deriva ve. We es mate the covariance of the (cid:1) x and (cid:2) y distribu ons for eachSNR bin by (cid:3) nding the MCD (Sec on 4.2.1). Three mes thegeometric mean of the resul ng eigenvectors ( (cid:4) and (cid:5) ) is used as avisual approxima on of the outer edge of the radial distribu on,denoted by red points in panel (a).The covariance matrix calculated using the MCD method is used totransform the distribu on in each SNR bin into a mul variatestandard normal distribu on. Distance from zero in this new spacecorresponds to distance from the mean, taking into account thecovariance of the original distribu on. This is called the Mahalanobis distance (Equa on 6). A$er every point has been expressed in terms of theMahalanobis distance, points across all bins are compareduniformly, seen clearly by the transforma on of the red points from panel a). This transforma on of the parent sample allows us to be%er decide which far-outlying points to cull (Sec on 4.2.1).The red points do not indicate our adopted thresholds. a. b. c. d. σ σ Mahalanobis distance D M σσ F i g u r e . A n ill u s t r a t i o nd e p i c t i n g t h e s t e p s t a k e n t o d e r i v e t h e M a h a l a n o b i s d i s t a n c e s o f t h e a s t r o m e t r i c o ff s e t s f o r e a c h s t a r i n t h e p a r e n t s a m p l e , a s d e s c r i b e d i n § . . . aint WISE
Debris Disks ~r W ,W and ~r W ,W centroid offsets varies as a function of SNR. Therefore, the rejection thresholdneeds to depend on SNR. Second, the positional x and y uncertainties are correlated in pixel coordinates because the WISE
PSF is not circularly symmetric. For example, the W ′′ and 6.1 ′′ . Consequently, the distribution of the centroid offsets ~r W ,W and ~r W ,W will not be centrally symmetric,and their ∆ x and ∆ y projections onto pixel coordinates will be correlated. Generally, the ∆ x and ∆ y distributionswill follow different degrees of correlation as a function of SNR.We illustrate these two considerations for the ~r W ,W centroid offsets in panels (a) and (b) of Figure 4. The bean-likecloud of data points in Figure 4a shows a clear trend for a widening distribution of ∆ r = ∆ x + ∆ y variances inthe ~r W ,W centroid offsets at lower W x vs. ∆ y in Figure 4b shows thecovariance expected from the centrally asymmetric shape of the WISE
PSF.4.2.1.
Eliminating SNR and Covariance Dependencies in the Astrometry
The covariance of the ∆ x and ∆ y offsets at any W r = ∆ x + ∆ y . Instead, we require a distance statistic that is independentof the covariance among ∆ x and ∆ y . In addition, because the covariance of the ∆ x and ∆ y offsets depends on SNR,the covariance matrix must be calculated at different W W W | ~r | = ∆ r space. The binning is illustratedin Figure 4a. The bins are not equally spaced, but are instead chosen such that all bins contain an equal number ofstars, which in turn ensures that there are no under-represented bins. To determine the optimal number of bins, wefirst start with a small number (e.g., 4) of bins, and in each bin calculate the geometric mean of the variances along theprincipal axes of the 2D ∆ x vs. ∆ y distribution: i.e., the eigenvalues of the covariance matrix. The geometric meanapproximates what the (joint) variance would be if the positional offsets in ∆ x and ∆ y were uncorrelated and hadequal variance. The geometric means of the ∆ x and ∆ y variances for each bin are shown as red points in Figure 4a,where they are multiplied by 3 for illustrative purposes. We then increased the number of bins until the geometricmeans for all bins stopped forming a sequence that had a monotonically increasing derivative. For our analysis, wethus used nine equally populated bins. We expect the relationship between SNR and astrometric offsets to be smooth,and using more than nine bins results in a jagged approximation.We then need to determine how the empirical distribution of the geometric means of the ∆ x and ∆ y variancescan be used to set a probability threshold for contamination. Each population of | ~r | offsets in the W x and ∆ y offsets must be calculated for the statistically random sample while being insensitive to the presence ofoutliers. To this end, we adopt the minimum covariance determinant (MCD; Rousseeuw & Driessen 1999) method.The MCD method is optimized to selectively ignore data that are significantly distant from the center of thedistribution, such that the determinant of the resulting covariance matrix Σ ∆ x, ∆ y is minimized. Figure 4b illustratesthe covariance ellipses calculated by the MCD technique, for a given W ∆ x, ∆ y covariance matrices among the W D M using amatrix multiplication of the observed offset ∆ r = (∆ x, ∆ y ) and the distribution’s covariance matrix (Σ ∆ x, ∆ y ): D M = r T Σ − x, ∆ y r . (6)The calculation of the Mahalanobis distance is the multi-dimensional equivalent of subtracting the mean of thedistribution and dividing by the standard deviation. In essence, we are performing two separate transformations tothe 2-D ∆ x and ∆ y offset distributions: a rotation and scaling. The rotation is dictated by the eigenvectors of thecovariance matrix Σ − x, ∆ y , while its eigenvalues determine the magnitude of the scaling. The transformed 2-D offsetdistribution is then centrally symmetric, with the Mahalanobis distance D M describing the radial distance of eachdata point from the origin in units of the standard deviation of the distribution (see Figure 4c–d).We calculate the Mahalanobis distances separately for each bin, since the covariance matrices differ. Figure 4c showshow the 2-D ∆ x vs. ∆ y distribution for a given W W | ~r | distribution, where the | ~r | offsets have been expressed in terms of the dimensionless Mahalanobis distances. The See Table 1 in Section IV.4.c.iii.1 of the All-Sky Explanatory Supplement; http://wise2.ipac.caltech.edu/docs/release/allsky/expsup/sec4_4c.html Patel, Metchev, Heinze, Trollo 𝖣 𝖬 for 𝘞𝟥 vs. 𝘞𝟦 aperture positions N e g a t i v e P r e d i c t i v e V a l u e 𝖣 𝖬 for narrow vs. wide 𝘞𝟦 aperture positions N e g a t i v e P r e d i c t i v e V a l u e Figure 5 . The NPV distributions of the 120 pc parent sample stars as a function of the Mahalanobis distances between their( x, y ) positions in unWISE images. The horizontal dashed line is set at NPV=99.5%. The vertical dashed line indicates D M ,solved from equation 8. Stars with D M > D M (3.63 and 3.28 for the W W W W < .
995 are rejected as astrometric outliers.
Left:
NPV distribution for W W Right:
NPV distributionfor offsets between the narrow (2.5 pix) radius and wide (10 pix) radius apertures in W Mahalanobis distance distributions are identical (by design) across all bins, which allows us to set a uniform thresholdfor rejecting positional outliers. 4.2.2.
Adopting A Uniform Rejection Threshold
In the absence of contamination by nearby sources, the centroids of the majority of the stars would be distributedaccording to a multivariate normal distribution. Consequently, the Mahalanobis distances would follow a χ distribu-tion of two degrees of freedom. We aim to separate the population of uncontaminated stars from the outlier populationof contaminated stars whose centroids are offset because of nearby emission. As an estimate of the uncontaminatedpopulation, we select all stars with D M <
2. Since the population of uncontaminated stars dominates at such smalloffsets, and since the spatial distribution of its centroid offsets is expected to be narrower, we expect the set of D M < f ( x ) to be the probability density function of the χ distribution with two degrees of freedom representing the uncontaminated population, while N D M < is the numberof stars in this population. Thus, the uncontaminated distribution can be represented using the empirical data andscaled such that A Z f ( x ) dx = N D M < , (7)where A is the normalization factor.We then calculate A from Equation 7 and use it to compare the empirical D M distribution for the centroid offsetsto the expectation Af ( x ) for an uncontaminated distribution. We estimate the fraction of stars within a certain D M that are expected to be uncontaminated by calculating the negative predictive value (NPV) as a function of D M . Ifwe set a threshold D M beyond which we reject stars as astrometrically contaminated, then the NPV is defined as: N P V = A R D M f ( x ) dxN D M 5% and solve Equation 8 for D M by calculating the intersection of the right andleft hand side of Equation 8. We find D M thresholds of 3.63 and 3.28 for the W W W W . D M thresholds marked withvertical lines. Should the distribution of centroid offsets at D M < χ distributionwith two degrees of freedom, the NPV distributions would start at unity at D M = 0 and monotonically decreasetoward larger values of D M . However, since we are dealing with a real data set, the NPV distributions are noisy at aint WISE Debris Disks −1 𝖣 𝖬 for 𝘞𝟥 vs. 𝘞𝟦 aperture positions W S N R HIP78010HIP35198HIP63973 Rejected candidate debris disks, identified fro this study of PMH14Candidate debris disks Figure 6 . W W W unWISE centroids (see Sections 4.1–4.2). The black/graydensity cloud represents the density of 16927 Hipparcos 120 pc parent sample stars. The light-blue dots represent the candidateexcess stars. The vertical black-dotted line represents the NPV=99.5% threshold for rejecting astrometrically contaminatedexcesses. The unWISE images for the rejected stars are shown in Figure 8. small D M (fewer data points) and become monotonic only at larger D M . Therefore, while there are several possible D M values at which NPV = 99 . D M . We reject candidate excesses withMahalanobis distances above these thresholds.Figures 6 and 7 show the distribution of the Mahalanobis distances with respect to the W W W W W W W W Rejection Fidelity We would like to determine whether stars rejected by our automated positional analysis of unWISE images areindeed contaminated. The expectation is that if an extraneous point or extended source can randomly offset thecentroid positions (and hence contaminate the photometry) of a star, then the fraction of rejected (contaminated)stars among our candidate excesses should be higher than the fraction of rejected stars in an the non-excess portionof the science sample. This is because if a contaminating source is bright enough to influence the photocenter of thestar, it is likely to increase the flux of the star as well.To this end, we compare the fraction of astrometrically rejected stars in two complementary subsets of the sciencesample. On one hand we consider the population of 271 candidate excesses before any visual or automated rejection,and on the other hand we take its complement of 7666 non-excess stars. We use Welch’s t-test to determine whetherthe fractions of stars rejected from each subset by the centroid checks are significantly different from each other. Thus,this test will tell us whether the null hypothesis can be rejected. Specifically, the null hypothesis is that the means ofthe rejected and complementary science samples are equal.The result from this test yielded a p -value of 0.025, indicating that the probability of observing the difference in themeans of the two populations, assuming they are the same, is 2.5%. With this, we can reject the null hypothesis and4 Patel, Metchev, Heinze, Trollo −1 𝖣 𝖬 for narrow vs. wide 𝘞𝟦 aperture positions W S N R HIP28498HIP63973HIP20998HIP60074HIP68593HIP95793HIP19796HIP79881Bona-fide debris disk that appears extendedRejected candidate debris disks, identified from this study of PMH14Candidate debris disks Figure 7 . W W unWISE centroids in narrow (2.5 pix) and wide (10 pix) apertures(see Sections 4.1–4.2). The black/gray density cloud represents the density of 16927 Hipparcos 120 -pc parent sample stars.The light-blue dots represent the candidate excess stars. The vertical black-dotted line represents the NPV=99.5% thresholdfor rejecting astrometrically contaminated excesses. The contaminated objects include eight candidate debris disk excessesidentified in this study, and are marked with open square symbols. The unWISE images for the rejected excesses are shown inFigure 9. claim that the mean of the two populations are not equal. In other words, though this test does not determine whetherall stars astrometrically rejected excesses are contaminated, it does tell us that the astrometric rejection technique isindeed preferentially selecting stars that are selected as candidate excesses.Our automated checks for contamination by nearby point or extended sources are sensitive to systematic offsets assmall as 0.2 pix (0.6 ′′ ) at SNR > unWISE PSF: atenth at W W 4. The human eye may be challenged at discerning such small offsets. Nonetheless,it is always instructive to perform a visual inspection of the actual images of the rejected sources.Figures 8 and 9 show postage-stamp unWISE images of the rejected candidate excesses. Some of the automaticallyrejected sources clearly show contamination from nearby emission in the unWISE images. This is the case for twoof the candidates—HIP 20998, and HIP 63973—rejected by the W unWISE postage stamp image. However, theAll-Sky Atlas images show the star to be partially contaminated by cirrus. Indeed, Rebull et al. (2008) discusses thelack of a Spitzer /MIPS 24 µ m excess, attributing previous IRAS detections with the blending of the source and IRcirrus. In addition, Riviere-Marichalar et al. (2014) do not detect an excess at 70 µ m. These two studies corroborateour rejection of this excess detection. The images of HIP 35198, and HIP 78010, which possess the largest D M basedon their W W W 4, as may HIP 28498 andHIP 95793 (Figure 9). However, no visible contamination can be seen around most excess candidates rejected at D M . Spitzer . The latter, HIP 60074 (HD 107146), is a well-known cold debrisdisk that has been spatially resolved in scattered light by the Hubble Space Telescope (Ardila et al. 2004) and in the aint WISE Debris Disks NE Figure 8 . 44 ′′ × ′′ unWISE W W W ′′ ). The red and blue crosses showthe centroid locations calculated from the W W W ′′ ) radius aperture used to calculate the centroid position in both bands. submillimeter by the Atacama Large Millimeter Array (ALMA; Ricci et al. 2015). In our analysis of the narrow- vs.wide-aperture W D M threshold, below which it would be considered uncon-taminated. We note that the centroid offset for this star is ∆ r W = 1 . ′′ in the southwest direction. Ardila et al.(2004) identified a faint background spiral galaxy roughly 6 ′′ from HIP 60074 in the same direction as this offset. Theposition of the galaxy places it within the WISE W W W µ m emission from the background galaxy. Nosuch projected contaminants are known for the other three previously known debris disks that are rejected by ourcentroid offset analysis.It is very likely that some of the stars rejected by the centroid offset comparisons, and for which contaminationcannot be visually discerned, have bona-fide IR excesses from debris disks. Nonetheless, we retain the centroid checksas an unbiased and objective indicator of possible IR flux contamination. Our contamination thresholds are establishedempirically, from the larger parent sample. If a contaminant is well blended with the stellar PSF, the centroid offsetmay be the only reliable way to identify it.We also note that some of the stars that we reject upon visual inspection are not identified as contaminated by theautomated centroid offset comparisons. Among the twelve visually rejected stars in Table 3 (rejection reason equal to1), seven (HIP 13631, HIP 27114, HIP 79741, HIP 81181, HIP 82384, HIP 83251, HIP 111136) were not identified asbeing contaminated by our astrometric rejection method. Upon comparing the Atlas and unWISE images for each ofthese seven stars, we find visual differences in the structure of the cirrus, as the unWISE images show cirrus whichis less pronounced. This is caused mainly by the different smoothing kernels used between the Atlas and unWISE service. Thus, one of two explanations are plausible. The first is that our rejection technique has not been fully6 Patel, Metchev, Heinze, Trollo NE Figure 9 . 44 ′′ × ′′ unWISE W W ′′ ) and wide (blue circle, 10 pixels or27.5 ′′ ) apertures. The red and blue crosses in each image are the centroid locations calculated from their respective coloredapertures. customized to detect extended cirrus emission below a certain threshold, or more likely, that we are being conservativein our assessment of what is contaminated from a subjective visual inspection. RESULTSOur improved WISE IR excess identification procedure has uncovered 29 candidate excesses that we did not reportin PMH14. In Section 5.1.1 we argue that one of these excesses, associated with HIP 910, is likely spurious, which aint WISE Debris Disks Table 4 . Parameters of Stars with WISE Color Excesses Identified Since PMH14 HIP WISE SpTa Dist.b T ∗ R ∗ χ ∗ FW FW , ∗ FW FW , ∗ ∆ FW /FW 3c ∆ FW /FW W corr d W corr dID ID (pc) (K) ( R ⊙ ) (mJy) (mJy) (mJy) (mJy) (mag) (mag)1893 J002356.52-142047.4 G6V 53 5468 1.0 1.9 48.6 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Note — Hipparcos stars with detected mid-IR excesses at either W W 4. Unless otherwise noted, the stellar temperature and radius were obtained from photospheric model fits to the opticalthrough 4.5 µ m photometry, as described in Section 3 of PMH14. a Spectral types are from the Hipparcos catalog. Stars marked with asterisks have had their spectral types estimated from their BT − VT colors using empirical color relations from Pecaut & Mamajek(2013). b Parallactic distances from Hipparcos . c The quoted fractional excesses in W W fd of the dust (Table 5; see Section 3 of PMH14). d Saturation corrected W W leaves 28 candidate excess identifications not reported in PMH14. These are the 28 excesses whose detection specificsare listed in Table 2. Nineteen of the 28 excesses are new to the literature, and are addressed in more detail inSection 5.1.The 28 excesses newly identified by our color-selection methods include single-color only excesses (12 at W W W W W E for each star showsthat all of the new detections are fainter (smaller f d fractional excesses) than those found in PMH14: mainly becauseof the decrease of the Σ E CL confidence level in our updated FDR threshold determination (Sec. 3.1).The stellar and dust properties of the 28 candidate excesses are listed in Tables 4 and 5. These parameters are derivedfrom photospheric model fits to the optical and near-IR photometry from the Hipparcos catalogue and the Two MicronAll-Sky Sky Survey ( ), using a procedure similar to the one outlined in PMH14. The only update with respectto PMH14 is that after fitting the optical/IR SED with a photospheric model to determine the best-fit stellar effectivetemperature, we then scale the model to the weighted mean of the W W W σ upper limits to the W W W > σ below the photosphere. This8 Patel, Metchev, Heinze, Trollo is because we found that the empirically derived W − W W − W W W 2, the W W New Candidate Debris Disks Out of the 28 WISE candidate debris disks discovered since PMH14, 19 are completely new detections with nopreviously reported excesses at any wavelength. Eighteen of these occur at W 4, and are indicated with ‘Y-’ in thecolumn labeled ‘New?’ in Table 2. These are new excesses at 22 µ m with no significant 12 µ m excess emission. One ofthe 18 new W Table 5 . Debris Disk Parameters from Single-Temperature Blackbody Fits HIP ID T BB T BBlim R BB R BBlim θ f d f dlim Notes(K) (K) (AU) (AU) ( ′′ ) (10 − ) (10 − )1893 · · · < · · · > > > · · · < · · · > > > · · · < · · · > > > < 264 2.3 > > · · · < · · · > > > · · · · · · > · · · < · · · > > > · · · < · · · > > > · · · < · · · > > > · · · < · · · > > > · · · · · · · · · g39947 · · · < · · · > > > < 344 5.5 > > < 432 1.6 > > · · · < · · · > > > · · · · · · > · · · < · · · > > > · · · < · · · > > > · · · < · · · > > > · · · < · · · > > > · · · < · · · > > > · · · < · · · > > > · · · < · · · > > > · · · · · · > · · · · · · > · · · < · · · > > > · · · < · · · > > > > 283 0.31 < > 19 d,e Table 5 continued on next page aint WISE Debris Disks Table 5 (continued) HIP ID T BB T BBlim R BB R BBlim θ f d f dlim Notes(K) (K) (AU) (AU) ( ′′ ) (10 − ) (10 − ) Note —The columns list blackbody temperatures of thermal excesses, inferred separations fromthe star and fractional bolometric luminosities.Notes:a. W W > σ below the photosphere. Alimiting temperature and radius for the dust cannot be determined. See detailed explanation inSection 5.b. W W σ limit on the dust temperature and radius.c. W W W σ upper limit on the W σ limit on thedust temperature and radius.d. W W W σ upper limit on the W σ limit on thedust temperature and radius.e. A lower limit on the fractional luminosity was calculated for a blackbody with peak emissionat λ = 12 µm as described in Section 3 in PMH14.f. A lower limit on the fractional luminosity was calculated for a blackbody with peak emissionat λ = 22 µm as described in Section 3 in PMH14g. Significant excesses were found both at W W 4. The dust parameters are calculatedexactly using a blackbody for the excess. The remaining one of the 19 new candidate excesses, associated with HIP 117972, is significant only at W 3, andonly in the W − W E [ W − W = 2 . 73: just above the Σ E [ W − W = 2 . 66 confidence level threshold.It is not confirmed as a weighted-color excess at W W E [ W = 3 . 28. Given our adoption of a lower confidence level (98%) for detecting W W − W W − W W W ∼ 531 K dust excess (Figure 10, bottom left panel) at f d = 1 . × − of the stellar bolometricluminosity (Table 5). 5.1.1. New Disk Candidates with Archival IR Observations While none of the stars with new candidate excess detections discussed here have been previously identified as debrisdisk hosts in the literature, perusal of archival observations from IRAS Spitzer , Herschel , and AKARI reveals datafor HIP 910, HIP 20507, HIP 21783, and HIP 67837. HIP 20507 has only IRAS data at 25 µ m, though the detectionis too noisy to place useful constraints and hence we do not include it in our SED fit (Figure 10, bottom right panel).We discuss the other three candidate excesses with archival observations below, noting that the small HIP 910 W WISE excesses is in fact 19. HIP 910. — Among the four stars for which archival mid-IR data exist, only HIP 910 has been discussed in thedebris disk literature, where it has received considerable scrutiny as a nearby (19 pc; van Leeuwen 2007) near-solaranalog (F8V; Gray et al. 2006). Independent analyses of Spitzer /IRS low-resolution spectra (Beichman et al. 2006), Spitzer /MIPS 24 µ m and 70 µ m photometry (Trilling et al. 2008), and Herschel /PACS 100 µ m and 160 µ m photometry(Eiroa et al. 2013) all conclude that HIP 910 does not possess an excess. We find that HIP 910 has small but significant W − W . ± . 06 mag) and W − W . ± . 04 mag) excesses above the photosphere. As such, HIP 910 wouldbe a candidate for having a zodiacal dust debris disk analog. The inferred 19% excess at W ∼ σ significant in the MIPS24 observations of Trilling et al. (2008), hence the non-confirmation in MIPS is not surprising.However, the 15%–19% excess over 10–30 µ m would have been detected at ∼ σ significance in the Spitzer /IRS analysisof Beichman et al. (2006). Their low-resolution Spitzer /IRS observations cover a wide wavelength range, 6–38 µ m, andhave superior sensitivity to faint excesses compared to our WISE photometric analysis: because of the better stellarphotospheric estimation that is attainable with a larger number of independent short-wavelength data points. Giventhe lack of confirmation from the Spitzer /IRS observations, we conclude that the candidate W W > σ below the photosphere. HIP 910 may berepresentative of the very few ( . W Patel, Metchev, Heinze, Trollo exist. Because it is also unique in that it is not confirmed as a debris disk in the more sensitive Spitzer /IRS data,this raises the question whether some of our other candidates discussed here and in PMH14 may also be spurious. Todetermine whether the non-confirmation of WISE excesses from Spitzer /IRS observations is a common occurrence forany of our reported excesses, we searched the recent literature for all of the new excess stars discovered in PMH14.Nineteen of these have had Spitzer /IRS observations published since, all in Chen et al. (2014). All are confirmed tohave Spitzer /IRS excesses. Hence, we can conclude that the non-confirmation of HIP 910 is not typical of our WISE excess detections, and that the remaining 19 new candidate debris disks reported here and the 104 new candidates inPMH14 remain viable. HIP 21783. — This star is serendipitously included in a single MIPS 70 µ m pointing in Spitzer program GO 54777 (PI:T. Bourke). We measure a flux of 26 ± r =16 ′′ aperture photometry on the post-basic calibrated data(PBCD) images, after an aperture correction factor of 2.04. The MIPS70 measurement confirms the presence of athermal excess. A fit to the optical–IR SED (Figure 10, top left panel) reveals that the associated circumstellar dusthas a temperature of 84 K and a fractional luminosity of f d = 1 . × − . HIP 67837. — HIP 67837 is included in a Herschel /PACS 70 µ m and 160 µ m Open Time program (PI: D. Padgett).Its 70 µ m flux is 24 ± r = 5 ′′ aperture photometry on the Level 2.5-processed images,and applied an aperture correction factor of 1 / . 577 = 1 . 733 (following Table 2 of Balog et al. 2014). The PACS70 µ m measurement confirms the thermal excess (Figure 10, top right panel). The star is not detected at 160 µ m. Theinferred dust temperature is 76 K and the fractional dust luminosity is f d = 3 . × − .5.1.2. New Disk Candidates in Binary Systems Two of our new excess stars, HIP 2852 and HIP 70022, have M-dwarf companions (De Rosa et al. 2014). This maybe a cause for concern, as these companions might be responsible for the W M ⊙ companion, which corresponds to an M3/4 spectral type, at a separation of 0.93 ′′ ± ′′ (45 . ± . 49 au). HIP 70022 has a 0.18 M ⊙ (M5/6) companion that is also likely physical (De Rosa et al. 2014),separated by 1.84 ′′ (116 au) from the central star. Given ∆ K s ≥ W Confirmation of Previously Reported 22 µ m Faint Debris Disks In Section 5.1.1, we discussed all 19 new debris disks reported in the present work. We now discuss the nine additionaldebris disk excesses that have been published by other teams and that we recover here, but that were not identifiedin PMH14. Amongst them, is HIP 26395, a star for which we report a new small W W W WISE : four by Vican & Schneider (2014, ;HIP 12198, HIP 21091, HIP 78466 and HIP 115527) and one by Mizusawa et al. (2012, ;HIP 92270). We determineupper limits on the dust temperatures in these systems (Table 5) as we have done for the newly reported debris disks(Section 5) and in PMH14. Our dust temperature limits are consistent with, albeit generally more stringent (131–203 K) than reported in Vican & Schneider (2014) for the four stars in common. We use the individual 3- σ upperlimits on the W W W Spitzer . The longer-wavelength detections affirm the existence of debris disks around these stars,and provide greater constraints on the dust properties in these systems. Plavchan et al. (2009) reported MIPS 24 µ mand 70 µ m excess detections for HIP 42333 and calculated the dust temperature of the excess to be T < 91 K. Ourestimates of the blackbody dust temperature solely from the W W σ upper limit yield a hotter, yetconsistent result ( T BB < 344 K). HIP 42438 and HIP 100469 are both known to have excesses between 8–30 µ m from Spitzer /IRS and at 70 µ m from Spitzer /MIPS. Chen et al. (2014) report multi-temperature debris disks for both stars, After the publication of PMH14 we further recognized that some of the excesses that we had reported as new had already beenidentified as candidate debris disks from Spitzer /IRS spectra by Ballering et al. (2013). There are 14 such excesses: a subsample of the 19new PMH14 W Following Table 4.14 of the MIPS Instrument Handbook v. 3.0; http://irsa.ipac.caltech.edu/data/SPITZER/docs/mips/mipsinstrumenthandbook/ aint WISE Debris Disks (𝘮) −14 −13 −12 −11 −10 −9 −8 −7 −6 𝘍 [ 𝘦 𝘳 𝘨 𝘴 − 𝘤 𝘮 − ] HIP20507 A2V 𝘛 * = 8840K𝘛 𝘉𝘉 = 260K f d = 1.34x10 -4 f d = 3.12x10 -4 f d = 1.92x10 -4 Figure 10 . Example SEDs representative of newly detected excesses from this study. The blue dashed lines correspond tothe fitted NextGen photosphere models to photometry from the Hipparcos catalog (Johnson B, V ), catalog ( J, H, K s ),and WISE All-Sky Catalog ( W , W 2) photometry. For HIP 20507, we also fit the photosphere using W W W WISE photometry. The W W W W µ m in each plot. We fit blackbodycurves (magenta dashed-dot curves) to excess fluxes (open magenta diamonds) and 3 σ upper limits (red arrows) red-ward of W 3. The combined photosphere and excess emission for each star is plotted as solid black line. HIP 21783 and HIP 67837are new W W − W W − W Spitzer /MIPS 70 µ m and Herschel /PACS 70 µ m fluxes to further constrain the dust temperature fits for HIP 21783 andHIP 67837, respectively. The Spitzer and Herschel fluxes were obtained as described in Section 5.1.1. In addition, HIP 117972is a new W W − W W IRAS µ m flux is plotted, although it does not provide any useful constraints. with ∼ < 499 K warm dust components. Our single-population dust temperatureestimates from W W T BB < 432 K for HIP 42438 and T BB = 131 K for HIP 100469 (for whichwe measure a significant excess also at W W µ memission (Ballering et al. 2013). Here, we report the additional detection of a weighted W µ m excess seen in Spitzer /IRS data. Chen et al. find that HIP 26395 has amulti-temperature debris disk, similar to those around HIP 42438 and HIP 100469: a cold component at T=94 Kand a hot component at T=399 K. Again, our single-population dust temperature (146 K) is consistent with thetwo-population dust model of Chen et al. (2014). Notably, our detection of the weighted W Spitzer /IRS thanks to our increasedprecision in determining the level of the photosphere.5.3. Unconfirmed WISE 22 µ m Excess Candidates from the Literature Patel, Metchev, Heinze, Trollo Our study is constrained only to WISE excesses from B9–K main sequence Hipparcos stars within 75 pc and outsideof the galactic plane. We compare our findings to searches for WISE debris disks within this volume. The main compar-ison studies are those of McDonald et al. (2012); Mizusawa et al. (2012); Wu et al. (2013); Cruz-Saenz de Miera et al.(2014); Vican & Schneider (2014), and most recently, Cotten & Song (2016).Similarly to our approach, Mizusawa et al. (2012); Wu et al. (2013), and Cruz-Saenz de Miera et al. (2014) used WISE colors, at least in part, to seek mid-IR excesses from debris disks. As already discussed in PMH14, we reliablyrecover all of the excesses reported in Wu et al. (2013) and Cruz-Saenz de Miera et al. (2014) that pass our strictphotometric quality selection criteria. This is also largely the case for the Mizusawa et al. (2012) work, although wedo not recover five of their 22 candidates because they are either outside of our search region (HIP 55897 being inthe galactic plane) or suffer potential contamination: from a close binary companion (HIP 88399), from saturationin the three shortest-wavelength WISE bands (HIP 61174), from other sources based on their WISE confusion flags(HIP 18859 and HIP 100800), or as inferred from discrepant photometry between the reported WISE values and theaveraged single-frame measurements (HIP 18859; see Section 2.3 of Patel et al. 2014a).The set of studies by McDonald et al. (2012); Vican & Schneider (2014) and Cotten & Song (2016) follow a differ-ent excess search approach, comparing stellar photospheric models to optical-through-infrared SEDs that incorporatephotometry from multiple instruments and epochs. As we discussed in PMH14 and in Section 1, this method is vul-nerable to systematics induced by differences in photometric calibration among filter systems and by stellar variability.The presence of systematics is evident from the fact that (model plus) SED-based searches result in non-negligiblenumbers of large “negative” excesses, to the tune of − σ to − σ . Consequently, the reliability of positive outliers atcomparable numbers of standard deviations—which would be considered candidate excesses—is diminished.Our WISE -only color-based search overcomes these systematic issues. Because we only use the measured WISE colors we circumvent any instrument-to-instrument and epoch-to-epoch systematics. In addition, by empirically cali-brating the photospheric colors of stars in WISE , we have removed the spectral response dependence in estimating thestellar photosphere. This latter point is particularly important as the published WISE filter profiles carry a residualcolor term depending on the slope of the mid-IR SED (e.g., Brown et al. 2014).We do not recover substantial fractions of the excesses reported in SED-based searches: e.g., 41 of the 81 excessesin Vican & Schneider (2014) that pass our selection criteria. In some cases the W i − W i < 3) colors are infact significantly negative (PMH14), meaning that the apparent excesses are not confirmed in WISE data alone, andmay thus be the result of the systematic uncertainties in the WISE photometric zero points (Wright et al. 2010) or ofstellar variability between the WISE and prior photometric epochs. At the same time, it is not surprising that withour presently more aggressive color-excess detection thresholds (Section 3.1) relative to PMH14, we now recover someadditional candidate excesses (Section5.2) reported by Vican & Schneider (2014). A comparison to the much morecomprehensive Tycho-2-based WISE study of Cotten & Song (2016) is forthcoming. DISCUSSION: SINGLE- VS. WEIGHTED-COLOR EXCESS SEARCHESWe have presented an improved set of procedures for detecting IR excesses in individual WISE colors (Section 3.1),and also an approach to combining the individual colors and producing a weighted-color excess metric at W W WISE photometry in all four bands.The Venn diagrams in Figure 3 show the correspondence between the single- and weighted-color excess detectionsin this sample. The weighted excess metrics confirm all five of the single-color W W W W W i − W W WISE photometricuncertainty distributions (Figure 11) shows that the W W W i − W W WISE single-color excess is not confirmed by the weighted-color excess metric, then the single-color excess might be considered suspect. That is, the ten stars that are not detected in our weighted W aint WISE Debris Disks Photometric Uncertainty (mag) N u m b e r o f S t a r s Figure 11 . Distributions of photometric uncertainties for all four WISE bands for the 12654 stars in the weighted W W W σ W is expected becauseof the lower absolute flux levels in W 4. It is evident that the mean σ W is larger than the means of σ W or σ W . The W − W W − W (Figure 3b), might be false detections. Nonetheless, there are two reasons for which a star may not have a weighted W W E [ W of the W W W − W W − W W − W W − W W − W W W W W W − W W W W W W − W W W − W W − W W − W 4, and even in the weighted W W − W W W − W W W W 3: not surprising as all four stars are saturated in W W 2. Even though we correct the saturatedphotometry of these stars, the resulting photometric uncertainties will always be larger than those of unsaturatedstars.4 Patel, Metchev, Heinze, Trollo 𝘞𝟦 Excess Significance ( 𝘌 ) HIP1893HIP8987HIP13932HIP21918HIP43273HIP70022HIP82887HIP85354HIP92270HIP100469 𝘌[𝘞𝟣 − 𝘞𝟦] 𝘌[𝘞𝟤 − 𝘞𝟦] 𝘌[𝘞𝟥 − 𝘞𝟦] 𝘌[𝘞𝟦] Figure 12 . The excess significances for the ten stars with single-color W W W E [ W ) effectively averages theindividual single-color detection thresholds. The stars that are not confirmed in the weighted-color selection possess significantsingle-color excesses in only one or two colors. 7. CONCLUSIONWe have presented a series of techniques that improve the ability to detect and verify the existence of WISE mid-IRexcesses from debris disks around main sequence stars. First, we have implemented an improved assessment of theconfidence threshold beyond which stars with IR excesses can be identified based on their WISE colors. This hasrevealed 18 new potential debris disks around main-sequence Hipparcos stars within 75 pc.Second, we have presented a method that uses an optimally-weighted average of multiple WISE colors to identify W W WISE colors. Whilethe color weighting approach has the potential to identify fainter IR excesses, most of the excesses are expressed onlyat W 4: the band with the largest W W W W WISE imagesavailable through the unWISE service to assess the positions of the stellar centroids between W W 4, and be-tween W Spitzer /MIPS identified excess K S -[24]= 0.09 mags (Stauffer et al. 2010; Urban et al. 2012). However, given this star’s relatively small excess and that weidentified it as a an astrometric rejection, we feel the existence of its debris disk may be questionable. As we havestated previously, the rejection of any debris disk candidate using our astrometric technique, though it may indicatethe presence of a blended background source, does not necessarily discount the existence of a circumstellar debris disk.Although we do not eliminate visual checks of the WISE All-Sky images after excess identification, the automatedassessment of the stellar centroid offsets provides a sensitive and objective metric to assess contamination. aint WISE Debris Disks WISE colors improves the reliability of candidate IR excessdetections from individual WISE colors at the cost of potentially overlooking a remaining small population of faintW4 excesses. Even though the fraction of debris disk-bearing stars within 75 pc does not change significantly from thefindings in our previous study, the verification through weighted colors and the positional checks using higher angularresolution images provide confidence that the 19 new disks discovered here are real, and not spurious or contaminated.Thus, combined with the PMH14 results, we find a total of 9 W W < 75 pc Hipparcos stars in WISE . As of the current study, 107 of these represent previously unreported 10–30 µ m excesses, 101of which represent entirely new debris disk detections within 75 pc. This expands the 75 pc debris disk sample by 22%around Hipparcos main sequence stars and by 20% overall (including non-main sequence and non- Hipparcos stars).We thank Dustin Lang for help with downloading images for our entire sample from the unWISE image service.We would like to acknowledge assistance from Melissa Louie who provided suggestions to improve figure aesthetics.This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint projectof the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology,funded by the National Aeronautics and Space Administration. We also use data products from the Two MicronAll Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and AnalysisCenter/California Institute of Technology, funded by the National Aeronautics and Space Administration and theNational Science Foundation. This research has also made use of the SIMBAD database, operated at CDS, Strasbourg,France. This research has made use of the Washington Double Star Catalog maintained at the U.S. Naval Observatory.Most of the figures in this work were created using Matplotlib, a Python graphics environment (Hunter 2007). Thisresearch also made use of APLpy, an open-source plotting package for Python hosted at http://aplpy.github.com (Robitaille & Bressert 2012). This work is partially supported by NASA Origins of Solar Systems through subcontractNo. 1467483 to Dr. Stanimir Metchev at Stony Brook University, and by an NSERC Discovery award to Dr. StanimirMetchev at the University of Western Ontario. APPENDIX A. THE WEIGHTED-COLOR EXCESS METRICWe present the full derivation of Σ E [ W j ] for a star at a WISE mid-IR band W j , where j = 3 or 4. Starting withEquation 2, we arrive at a general form for the weighted-color excess by adding the individual color excess terms, andmultiplying by weights a i E [ W j ] = j − X i =1 a i E [ W i − W j ] (A1)= j − X i =1 a i ( W i − W j − W ij ( B T − V T )) . (A2)The weights a i are normalized and are unknown: j − X i =1 a i ≡ . (A3)Our general form for the S/N of the weighted average of the excess at W j is calculated by dividing equation A1 bythe uncertainty in the weighted average, σ E [ W j ] . The uncertainty is defined as the quadrature sum of each entry ofthe Jacobian matrix of E [ W j ] weighted by its respective uncertainty. The variance of the weighted average is σ E [ W j ] = X α σ α ∂E [ W j ] ∂α ! + O ( σ W i,W ij ) + O ( σ W i,W j ) , (A4)where α ∈ { W i, W j, W ij ( B T − V T ) } are the terms on the right hand side of Equation A2. The cross terms in theJacobian matrix, O ( σ W i,W ij ) and O ( σ W i,W j ) are proportional to the covariance of the uncertainties in the WISE photometry and the mean WISE colors. We ignore the first term, O ( σ W i,W ij ), because σ W ij ∼ . σ W i and W ij is6 Patel, Metchev, Heinze, Trollo only a shallow function of B T − V T . We also ignore O ( σ W i,W j ) because the errors on W i and W j are not correlatedand hence σ W i,W j ∼ 0. Thus, Equation A4 reduces to σ E [ W j ] ≃ X α σ α ∂E [ W j ] ∂α ! , (A5)where α ∈ { W i, W j } , after removing the photospheric uncertainties from the calculation. We define the significanceof the weighted-color excess at W j in the same form as in Equation 4:Σ E [ W j ] = E [ W j ] σ E [ W j ] . (A6)We proceed with solving for the weights in equation A1. Using j = 4 as an example, we can expand equation A1 as E [ W 4] = a E [ W − W 4] + a E [ W − W 4] + a E [ W − W 4] (A7)= a ( W − W − W ) + a ( W − W − W ) + a ( W − W − W ) , (A8)Inserting a = 1 − a − a into Equation A7 produces E [ W 4] = a W − a W + a W − a W + W − W − W − a W a W − a W a W . (A9)The variance of E [ W 4] is calculated using Equation A5, σ E [ W = a σ W + a σ W + (1 − a − a ) σ W + σ W . (A10)Next we seek solutions for a and a that minimize the dependence of σ E [ W on these weights. Thus, by calculating ∂σ E [ W ∂a ! = 0 = 2 a σ W − σ W + 2 a σ W + 2 a σ W , (A11) ∂σ E [ W ∂a ! = 0 = 2 a σ W − σ W + 2 a σ W + 2 a σ W (A12)We solve for a and a a = σ W σ W σ W σ W + σ W σ W + σ W σ W , (A13) a = σ W σ W σ W σ W + σ W σ W + σ W σ W . (A14)Now, using Equations A13 and A14, we recover a , a = σ W σ W σ W σ W + σ W σ W + σ W σ W . (A15)To reduce the form of these weights, we multiply and divide each by σ W σ W σ W , to finally obtain the general formfor each weight a i = 1 /σ W i P j − i =1 /σ W i . (A16)This is valid for either weighted W j = 3) or weighted W j = 4) excesses. We then set A = P j − i =1 /σ W i , substituteequation A16 into equation A10 to obtain a reduced expression for the variance of the excess ( σ E [ W ), and then place aint WISE Debris Disks j = 3 or j = 4 is Σ E [ W j ] = A j − P i =1 E [ W i − W j ] σ i q σ j + 1 /A . (A17)Equation A17 is the same result for Σ E [ W j ] as presented in equation 4.8 Patel, Metchev, Heinze, Trollo