Does the Debris Disk around HD 32297 Contain Cometary Grains?
Timothy J. Rodigas, John H. Debes, Philip M. Hinz, Eric E. Mamajek, Mark J. Pecaut, Thayne Currie, Vanessa Bailey, Denis Defrere, Robert J. De Rosa, John M. Hill, Jarron Leisenring, Glenn Schneider, Andrew J. Skemer, Michael Skrutskie, Vidhya Vaitheeswaran, Kimberly Ward-Duong
aa r X i v : . [ a s t r o - ph . E P ] J a n Draft version October 4, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
DOES THE DEBRIS DISK AROUND HD 32297 CONTAIN COMETARY GRAINS? *+ Timothy J. Rodigas , John H. Debes , Philip M. Hinz , Eric E. Mamajek , Mark J. Pecaut , Thayne Currie ,Vanessa Bailey , Denis Defrere , Robert J. De Rosa , John M. Hill , Jarron Leisenring , Glenn Schneider ,Andrew J. Skemer , Michael Skrutskie , Vidhya Vaitheeswaran , Kimberly Ward-Duong Draft version October 4, 2018
ABSTRACTWe present an adaptive optics imaging detection of the HD 32297 debris disk at L ′ (3.8 µ m) obtainedwith the LBTI/LMIRcam infrared instrument at the LBT. The disk is detected at signal-to-noise perresolution element (SNRE) ∼ ∼ . ′′ . ′′ L ′ is bowed, as wasseen at shorter wavelengths. This likely indicates the disk is not perfectly edge-on and contains highlyforward scattering grains. Interior to ∼
50 AU, the surface brightness at L ′ rises sharply on bothsides of the disk, which was also previously seen at Ks band. This evidence together points to thedisk containing a second inner component located at .
50 AU. Comparing the color of the outer(50 < r /AU < L ′ with archival HST/NICMOS images of the disk at 1-2 µ m allows us to test the recently proposed cometary grains model of Donaldson et al. (2013). Wefind that the model fails to match the disk’s surface brightness and spectrum simultaneously (reducedchi-square = 17.9). When we modify the density distribution of the model disk, we obtain a betteroverall fit (reduced chi-square = 2.9). The best fit to all of the data is a pure water ice model (reducedchi-square = 1.06), but additional resolved imaging at 3.1 µ m is necessary to constrain how much (ifany) water ice exists in the disk, which can then help refine the originally proposed cometary grainsmodel. Subject headings: instrumentation: adaptive optics — techniques: high angular resolution — stars:individual (HD 32297) — circumstellar matter — planetary systems INTRODUCTION
Debris disks, which are thought to be continuallyreplenished by collisions between large planetesimals(Wyatt 2008), can point to interesting planets in severalways: with warps and/or gaps (Lagrange et al. 2010), * Based on observations made at the Large Binocular Tele-scope (LBT). The LBT is an international collaboration amonginstitutions in the United States, Italy and Germany. LBT Cor-poration partners are: The University of Arizona on behalf ofthe Arizona university system; Istituto Nazionale di Astrosica,Italy; LBT Beteiligungsgesellschaft, Germany, representing theMax-Planck Society, the Astrophysical Institute Potsdam, andHeidelberg University; The Ohio State University, and The Re-search Corporation, on behalf of The University of Notre Dame,University of Minnesota and University of Virginia. + Based on observations made using the Large Binocular Tele-scope Interferometer (LBTI). LBTI is funded by the NationalAeronautics and Space Administration as part of its ExoplanetExploration program. Steward Observatory, The University of Arizona, 933N. Cherry Ave., Tucson, AZ 85721, USA; email: [email protected] Carnegie Postdoctoral Fellow; Department of TerrestrialMagnetism, Carnegie Institute of Washington, 5241 BroadBranch Road, NW, Washington, DC 20015, USA Space Telescope Science Institute, Baltimore, MD 21218,USA Department of Physics and Astronomy, University ofRochester, Rochester, NY 14627-0171, USA Rockhurst University, 1100 Rockhurst Rd, Kansas City, MO64110, USA University of Toronto, 50 St George St., Toronto, ON M5S1A1, Canada School of Earth and Space Exploration, Arizona State Uni-versity, PO Box 871404, Tempe, AZ 85287-1404, USA Large Binocular Telescope Observatory, University of Ari-zona, Tucson, AZ 85721, USA University of Virginia, Department of Astronomy, 530 Mc-Cormick Road, Charlottesville, VA 22903, USA sharp edges (Schneider et al. 2009; Chiang et al. 2009),and with their specific dust grain compositions. Sincemany outer solar system bodies contain copious amountsof water ice and organic materials, finding other debrisdisk systems that contain water ice and/or organic mate-rials (Debes et al. 2008a) would point to planetary sys-tems that might contain the ingredients necessary forEarth-like life. Therefore constraining the dust graincompositions in debris disks is crucial.Narrow and broadband scattered light imaging is a par-ticularly powerful tool for constraining composition be-cause it can substitute for spectra that would otherwisebe too difficult to obtain. The wavelength range between1-5 µ m, in particular, contains strong absorption featuresfor water ice and organics like tholins (both near 3.1 µ m;Inoue et al. (2008); Buratti et al. (2008)). Imaging atthese wavelengths from the ground using adaptive op-tics (AO) also offers high Strehl ratios, allowing for moreprecise characterization of faint extended sources close totheir host stars.Obtaining high signal-to-noise (S/N) detections offaint debris disks at these wavelengths from the groundis challenging due to the bright thermal background ofEarth’s atmosphere, as well as the warm glowing sur-faces in the optical path of the telescope. An AO sys-tem that suppresses unwanted thermal noise is necessaryto overcome these obstacles. The Large Binocular Tele-scope (LBT), combined with the Large Binocular Tele-scope Interferometer (LBTI, Hinz et al. (2008)), is onesuch system. The LBT AO system (Esposito et al. 2011)consists of two secondary mirrors (one for each primary)that can each operate with up to 400 modes of correction,resulting in very high Strehl ratios ( ∼ H band, ∼
90% at Ks band, and >
90% at longer wavelengths). Rodigas et al.This equates to very high-contrast, high-sensitivity imag-ing capabilities, allowing detections of planets and debrisdisks that were previously too difficult.HD 32297 is a young A star located 112 pc away(van Leeuwen 2007) surrounded by a bright edge-on debris disk. The disk has recently been re-solved at Ks band (2.15 µ m) by Currie et al. (2012),Boccaletti et al. (2012), and Esposito et al. (2013). Thedisk has also been detected in the far-infrared (FIR)by Herschel (Donaldson et al. 2013, hereafter D13), whomodeled the disk as consisting of porous cometary grains(silicates, carbonaceous material, water ice).To further test this model, we have obtained ahigh S/N image of the disk at L ′ (3.8 µ m) withLBTI/LMIRcam. Using this new image, along witharchival HST/NICMOS images of the disk at 1-2 µ m from Debes et al. (2009) , we determine how wellthe D13 cometary grains model matches the scatteredlight of the disk at 1-4 µ m.In Section 2 we describe the observations and datareduction. In Section 3 we present our results on thedisk’s surface brightness (SB) from 1-4 µ m, analysis ofthe disk’s morphology, and our detection limits on plan-ets in the system. In Section 4 we present our modelingof the disk. In Section 5 we discuss the implications ofour results on the disk’s structure and composition, andin Section 6 we summarize and conclude. OBSERVATIONS AND DATA REDUCTION
Observations
We observed HD 32297 on the night of UT November4 2012 at the LBT on Mt. Graham in Arizona. We usedLBTI/LMIRcam and observed at L ′ (3.8 µ m). LMIR-cam has a field of view (FOV) of ∼ ′′ on a side anda plate scale of 0 . ′′ ∼ . ′′ ∼ While resolved images of the disk have also been obtainedfrom the ground at these wavelengths, the HST data are preferredbecause they do not suffer from the biases inherent in ADI/PCAdata reduction. with the core of the star saturated out to 0 . ′′
1. After fil-tering out images taken while the AO loop was open ,the final dataset consisted of 726 images, resulting in 2.99hours of continuous integration (not including the min-imum exposure photometric images). Throughout theobservations, which began just after the star’s transit,the FOV rotated by 50.84 ◦ , enabling the star itself toact as the point spread function (PSF) reference for sub-traction during data reduction. Data reduction
All data reduction discussed below was performed withcustom Matlab scripts. We first divided each scienceexposure image by the number of coadds (15) and in-tegration time (0.99 s) to obtain units of counts/s foreach pixel. Next we corrected for bad pixels and sub-tracted opposite chop beam images of the star to removedetector artifacts and the sky background, resulting inflat images with ∼ . ′′ We then registered each image so that the star’s locationwas at the exact center of each image. We binned eachimage by a factor of 2 to ease the computational loadrequired in processing 726 images, which is not a prob-lem because the PSF is still oversampled by more than afactor of 4. To reduce the level of the patchy sky back-ground, for each image we subtracted a 15 pixel (0 . ′′ . ′′ . ′′ ∼ Filtering out images of poor quality can be accomplished inseveral ways: the fits headers contain keywords relating to thestatus of the AO loop, which a user can check in the data reduction;the raw images themselves can be examined by the user to checkthe appearance of the PSF (pointy vs. blurry); or the user cancheck the log of the observations, which should denote when/whereproblems with the AO occurred. We used the first and third optionsto filter out open loop data on HD 32297. Since the PSF is only saturated out to 0 . ′′
1, it contributesvery little to the center of light calculation; we have demonstratedsub-pixel accuracy using this method in Rodigas et al. (2012).
As a first check on the efficacy of the steps describedabove, we performed classical ADI subtraction by sub-tracting a median-combined master PSF image from allthe images, and then derotating the images by theirparallactic angle at the time of the exposure. The re-sulting image revealed edge-on disk structure at the ex-pected position angle (PA) of ∼ ◦ (Debes et al. 2009;Mawet et al. 2009).To obtain the highest possible S/N detection ofHD 32297’s debris disk, we reduced the images us-ing principal component analysis (PCA, Soummer et al.(2012)). PCA has recently been shown to pro-duce equal-to or higher S/N detections of plan-ets and disks (Thalmann et al. 2013; Bonnefoy et al.2013; Boccaletti et al. 2013; Soummer et al. 2012;Meshkat et al. 2013) than LOCI (Lafreni`ere et al. 2007),though this may be a result of LOCI’s tunable pa-rameters not being optimized correctly (C. Marois, pri-vate communication). We did also reduce the data us-ing conventional LOCI algorithms (Rodigas et al. 2012;Currie et al. 2012; Thalmann et al. 2011) but found thatthe gain in computational speed for PCA with no lossin S/N warranted the ultimate preference of PCA overLOCI for this dataset.We followed the prescription outlined inSoummer et al. (2012), with the main tunable pa-rameter being K , the number of modes to use for agiven reduction. Increasing K reduces the noise inthe final image but also suppresses the flux from thedisk; therefore this parameter must be optimized. Afterexamining the average S/N per resolution element(SNRE) over the disk’s spatial extent for varyingvalues of K , we determined the optimal number ofmodes to be K = 3 (out of a possible 726). We thenfed all the images through our PCA pipeline, rotatedthe images by their corresponding PAs clockwise toobtain North-up East-left, and combined the imagesusing a mean with sigma clipping. Fig. 1a shows thisfinal image, and Fig. 1b shows the corresponding SNREmap. We detect the disk from ∼ . ′′ . ′′ ∼ L ′ imaging of HD 15115 (Rodigas et al.2012). The detection of the disk at high S/N allows usto more precisely measure its SB, which in turn resultsin better constraints on the composition and size of thedust grains producing the observed scattered light. RESULTS
Calculation of Uncertainties
For all the images analyzed in this study, the uncer-tainties are dominated by residuals left over from PSFsubtraction. Specifically, both the HST and LBT datasuffer from azimuthal and radial residual structures. Forthe LBT data, we computed the standard deviation ofthe equivalent SB measurements all around the star (ex-cluding the disk). For the HST data, we calculated theerrors in two ways: by computing the equivalent SB mea-surements 90 ◦ away from the real disk; and by computing As in Rodigas et al. (2012), the SNRE map is calculated byconvolving the final image by a Gaussian with full-width half-maximum = 0 . ′′ the standard deviation of the equivalent SB measurmentsall around the star (excluding the disk). We found thatboth methods resulted in comparable errors, therefore wechose to use the second method since this method wasalso used for computing the errors on the LBT data. Surface Brightness Profiles
In addition to the image of the disk at L ′ , we also re-analyzed archival, reduced images of the disk at ∼ µ m from HST/NICMOS presented inDebes et al. (2009). For each image, we rotated thedisk by 47 ◦ counterclockwise so that its midplane was ap-proximately horizontal in the image. We measured theSB in all the HST/NICMOS images by taking the me-dian value in 3 pixel (0 . ′′ µ m) images, these boxes were centered onthe brightest pixel at each specific pixel distance fromthe star (0 . ′′ . ′′ µ m) and theF205W (2.05 µ m) images, the boxes were centered on thesame pixel locations as were used in the F110W image.We converted the image counts/s to mJy/arcsecond us-ing the reported photometric conversions given on theSpace Telescope Science Institute website and appliedthe appropriate correction factors to the data (see theAppendix for a detailed description of these correctionfactors).For the final L ′ image, we calculated the mediancounts/s in a 5 pixel (0 . ′′ . ′′ . ′′ . ′′ L ′ data than for theHST/NICMOS data due to the disk appearing thinner(FWHM ∼ . ′′ ≈ λ /D) at L ′ , and to avoid the largenegative residuals above and below the disk close to thestar. We converted these values to mJy/arcsecond usingthe total measured flux in the unsaturated photometricimage of HD 32297 and applied the appropriate correc-tion factors to the data (see the Appendix for a detaileddescription of these correction factors).Fig. 2 shows the final, corrected SB of the disk at1-2 µ m and at 3.8 µ m. The star’s magnitude at 1-2 µ m (7.7) and L ′ (7.59) has been subtracted from the diskmagnitude/arcsecond to yield the intrinsic disk color ateach wavelength. We find that the SB profile is asym-metric from ∼ . ′′ . ′′ L ′ , in agreementwith the asymmetry at Ks band reported by Currie et al.(2012) and Esposito et al. (2013). We do not find evi-dence for asymmetry interior to 0 . ′′ Ks band byCurrie et al. (2012). Exterior to 0 . ′′ ∼ equal SB at L ′ . The HST data are gen-erally consistent from 1-2 µ m, within the uncertainties,except for interior to 0 . ′′ σ of each other for the outer portionof the disk (0 . ′′ < r < . ′′ ∼ -1.3 and -1.5. Interior to 0 . ′′
4, the disk is not detected We refer the reader to Debes et al. (2009) for these imagesand descriptions of how they were reduced.
Rodigas et al. arcseconds a r cs e c ond s −1 −0.5 0 0.5 1−1−0.500.51 −0.200.20.40.60.8 (a) arcseconds a r cs e c ond s −1 −0.5 0 0.5 1−1−0.500.51 01234567 (b) Fig. 1.—
Left : Final reduced L ′ image of the HD 32297 debris disk, in units of detector counts/s, with North-up, East-left. The white dotmarks the location of the star and represents the size of a resolution element at L ′ . A 0 . ′′ ∼ brighter than the northeast side from 0 . ′′ . ′′ Ks band (Currie et al. 2012). However there is no brightness asymmetry at the location of the mm peak first identified byManess et al. (2008) and later seen at Ks band by Currie et al. (2012). Right : SNRE map of the final image. Both sides of the disk aredetected from ∼ . ′′ . ′′ ∼ distance from star (arcseconds) S u r f a c e B r i gh t ne ss ( ∆ m ag s / a r cs e c ond ) northeast L’F110WF160WF205W (a) distance from star (arcseconds) S u r f a c e B r i gh t ne ss ( ∆ m ag s / a r cs e c ond ) southwest L’F110WF160WF205W (b)
Fig. 2.—
Left : SB profiles for the HD 32297 debris disk for the 1-2 µ m HST/NICMOS and 3.8 µ m LBTI data for the northeastern lobe. Right : The same except for the southwestern lobe of the disk. Interestingly, the SB asymmetry at 0 . ′′ . ′′ L ′ data. Inward of 0 . ′′
5, the disk’s SB declines more steeply than at larger stellocentric separations,and we do not find evidence for an asymmetry near 0 . ′′ . ′′ µ m data are generally consistent with the L ′ data within the uncertainties. at 1-2 µ m with HST/NICMOS but is detected at L ′ .At these close distances, the disk SB clearly falls faster,declining like ∼ r − . . We do not compare our reportedpower-law indices to indices reported in other works mea-sured farther from the star because the disk is thoughtto have a break in the SB distribution near 110 AU (1 ′′ ;Boccaletti et al. 2012; Currie et al. 2012). Midplane Offset Measurements
Currie et al. (2012) measured the PA of the HD 32297debris disk as a function of separation from the star at Ks band and found that the disk was bowed close to thestar. Similar bowing was reported by Boccaletti et al.(2012) and Esposito et al. (2013). To test whether thebow shape is seen at L ′ , we measured the offset of the disk relative to the midplane as a function of distancefrom the star. We measure the midplane offset, as op-posed to the disk’s PA, because the former is a moreintuitive indicator of a bow-shaped disk. The offsetswere measured in manners analogous to those describedin Rodigas et al. (2012) and Currie et al. (2012). Fig. 3shows these offsets for the northeastern and southwesternlobes, along with the midplane offsets for the Ks banddata from Currie et al. (2012) for reference. The diskis clearly bowed at L ′ , with the offsets increasing closerto the star on both sides of the disk to a peak value of ∼ . ′′
04 (4.5 AU). This is comparable to the peak mid-plane offset reported by Esposito et al. (2013) and agreeswith the peak offsets in the Ks band data (Fig. 3c andFig. 3d). TABLE 1Surface Brightness Profile Power-law Indices µ m 2.05 µ m 1.6 µ m 1.1 µ mnortheast outer (0 . ′′ < r < . ′′
1) -1.5 (-2.45, -0.55) ∗ -1.83 (-2.12, -1.53) -1.56 (-1.99, -1.13) -1.33 (-1.73, -0.93)southwest outer (0 . ′′ < r < . ′′
1) -1.3 (-1.86, -0.72) -1.56 (-1.88, -1.24) -1.55 (-1.92, -1.17) -1.32 (-1.52, -1.11)northeast inner ( r < . ′′
5) -2.45 (-3.36, -1.53) – – –southwest inner ( r < . ′′
5) -2.72 (-10.74, 5.3) – – – ∗ These and all other parenthetical values denote 95% confidence bounds. distance from star (arcseconds) m i dp l ane o ff s e t ( a r cs e c ond s ) northeast (a) distance from star (arcseconds) m i dp l ane o ff s e t ( a r cs e c ond s ) southwest (b) distance from star (arcseconds) m i dp l ane o ff s e t ( a r cs e c ond s ) (c) distance from star (arcseconds) m i dp l ane o ff s e t ( a r cs e c ond s ) (d) Fig. 3.—
Top left : Disk midplane offset as a function of distance from the star at 3.8 µ m for the northeastern lobe. Top right : The sameexcept for the southwestern lobe of the disk.
Bottom row : the same as the top row, except the offsets are measured on the Ks band datafrom Currie et al. (2012). The offset from the midplane increases closer to the star at both L ′ and Ks band, indicating a bow-shaped disk.The offsets peak at ∼ . ′′ . ′′
06 (4.5-7 AU).
Revised Spectral Classification, Luminosity, Mass,and Age of HD 32297
Estimating the masses of exoplanets detected via di-rect imaging requires atmospheric models, which dependheavily on the age of the planet and therefore on the hoststar. The age of HD 32297, like many stars, is poorlyconstrained. Estimates of the star’s spectral type, whichcan be used to constrain its age, have ranged from A0(Torres et al. 2006) to A5 (Heckmann 1975). Based onan archival optical spectrum of the star taken on 2 Febru-ary 2006 with the 300 line grating of the FAST spectro-graph on the Tillinghast telescope , and comparison of the spectrum to a dense grid of MK standard stars usingthe python tool “sptool” , we estimate the star’s spec-tral type to be kA3hA6mA6 V (see Fig. 4a). The oft-quoted spectral type for the star of A0 is clearly too hot.Based on the hydrogen type of A6, we adopt an effectivetemperature of T eff = 8000 ±
150 K on the modern dwarfT eff vs. spectral type scale from Pecaut & Mamajek(2013). Plotting the star’s updated position on an HRdiagram (Fig. 4b), along with isochrones from the evolu- http://rumtph.org/pecaut/sptool/ Each of the lower-case prefix letters corresponds to a differentspectral typing method; “k” refers to the star’s spectral type basedon Ca K absorption; “h” refers to the star’s hydrogen type; “m”refers to the star’s metal-type.
Rodigas et al. (a)(b)
Fig. 4.—
Top : Visible spectrum of HD 32297, used for deter-mining its spectral type, which we classify as A6V.
Bottom : HD32297’s position on an HR diagram with pre-main sequence andmain sequence isochrones from Bressan et al. (2012) for an as-sumed protosolar composition with Helium mass fraction Y = 0.27and metal mass fraction Z = 0.017. The star is likely older than ∼
15 Myr and younger than ∼
500 Myr. In this study, we take theage of the star to be 100 Myr. tionary tracks of Bressan et al. (2012), we estimate thatHD 32297 is older than ∼
15 Myr and younger than ∼ ∼ ⊙ ) =0.79 ± eff and log(L) points that were “physical” (i.e. notbelow the zero age main-sequence), and assuming proto-solar composition, we determine the mass of HD 32297to be 1.65 ± ⊙ . This is much smaller than the oft-quoted higher mass value ( ∼ ⊙ ) that corresponds toa star of spectral type A0. Limits on Planets
In addition to being sensitive to scattered light fromdebris disks at L ′ , imaging at this wavelength is alsoparticularly sensitive to self-luminous planets, which areexpected to become redder (from 1-5 µ m) as they ageand cool (Burrows et al. 2003; Baraffe et al. 2003). Un-derstanding the connection between massive planets anddebris disks is critical to constraining planetary systemarchitectures and consequently planet formation.By inspection of the SNRE map in Fig. 1b, only onesource stands at 5 σ above the noise (the typical minimumthreshold for detecting imaged exoplanets). However thisfeature, located ∼ ′′ below the star to the southeast, isnot point-like in the final reduced image (Fig. 1a), isnot very symmetrical, and does not persist for differentreduction methods (e.g., varying the number of modesused in PCA). Therefore we do not treat this as a realastronomical source. Other than this feature, there areno point-source features outside the disk at S/N > L ′ image.To ascertain what planets we could have detected, weassume that any planets in the HD 32297 system mustcurrently reside within the debris disk itself and there-fore insert artificial planets into the midplane of the disk.The insertion of artificial sources into the disk is a validmethod because the disk is likely to be optically thin, sothe signals from any real embedded planets should travelto Earth relatively unimpeded. We vary the brightnessesof the artificial planets and re-reduce the data until eachis recovered at ≥ σ confidence. The S/N is calculatedas the peak pixel value in the SNRE map at a given posi-tion. Artificial planets are made by extracting the central0 . ′′
094 (=FWHM at L ′ ) of the unsaturated photometricimage of HD 32297. The reduction pipeline for the plan-ets uses the same parameters as were used to detect thedisk at high S/N except that we set K = 5.When calculating the S/Ns of the recovered planets, wehave to be careful about how we interpret the values sincesignals from the planets lie on top of the signal from thedisk. Therefore any measurement of a recovered planet’sS/N must first subtract out the S/N of the recovereddisk. After doing this, only planets at a contrast level of2 . × − (11.5 mags) were detected at 5 σ confidencebeyond 1 . ′′
25. At a contrast level of 5 × − , all planetswith separations ≥ . ′′
75 were successfully detected, andat 5 . × − all planets at ≥ . ′′ . ′′
5, only planets 100 times fainter than the star couldbe detected at > σ confidence, and even these becomehighly elongated due to the increased self-subtraction soclose to the star. This self-subtraction could in prin-ciple be removed by reducing the data more carefully(e.g., including a minimum azimuthal field rotation be-fore subtracting a PSF image), but such an exhaustiveoptimization of PCA is unnecessary since it would prob-ably not increase contrast levels here by more than afactor of 10. Fig. 5 shows three example images, alongwith their S/N maps, of artificial planets inserted intothe disk. Fig. 6 summarizes all the planet detection re-sults. Adopting a stellar age of 100 Myr and using thehot-start atmospheric models of Baraffe et al. (2003), werule out planets more massive than 8 M J at projectedseparations ≥ . ′′ ∼ J beyond 1. . ′′
25 (140 AU). MODELING THE DEBRIS DISK’S DUST arcseconds a r cs e c ond s −1 −0.5 0 0.5 1−1−0.500.51 −0.200.20.40.60.81 (a) arcseconds a r cs e c ond s −1 −0.5 0 0.5 1−1−0.500.51 −0.200.20.40.60.81 (b) arcseconds a r cs e c ond s −1 −0.5 0 0.5 1−1−0.500.51 −0.200.20.40.60.81 (c) arcseconds a r cs e c ond s −1 −0.5 0 0.5 1−1−0.500.51 0123456789 (d) arcseconds a r cs e c ond s −1 −0.5 0 0.5 1−1−0.500.51 0123456789 (e) arcseconds a r cs e c ond s −1 −0.5 0 0.5 1−1−0.500.51 0123456789 (f) Fig. 5.—
Artificial planets of varying brightnesses inserted into the HD 32297 debris disk and recovered. The top row consists of there-reduced images with the planets inserted, and the bottom row is the corresponding S/N of the detections (after subtracting the S/N ofthe disk itself). From left to right, the brightnesses of the planets increase, with the leftmost panel showing no 5 σ detections (planets thatare 10 − times fainter than the star), the middle panel showing detections beyond 0 . ′′
75 (contrast level of 5 × − ), and the rightmostshowing successful detections for all planets at ≥ . ′′ . × − ). distance from star (arcseconds) σ c on t r a s t ( m ag s ) J , 100 Myr5 M J , 100 Myr Fig. 6.—
Limits on the masses of planets that could have beendetected at 5 σ confidence in our L ′ dataset (solid black line). Thedashed lines correspond to the contrast (in mags) 100 Myr oldplanets would have in this system from Baraffe et al. (2003). Werule out planets more massive than 8 M J at projected separations ≥ . ′′
5, and planets more massive than ∼ J beyond 1 . ′′ The high S/N images of HD 32297 debris disk at mul-tiple wavelengths provide a unique window into the dustgrain properties within the disk. Under the assumptionthat a single population of grains can explain all the ob-servations, we set out to test the recent models of theHD 32297 disk from D13, which are constrained by ob-servations of the disk at Ks band (Boccaletti et al. 2012)along with detailed FIR SED modeling. The primarystructure of their modeled debris disk is that of at leastone component with a sharp edge at 110 AU and a drop-off in surface density with increasing radius. An interior, warmer component is preferred to fit an additional hotcomponent of dust (D13, Currie et al. (2012)), but thisis unobservable at the current inner working angles. Anymodel must be able to reproduce the SB distributions inFig. 2. Scattered light model of an optically-thin edge-ondisk
We construct a model of the disk in a similar fashionto Currie et al. (2012) (and references therein). An an-alytical density distribution of dust is generated in a 3dimensional array and sampled in a Monte Carlo fash-ion with 2 million particles representing a model dustpopulation. Scattering angles are calculated for the den-sity distribution with a given PA and inclination. Inputsto the model include a cross-sectional averaged asym-metry parameter < g > , which can be used to modelthe forward scattering nature of a grain model in a self-consistent fashion assuming a specific grain size distri-bution (Augereau & Beust 2006; Wolf & Voshchinnikov2004): < g > = R a max a min n ( a ) C sca ( a ) g ( a ) d a R a max a min n ( a ) C sca ( a ) d a , (1)where n is the density of the dust in the disk and C sca is the scattering cross-section. The variable < g > cancreate an approximate phase function as a function ofscattering angle Φ( θ ) for the dust under the assumptionof a Henyey-Greenstein (HG) functional form:Φ( θ ) = 14 π (1 − < g > )(1+ < g > − θ ) . . (2)The code can include linear combinations of < g > Rodigas et al. −3 wavelength ( µ m) SB d i sk / F s t a r ( a r cs e c ond s − )
59 AU (a) −3 wavelength ( µ m) SB d i sk / F s t a r ( a r cs e c ond s − )
68 AU (b) −3 wavelength ( µ m) SB d i sk / F s t a r ( a r cs e c ond s − )
76 AU (c) −3 wavelength ( µ m) SB d i sk / F s t a r ( a r cs e c ond s − )
85 AU (d) −3 wavelength ( µ m) SB d i sk / F s t a r ( a r cs e c ond s − )
93 AU (e)
Fig. 7.—
HD 32297 debris disk spectrum from 59-93 AU, averaged at each distance between the northeast and southwest lobes (blackstars), along with the D13 model spectrum (solid purple lines), the modified D13 model (dashed purple lines), and the pure water ice model(solid blue lines). The horizontal black lines denote the filter widths at each wavelength. The original D13 model agrees poorly with thedisk’s spectrum, with a reduced chi-square of 17.9. The modified D13 model is a better match, with a reduced chi-square of 2.87. The bestmatch to the data is the pure water ice model, with a reduced chi-square of 1.06. parameters, which might be appropriate for debrisdisks and can reproduce the phase function that hasbeen found for the zodiacal dust in the solar system(Currie et al. 2012; Hong 1985). To convert an observeddisk SB into a mass, one must solve for the combina-tion of both the phase function of the dust and the size-averaged cross section of the dust < C sca > : < C sca > = Z a max a min n ( a ) C sca ( a ) d a. (3)We calculated scattering cross-sections < C sca > and < g > using the real and imaginary parts of the complexindices of refraction for the best-fitting grain model (pro-vided kindly by J. Donaldson, private communication)from the code miex , which has been designed specifi-cally for fast modeling of debris disks with a size distri-bution of dust (Wolf & Voshchinnikov 2004; Ertel et al.2011). The grain model used here (and by D13) is a 1:2:3mixture of 90% porous silicates, carbon, and water icegrains 2.1-1000 µ m in size; such compositions may also beappropriate for other debris disks (e.g., Lebreton et al.2012). Models were generated for each image (wave-length) with the appropriate pixel scale and sampled in asimilar fashion to our SB profiles (Section 3.2). A scalingfactor for each lobe of the disk was calculated by ratioingthe models with the observed disk SB profiles as a func-tion of wavelength. For the disk’s density distribution,we used the best-fitting distribution in Boccaletti et al.(2012), based on analysis of their Ks band disk data,because D13 also used this model for their geometrical constraints: n ( r ) = n √ (cid:18)(cid:16) r (cid:17) − α out + (cid:16) r (cid:17) − α in (cid:19) − / , (4)where n is the midplane number density at the referencedistance of 110 AU, and α out = − α in = 2. Wealso kept their assumption of < g > = 0.5, which issomewhat degenerate with the choice of an interior steeppower law drop-off in density interior to 110 AU. It isalso not consistent with Mie calculations of the expected < g > , which is closer to 0.99. Comparison to original D13 cometary grains model
For the D13 model to be accepted as a good match tothe data, it must reproduce the disk’s SB at all wave-lengths and distances from the star. This can be mea-sured by calculating the reduced chi-square. We accom-plish this by summing up the squared difference betweenthe model disk SB and the real disk SB at all wave-lengths and at all disk locations, divided by the numberof degrees of freedom and the uncertainties squared. Wemeasured this value to be 17.9, indicating a poor fit. Toillustrate, Fig. 7 shows the spectrum of the disk at 59-93AU (black stars), along with the D13 cometary grainsmodel (solid purple lines). The SB values for the north-east and southwest lobes of the disk have been averagedat each wavelength because the D13 model is axisym-metric.In general, this model overpredicts the disk’s SB and istherefore a poor overall fit. However, at ∼ . ′′ L ′ image). Comparison to modified D13 cometary grains model
Seeking to obtain an alternate model fit to the data,we modified the density distribution of the original D13cometary grains model. This is necessary because thedisk’s actual SB at 1-2 µ m is shallower (lower SB power-laws) than the model disk’s SB. Therefore we modifiedthe model’s dust distribution to better reproduce thedata. Specifically we tested different values of α out and α in , picking α out = − α in = 5 based on chi-squareminimization. This modification resulted in a much im-proved reduced chi-square value of 2.87. This model isshown in Fig. 7 as the dashed purple lines. Comparison to pure water ice model wavelength ( µ m) no r m a li z ed SB d i sk / F s t a r combined Fig. 8.—
Combined spectrum of the disk from 59-93 AU, ob-tained by normalizing the spectra from Fig. 7 at 1.1 µ m and thentaking the median value at each wavelength (black stars). The hor-izontal black lines denote the filter widths at each wavelength. Thesolid purple line corresponds to the D13 model spectrum, adjustedsuch that the residuals between the data and the model are at aminimum. The solid blue line corresponds to the pure water icemodel spectrum, adjusted in the same fashion. After scaling theD13 model spectrum, the pure water ice model has a chi-squarevalue ∼ × lower, indicating a better spectral fit to the data, butadditional data at 3.1 µ m is required to help distinguish betweencomets and pure water ice. We also tested a pure water ice model, since the inclu-sion of water ice significantly improved the model fits tothe FIR SED of the disk (D13). Simpler compositionslike astronomical silicates are not modeled because theseproduced poor fits to the FIR SED data (D13), and morecomplex models like tholins (Debes et al. 2008a) resultedin poor fits to the data . The pure water ice model diskhad the same density distribution as the modified D13model ( α out = − α in = 5), except the dust grains were hard spheres 3 µ m in size. This model is the bestfit to all of the available NIR data (Fig. 7; reduced chi-square = 1.09).If we ignore the requirement that the models mustmatch the disk’s SB distribution, allowing the modelspectra to be arbitrarily scaled to match the disk’s spec-trum, we can determine which model is the best spectral fit to the data. To increase the S/N of the data, we nor-malized the disk spectra from 59-93 AU at 1.1 µ m andcomputed the median value at each wavelength. Thesevalues are shown in Fig. 8 (black stars). We then scaledthe original D13 model spectrum until the residuals be-tween the data and model were minimized. This is shownas the solid purple line in Fig. 8. After optimizing thespectral fit, the D13 model is blue and underpredicts thedisk’s SB at 3.8 µ m, while the real disk’s spectrum is graywithin the uncertainties. We repeated this procedure forthe pure water ice model. The chi-square value for thewater ice model is ∼ × lower than the D13 model, in-dicating this model is still preferred over the cometarygrains model based on the available data. DISCUSSION
Disk Structure
Fig. 2 and Fig. 3 allow us to characterize the struc-ture of HD 32297’s debris disk. The SB asymmetry be-tween the two sides of the disk from 0 . ′′ . ′′ L ′ (and Ks band from Currie et al. (2012)) suggeststhat the northeastern lobe of the disk has a deficit of dustgrains here. Furthermore, by inspection of the SB profilepower-law indices in Table 1, we can see that interior to0 . ′′ Ks band (Currie et al.2012), corroborating this feature. The inner componentcould be located at .
50 AU but needs to be confirmedwith additional imaging that is sensitive to scatteredlight close to the star.This is not the first time a second inner disk componenthas been suggested for the HD 32297 debris disk. D13favored a warm inner component for their modeling, andFitzgerald et al. (2007) used 11 µ m images to suggesta population of dust grains that peaks near ∼
60 AU.Such thermally-emitting grains may also be contribut-ing to the scattered light that has been detected at 2-4 µ m. Currie et al. (2012) also preferred multiple belts,including a component at ∼
45 AU, to explain the disk’sobserved SB and SED. Our L ′ data appear to supportthe notion of a second interior belt, but additional datawith very small inner working angles would help validatethis explanation.The midplane offset profiles show that the disk isbowed close to the star, agreeing with similar find-ings at Ks band (Currie et al. 2012; Boccaletti et al.2012; Esposito et al. 2013). We do not explicitlymodel this phenomenon because we have already showed0 Rodigas et al.that it can be explained (for both HD 15115 andHD 32297) by a highly-inclined ring-like disk consist-ing of forward-scattering grains (Rodigas et al. 2012;Currie et al. 2012).No high-mass (8 M J ) planets at projected separa-tions &
56 AU currently reside in the disk based onour L ′ imaging. If such planets exist in this system,their projected separations must be very small, imply-ing either small semimajor axes or an unlucky epochof imaging. The null detection of high-mass planets inthis system, though disappointing, should not be surpris-ing, since there is now copious evidence that such plan-ets are rare at large separations from their stars (e.g.,Wahhaj et al. 2013). While lower-mass planets may stillreside in the HD 32297 system, detecting them will re-quire more advanced imaging capabilities than are cur-rently available. This is further complicated by the like-lihood of such planets residing in the midplane of thedisk, which if bright enough, can hide planets. Residualsfrom PSF subtraction (especially in ADI datasets) canthemselves also resemble point sources, and since theycan be found anywhere in an image (Fig. 1b), includ-ing in the midplane of the disk, distinguishing betweenreal and artificial planets is difficult for systems like HD32297. Future imaging searches for planets around thisstar must adequately take into account the effects of boththe disk itself and the PSF residuals. Dust Grain Composition
D13 found that comet-like porous grains consisting ofsilicates, carbon, and water ice were the best match tothe HD 32297 disk SED at wavelengths longer than 25 µ m. Based on our analysis of the disk’s 1-4 µ m SB andspectrum, we cannot lend further evidence to supportthis claim, at least with respect to their original model.The overall agreement between the data and the D13model is poor (reduced chi-square = 17.9).This does not necessarily exclude comet-like materialsfrom being present in the disk. We were able to achievea much better fit simply by altering the dust densitydistribution in the original cometary grains model. Itmay be that additional tweaking of model parameterswill yield an even better fit. Furthermore D13 reportedonly one “comet” combination; other combinations withdiffering ratios of carbon/silicates/water ice and perhapsthe dust’s porosity might better match the disk’s spec-trum at λ > µ m. Because the spectral coverage iscurrently sparse from 1-4 µ m, complex cometary grainmodeling is beyond the scope of this paper.The best fit to the data is achieved by a pure wa-ter ice model, likely due to the fact that the model isgray from 1-4 µ m, like the disk. This model has a verydeep absorption feature near 3.1 µ m, evident in Fig. 8.The feature is also evident in the cometary grains model,though it is much shallower. Therefore a key additionaltest of the disk’s dust grain composition would be ob-taining very high S/N photometry of the disk using anarrowband filter centered around 3.1 µ m. This wouldhelp determine if the disk’s dust contains any water ice(e.g., Honda et al. 2009), which could then be used torefine the D13 cometary grains model.Other dust grain compositions not tested in this workmay also better support the available data. For example,a perfectly flat/gray model spectrum might better fit the disk’s NIR spectrum, even if such a dust compositionis not easily explained. This is why obtaining a diskdetection at 3.1 µ m is crucial; it can help distinguishbetween various dust models that might fit the availableNIR data. Limitations
While our pure water ice model is the best match to thescattered light data, it may not be for the FIR data (usedby D13). Our model must reproduce all of the availablephotometry at all stellocentric distances to be acceptedas valid; therefore our scattered light modeling shouldnot be considered final. This is especially true becausewe currently lack data near 3.1 µ m, where our preferredmodel has a very deep absorption feature. We stressthat the goal of this study was to test the originally-proposed D13 cometary grains model; if that failed to fitthe data, the goal was to find a reasonable alternative.Pure water ice is one such alternative composition, andit makes predictions that are testable with future data,which can then help refine the original cometary grainsmodel.We also note that producing scattered light models ofdebris disks comes with several problems. The scatter-ing asymmetry parameter, < g > , is not self-consistentwhen computed using the Mie formalism. Additionallythe commonly assumed single component HG formalismmay not be appropriate for this disk (Currie et al. 2012).This would immediately make modeling the dust compo-sition more complicated and beyond the scope of this ini-tial effort. Finally the increasing evidence that the diskmay have an inner component at .
50 AU further com-plicates the modeling process, since we would then haveto consider the possibility of two separate dust popula-tions with two different dust compositions. At this time,it is unclear what the underlying distribution of dust isaround HD 32297. Lacking this knowledge, assuming asingle disk component as we have in this study is a rea-sonable starting point. SUMMARY
We have presented an imaging detection of the HD32297 debris disk at L ′ . The disk is detected at high S/Nfrom ∼ . ′′ . ′′ L ′ imaging,we show that the system does not contain any planetsmore massive than ∼ J beyond 0 . ′′ L ′ is bowed, as was seen at Ks band.This likely indicates that the disk is inclined by afew degrees from edge-on and contains highly forward-scattering grains (Rodigas et al. 2012). The SB at L ′ in-terior to 50 AU rises sharply, as was also seen at Ks band(Currie et al. 2012). This evidence together suggeststhat the disk may contain a second inner component lo-cated at <
50 AU.Comparing the disk’s color at 1-4 µ m over the outerportion of the disk ( >
50 AU) with the recently pro-posed cometary dust grain model of D13 shows that thismodel is a poor overall fit to the disk’s SB distributionand spectrum (reduced chi-square = 17.9). A modifiedversion of this model produces a much better overall fitto all the data (reduced chi-square = 2.87). The bestfit to the data is achieved with a pure water ice model,though this model is not the only possible dust compo-sition. Additional imaging of the disk near 3.1 µ m can1help constrain the fractional amount of water ice in thedust. This will then help determine how similar the HD32297 dust grains are to comet-like grains.We thank the anonymous referee for helpful commentsthat improved this paper. We thank Jessica Donaldsonfor sharing her disk model and for helpful discussions.We thank the LBT observatory staff for their help oper- ating and maintaining the telescope and its powerful in-struments. We acknowledge support for LMIRcam fromthe National Science Foundation under grant NSF AST-0705296. T.J.R. acknowledges support from the NASAEarth and Space Science Fellowship (NESSF) during histime at the University of Arizona. VB is funded bythe NSF Graduate Research Fellowship Program (DGE-1143853). APPENDIX
SURFACE BRIGHTNESS CORRECTIONS
Determining the SB of the disk as a function of distance from the star at multiple wavelengths requires several stepsto ensure the correct quantities are measured (Debes et al. 2008b). The true SB of an edge-on debris disk a distance r away from the star is computed as follows:SB true ( r ) = SB measured ( r ) × (PSF convolution correction) × (aperture size correction) × (reduction bias correction) , (A1)where the PSF convolution correction (often referred to as “aperture correction”) is employed to account for non-infinite photometric apertures, and the latter two corrections are only necessary if different aperture sizes are used atdifferent wavelengths and if the data reduction pipeline alters the SB of the disk as a function of distance from thestar.We computed the appropriate corrections necessary for the HST/NICMOS and LBTI/LMIRcam L ′ data. ThePSF convolution correction was computed as follows. We produced unconvolved and convolved model disk images(with parameters determined from the best-fitting model used in Boccaletti et al. 2012). In total, we generated oneunconvolved model image for the HST/NICMOS data (since all the HST data was taken at the same plate scale),and one unconvolved model image for the higher-resolution LBTI/LMIRcam data. Four convolved images (one foreach wavelength) were produced by convolving the corresponding unconvolved model image with the appropriate PSFtemplate (either HST/NICMOS or LBTI/LMIRcam).We measured the SB in all the HST/NICMOS model images using the same 3 pixel (0 . ′′ arcseconds a r cs e c ond s −1 −0.5 0 0.5 1−1−0.500.51 −0.2−0.100.10.20.30.40.50.60.70.8 (a) distance from star (arcseconds) P C A / A D I b i a s c o rr e c t i on f a c t o r (b) distance from star (arcseconds) ape r t u r e s i z e c o rr e c t i on × PS F c on v o l u t i on c o rr e c t i on (c) Fig. 9.—
Left : Final reduced L ′ image of the HD 32297 debris disk along with three artificial disks, all in units of detector counts/s, withNorth-up, East-left. A 0 . ′′ ∼ ◦ . All threemodel disks are easily recovered by the PCA pipeline, allowing correction factors for the real disk’s surface brightness to be calculated. Middle : PCA/ADI reduction bias correction factors as a function of distance from the star, with a fitted function (dashed line).
Right :the same, except for the aperture size correction factor × the PSF convolution correction factor. The correction changes with separationfrom the star because a non-uniform structure that changes with distance is being convolved with a PSF (Debes et al. 2008b). The aperture size correction was only needed for the L ′ data, since a smaller photometric aperture was used. Wecompared the median SB in the unconvolved model HST image (computed using the 3 pixel (0 . ′′ L ′ image (computed using the 5 pixel (0 . ′′ × the PSF convolution corrections for the L ′ data.Finally, the L ′ data required a correction to account for the biases inherent in PCA + ADI data reduction (e.g.,Rodigas et al. 2012; Currie et al. 2012). We measured these biases by inserting artificial disks into the raw images2 Rodigas et al.at differing PAs, re-reducing the data, and computing the correction factors based on how the SB of the artificialdisks changed. We inserted three artificial disks (the best-matching model from Boccaletti et al. 2012) of varyingbrightness and PA into the raw images. Specifically, the first disk was slightly brighter than the real disk and located ∼ ◦ away; the second was 10% fainter than the first and located ∼ ◦ away; and the third was 25% fainter than thefirst and located ∼ ◦ away. We chose to insert disks of varying SB and PA to better account for the biases inherentin the PCA reduction.After recovering both the real and artificial disks (Fig. 9a), we measured the PCA correction factors as a functionof separation from the star by comparing the median counts/s in the same 5 pixel (0 . ′′ REFERENCESAugereau, J.-C., & Beust, H. 2006, A&A, 455, 987Baraffe, I., Chabrier, G., Barman, T. S., Allard, F., & Hauschildt,P. 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C. 2008, ARA&A, 46, 339 Esposito et al. (2013) showed that forward-modeling was apotentially more accurate method for determining the true SB ofedge-on disks. However their method currently requires the use ofLOCI, rather than PCA, therefore we do not employ their methodin this study. For two of the artifical disks, the azimuthal separation from the real disk is less than the total parallactic angle rotation(50.84 ◦◦