The Frequency of Debris Disks at White Dwarfs

The Frequency of Debris Disks at White Dwarfs

Sara D. Barber11affiliation: Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, 440 W. Brooks St., Norman, OK, 73019, USA 55affiliation: barber@nhn.ou.edu , Adam J. Patterson11affiliation: Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, 440 W. Brooks St., Norman, OK, 73019, USA , Mukremin Kilic11affiliation: Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, 440 W. Brooks St., Norman, OK, 73019, USA , S. K. Leggett22affiliation: Gemini Observatory, 670 N. A’ohoku Place, Hilo, HI 96720, USA , P. Dufour33affiliation: Département de Physique, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec H3C 3J7, Canada , J. S. Bloom44affiliation: Department of Astronomy, University of California, Berkeley, CA 94720, USA , D. L. Starr44affiliation: Department of Astronomy, University of California, Berkeley, CA 94720, USA
Abstract

We present near- and mid-infrared photometry and spectroscopy from PAIRITEL, IRTF, and Spitzer of a metallicity-unbiased sample of 117 cool, hydrogen-atmosphere white dwarfs from the Palomar-Green survey and find five with excess radiation in the infrared, translating to a  frequency of debris disks. This is slightly higher than, but consistent with the results of previous surveys. Using an initial-final mass relation, we apply this result to the progenitor stars of our sample and conclude that M stars have at least a 4.3% chance of hosting planets; an indirect probe of the intermediate-mass regime eluding conventional exoplanetary detection methods. Alternatively, we interpret this result as a limit on accretion timescales as a fraction of white dwarf cooling ages; white dwarfs accrete debris from several generations of disks for 10Myr. The average total mass accreted by these stars ranges from that of 200km asteroids to Ceres-sized objects, indicating that white dwarfs accrete moons and dwarf planets as well as Solar System asteroid analogues.

infrared: planetary systems — infrared: stars — white dwarfs

1 Introduction

The study of extrasolar planetary systems has become a very active field that will continue to grow in the coming years and decades. Over the last two decades, several hundred exoplanets have been discovered, proving planet formation to be a robust process in the Galaxy. The vast majority of known exoplanets have been discovered using just two techniques; namely, radial velocity and transits. To date, radial velocity studies have revealed the presence of well over five hundred planets and the number of transiting systems has passed the two hundred mark (see http://exoplanet.eu and Schneider et al. 2011).

A cursory examination of these planet-hosting stellar systems reveals a curious trend. The frequency of Jovian planets increases from 3% for M dwarfs to 14% for 2M stars (Johnson et al. 2010; Bowler et al. 2010). In addition, the distribution of known exoplanets as a function of host stellar mass has a strong cutoff at 3M, above which no exoplanets have been found. Could it be that planets do not form around intermediate-mass stars, or is this a selection effect? The planet formation models of Kennedy & Kenyon (2008) suggest the latter. They predict that the fraction of stars with giant planets shows a steady increase with mass up to 3M. In addition, the mass of the planets and the width of the regions where they form are predicted to increase with stellar mass. Probing intermediate-mass stellar systems for planets could help test these planet formation models. Since most exoplanet detection methods tend to break down in the intermediate-mass range, one can look at these systems in post main-sequence where the contrast between the planet’s photometric signal and that of its host is greatly decreased. This work examines a sample of white dwarfs decedent from stars and constrains the frequency of planetary systems in the elusive intermediate-mass regime.

If planets survive post-MS evolution, they should be detectable around WDs (Burleigh et al. 2002; Gould & Kilic 2008). Unfortunately, there are still no confirmed planets around single WDs. The candidate planet around the pulsating WD GD 66 (Mullally et al. 2007a) is currently disputed (J. J. Hermes 2012, private communication). Perhaps an easier way to detect remnant planetary systems around WDs is to look for the tidally disrupted remains of exoplanets and moons in the form of circumstellar debris disks (Debes & Sigurdsson 2002; Jura 2003; Kilic et al. 2006). There are now two dozen WDs known to host dust and/or gas disks. Photospheric abundance analyses of these WDs show that the accreted metals originate from tidally disrupted minor bodies similar in composition to that of bulk Earth (Zuckerman et al. 2007; Klein et al. 2010, 2011; Dufour et al. 2010, 2012). Since at least one giant planet is required to perturb minor bodies out of their stable orbits (Debes et al. 2012), photospheric pollution as well as circumstellar debris disks serve as tracers for giant planets at WDs. Therefore, the frequency of debris disks around WDs can be taken as a lower limit on the frequency of planets around WD remnants of intermediate-mass stars.

The search for debris disks around WDs begins as a search for excess emission in the infrared. Over the last two decades, several hundreds of WDs have been surveyed for infrared excess due to substellar companions or circumstellar disks. The first dusty WD, G29-38, was identified by Zuckerman & Becklin (1987), see also Graham et al. (1990). Zuckerman & Becklin (1992) examined 200 WDs for excesses in the K-band, while Farihi et al. (2005) surveyed 371 WDs of all spectral types and constrained the frequency of substellar companions to less than 0.5%. The discovery of the second dusty WD, GD 362, (Kilic et al. 2005; Becklin et al. 2005) lead to the realization that dusty WDs may be found more readily by looking at metal-rich WDs.

Previous surveys for debris disks around WDs focused on metal-rich WDs since so far all known WDs with disks also show metal absorption lines in their optical and ultraviolet spectra; DAZ and DBZ spectral types. The Poynting-Robertson drag timescale is significantly shorter than the evolutionary timescales for WDs (von Hippel et al. 2007; Rafikov 2011b), hence we expect every WD with dust/gas disks to accrete metals from these disks and appear metal-rich. Zuckerman et al. (2003, 2010) find that about 30% of DA and DB WDs show trace amounts of metals in their photospheres. However, only % of DAZs, the ones with the highest accretion rates, host dust (Kilic et al. 2008; Farihi et al. 2009). The source of metals for the other DAZs remains uknown, but it is likely that the majority of DAZs accrete many small asteroids that do not form a large debris disk (Jura 2008).

Mullally et al. (2007a) survey 124 WDs with K using mid-infrared Spitzer photometry. Their search for infrared excess finds 2 dusty WDs for a disk frequency of 1.6%. However, this survey extends beyond the temperature range within which solid dust orbiting interior to the tidal radius can persist. Based on Spitzer observations of mostly metal-rich WDs, Farihi et al. (2009) estimate a debris disk frequency of 1% to 3% for WDs younger than 500Myr. Debes et al. (2011) recently searched for infrared excesses amongst an unbiased (in terms of metallicity) WD sample using the Wide-field Infrared Survey Explorer (WISE, Wright et al. 2010) data. They found about % of these WDs to be dusty. However, the large beam size of WISE allows for many false positives due to background contamination, and many of these dusty WD candidates need follow-up higher spatial resolution infrared imaging data to confirm the observed infrared excess.

Here we present a near- and mid-infrared photometric and spectroscopic survey of an unbiased (in terms of metallicity) sample of DA WDs from the Palomar-Green (PG) survey. Our survey does not focus on metal-rich WDs and thus constrains the disk frequency representative of the general WD population. We target 117 PG WDs with accurate temperature, mass, and age estimates (Liebert et al. 2005) and K. With 117 objects we sample temperatures at which solid dust can persist within the tidal radius and thus improve upon the constraint obtained by Mullally et al. (2007a) whose sample includes 69 WDs in this temperature range. The WDs in our sample are the descendants of MS stars with masses between M, so this study extends the search for planets well beyond the mass range available to conventional exoplanet detection methods. Section 2 describes our near- and mid-infrared photometry and spectroscopy data, while Section 3 presents the spectral energy distributions (SEDs) and the dusty WDs in the PG survey. Section 4 presents a discussion of the frequency of disks and planets around WDs and their progenitor MS stars.

2 Observations

2.1 The Sample

Almost all known dusty WDs are relatively young with cooling ages of Gyr and temperatures in the range K (with the exception of G166-58, Farihi et al. 2008). This is probably because a second heavy bombardment phase occurs around intermediate-mass stars in their post-MS evolution due to planetary migration around the mass-losing star (Debes et al. 2012; Bonsor & Wyatt 2012). We would expect to see a peak in the frequency of collisions, tidal disruptions, and disks around the younger WD remnants of such stars (Debes & Sigurdsson 2002).

Consider the disk around G29-38 as a typical system. Jura (2003) models the disk emission and obtains a ring of dust extending from to and K. Such a disk around a star twice or three times as hot as G29-38 would be sublimated and invisible in the IR. Thats why our target selection using effective temperature gives a better measurement of the real frequency of disks.

We select 117 apparently single DA WDs from the PG survey with K, where we are most efficient in finding the disks using near- and mid-infrared data. Liebert et al. (2005) performed a detailed model atmosphere analysis of all DA WDs in the PG survey and provided temperature, surface gravity, mass, and age estimates. Their spectroscopy did not have enough resolution to detect the metal-rich DAZs among these targets; our survey does not have a metallicity bias, and hence it has the potential to reveal the true frequency of dusty disks without knowing the fraction of metal-rich WDs among the nearby WD population.

2.2 Near-infrared Photometry

We obtained simultaneous JH imaging of 78 WDs using the Peters Automated Imaging Telescope (PAIRITEL, Bloom et al. 2006) between 2009 Feb and 2010 Apr. PAIRITEL is the old Two Micron All Sky Survey (2MASS, Cutri et al. 2003) telescope and it uses the same camera and filter set. The total exposure time for our targets ranged from 70 s to 1,500 s depending on the expected brightness of each target. We use the PAIRITEL pipeline version 3.3 processed images and standard IRAF DAOPHOT routines to perform aperture photometry on every 2MASS source detected in the images. We use the 2MASS stars to calibrate the photometry for each object.

Table 1 presents the PAIRITEL photometry (and the 2MASS photometry of a few relatively bright targets) for our sample along with the physical parameters obtained from the model atmosphere analysis of Liebert et al. (2005). We compare our PAIRITEL photometry to that of 2MASS in Figure 1. Only about half of our targets are detected by 2MASS in the K-band, and usually with large photometric errors. Our survey goes significantly deeper than 2MASS, and provides improved photometry with smaller errors, which is essential for identifying objects with slight band excesses. This figure demonstrates that the PAIRITEL photometry agrees fairly well with the 2MASS photometry and that it can be used reliably to constrain the near-infrared SEDs of our targets.

Figure 2 shows and colors of our sample of stars as a function of their effective temperatures. The colors for the majority of our targets follow the model predictions of mag, though with some scatter. There are four WDs with excesses, though with relatively noisy 2MASS photometry. However, from the available mid-infrared photometry from Spitzer and/or WISE, we conclude that there is no evidence of excess in these objects. The photometry for the rest of the targets are consistent with the emission from single WDs. Several of these apparently single WDs have positive colors, suggesting extra emission from a cool companion or a circumstellar debris disk. We chose to further examine those objects with positive colors by obtaining near-infrared spectra and mid-infrared photometry. Objects with apparently red colors were targeted however, depending on the timing of the observing runs and conditions, some of the objects with blue colors were also followed up as a sanity check.

2.3 Near-infrared Spectroscopy

We obtained low-resolution near-infrared spectra of 41 WDs over several nights in 2011 April, August, and September using the 3-m NASA InfraRed Telescope Facility (IRTF) equipped with the Micron Medium-Resolution Spectrograph and Imager (Spex; Rayner et al. 2003). The observing setup and procedures are similar to those of Kilic et al. (2012). We use a slit to obtain a resolving power of 90-210 over the range. The observations are taken in two different positions on the slit separated by . We use internal calibration lamps (a 0.1W incandescent lamp and an Argon lamp) for flat-fielding and wavelength calibration, respectively. To correct for telluric features and flux calibrate the spectra, we use the observations of nearby A0V stars at a similar airmass to the target observations. We use the IDL-based package SPEXTOOL version 3.4 (Cushing et al. 2004) to reduce the data.

To demonstrate that our near-infrared observations and reductions are reliable, we also obtained a near-infrared spectrum of the previously known dusty WD GALEX J193156.8+011745 (hereafter J1931+0117; Vennes et al. 2010; Debes et al. 2011; Melis et al. 2011). Figure 3 shows the near-infrared photometry and our IRTF spectrum of this object. There are two nearby red sources within 2 of the WD (Melis et al. 2011). Our IRTF observations were obtained under average seeing conditions of 0.8 and our 0.5 slit minimizes the contamination from the nearby sources. A slight excess is clearly detected redward of 2.1, typical of dusty WDs (Kilic et al. 2006). Melis et al. (2011) also obtained a near-infrared spectrum of J1931+0117 on the Magellan 6.5m Baade telescope, which shows a significantly larger excess redward of 1.6. Those authors discuss the potential problems with the flux calibration of their spectra. They model the excess around J1931+0117 with a flat disk model with inner and outer temperatures of 1400 and 1200 K, essentially a narrow ring of dust. Our IRTF spectrum demonstrates that the excess around J1931+0117 mostly shows up redward of 2.1 and it is similar to the other dusty WDs with extended (up to 1) disks. Of course, the outer edge of the disk around J1931+0117 is currently unconstrained due to the lack of uncontaminated mid-infrared photometry. Regardless of these issues, this figure demonstrates that we are able to identify dusty WDs even with slight band excesses.

2.4 Spitzer Photometry

We used the warm Spitzer equipped with the InfraRed Array Camera (IRAC; Fazio et al. 2004) to obtain infrared photometry of 11 WDs between 2010 Sep and 2011 Feb for program number 70023. Based on our preliminary analysis of the PAIRITEL data, these 11 sources appeared to have slight band excesses indicative of debris disks. We obtained 3.6 and 4.5 images with integration times of 30 s or 100 s for nine dither positions. We use the IDL ASTROLIB packages to perform aperture photometry on the individual corrected basic calibrated data frames from the S18.18.0 pipeline reduction.

Following the IRAC calibration procedures, we correct for the location of the source in the array before averaging the fluxes of each of the dithered frames at each wavelength. We also correct the Channel 1 (3.6µm) photometry for the pixel phase dependence. We estimate the photometry error bars from the observed scatter in the nine images corresponding to the dither positions. We add the 3% absolute calibration error in quadrature (Reach et al. 2005). Finally, we divide the estimated fluxes by the color corrections for a Rayleigh-Jeans spectrum, except for the dusty WDs in our sample. Table 2 presents our Spitzer IRAC photometry for 11 PG WDs.

3 Results

Our near-infrared photometric observations revealed several sources with potential band excesses. We followed up 11 of the most interesting targets with Spitzer IRAC and 41 stars in total at the IRTF. Figure 4 shows the SEDs of the 41 stars observed at the IRTF. Here, and in the rest of the figures, the PAIRITEL and 2MASS photometry are shown as blue and green points, respectively. The black lines show the observed spectra and the red solid lines show the predicted photospheric emission for each star assuming a blackbody. The IRTF spectra display telluric correction problems around 1.4 and 1.9, but otherwise they closely follow the predicted blackbody distributions for the majority of the targets in our sample. PG 0048+202 and PG 1720+361 are two of the stars for which our PAIRITEL photometry indicated band excesses, but our IRTF spectra show that there are no significant excesses in the band for these two stars. There is only one WD in our IRTF sample where a significant band excess is detected, PG 1541+651. The observed flux stays essentially constant between 2.0 and 2.5 , which is typical of dusty WDs. The detection of Ca II 3933 Å  absorption in the HIRES spectrum of this object (Xu et al. in preparation) corroborates the presence of circumstellar debris.

Figure 5 shows the near- and mid-infrared data on 11 WDs that we targeted with Spitzer, including PG 1541+651. Eight of these stars also have IRTF spectroscopy available. Our Spitzer observations confirm the results from the IRTF observations; only PG 1541+651 shows a significant infrared excess that is compatible with a debris disk (see Kilic et al. 2012). The SEDs for the other ten objects in this figure are consistent with photospheric emission from each star.

There are four other previously known dusty WDs in our sample; PG 1015+161, PG 1116+026, PG 1457086, and PG 2326+049. Figure 6 displays the SEDs for these four WDs plus PG 1541+651. PG 2326+049 has the most prominent excess, while the excess at PG 1457086 is the most subtle. The variation in the strength of these excesses is likely due to a variation in the disk geometry from object to object. There is another known dusty WD in the Liebert et al. (2005) DA WD sample, PG 1456+298 (G166-58, Farihi et al. 2008) that is cooler than the lower temperature limit of our sample and hence it is not included in Figure 6.

Out of the 117 DA WDs in our sample, the majority have SEDs that closely follow a single blackbody curve, while five WDs show a significant deviation from their blackbody model in the near- to mid-infrared (see Figure 6). In light of the recent WISE All-Sky Data Release, we examine our sample of objects for infrared excesses in the WISE data and plot these results in Figure 7. Four of the five dusty WDs in our sample clearly show infrared excesses in the WISE bands. The fifth dusty WD, PG 1457086, is also detected in the WISE observations, but with large photometric errors. There is another target, PG 1519+384, with positive and colors. However, there are two nearby sources within several arcseconds of this target in the Sloan Digital Sky Survey images. The WISE photometry for PG 1519+384 is likely contaminated by these background sources. Hence, the WISE data do not reveal any new dusty WDs in our sample other than the five systems known.

Farihi et al. (2005) finds a frequency of less than 0.5% for brown dwarf companions of WDs. Given our sample size of 117 we would expect to find less than one brown dwarf companion in our sample. It is not surprising, then, that we do not find any substellar companions. Through the initial selection process, we excluded objects with potential M-dwarf companions.

4 Discussion

4.1 The Frequency of Debris Disks Around WDs

Out of the 348 DA WDs analyzed by Liebert et al. (2005), 308 are apparently single. Six of these PG WDs are known to host dust disks, corresponding to a debris disk frequency of 1.9%. This is similar to the frequency of disks, 1.6%, around the nearby bright WD sample of Mullally et al. (2007a). Of course, these estimates ignore the fact that most disks occur around young WDs (see Kilic et al. 2009b). The process that creates the debris disks around WDs seem to be more efficient at younger ages.

We use the binomial probability distribution to compute the upper and lower limits on the frequency () of disks. The binomial distribution function gives the discrete probability distribution of obtaining exactly successes out of trials (where the result of each trial is true with probability and false with probability ). The probability, , that a survey of WDs will detect debris disks, when the true frequency of disks is is given by (Burgasser et al. 2003, Appendix)

(1)

Since this probability function is not symmetric about its maximum value, we report the range in that delimits 68% of the integrated probability function, equivalent to 1 Gaussian limits. For and , there is a 68% chance of being between 3.1% and 7% (see Figure 8). Thus, . This frequency estimate is slightly higher than, but consistent with, the 3% disk frequency derived by Farihi et al. (2009).

4.2 Planets Around Intermediate-Mass Stars

The 117 WDs in our sample have an average mass of and mass range of . We estimate the progenitor MS masses using the initial-final mass relation derived by Kalirai et al. (2008) and Williams et al. (2009). We obtain an average progenitor mass of and mass range of (see Table 1) where we neglect WDs below 0.5. Based on the observed frequency of disks around our WD targets, we find that the probability of finding planetary systems around their progenitor MS stars is at least . This result serves as an indirect probe of the intermediate-mass stellar systems which have thus far challenged conventional planetary detection techniques (Gould & Kilic 2008).

The dusty WDs in our sample, PG 1015+161, 1116+026, 1457086, 1541+651, and 2326+049 are the descendants of MS stars. At first glance, this argues that planet formation may be most efficient around stars. However, given the age and star formation history of the Galactic disk, our sample is dominated by the WD remnants of MS stars. In fact, 80% of our sample consists of WD descendants of MS stars. Hence, the lack of discoveries of dusty disks, and therefore remnant planetary systems, around the massive WD remnants of stars may be due to small number statistics. There are 22 systems in our sample with progenitors, we would expect to find 1 dusty WD in a sample of 22 stars. The probability of finding zero dusty WDs in a sample of 22, when the expected number is one, is 30% (see Equation 1). Hence, larger surveys of massive WDs are required to detect disks around them and to constrain the frequency of planets around their intermediate-mass progenitor MS stars.

4.3 Disk Lifetimes

An alternative interpretation of the 4.3% disk frequency around WDs is that perhaps 100% of WDs have remnant planetary systems that can create debris disks, but the disks only persist for 4.3% of the cooling age of the WD. For the average cooling age of our sample of WDs, 300Myr, this implies that disks survive around typical WDs for 10Myr. We note that this is the total time a WD accretes from circumstellar debris disks, even though individual disks may last for a significantly shorter amount of time. Kilic et al. (2008) and Farihi et al. (2009) estimate typical disk lifetimes of yr. Hence, up to 100 tidal disruption events that create circumstellar debris disks may occur for any given WD.

von Hippel et al. (2007) use a geometrically thin, optically thick disk model to determine typical accretion rates of WDs. Their result ( g s) means a WD with the disk lifetime typical of our sample will accrete a total mass equivalent to a 400 km Solar System asteroid (assuming an asteroid density of 3 g cm). Rafikov (2011a) demonstrate that the Poynting-Robertson drag can explain accretion rates of around g s from circumstellar debris disks onto the WDs. Taken at face value, this implies a total accreted mass of g, a 200km asteroid, over the disk-hosting lifetime of a WD. However, dusty WDs show accretion rates of up to g s (Dufour et al. 2012). To explain the observed high accretion rates, Rafikov (2011b) and Metzger et al. (2012) propose a runaway accretion scenario where rapid transport of metals from the disk results from interaction between spatially coexisting dust and gas disks. In this scenario, a WD accretes g of metals in years. Hence, typical WDs may accrete up to g of metal over 10Myr, the total time they host circumstellar disks. This is comparable to the mass of the dwarf planet Ceres and Pluto’s moon Charon. Of course, if the tidally disrupted object is icy, the total accreted mass may be significantly higher (although see Jura & Xu 2012). Therefore, the debris surrounding WDs is likely supplied through disruption of Solar System asteroid analogues, moons, and dwarf planets.

5 Conclusions

We present near- and mid-infared observations and a comprehensive study of the SEDs of a metallicity-unbiased sample of 117 DA WDs from the PG survey. Only five of our targets show excess radiation from debris disks, indicating a debris disk frequency of  which fits in well with previous surveys of this kind. We interpret this frequency as a lower limit to the frequency of planets around the progenitor MS stars; an indirect result for the intermediate-mass regime in which conventional exoplanetary detection methods are insensitive. Alternatively, we interpret the observed frequency of disks as the fraction of time a WD accretes from its debris disks over the entire cooling age of the star. We estimate that typical WDs may accrete metals from several generations of disks for 10Myr, corresponding to accretion of metals up to g. This means WDs are capable of accreting bodies as large as dwarf planets as well as Solar System asteroid analogues.

This work is based, in part, on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. Support for this work was provided by NASA. The PAIRITEL is operated by the Smithsonian Astrophysical Observatory (SAO) and was made possible by a grant from the Harvard University Milton Fund, the camera loan from the University of Virginia, and the continued support of the SAO and UC Berkeley. The PAIRITEL project and JSB are further supported by NASA/Swift Guest Investigator Grant no. NNG06GH50G. We thank M. Skrutskie for his continued support of the PAIRITEL project. The IRTF is operated by the University of Hawaii under Cooperative Agreement no. NNX-08AE38A with the National Aeronautics and Space Administration, Science Mission Directorate, Planetary Astronomy Program. We thank A. Gianninas for his helpful comments, J. Farihi for useful discussions, and C. Blake, M. Skrutskie, and E. Falco for helping with the PAIRITEL observations. We also thank the referee, Marc Kucher, for insightful suggestions.

References

  • Becklin et al. (2005) Becklin, E. E., Farihi, J., Jura, M., et al. 2005, ApJ, 632, L119
  • Bergeron et al. (2011) Bergeron, P., Wesemael, F., Dufour, P., et al. 2011, ApJ, 737, 28
  • Bloom et al. (2006) Bloom, J. S., Starr, D. L., Blake, C. H., Skrutskie, M. F., & Falco, E. E. 2006, in Astronomical Society of the Pacific Conference Series, Vol. 351, Astronomical Data Analysis Software and Systems XV, ed. C. Gabriel, C. Arviset, D. Ponz, & S. Enrique, 751
  • Bonsor & Wyatt (2012) Bonsor, A., & Wyatt, M. C. 2012, MNRAS, 420, 2990
  • Bowler et al. (2010) Bowler, B. P., Johnson, J. A., Marcy, G. W., et al. 2010, ApJ, 709, 396
  • Burgasser et al. (2003) Burgasser, A. J., Kirkpatrick, J. D., Reid, I. N., et al. 2003, ApJ, 586, 512
  • Burleigh et al. (2002) Burleigh, M. R., Clarke, F. J., & Hodgkin, S. T. 2002, MNRAS, 331, L41
  • Cushing et al. (2004) Cushing, M. C., Vacca, W. D., & Rayner, J. T. 2004, PASP, 116, 362
  • Cutri et al. (2003) Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003, 2MASS All Sky Catalog of point sources.
  • Debes & Sigurdsson (2002) Debes, J. H., & Sigurdsson, S. 2002, ApJ, 572, 556
  • Debes et al. (2011) Debes, J. H., Hoard, D. W., Wachter, S., Leisawitz, D. T., & Cohen, M. 2011, ApJS, 197, 38
  • Debes et al. (2012) Debes, J. H., Walsh, K. J., & Stark, C. 2012, ApJ, 747, 148
  • Dufour et al. (2010) Dufour, P., Kilic, M., Fontaine, G., et al. 2010, ApJ, 719, 803
  • Dufour et al. (2012) —. 2012, ApJ, 749, 6
  • Farihi et al. (2005) Farihi, J., Becklin, E. E., & Zuckerman, B. 2005, ApJS, 161, 394
  • Farihi et al. (2008) Farihi, J., Zuckerman, B., & Becklin, E. E. 2008, ApJ, 674, 431
  • Farihi et al. (2009) Farihi, J., Jura, M., & Zuckerman, B. 2009, ApJ, 694, 805
  • Fazio et al. (2004) Fazio, G. G., Hora, J. L., Allen, L. E., et al. 2004, ApJS, 154, 10
  • Gould & Kilic (2008) Gould, A., & Kilic, M. 2008, ApJ, 673, L75
  • Graham et al. (1990) Graham, J. R., Matthews, K., Neugebauer, G., & Soifer, B. T. 1990, ApJ, 357, 216
  • Johnson et al. (2010) Johnson, J. A., Aller, K. M., Howard, A. W., & Crepp, J. R. 2010, PASP, 122, 905
  • Jura (2003) Jura, M. 2003, ApJ, 584, L91
  • Jura et al. (2007) Jura, M., Farihi, J., & Zuckerman, B. 2007, ApJ, 663, 1285
  • Jura (2008) —. 2008, AJ, 135, 1785
  • Jura & Xu (2012) Jura, M., & Xu, S. 2012, AJ, 143, 6
  • Kalirai et al. (2008) Kalirai, J. S., Hansen, B. M. S., Kelson, D. D., et al. 2008, ApJ, 676, 594
  • Kennedy & Kenyon (2008) Kennedy, G. M., & Kenyon, S. J. 2008, ApJ, 673, 502
  • Kilic et al. (2005) Kilic, M., von Hippel, T., Leggett, S. K., & Winget, D. E. 2005, ApJ, 632, L115
  • Kilic et al. (2006) —. 2006, ApJ, 646, 474
  • Kilic et al. (2008) Kilic, M., Farihi, J., Nitta, A., & Leggett, S. K. 2008, AJ, 136, 111
  • Kilic et al. (2009a) Kilic, M., Gould, A., & Koester, D. 2009a, ApJ, 705, 1219
  • Kilic et al. (2009b) Kilic, M., Kowalski, P. M., Reach, W. T., & von Hippel, T. 2009b, ApJ, 696, 2094
  • Kilic et al. (2010) Kilic, M., Brown, W. R., & McLeod, B. 2010, ApJ, 708, 411
  • Kilic et al. (2012) Kilic, M., Patterson, A. J., Barber, S., Leggett, S. K., & Dufour, P. 2012, MNRAS, 419, L59
  • Klein et al. (2010) Klein, B., Jura, M., Koester, D., Zuckerman, B., & Melis, C. 2010, ApJ, 709, 950
  • Klein et al. (2011) Klein, B., Jura, M., Koester, D., & Zuckerman, B. 2011, ApJ, 741, 64
  • Liebert et al. (2005) Liebert, J., Bergeron, P., & Holberg, J. B. 2005, ApJS, 156, 47
  • Melis et al. (2011) Melis, C., Farihi, J., Dufour, P., et al. 2011, ApJ, 732, 90
  • Metzger et al. (2012) Metzger, B. D., Rafikov, R. R., & Bochkarev, K. V. 2012, MNRAS, 423, 505
  • Mullally et al. (2007a) Mullally, F., Kilic, M., Reach, W. T., et al. 2007a, ApJS, 171, 206
  • Rafikov (2011a) Rafikov, R. R. 2011a, ApJ, 732, L3
  • Rafikov (2011b) —. 2011b, MNRAS, 416, L55
  • Rayner et al. (2003) Rayner, J. T., Toomey, D. W., Onaka, P. M., et al. 2003, PASP, 115, 362
  • Reach et al. (2005) Reach, W. T., Kuchner, M. J., von Hippel, T., et al. 2005, The Astrophysical Journal Letters, 635, L161
  • Reach et al. (2005) Reach, W. T., Megeath, S. T., Cohen, M., et al. 2005, PASP, 117, 978
  • Reach et al. (2009) Reach, W. T., Lisse, C., von Hippel, T., & Mullally, F. 2009, ApJ, 693, 697
  • Schneider et al. (2011) Schneider, J., Dedieu, C., Le Sidaner, P., Savalle, R., & Zolotukhin, I. 2011, A&A, 532, A79
  • Vennes et al. (2010) Vennes, S., Kawka, A., & Németh, P. 2010, MNRAS, 404, L40
  • von Hippel et al. (2007) von Hippel, T., Kuchner, M. J., Kilic, M., Mullally, F., & Reach, W. T. 2007, ApJ, 662, 544
  • Williams et al. (2009) Williams, K. A., Bolte, M., & Koester, D. 2009, ApJ, 693, 355
  • Wright et al. (2010) Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868
  • Xu & Jura (2012) Xu, S., & Jura, M. 2012, ApJ, 745, 88
  • Zuckerman & Becklin (1987) Zuckerman, B., & Becklin, E. E. 1987, Nature, 330, 138
  • Zuckerman & Becklin (1992) —. 1992, ApJ, 386, 260
  • Zuckerman et al. (2003) Zuckerman, B., Koester, D., Reid, I. N., & Hünsch, M. 2003, ApJ, 596, 477
  • Zuckerman et al. (2007) Zuckerman, B., Koester, D., Melis, C., Hansen, B. M., & Jura, M. 2007, ApJ, 671, 872
  • Zuckerman et al. (2010) Zuckerman, B., Melis, C., Klein, B., Koester, D., & Jura, M. 2010, ApJ, 722, 725
WD Mass MS Mass J H K
PG (K) () () (Myr) (mag) (mag) (mag) Ref. Data
0000+172 20210 7.99 0.62 2.1 85 16.262 0.016 16.299 0.035 16.237 0.154 1 I, P
0033+016 10980 8.83 1.12 6.7 2089 15.625 0.014 15.659 0.030 15.649 0.086 1 I, P
0048+202 20160 7.99 0.62 2.1 85 15.795 0.020 15.831 0.041 15.637 0.092 1 I, P
0059+258 21370 8.04 0.65 2.3 78 16.252 0.018 16.266 0.033 16.325 0.135 1 I, P
0107+268 13880 7.87 0.54 1.3 245 15.392 0.015 15.420 0.030 15.528 0.111 1 I, P
0132+254 19960 7.45 0.41 0.1 63 16.446 0.128 1, 9
0816+297 16660 7.84 0.53 1.2 129 16.141 0.105 15.921 0.184 1, 10
0819+364 18740 8.03 0.64 2.3 123 16.026 0.088 15.781 0.228 1, 10
0821+633 16770 7.82 0.52 1.2 123 16.221 0.009 16.238 0.018 16.342 0.045 1 P
0826+455 10370 7.86 0.52 1.2 513 15.001 0.006 14.947 0.009 14.927 0.018 1 I, S, P
0852+659 19070 8.13 0.70 2.8 141 15.876 0.079 15.826 0.184 1, 8
0854+405 22250 7.91 0.58 1.7 46 15.419 0.009 15.496 0.014 15.553 0.029 1 I, P
0908+171 17340 7.92 0.57 1.6 129 16.403 0.013 16.458 0.024 16.573 0.064 1 P
0915+526 15560 7.96 0.60 1.9 200 15.809 0.009 15.894 0.018 15.977 0.039 1 P
0933+729 17380 8.00 0.62 2.1 148 16.074 0.009 16.067 0.018 16.108 0.045 1 P
0938+286 14490 7.82 0.52 1.2 200 15.742 0.016 15.750 0.027 15.924 0.060 1 P
0938+550 18530 8.10 0.68 2.6 148 15.153 0.025 15.306 0.033 15.396 0.053 1 I, P
0943+441 12820 7.55 0.41 0.1 339 13.643 0.028 13.707 0.041 13.722 0.046 1, 9
0947+326 22060 8.31 0.82 3.9 117 16.022 0.015 16.044 0.023 15.841 0.069 1 I, P
0950+078 14770 7.95 0.59 1.8 229 16.148 0.011 16.280 0.021 16.280 0.049 1 P
0954+697 21420 7.91 0.58 1.7 54 16.427 0.016 16.612 0.042 16.548 0.078 1 P
0956+021 15670 7.80 0.51 1.1 151 16.007 0.012 16.073 0.022 16.130 0.049 1 S, P
1000002 19470 7.99 0.62 2.1 98 16.474 0.019 16.558 0.054 16.614 0.094 1 P
1003023 20340 7.95 0.60 1.9 76 15.677 0.014 15.733 0.030 15.845 0.057 1 P
1005+642 19660 7.93 0.58 1.7 81 14.232 0.029 14.330 0.050 14.356 0.052 1
1015+161 19540 8.04 0.65 2.3 110 15.950 0.010 15.944 0.018 15.906 0.036 1, 4 P
1017+125 21670 7.94 0.60 1.9 56 16.236 0.096 15.856 0.177 15.875 0.253 1, 10
1019+129 18020 8.00 0.62 2.1 132 16.101 0.017 16.048 0.031 15.981 0.058 1 I, P
1022+050 11680 7.64 0.44 0.4 490 14.193 0.035 14.237 0.033 14.185 0.065 1
1026+024 12570 7.98 0.60 1.9 363 14.433 0.011 14.447 0.017 14.362 0.031 1 I, P
1031+063 20750 7.87 0.56 1.5 58 16.726 0.025 16.912 0.061 16.647 0.093 1 I, P
1031+234 15000 8.50 0.93 4.9 550 16.044 0.009 16.108 0.016 16.123 0.049 1 P
1034+492 20650 8.17 0.73 3.1 11 15.778 0.063 16.127 0.212 16.061 0.287 1, 8
1036+086 22230 7.49 0.42 0.2 46 16.654 0.015 16.810 0.034 16.471 0.066 1 I, S, P
1046+282 12610 7.97 0.59 1.8 363 15.479 0.016 15.438 0.028 15.349 0.057 1 I, P
1102+749 19710 8.36 0.85 4.2 182 15.530 0.010 15.574 0.023 15.746 0.044 1 P
1108+476 12400 8.31 0.80 3.7 603 15.657 0.054 15.350 0.092 15.618 0.222 1, 8
1115+166 22090 8.12 0.70 2.8 81 15.466 0.055 15.657 0.159 15.463 0.208 1
1116+026 12290 8.05 0.63 2.2 427 14.745 0.014 14.668 0.021 14.718 0.032 1, 4 P
1122+546 14380 7.83 0.52 1.2 209 15.697 0.015 15.704 0.034 15.590 0.053 1 I, S, P
1129+072 13360 7.91 0.56 1.5 288 15.298 0.012 15.158 0.018 15.266 0.033 1 P
1129+156 16890 8.19 0.73 3.1 224 14.443 0.034 14.493 0.052 14.565 0.094 1, 8
1134+301 21280 8.55 0.96 5.2 200 12.993 0.024 13.105 0.031 13.183 0.028 3
1147+256 10200 8.14 0.69 2.7 794 15.548 0.012 15.555 0.020 15.668 0.047 1 P
1149+058 11070 8.15 0.69 2.7 646 14.985 0.015 14.962 0.021 14.861 0.035 1 I, S, P
1149+411 14070 7.84 0.53 1.2 224 16.365 0.017 16.431 0.037 16.398 0.064 1 P
1158+433 14050 7.85 0.53 1.2 224 16.170 0.011 16.197 0.020 16.169 0.043 1 P
1159098 9540 8.81 1.10 6.5 2692 15.533 0.018 15.491 0.032 15.419 0.090 1 I, P
1201001 19770 8.26 0.78 3.5 155 15.680 0.057 15.846 0.098 15.706 0.231 1, 8
1216+036 13800 7.85 0.53 1.2 245 16.284 0.101 16.198 0.187 1, 10
1229013 19430 7.47 0.41 0.1 71 14.925 0.032 15.044 0.070 15.349 0.229 1, 9
1230+418 19520 7.98 0.61 2.0 95 16.161 0.014 16.180 0.027 16.337 0.055 1 P
1232+479 14370 7.82 0.52 1.2 204 14.937 0.011 14.760 0.014 14.725 0.024 1 I, P
1237029 10240 8.58 0.98 5.4 1660 15.828 0.011 15.761 0.018 15.955 0.040 1 P
1244+149 10680 8.06 0.64 2.3 631 15.740 0.015 15.714 0.029 15.729 0.058 1 P
1257+032 17290 7.79 0.51 1.1 105 16.090 0.092 15.956 0.159 1, 10
1258+593 14480 7.87 0.54 1.3 214 15.645 0.012 15.607 0.021 15.621 0.051 1 P
1307+354 11180 8.15 0.70 2.8 631 15.344 0.051 15.398 0.096 1, 8
1310+583 10560 8.32 0.80 3.7 912 14.016 0.028 14.004 0.045 14.081 0.073 1, 8
1319+466 13880 8.19 0.73 3.1 398 14.867 0.035 14.859 0.075 14.767 0.083 1, 8
1325+168 17970 8.18 0.73 3.1 186 16.426 0.016 16.640 0.045 16.499 0.063 1 I, S, P
1328+344 16300 7.90 0.56 1.5 155 15.495 0.008 15.528 0.015 15.654 0.030 1 P
1330+473 22460 7.95 0.60 1.9 48 15.772 0.011 15.710 0.017 15.912 0.042 1 P
1335+369 20510 7.78 0.51 1.1 51 15.122 0.010 15.152 0.016 15.188 0.029 1 P
1337+705 20460 7.90 0.57 1.6 66 13.248 0.024 13.357 0.027 13.451 0.035 1, 3,
1344+573 13390 7.94 0.58 1.7 295 13.704 0.022 13.821 0.035 13.757 0.041 1
1349+144 16620 7.68 0.46 0.6 145 15.550 0.009 15.629 0.017 15.664 0.036 1 P
1349+552 11800 7.87 0.54 1.3 380 15.830 0.015 15.967 0.028 15.800 0.060 1 I, P
1350+657 11880 7.91 0.55 1.4 389 15.688 0.068 15.419 0.136 15.304 0.175 1
1350090 9520 8.36 0.83 4.0 1318 14.191 0.007 14.082 0.009 14.140 0.013 1 P
1407+425 10010 8.21 0.73 3.1 912 14.998 0.044 14.870 0.064 14.892 0.095 1, 5
1408+324 18150 7.95 0.59 1.8 117 14.396 0.031 14.484 0.054 14.431 0.073 3
1410+425 15350 7.87 0.54 1.3 178 16.343 0.016 16.337 0.025 16.467 0.069 1 P
1431+154 13550 7.95 0.58 1.7 302 16.130 0.014 15.985 0.022 15.895 0.053 1 I, P
1448+078 14170 7.75 0.48 0.8 195 15.854 0.016 15.755 0.027 15.788 0.072 1 I, P
1449+168 21600 7.88 0.56 1.5 49 15.973 0.010 16.077 0.018 15.861 0.044 1 I, P
1457086 21450 7.97 0.62 2.1 63 16.041 0.098 16.212 0.233 15.614 0.228 1, 7
1501+032 13770 7.88 0.54 1.3 257 15.856 0.018 15.847 0.033 15.900 0.063 1 P
1502+351 18120 8.13 0.70 2.8 166 16.239 0.024 16.386 0.038 16.305 0.072 1 I, P
1507+021 19580 7.87 0.56 1.5 76 16.601 0.115 16.451 0.209 1, 10
1507+220 19340 7.91 0.57 1.6 85 15.445 0.015 15.525 0.021 15.698 0.055 1 P
1508+549 16970 7.86 0.54 1.3 126 16.125 0.009 16.136 0.019 16.278 0.051 1 P
1508+637 10450 8.12 0.68 2.6 724 14.689 0.015 14.660 0.023 14.823 0.046 1 P
1509+323 13970 7.98 0.60 1.9 282 14.436 0.030 14.574 0.055 14.572 0.089 3
1515+669 10320 8.40 0.86 4.3 1122 15.295 0.053 15.240 0.112 15.180 0.198 1, 8
1519+384 19620 7.98 0.61 2.0 93 16.207 0.015 16.359 0.032 16.176 0.080 1 I, P
1527+091 21520 8.02 0.64 2.3 71 14.814 0.012 14.922 0.018 15.003 0.037 1 P
1531023 18620 8.41 0.88 4.5 234 14.395 0.040 14.484 0.053 14.618 0.101 3
1533057 20000 8.50 0.94 5.0 245 15.876 0.013 15.951 0.031 16.082 0.059 1 P
1537+652 9740 8.15 0.69 2.7 912 14.438 0.006 14.426 0.009 14.372 0.014 1 I P
1541+651 11600 8.10 0.67 2.5 537 15.625 0.013 15.590 0.025 15.450 0.048 1 I, S, P
1548+149 20520 7.89 0.57 1.6 65 15.656 0.013 15.844 0.029 15.821 0.061 1 I P
1550+183 14260 8.25 0.77 3.4 389 15.170 0.050 15.311 0.107 15.278 0.131 1, 8
1601+581 14670 7.84 0.53 1.2 200 14.116 0.010 14.151 0.013 14.209 0.021 1 P
1605+684 21090 7.97 0.61 2.0 68 16.404 0.010 16.474 0.026 16.276 0.054 1 S, P
1610+167 14390 7.84 0.52 1.2 209 16.047 0.011 16.033 0.024 16.027 0.065 1 I, P
1614+137 22430 7.33 0.40 0.1 30 15.704 0.059 15.896 0.141 1
1620+513 20890 7.92 0.58 1.7 63 16.251 0.093 16.181 0.213 1, 10
1626+409 21370 8.02 0.64 2.3 72 16.647 0.027 16.933 0.068 16.851 0.146 1 I, P
1632+177 10100 7.96 0.58 1.7 617 13.049 0.021 12.989 0.027 13.076 0.029 1, 5
1637+335 10150 8.17 0.71 2.9 832 14.551 0.031 14.467 0.045 14.424 0.081 3
1641+388 15570 7.95 0.59 1.8 195 14.958 0.008 15.066 0.014 15.024 0.037 1 I, P
1647+376 21980 7.89 0.57 1.6 46 15.494 0.007 15.533 0.016 15.782 0.051 1 I, P
1654+637 15070 7.63 0.44 0.4 204 16.167 0.103 15.688 0.146 15.565 0.179 1, 9
1659+303 13600 7.95 0.58 1.7 295 15.315 0.011 15.328 0.025 15.435 0.045 1 I P
1720+361 13670 7.83 0.52 1.2 245 15.476 0.023 15.592 0.046 15.136 0.075 1 I, S, P
2226+061 15280 7.62 0.44 0.4 191 15.178 0.045 15.217 0.067 15.227 0.142 1, 9
2246+223 10650 8.80 1.10 6.5 2188 14.341 0.029 14.317 0.047 14.360 0.090 3
2303+243 11480 8.09 0.66 2.4 550 15.398 0.028 15.509 0.042 15.363 0.073 1 S, P
2306+125 20220 8.05 0.66 2.4 98 15.672 0.012 15.642 0.024 15.735 0.068 1 I, P
2306+131 13250 7.92 0.56 1.5 295 15.567 0.013 15.553 0.026 15.299 0.065 1 I, S, P
2322+207 13060 7.84 0.52 1.2 282 15.745 0.013 15.708 0.026 15.354 0.066 1 I, P
2324+060 15750 7.90 0.56 1.5 174 15.744 0.028 15.879 0.063 16.051 0.249 1 I, P
2326+049 11820 8.15 0.70 2.8 550 13.132 0.029 13.075 0.022 12.689 0.029 1, 2, 3, 5, 6
2328+108 21910 7.84 0.55 1.4 42 15.900 0.013 15.911 0.023 16.046 0.109 1 I, P
2329+267 11730 8.98 1.18 7.2 2042 15.126 0.011 15.093 0.020 14.908 0.088 1 I, P
2336+063 16520 8.03 0.63 2.2 186 15.903 0.017 15.959 0.032 16.140 0.135 1 I, P

Note. – Data sources: (I) IRTF; (S) Spitzer; (P) PAIRITEL References. – (1) this work; (2) Reach et al. 2005; (3) Mullally et al. 2007a; (4) Jura et al. 2007; (5) Farihi et al. 2008; (6) Reach et al. 2009; (7) Farihi et al. 2009; (8) Kilic et al. 2009a; (9) Kilic et al. 2010; (10) Xu & Jura 2012

Table 1: Sample Properties
3.6 m 4.5 m
PG (Jy) (Jy)
0826+455 268.6 8.7 172.0 5.9
0956+021 88.6 3.5 53.7 2.8
1036+086 42.5 1.5 26.6 1.3
1122+546 118.2 4.3 77.6 3.1
1149+058 248.0 8.1 163.4 5.7
1325+168 64.7 2.2 42.3 1.7
1541+651 435.4 13.5 483.9 15
1605+684 60.9 2.7 41.2 2.2
1720+361 155.9 5.4 97.6 3.7
2303+243 170.8 5.9 110.1 4
2306+131 146.2 5.2 92.0 3.5

Note. – Spitzer Cycle 7 photometry fluxes in IRAC Channels 1 (3.6 m) and 2 (4.5 m).

Table 2: Spitzer IRAC Photometry
Figure 1: The PAIRITEL vs. 2MASS photometry for our sample. The PAIRITEL data agrees fairly well with the 2MASS photometry.
Figure 2: and colors vs. temperature for our sample of DA WDs from the PG survey. Red squares and blue triangles show the confirmed dusty WDs and objects with follow-up IRTF spectroscopy, respectively. Solid lines show the predicted sequences for DA WDs (Bergeron et al. 2011).
Figure 3: Spectral energy distribution of the known dusty WD GALEX J1931+0117. Green points represent 2MASS photometry, while blue points represent the photometry from Melis et al. 2011. The IRTF spectrum is shown in black and the red line represents the predicted contribution from a blackbody stellar photosphere. The noise near 1.9 and 2.5 m falls in regions of poor telluric correction. The 1.28 m feature is Pa absorption. The detection of slight K-band excess around this target demonstrates that our near-infrared observations and reductions are reliable.
Figure 4: Spectral energy distributions of 41 WDs observed at the IRTF. The PAIRITEL and 2MASS photometry are shown as blue and green points, respectively. The black lines show the observed spectra and the red solid lines show the predicted photospheric emission for each star assuming a blackbody. The IRTF spectra display telluric correction problems around 1.4 and 1.9 m.
Figure 5: SEDS of the 11 WDs with new Spitzer photometry (shown in purple). The symbols are the same as in Figure 3. The IRTF spectra display telluric correction problems around 1.4 and 1.9 m. Our Spitzer observations confirm the results of the IRTF observations; only PG1541+651 shows a significant infrared excess.
Figure 6: SEDs of the five dusty WDs in our sample. The symbols are the same as in Figure 5. The IRTF spectra display telluric correction problems around 1.4 and 1.9 m.
Figure 7: Color-color diagrams using PAIRITEL/2MASS and WISE photometry for our WD sample. Red triangles mark the dusty WDs. Four of the five dusty WDs in our sample clearly show infrared excesses in the WISE bands. The fifth dusty WD, PG 1457086, is also detected in the WISE observations, but with large photometric errors.
Figure 8: Probability function for WDs with debris disks. Probability, , of finding debris disks as a function of assumed true debris disk frequencies, , where . Dashed lines delineate the region containing 68% probability, equivalent to 1 Gaussian limits. The solid line indicates the peak of the distribution. The derived frequency is
Comments 0
Request Comment
You are adding the first comment!
How to quickly get a good reply:
  • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
  • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
  • Your comment should inspire ideas to flow and help the author improves the paper.

The better we are at sharing our knowledge with each other, the faster we move forward.
""
The feedback must be of minimum 40 characters and the title a minimum of 5 characters
   
Add comment
Cancel
Loading ...
171612
This is a comment super asjknd jkasnjk adsnkj
Upvote
Downvote
""
The feedback must be of minumum 40 characters
The feedback must be of minumum 40 characters
Submit
Cancel

You are asking your first question!
How to quickly get a good answer:
  • Keep your question short and to the point
  • Check for grammar or spelling errors.
  • Phrase it like a question
Test
Test description