Echoes of a decaying planetary system: the gaseous and dusty disks surrounding three white dwarfs
aa r X i v : . [ a s t r o - ph . S R ] J u l Echoes of a decaying planetary system: the gaseous and dustydisks surrounding three white dwarfs
C. Melis , , M. Jura , L. Albert , B. Klein , B. Zuckerman [email protected] ABSTRACT
We have performed a comprehensive ground-based observational programaimed at characterizing the circumstellar material orbiting three single whitedwarf stars previously known to possess gaseous disks. Near-infrared imagingunambiguously detects excess infrared emission towards Ton 345 and allows usto refine models for the circumstellar dust around all three white dwarf stars.We find that each white dwarf hosts gaseous and dusty disks that are roughlyspatially coincident, a result that is consistent with a scenario in which dustyand gaseous material has its origin in remnant parent bodies of the white dwarfs’planetary systems. We briefly describe a new model for the gas disk heatingmechanism in which the gaseous material behaves like a “Z II” region. In thisZ II region, gas primarily composed of metals is photoionized by ultraviolet lightand cools through optically thick allowed Ca II-line emission.
Subject headings: circumstellar matter — planet-star interactions — stars: in-dividual (Ton 345, SDSS J122859.93+104032.9, SDSSJ104341.53+085558.2) —white dwarfs
1. Introduction
White dwarfs represent the endstate of stellar evolution for the majority of stars withinour galaxy. Most stars with mass less than ∼ ⊙ will end up as these exposed cores ofnuclear ash that slowly cool over time as they radiate away their energy. The planetary Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1547, USA Current address: Center for Astrophysics and Space Sciences, University of California, San Diego, CA92093-0424, USA CFHT Resident Astronomer, 65-1238 Mamalahoa Highway, Kamuela, HI 96743, USA et al. et al. ∼
10 Gyr. Less massive progenitor stars are more likely tohave giant planets with stable orbits at the end of their stellar evolution. However, these lessmassive progenitor stars are also expected to obliterate any terrestrial-like planets orbitingwithin ∼ et al. et al. et al. et al. et al. et al. et al. et al. −
38 hosted infrared excess. This infrared excess was interpreted by Zuckerman & Becklin 3 –(1987) to probably be the signature of a brown dwarf companion. However, subsequent ob-servations of G29 −
38 found evidence for a silicate emission feature at ∼ µ m (Graham et al. et al. et al. et al. et al. et al. et al. et al. (2009) compiledall previous Spitzer observations and found that ∼ . eff ∼ ∼
50% of white dwarfswith implied metal accretion rates of ˙
M > × g s − have dusty material orbiting them.All white dwarfs discussed above have debris disks contained almost entirely within theirrespective white dwarf’s Roche radius indicating disrupted rocky objects.Contemporaneous with the Spitzer white dwarf disk searches, G¨ansicke et al. (2006)noted peculiar double-peaked gas emission lines from a hot (T eff =22,000 K) white dwarfobserved as part of the Sloan Digital Sky Survey (SDSS; York et al. et al. (hereafter SDSS1228) show that this gas disk-hosting white dwarf is also orbitedby dusty material that coincides positionally with the gaseous material (Brinkworth et al. Farihi et al. (2010) performed AKARI observations of Ton 345 that indicate there is excess infraredemission at 2.3, 3.2, and 4.3 µ m; these observations are contaminated by a nearby background objectdiscussed in Section 2. et al. (2006, 2007, 2008a) were performed and are reported herein.
2. Observations2.1. WIRCam Imaging at the CFHT
Initial near-infrared (NIR) images of Ton 345 and SDSS1043 were obtained with WIRCammounted on the 3.6-m CFHT telescope (Puget et al. ′′ offsets between dithers. For Ton 345 we took exposures in the J, H, and K s bands with 45,15, and 25 seconds per dither (yielding total integration times of 270, 630, and 450 seconds,respectively). The H-band observations for Ton 345 were repeated on UT 25 February 2008in better sky brightness conditions. Both H-band data sets yielded the same result. ForSDSS1043 we took exposures only in the K s -band; these observations were performed ina manner similar to that described for Ton 345. Images were preprocessed, non-linearitycorrected, and sky subtracted at CFHT with the ‘I‘iwi pipeline and median-stacked usingthe suite of Terapix software ( sextractor - Bertin & Arnouts (1996), scamp - Bertin (2006),and swarp ) with the 2MASS point-source catalogue as the reference for external astrome-try. Photometry of the two white dwarfs and all 2MASS sources was performed using the FLUX_AUTO measurement in SExtractor, version 2.4.4. Absolute photometry was anchoredon the 2MASS system using a weighted average of all ( > σ outlier rejection. The uncertainty on this calibrationis ∼ ∼ s for objects similar in flux to SDSS1043.WIRCam data for Ton 345 are summarized in Table 1 which also includes SDSS andGALEX fluxes. Images of Ton 345 and a ∼ ′′ separation background source, presumably agalaxy, are displayed in Figure 1. Large beam instruments (like Spitzer or AKARI) would becontaminated by this red background object. The WIRCam result for SDSS1043 is presented Follow-up observations of Ton 345 were obtained with NIRI (Hodapp et al. s with total integration times of 105, 120, and 150 seconds,respectively. A 4-point dither pattern was repeated for L ′ until we accrued a total integrationtime of 2520 seconds.After pre-processing to correct for the known NIRI non-linearity , data were reducedusing in-house IDL software routines. For each filter, science frames were median combinedto generate a “sky-median” frame which was then subtracted from each science frame. Sky-subtracted frames were then flat-fielded using exposures of the illuminated telescope domefor J, H, and K s . L ′ frames were flat-fielded using the median stack of all science framesnormalized to unity. Reduced science frames were registered by reversing the header-recordedvalues for the telescope offsets between dithers.Photometric measurements for Ton 345 were calibrated by comparing extracted fluxesfor each filter to standard stars fluxes (Leggett et al 2003, 2006) observed and reduced in asimilar fashion. For JHK s the standard star was FS 15, for L ′ it was HD 84800. We notethat HD 84800 appears to have a ∼ ′′ extent in our L ′ images; no telescope problems werenoted at the time of observation. JHK s fluxes were extracted with an aperture that yielded ∼
85% encircled energy (with a negligible difference between Ton 345 and FS 15). For L ′ fluxcalibration we used a 2.0 ′′ diameter aperture to extract the flux of HD 84800 and Ton 345.Uncertainties for JHK s fluxes were determined by examining the dispersion of the extractedfluxes for each of the individual reduced science frames. Since this was not possible in our L ′ imaging sets, we instead made ten randomly placed extractions on the final, median-stackedL ′ image using the same aperture that was used to extract the flux for Ton 345. The standarddeviation of this set of values was adopted as the flux measurement uncertainty. The finalsignal-to-noise ratio (S/N) is ∼
50 for JHK s while for L ′ it is ∼ ∼ ′′ separated galaxy. Table 3 lists fluxes for the galaxy extracted usingsimilar apertures and procedures as for Ton 345. http://staff.gemini.edu/~astephens/niri/nirlin/ Observations of SDSS1043 in the J-band were performed UT 10 October 2008 with theGemini Twin-Arrays Infrared Camera (McLean et al. ∼ ′ field-of-view of the Gemini instrument enabled simultaneous observations of two 2MASSstars for use in flux calibration. Although Gemini hosts two infrared cameras, data for thelonger wavelength chip were unusable due to instrumental difficulties.Data were reduced and fluxes extracted much like that described above for the Ton 345NIRI data. Exceptions include no non-linearity correction, the use of twilight flats insteadof dome flats, and image registration using bright point sources within the field. The GeminiJ-band flux for SDSS1043 is reported in Table 2. Keck HIRES (Vogt et al. ∼ λ
3. Results3.1. Imaging
Table 1 lists measured near-infrared fluxes for Ton 345 from the CFHT and GeminiNorth data sets. To place these near-infrared measurements in context we queried SDSSDR7 (Abazajian et al. ugriz and ultraviolet fluxes, respectively. Fromthe measured magnitudes alone it is apparent that Ton 345 hosts significant near-infraredexcess (see Section 4).Table 2 lists GALEX ultraviolet fluxes, SDSS ugriz , and the ground-based near-infraredphotometry for SDSS1043. Our data alone do not conclusively show that there is infraredexcess emission towards SDSS1043. But, when these ground-based near-infrared measure-ments are combined with Spitzer photometry at longer wavelengths (C. Brinkworth et al .2010, in preparation), significant excess infrared emission is apparent (see Section 4).
Double-peaked metallic gas emission lines are detected towards all three white dwarfs.Emission lines from Ca II and Fe II are shown in Figures 3 and 4. Ca II H & K emissionlines are detected only for SDSS1228 (Figure 3 and Table 5). Fe II λ λ et al. (2006) are not detected. Measurablequantities from emission features in the spectra, and associated derived quantities, can befound in Tables 5 and 6. We defer quantitative analysis of absorption feature equivalentwidths and elemental abundances to future publications.Table 5 contains information on the velocity separation between emission peaks of thesame transition, the full velocity width at zero power of each double-peaked emission feature,the “peak midpoint”, and the maximum velocity gas detected in the blue and red wings of thedouble-peaked emission features (v max sin i ). We estimate the wavelength centroid positionof emission peaks by fitting either Gaussian or Lorentzian profiles over a ∼ et al. et al. et al. WD /Dist parameter from our model fits (see Section4 and Table 7) and the gravity values given in G¨ansicke et al. (2006, 2007, 2008a). We adoptan uncertainty of 10% for the distances. With multiple epochs of spectra, and by comparison to the Ca II IRT emission linespresented in G¨ansicke et al. (2006, 2007, 2008a), we can probe variability in emission linestrength and morphology. Table 5 contains emission line equivalent widths, velocity sep-aration between emission peaks of a given transition, and the full width at zero power ofemission lines for each epoch a gas emission line was observed. Figure 4 shows multipleepochs of Fe II λ et al. (2008a) in which the equivalent width of the sum of thethree Ca II IRT lines decreases by a factor of ∼ et al. (2008a) 2008 Jan value to within the 1 σ errors. Although speculative, this might suggestthat an episodic disk feeding event occurred before the 2004 Dec epoch and that the 2008measurements are probing a “quiescent” phase.Comparing the HIRES observations of SDSS1228’s Ca II IRT complex to those presentedin G¨ansicke et al. (2006, 2007) suggests the stronger of the two emission peaks has switchedfrom the red side of the double peaked emission complex (as seen in G¨ansicke et al. et al. et al. (2006, 2007) spectra have epochs of 2003Mar (SDSS) and 2006 Jul (WHT). The morphological appearance of the Ca II IRT emissionlines in the SDSS and WHT spectra suggests little change between these two epochs. Itis not clear what would change the parity in the emission peak strength between the 2006WHT epoch and the 2008 HIRES epoch. One possibility is that the disk is clumpy and wehave witnessed the clumps orbiting around SDSS1228. Additional spectroscopic monitoringof SDSS1228 is necessary to confirm and characterize such orbiting clumps.
4. Dust Disk Parameters
Ton 345’s photometry suggests near-infrared emission in excess of what one would ex-pect from the photosphere of the white dwarf star alone. The comprehensive data set inTable 1 is modeled as a flat, passive, opaque disk (Jura 2003b; Jura et al. ∼ ′ , the temperature at the outer edge of the dust diskis observationally unconstrained. In the model shown in Figure 5 and Table 7 we assumeT outer of the disk is 1000 K. T outer could be, and likely is, smaller than this value (see be-low). Further observational constraint of the disk outer edge temperature will require longerwavelength data that is uncontaminated by the nearby background object.In the interest of comparing a homogeneous set of disk model parameters, we refitthe data for SDSS1228 presented in Brinkworth et al. (2009) and the data for SDSS1043presented in C. Brinkworth et al . (2010, in preparation) in the same manner as Ton 345.These model fits and measured fluxes are shown in Figures 6 and 7 with model parametersreported in Table 7. It is noted that SDSS1043’s outer disk temperature is poorly constrainedeven with the inclusion of IRAC photometry. In an effort to illustrate the range of viablemodel parameters that can fit the measured infrared excesses, we plot in Figure 6 threemodels for SDSS1228 that have different dust disk parameters (Table 7). The resultantparameter extremes reported in Table 7 are taken to be the ∼ σ confidence limit on eachmodel parameter. We then derive the 1 σ model parameter uncertainties by dividing thedifference between parameter extremes by five; these uncertainties are reported along with 10 –SDSS1228’s best fit model parameters in Table 7.For the case of optically thick, flat dust disks Eq. 1 from Jura (2003b) can be used todetermine at what radial distance from each white dwarf dust particles of certain temper-atures reside. As previously mentioned, for Ton 345 and SDSS1043 the temperature of theouter region of their orbiting dusty material is poorly constrained by observations. Ratherthan take the model outer disk temperatures for Ton 345 and SDSS1043 (which are betterinterpreted as upper limits), we instead estimate their outer disk temperatures under theassumption of an asteroidal debris model for the origin of the dusty disk. Such a scenario re-quires a rocky object to fall within the Roche radius of the white dwarf (Debes & Sigurdsson2002; Jura 2003b). The following expression for the Roche radius is used (Davidsson 1999): R tide = C tide (cid:18) ρ ∗ ρ a (cid:19) / R ∗ where within R tide (the radial separation from a star of radius R ∗ and density ρ ∗ ) a rockyobject of density ρ a would be disrupted. The factor C tide is a constant of order unity thatis determined by the tensile strength, shape, rotation rate, and orbital parameters of therocky object (Davidsson 1999; Holsapple & Michel 2008). It is unlikely that all objects thatwere tidally shredded around SDSS1228, Ton 345, and SDSS1043 had the same physicalparameters; however, in the absence of any such information it is assumed that this is thecase. Such an assumption can potentially introduce a significant systematic offset in thederived outer dust disk radii. Using the well-modeld data for SDSS1228 (Table 7) andassuming an asteroid density of ∼ − a value of 1.45 for C tide is estimated. Combiningthese values with the mass and radius of the white dwarfs (see Table 6) from G¨ansicke et al. (2006, 2007, 2008a) we calculate the tidal radii for each white dwarf. These values for Ton345 and SDSS1043 are reported as R outer,dust in Table 8. The value reported for SDSS1228in Table 8 is the disk outer radius as derived from fitting its Spitzer data.
5. Gas Disk Parameters
Using the HIRES optical spectra we can estimate the radial extent of the gaseous disksorbiting the three white dwarfs. This is done by measuring the highest velocity gas emissionin the HIRES spectra (v max sin i in Table 5), emission that corresponds to the innermost orbitof the emitting gas-phase metals around the white dwarf (e.g., Horne & Marsh 1986). How-ever, this value is degenerate with the inclination angle of the disk, i , where the degeneracyis v sin i ( i of 0 ◦ would correspond to a face-on disk). The dust disk model fits (Section 4) canhelp constrain the disk inclination angle assuming the dust and gas disks are coplanar. It is 11 –noted that the inclination angles as derived from the dust disk fitting can vary by ∼ σ ; see Table 7 and Section 4). Line-of-sight gas disk velocities forthe three white dwarfs are corrected using the dust disk model best-fit inclination angles.Assuming Keplerian orbits of the gas and dust disks, we use the white dwarf masses andradii (see Table 6) as modeled by G¨ansicke et al. (2006, 2007, 2008a) to derive the gas diskinner radius in units of white dwarf radii. We obtain the full dimensions of the gaseous disksby combining these measurements with the G¨ansicke et al. (2006, 2007, 2008a,b) models (seeSection 6) in which the gas disk outer radii have been estimated. These results are reportedin Table 8 and illustrated in Figure 8.We note the discrepancy between our inferred gas disk inner radius for SDSS1228 andthe same as quoted in Brinkworth et al. (2009). The origin of this discrepancy has to dowith two factors. The first factor is responsible for the smaller gas disk inner radius quotedin Brinkworth et al. (2009) − R inner,gas ∼
27 R WD − and results from use of the maximumCa II infrared triplet (IRT) gas emission velocity of ∼ − as reported in Table 1 inG¨ansicke et al. (2006). Re-measurement of the spectra presented in G¨ansicke et al. (2006)provides a maximum gas emission velocity more in line with that measured herein (Table5; use of the G¨ansicke et al. max sin i will reduce the gas disk inner radiusby a factor of ∼ et al. (2006) . The second factor is a 20% increasein the inner disk radius relative to that presented herein (where the ratio of 1.8/1.2=1.5 isthe ratio between our inferred gas disk inner radius and that of Brinkworth et al. et al. (2006) . Here a novel method of estimating the gravitational redshift for the gas disk-hostingwhite dwarf stars is attempted. This method employs the gas disk emission lines (fromwhich we seek to measure the white dwarf systemic velocity) and photospheric absorptionlines (which contain velocity components from the systemic velocity and the gravitationalredshift from the compact white dwarf). To estimate the gravitational redshift we measuredthe photospheric absorption line radial velocity for each white dwarf (see RV obs in Table The values reported in the main article text and tables of G¨ansicke et al. (2006) are different from thosereported in the supplementary online material.
12 –6) and the systemic radial velocity for each white dwarf-disk system from gaseous emissionlines (see “Peak Midpoint Velocity” in Table 5 and discussion in Section 3.2). Our estimatedgravitational redshift for SDSS1228 (RV obs − [Peak Midpoint Velocity] avg = 55 ± − ;based only on the Ca II IRT emission lines) reproduces well the expected gravitationalredshift (44 km s − , see Table 6). Estimates for SDSS1043 are inconclusive due to the lowS/N in the gas emission lines. However, our estimate for Ton 345 (RV obs − [Peak MidpointVelocity] avg = 131 ± − ; based only on the Ca II IRT emission lines) is quite differentfrom the expected gravitational redshift (44 km s − ).Why does this method fail for Ton 345? A clue comes from considering the agreement ofSDSS1228’s gravitational redshifts as measured from the two different methods. As modeledby G¨ansicke et al. (2006, 2008a), the gas disk orbiting SDSS1228 has negligible eccentricitywhile for Ton 345 the disk eccentricity is large ( e ∼ − e ∼ et al.
6. Gas Disk Models
When observed at high spectral resolution the relatively clean-cut morphologies of thegaseous emission lines presented in G¨ansicke et al. (2006, 2007, 2008a) resolve into complexstructures. A common feature of the HIRES observed Ca II IRT emission lines for all threewhite dwarfs is a profile having the typical peak and wing structure (e.g., see Figure 1 inHorne & Marsh 1986) on one side of the emission (red side of the double peaked Ca IIemission features for SDSS1228 and Ton 345 and the blue side for SDSS1043 in Figure 3)while having a peak with a sharp cut-off in emission (i.e., no wing) on the other side (blueside of the double peaked Ca II emission features for SDSS1228 and Ton 345 and the red sidefor SDSS1043 in Figure 3) of the emission. One could imagine that such an emission-linemorphology would still be well reproduced by modeling the disks with families of ellipticalrings as was done by G¨ansicke et al. (2006, 2007, 2008a).Werner et al. (2009) present a physical model to explain the gas emission lines observedin SDSS1228’s spectrum; their model relies on an active disk that is heated by viscous 13 –dissipation of disk energy. We use the HIRES spectra to test the predictions of this model.In particular, we compare the HIRES spectra covering the Ca II H, K, and IRT transitions(Figure 3) to the predictions in Figure 6 of Werner et al. (2009). Werner et al. (2009) predictthat the summed Ca II H & K emission complex should have flux that is a factor of ∼ et al. (2009) model.For each emission line the continuum flux is subtracted and the line flux summed. Extractionof the Ca II H emission line flux is not attempted as this complex is contaminated by theH ǫ absorption line. We instead assume that the emission line flux is the same for both ofthe Ca II H & K transitions and multiply the measured Ca II K emission line flux by 2 as aproxy for the sum of the emission line flux for both transitions. Examination of SDSS1228’semission line flux for the Ca II H, K, and IRT transitions indicates that the summed Ca IIH & K emission line flux is ∼ ∼
17 from that expected inthe Werner et al. (2009) model. It is noted that the total flux in line emission is ∼ × − times the bolometric flux emitted by SDSS1228.Assuming the line emission is optically thick (as is determined in the modeling pre-sented in the supplemental material to G¨ansicke et al. ∼ The Werner et al. (2009) model does not provide a good match to the HIRES data. Assuch, we briefly describe an alternative model for the disk heating mechanism. We envisiona model where the gas is photoionized by ultraviolet photons from the white dwarf. Theidea would be akin to an H II region, but since this is a gas that is extremely deficient in Hor He (G¨ansicke et al. >> cm − ) that forbidden line cooling is unimportantand that gas instead cools through emission lines like the Ca II IRT.We expect that the gas disk scale height will be significantly larger than the dust diskscale height (see Section 6.1.1). As a result, collisional energy transfer from gaseous atomicspecies to dust particles (e.g., Goldreich & Kwan 1974) will be negligible compared to theabove three energy balance points. Hence, it is expected that the gas and dust temperaturesare decoupled.Here we provide details for a highly idealized Z II region model. We consider a flatpassive disk (see Jura 2003b) whose thickness is a small fraction of the radius ( R ∗ ) of theilluminating star. The star is assumed to have effective temperature T ∗ and photosphericemission well described by a blackbody B ν ( T ∗ ). At radial distance D from the star, wecompute the effective disk-heating flux of stellar photons above energy threshold hν withfrequencies between ν and ν , F − ( ν , ν ) in the limit that D >> R ∗ , as: F − ( ν , ν ) ≈ (cid:18) R ∗ D (cid:19) (cid:18)Z ν ν B ν ( T ∗ ) hν [ hν − hν ] dν (cid:19) (1)If there is no gas in the system, then all the incident stellar flux heats the dust so that ν = 0 and ν = ∞ . In a system with both dust and gas where, for simplicity, it is assumedthat all gas atoms have the same average ionization potential hν I , then the grains absorb allthe photons with ν < ν I while the gas absorbs all the photons with ν > ν I . Therefore, theflux heating the dust, F − dust , is computed from Equation (1) for ν = 0 and ν = ν I . Sincewe consider environments where hν I >> kT ∗ , most stellar photons are absorbed by grains,and the expected dust temperature is nearly the same as if no gas was present. For theflux heating the gas, F − gas , we use Equation (1) with ν = ν I and ν = ∞ . Using the Wienapproximation for the Planck curve we find: F − gas ≈ (cid:18) R ∗ D (cid:19) hc (cid:18) k T ∗ h (cid:19) Z ∞ x I ( x − x I x ) e − x dx (2)where: x I = hν I k T ∗ . (3)From expressions (1) and (2), we find: 15 – F − gas F − dust ≈ ( x I + 4 x I + 6) e − x I π / . (4)The value of hν I is determined from the metallic constituents in a gaseous disk. Hence,knowledge of the gas disk composition is imperative in calculating this average energy of aphotoelectron and the distribution of its energy into the gaseous material. G¨ansicke et al. (2006, 2007, 2008a) report emission lines from Ca in all three white dwarfs and Fe inSDSS1228 and Ton 345, absorption lines of Mg in all three white dwarfs, and Ca and Siabsorption in Ton 345. Under the assumption that heavy elements in the photospheres ofthese white dwarfs were accreted from their disks (see e.g., Zuckerman et al. et al. ∼ T ∗ = 20,000 K and hν I =8 eV, we compute F − gas /F − dust ≈ × − , 4 × − , and 2 × − erg cm − s − , respectively. For these samethree stars, the fluxes from the dust can be very roughly approximated as νF ν evaluated at3.6 µ m, or 2 × − , 2 × − , and 3 × − erg cm − s − . Therefore, for each of the threewhite dwarfs, the ratio of the flux received in the calcium triplet line emission compared tothe flux received from the dust is ∼ F + gas is: F + gas = X π B ν ( T gas ) ∆ ν (5)In this expression, the sum is performed over all important cooling lines, here assumed tobe the three members of the calcium triplet. Although the disk is orbiting rapidly, weassume that each portion of the gas is in vertical hydrostatic equilibrium and that the localmicroscopic gas motions are mainly thermal. Therefore:∆ ν = β line (cid:18) k T gas m ( Ca ) (cid:19) / ν L c (6) 16 –where ν L is the line frequency, m ( Ca ) is the mean atomic weight of calcium, and β line is acoefficient of order unity. We compute the gas temperature by finding the value of T gas suchthat: F + gas ( T gas ) = F − gas . (7)With considerable simplifications, we compute an analytic solution to Equation (6). Weassign the same frequency to all three members of the calcium triplet and take β line = 4.Combining the previous equations we find: F + gas ≈ (cid:18) k T gas m ( Ca ) (cid:19) / π h ν L c e − hν L /kT gas . (8)For convenience, we define A such that: A = 118 π (cid:18) R ∗ D (cid:19) c (cid:18) m ( Ca )2 k T gas (cid:19) / (cid:18) ν ∗ ν L (cid:19) (cid:0) x I + 4 x I + 6 (cid:1) (9)where hν ∗ = k T ∗ . Combining the above equations, we find: T gas ( D ) = T ∗ (cid:18) ν I ν L − ν ∗ ν L ln A (cid:19) − . (10)Gas temperatures are calculated as a function of distance from the star using the analyticsolution in Equation (10) and are plotted for specific cases in Figure 9. We assume in thesecalculations that m ( Ca ) = 40 atomic mass units. For D << R ∗ , the simple model failsbecause there is insufficient cooling. However, for D >> R ∗ and T eff = 20,000 K, we seethat the gas temperature ranges from 6000 K to 3000 K, depending upon the exact distancefrom the star. Such gas disk temperatures are roughly in agreement with those estimatedfrom observations of the three gas disk-hosting stars. In our scenario for tidally-disrupted disks orbiting white dwarfs, the gas temperatureand the dust temperature are distinct because the gas and dust are spatially separated. Thedust is assumed to be confined to a flat disk somewhat analogous to Saturn’s ring. Dependingupon the mass of the tidally-disrupted rocky object and the extent of the radial zone where 17 –the material is located, the vertical thickness of the dust may be only 1 cm. In contrast, thegas is pictured to be in vertical hydrostatic equilibrium and therefore: ρ gas = ρ (0) e − z /H (11)where ρ (0) is the midplane density. For gas orbiting at radial distance D from the star ofmass M ∗ : H = (cid:18) k T gas D G M ∗ µ (cid:19) / . (12)With D = 10 cm, T gas ∼ M ∗ = 0.6 M ⊙ , and adopting µ = 2.4 × − g asrepresentative of an ionized gas of heavy atoms, we estimate H ≈ × cm. Thus, thebulk of the gas is very far from the dust and their temperatures may be different.
7. Discussion
From the imaging and spectroscopic data we have estimated inner and outer radii forboth the gas and dust disks using as few assumptions as possible to connect the dust andgas disk results. Now, the two disk parameter sets are combined to understand how the gasand dust are related, and what that can tell one about their origin and evolution.Dust disk inner radii are close to what is expected to correspond to the sublimationtemperature for silicate dust particles. Spitzer IRS observations presented in Jura et al. (2009) suggest white dwarfs with circumstellar disks have orbiting dust composed of olivine.The limited wavelength coverage of these spectra preclude more complete compositionalanalyses (but see Reach et al. et al. et al. (2009), if a warp were present in a dust disk then its grains could be coolerand located farther from their host white dwarf star while still reproducing the observedexcess infrared emission. Warps for the dust disk-hosting white dwarfs GD 362 and GD 56have been suggested by Jura et al. (2007b, 2009). A slight warp in the dust disk of SDSS1228or Ton 345 could inflate the inner radius by a factor & et al. et al. et al. et al.
8. Conclusion
We have obtained a suite of ground-based optical and near-infrared measurements ofthree gas-disk hosting white dwarfs. Unambiguous infrared excess emission is identifiedtowards Ton 345, confirming that this white dwarf hosts a dusty disk in addition to itsgaseous disk. Characterization of these three gaseous and dusty disk systems indicates thatthe gas and dust disks are spatially coincident at their outer radii and likely their innerradii. Disk parameterization results are consistent with a scenario where both dust and gasdisks have their origin in the dissolution of rocky objects from the white dwarfs’ remnantplanetary systems.Detection of the Ca II H & K and Ca II IRT lines in emission towards SDSS1228 enablesthe development of a new model for the gas disk heating mechanism. This model relies onphotoionization of metallic atoms in a metal-dominiated region around the hot white dwarfsand cooling of the gaseous material through optically thick emission lines.C.M. acknowledges support from the Spitzer Visiting Graduate Student program andfrom a LLNL Minigrant to UCLA. We would like to thank the observers and queue co-ordinators who carried out service observations at CFHT (programs 08AD96). We thankDetlev Koester for providing atmospheric models for SDSS1228 and SDSS1043 and JayFarihi for helpful discussion. We thank Carolyn Brinkworth for useful discussion and forallowing us to use unpublished Spitzer results for SDSS1043. Based on observations ob-tained with WIRCam, a joint project of CFHT, Taiwan, Korea, Canada, France, at theCanada-France-Hawaii Telescope (CFHT) which is operated by the National Research Coun-cil (NRC) of Canada, the Institute National des Sciences de l’Univers of the Centre Nationalde la Recherche Scientifique of France, and the University of Hawaii. Based on observationsobtained at the Gemini Observatory, which is operated by the Association of Universities 20 –for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf ofthe Gemini partnership: the National Science Foundation (United States), the Science andTechnology Facilities Council (United Kingdom), the National Research Council (Canada),CONICYT (Chile), the Australian Research Council (Australia), Ministrio da Cincia e Tec-nologia (Brazil) and Ministerio de Ciencia, Tecnologa e Innovacin Productiva (Argentina).We are grateful to the Director of the Gemini North telescope for granting us observing time.Some of the data presented herein were obtained at the W.M. Keck Observatory, which isoperated as a scientific partnership among the California Institute of Technology, the Univer-sity of California and the National Aeronautics and Space Administration. The Observatorywas made possible by the generous financial support of the W.M. Keck Foundation. Thispublication makes use of data products from the Two Micron All Sky Survey, which is ajoint project of the University of Massachusetts and the Infrared Processing and AnalysisCenter/California Institute of Technology, funded by the National Aeronautics and SpaceAdministration and the National Science Foundation. Funding for the SDSS and SDSS-IIhas been provided by the Alfred P. Sloan Foundation, the Participating Institutions, theNational Science Foundation, the U.S. Department of Energy, the National Aeronauticsand Space Administration, the Japanese Monbukagakusho, the Max Planck Society, andthe Higher Education Funding Council for England. Based on observations made with theNASA Galaxy Evolution Explorer. GALEX is operated for NASA by the California Instituteof Technology under NASA contract NAS5-98034. This research was supported in part byNASA and NSF grants to UCLA.
Facilities:
CFHT (WIRCam), Gemini:North (NIRI), Keck:I (HIRES), Shane (Gemini)
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24 –Fig. 1.—
Top panels:
CFHT WIRCam images of Ton 345 in the J-, H-, and K s -bands (fromleft to right) with a linear stretch. The image orientation and scale is the same for all threebands. Note the fainter source located ∼ ′′ to the NE of Ton 345. This faint backgroundsource does not contribute a significant amount of flux to the CFHT measured magnitudes ofTon 345. Bottom panels:
Gemini North NIRI images of Ton 345 in the J-, H-, and K s -bands(from left to right) presented on a linear stretch. Images were smoothed over with a 7-pixelboxcar to enhance the faint background object contrast. The image orientation and scale isthe same for all three bands. The background source, presumably a galaxy, is now clearlydetected in the H- and K s -bands. 25 –Fig. 2.— Gemini North NIRI image of Ton 345 in the L ′ -band presented on a linear stretchafter being smoothed over with a 7-pixel boxcar. The fluctuations in the background aroundTon 345 are representative of the 1 σ noise level. The background galaxy is not detected, itis likely too diffuse for the sensitivity threshold of this imaging set. 26 – N o r m a li ze d F l ux + C on s t a n t SDSS1043Ton 345SDSS12285140 5150 5160 5170 5180 5190 5200Wavelength (Å)0.81.01.21.41.61.8 N o r m a li ze d F l ux + C on s t a n t SDSS1043Ton 345SDSS12283925 3930 3935 3940Wavelength (Å)0.81.01.21.41.61.8 N o r m a li ze d F l ux + C on s t a n t SDSS1043Ton 345SDSS1228
Fig. 3.—
Gas emission lines detected in HIRES optical spectra for SDSS1228, Ton 345, and SDSS1043.
TopPanel:
Ca II infrared triplet region. Combined spectra from the 2008 November run are plotted. The lack ofdata around ∼ Middle Panel:
Fe II λ Bottom Panel:
Ca II K region. Plotted spectra are from the 2007May run for SDSS1228 and SDSS1043, and from the 2008 February run for Ton 345. Emission lines are seenonly in SDSS1228 (Ca II H emission for SDSS1228 is detected but not shown). The weak, blueshifted Ca IIabsorption components are likely interstellar in nature based on comparison to known interstellar Ca II Kline strengths and velocities in the direction towards each white dwarf (Albert et al.
27 – N o r m a li ze d F l ux + C on s t a n t N o r m a li ze d F l ux + C on s t a n t N o r m a li ze d F l ux + C on s t a n t Fig. 4.—
Multiple epochs of gas emission lines detected in the HIRES spectra.
Top Panel:
Fe II λ Middle Panel:
Ca II infrared triplet emissionlines for Ton 345. All measurable parameters for the two epochs agree to within their respectiveerrors.
Bottom Panel:
Fe II λ
28 –Fig. 5.— SED for the DBZ white dwarf Ton 345. Overplotted is a model for the whitedwarf photospheric emission (a blackbody with T eff ∼ s and L ′ arein excess of what one would expect from the photosphere of the white dwarf alone. 29 –Fig. 6.— SED for the DAZ white dwarf SDSS1228. Overplotted are models for an at-mosphere of a T eff =22,020 K, log( g )=8.24, DA white dwarf (dotted line; D. Koester, 2009private communication) with an orbiting flat, passive, opaque dust disk (dashed line). Inputinfrared fluxes are taken from Brinkworth et al. (2009). Three different disk models are dis-played to illustrate a range of viable model parameters. The black model curve (the middleof the three) is the best fit and the model whose parameters we adopt for SDSS1228’s dustydisk (see Table 7). Optical fluxes were obtained from SDSS while ultraviolet fluxes weretaken from the GALEX AIS catalog. One possible explanation for the relatively high fluxat 16 µ m is that the source possesses a strong silicate emission feature (Brinkworth et al. eff =18,330 K, log( g )=8.09, DA white dwarf (dotted line; D. Koester, 2009 private com-munication) with an orbiting flat, passive, opaque dust disk (dashed line). The model UVfluxes are reddened using the Cardelli et al. (1989) extinction curve assuming E(B − V)=0.03.Fluxes can be found in Table 2 and the model parameters are presented in Table 7. Datapoints longward of 2 µ m are IRAC measurements reported in C. Brinkworth et al. (2010,in preparation). Optical fluxes were obtained from SDSS while ultraviolet fluxes were ob-tained from the GALEX AIS catalog. When plotted with the Spitzer IRAC data, the K s measurement suggests an excess beginning at ∼ µ m. 31 – WD )SDSS1043Ton 345SDSS1228 Fig. 8.— Sketch illustrating the results presented in Table 8. The dimensions of each whitedwarf’s dusty and gaseous disks are plotted in units of each white dwarf’s radius. Trueblue colored regions correspond to gas disks while cardinal red colored regions correspond todust disks. The vertical scale heights of the gas disks are expected to be larger than thoseof the dust disks (Section 6.1.1). Gold, horizontally hatched regions correspond to the 1 σ uncertainty for the dust disk inner and outer radii as reported in Table 8. Gold, verticallyhatched regions correspond to the 1 σ uncertainty for the gas disk inner radii as reported inTable 8. 32 –Fig. 9.— Disk temperature as a function of radial separation from its host white dwarfstar in units of stellar radii. The solid lines are for the gas disk temperature as calculatedusing the analytical Z II region model outlined in Section 6.1. Dashed lines are dust disktemperatures as described in Section 4. The red, green, and blue curves are for stellareffective temperatures of 20,000 K, 15,000 K, and 10,000 K respectively. We note that thegas disk model predictions fail for D/R ∗ <
20 (see Section 6.1). 33 –Table 1. Broad-band Fluxes for Ton 345
Band λ mag Flux Densitynm (mJy)NIRWIRCam b NIRI b Average F obs F ∗ a F excess L ′ − ± − ±
28% 0.075 0.135 ± s ± ± ± ±
2% 0.19 0.076 ± ± ± ± ±
7% 0.29 0.036 ± ± ± ± ±
2% 0.45 0.00SDSS DR7 − Optical z ± ± i ± ± r ± ± g ± ± u ± ± b − UltravioletNUV 227.1 15.50 ± ± ± ± a F ∗ is the predicted photospheric flux density in the given bandpass assuming Ton 345is a blackbody with T eff of 18,600 K and that the J-band monochromatic flux is entirelyphotospheric in nature. b WIRCam and NIRI magnitudes are in the Johnson system. GALEX measurements arein AB magnitudes. GALEX uncertainties are as suggested in Morrissey et al. (2007).
34 –Table 2. Broad-band Fluxes for SDSS1043Band λ mag F obs nm (mJy)WIRCam/Gemini a ,b − NIRK s ± ± ± ± − Optical z ± ± i ± ± r ± ± g ± ± u ± ± b − UltravioletNUV 227.1 17.07 ± ± ± ± a K s -band data are from CFHT WIRCamobservations while J-band data are from LickGemini observations (see Section 2). b WIRCam and Gemini magnitudes are inthe Johnson system. GALEX measurementsare in AB magnitudes. GALEX uncertaintiesare as suggested in Morrissey et al. (2007). 35 –Table 3. NIRI Fluxes For Background Galaxy Companion to Ton 345Band mag Flux Density( µ Jy)J > < ± ± s ± ± ′′ separation from Ton 345 ap-pears to be a J-band drop-out galaxy.Comparing to galaxy models (e.g.,see Figure 11 of Sanders et al. z ∼ Table 4. HIRES Observations SummaryUT Date Setup Coverage Integration Time (sec) S/N a SDSS1228
05 May 2007 UV Collimator 3120-5950 ˚A 3000 2214 Nov 2008 Red Collimator 4500-9000 ˚A 1800 1215 Nov 2008 Red Collimator 4500-9000 ˚A 1600 1316 Nov 2008 Red Collimator 4500-9000 ˚A 1900 12
Ton 345
13 Feb 2008 UV Collimator 3130-5960 ˚A 2 × b
14 Feb 2008 UV Collimator 3130-5960 ˚A 2 × b
26 Feb 2008 Red Collimator 4600-9150 ˚A 3600 4214 Nov 2008 Red Collimator 4500-9000 ˚A 2 × b
16 Nov 2008 Red Collimator 4500-9000 ˚A 1800 32
SDSS1043
05 May 2007 UV Collimator 3120-5950 ˚A 3000 1315 Nov 2008 Red Collimator 4500-9000 ˚A 2 × b
16 Nov 2008 Red Collimator 4500-9000 ˚A 1500 & 1700 14 b Note. — A resolving power of ∼ a S/N measured at 5750 ˚A. b S/N for combined exposures.
Table 5. Gas-disk Emission Line Measurements
Transition UT Date a Equivalent Width Peak Separation b Full Width c Peak Midpoint Velocity b v max sin i b (˚A) (km s − ) (km s − ) (km s − ) (km s − ) SDSS 1228
Ca II K 05 May 2007 0.6 ± ±
20 1014 ±
44 -35 ±
10 455 ± ± − f ±
18 1020 ±
53 -22 ± ± ± λ g
05 May 2007 1.3 ± − − − − ± − − − − Ca II λ ± ± ±
16 -22 ± ± ± λ ± ± ± ± ± ± λ ± e ± ±
35 -18 ± ± ± Ton 345
Fe II λ d ± ±
14 1349 ±
87 -79 ± − ± ±
18 1305 ±
96 -69 ± − Ca II λ ± ±
20 1305 ±
49 -90 ±
11 671 ± ± ± ±
18 1252 ±
73 -104 ± ± ± λ ± ±
16 1281 ±
63 -98 ± ± ± ± ±
13 1211 ±
56 -89 ± ± ± λ ± ±
17 1298 ±
75 -99 ± ± ± ± e ±
25 1263 ±
71 -89 ±
12 611 ± ± SDSS1043
Ca II λ ± ±
38 1482 ±
50 39 ±
19 786 ± ± λ ± ±
49 1439 ±
50 52 ±
25 811 ± ± λ ± e ±
48 1402 ±
109 42 ±
24 802 ± ± a Spectra have been combined when multiple days are listed. b See Sections 3.2 and 5 for description of these quantities. The two different values reported for v max sin i correspond to the maximumvelocity gas seen in the blue and red wings of the double-peaked emission features, respectively. c Full velocity width of emission feature, from continuum blueward of the blue emission peak to continuum redward of the red emissionpeak. d To within the noise of each individual exposure the 13,14 Feb 2008 and 26 Feb 2008 Fe II λ e Measurement may be contaminated by second order blue light leak, see Section 2.4. f Photospheric Balmer H ǫ absorption in SDSS1228 prevents an accurate continuum estimation for the Ca II H emission complex. g The Fe II λ Table 6. Kinematics of Gas-disk White Dwarfs
WD Name RV obsa M WD R WD v gravb Distance pmRA pmDE U V W(km s − ) (M ⊙ ) (R ⊙ ) (km s − ) (pc) (mas yr − ) (mas yr − ) (km s − ) (km s − ) (km s − )SDSS1228 +37 ± ± − ± − ± − − − ± ± − ± − ± − − ± ±
19 +38.0 ± − ± −
27 +6 a RV obs is the observed radial velocity as measured from the absorption lines of each white dwarf. It has not been correctedfor each white dwarf’s gravitational redshift. b Gravitational redshift as computed from the model-determined mass and radius reported for each white dwarf in columns 3and 4.Note. — See Section 3.2 for discussion of input and output parameters. For the UVW space motions positive U is towardsthe Galactic center, positive V is in the direction of Galactic rotation, and positive W is toward the north Galactic pole.
41 –Table 7. Dust Disk ModelsSDSS1228 Ton 345 SDSS1043Stellar ParametersT eff (K) 22,020 18,600 18,330R WD /Dist 2.0 × − × − × − Disk Parameters a T inner (K) 1100 1300 ±
50 1350 1500 1200T outer (K) 700 500 ±
70 350 1000 1100 i ( ◦ ) 60 73 ± a The three different parameter sets for SDSS1228 correspondto the three curves plotted in Figure 6. The parameters are forthe red, black, and blue curves respectively. We adopt the middleparameter set (having T inner of 1300 K) for SDSS1228’s dust diskproperties (corresponding to the black curve in Figure 6). Fromthe three curves we estimate the 1 σ uncertainties on the modelparameters (see Section 4) which are reported with SDSS1228’sbest fit parameters.Note. — The effective temperatures for the three white dwarfscome from G¨ansicke et al. (2006, 2007, 2008a). The ratio of theradius of the white dwarf to the distance of the white dwarf fromEarth, R WD /Dist; temperature at the inner edge of the disk,T inner ; and inclination angle, i , come from the model fit to theUV, optical, and infrared photometry. See Section 4 for a discus-sion of the temperature at the outer edge of the disk (T outer ). 42 –Table 8. Disk DimensionsGas Disks Dust DisksName v max R inner,gas R outer,gas R inner,dust R outer,dust T outer (km s − ) (R WD ) (R WD ) (R WD ) (R WD ) (K)SDSS1228 575 ±
17 40 ± ± ±
17 500Ton 345 709 ±
20 27 ± ∼
100 17 ± ±
18 400SDSS1043 923 ±
52 12 ± ± ±
15 470Note. —
All quoted uncertainties are 1 σ (see below). Gas disks: v max comesfrom the average of the blue or red wing values (whichever is higher) listed inthe “v max sin i ” column of Table 5. This average value is then divided by the sineof the inclination angle reported in Table 7. R inner,gas is derived directly fromthe value reported in the “v max ” column. The quoted uncertainties for R inner,gas also include the statistical uncertainties for the white dwarf masses and radii asquoted in G¨ansicke et al. (2006, 2007, 2008a). There may be additional systematicuncertainties that are not included. R outer,gas is taken from G¨ansicke et al. (2006,2007, 2008a,b). Dust disks:
See Section 4 for a description of how R inner,dust andR outer,dust are derived. T outer corresponds to the outer dust radius shown. Theuncertainties for R inner,dust and R outer,dust are estimated from the range of possibledisk parameters modeled for the SDSS1228 data set and the suggested uncertaintyfor each star’s effective temperature as quoted in G¨ansicke et al. (2006, 2007, 2008a).
Table 9. Ca II Emission Line Flux
Name Ca II K Ca II λ λ λ a (10 − ergs cm − s − ) F IRT /F HK Temperature (K)SDSS1228 1.4 2.6 3.6 3.7 ∼ ∼ < b > b < < b > b < a These values are computed by multiplying emission line EW measurements reported in Table 5by the stellar continuum flux at the emission line location. bb