SHOCKS AND A GIANT PLANET IN THE DISK ORBITING BP PISCIUM?

Acke et al. (2009) and Furlan et al. (2006) validated the use of IRS-based spectral indices to study disk structure by comparing indices computed from data to those computed from disk models. We seek to gain insight into BP Psc's disk structure by comparing its IRS spectral indices to those computed for the disks studied by Acke et al. (2009) and Furlan et al. (2006). We calculate the value of the following indices: an excess at 7 μm of 4.55 mag, the ratio of flux at 13.5 μm to that at 7 μm ([13.5/7]) of 0.69 mag, and the ratio of flux at 30 μm to that at 13.5 μm ([30/13.5]) of 0.96 mag (see Acke et al. 2009 for how these values are derived); the ratio of integrated continuum flux near 6 μm to that near 13 μm (n_6–13) of 2.10, the ratio of integrated continuum flux near 13 μm to that near 25 μm (n_13–25) of 1.93, and the ratio of integrated continuum flux near 6 μm to that near 25 μm (n_6–25) of 2.03 (see Furlan et al. 2006 for how these values are derived). These values suggest that BP Psc has strong near-infrared excess emission and steeply rising flux toward longer wavelengths (consistent with BP Psc's SED; see Figure 2 herein and Figure 6 of Z08). As mentioned above, the real power of these indices to constrain the structure of BP Psc's disk comes from comparing them to indices derived for other well-modeled disk-bearing objects. Such comparisons are presented in Section 4.

The IRS spectrum of BP Psc shows several broad emission lines from solid-state transitions (Figures 1–3). To model these features, and hence deduce the nature of the emitting particles, we proceed in fitting the spectrum via two paths. In one path, we attempt to identify grain species by subtracting the most obvious contributor and searching for residuals indicative of additional grain species (as was done successfully for HD 100546 by Malfait et al. 1998). During these subtraction fits we try various grain shapes and sizes (using the absorption coefficients of Min et al. 2007) to identify the best shape distribution and grain size to use. In parallel with these subtraction fits, we fit the data using the χ² minimization routine described in Gielen et al. (2008). We refer the interested reader to their work, and references cited therein, for details about model inputs. The strategy employed by Gielen et al. (2008) assumes that solid-state emission features originate in an optically thin disk atmosphere. They attempt to fit mid-infrared spectra with a blackbody model for the disk continuum emission and an emission feature model computed from the linear combination of dust absorption coefficients multiplied by different blackbody temperatures. The χ² of the model fit to the data is then minimized by adjusting various parameters; e.g., grain temperature, grain species, and intensity of grain emission. Both the preliminary χ² fit and subtraction fits indicate that the grains producing the emission features in BP Psc's spectrum are sub-micron (∼0.1–1.0 μm) in size. We also find that both methods obtain consistent results in grain species identified. Similar to what was found by Gielen et al. (2008), we find that dust emission features cannot be reproduced with spherical grains (e.g., Mie theory), but are instead best reproduced with absorption coefficients calculated using the Gaussian random-field (GRF) theory for the grain shape distribution (Shkuratov & Grynko 2005; Min et al. 2007, and references therein) and the discrete dipole approximation (Draine 1988). It is noted that the grain shape approximations used sometimes do not reproduce exactly the grain emission features (and hence likely are not a complete match to the true grain shapes); see the discussion in Gielen et al. (2008). In the following three paragraphs we describe the resulting grain species identified from these two methods.

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Three features—with wavelengths near 33, 28, and 23 μm—stand out in BP Psc's IRS spectrum. These features are typically associated with crystalline, magnesium-rich olivine grains (forsterite, Mg₂SiO₄). Fits to the forsterite features leave significant residual emission in the 20–35 μm range. Experimentation with various grain species indicates a contribution from crystalline, magnesium-rich pyroxene (hereafter enstatite, MgSiO₃). Fits including enstatite leave little residual solid–state emission in the 23–35 μm range.

Our forsterite and enstatite fits alone cannot reproduce the feature near 10 μm. The ∼10 μm feature is typically associated with amorphous dust of the pyroxene or olivine species. Experimentation with the two suggests that amorphous, magnesium-rich pyroxene (hereafter pyroxene, MgSiO₃) provides a better fit.

The remaining residual emission—near wavelengths of 9, 13, 16, and 21 μm—is reminiscent of the features produced by annealed, crystalline silica (hereafter cristobalite, SiO₂; see Sargent et al. 2009b and references therein). It is noted that the 9 and 16 micron complexes are marginally detected in the residual spectrum. In light of this fact, and in the interest of completeness, we reviewed other polymorphs of silica to see if they could reproduce the remaining spectral features. α-quartz is ruled out by its characteristic 25 μm feature which would be quite strong if present (Gervais & Piriou 1975). β-quartz is ruled out by the high temperatures necessary to excite its resonances (T_dust ≳ 850 K; Gervais & Piriou 1975); our above analysis suggests the small dust grains seen in BP Psc's IRS spectrum are significantly cooler (see also below). The polymorphs coesite and stishovite are also ruled out due to their unique emission spectra (see Sargent et al. 2009b and references therein). This leaves cristobalite, amorphous silica, and obsidian as potential silica polymorphs to explain the residual emission. Since obsidian and amorphous silica have similar spectral features (see Figure 3 of Sargent et al. 2009b), we use amorphous silica to represent both polymorphs. To model silica emission features we adopt optical constants from Min et al. (2007) for amorphous silica (hereafter silica) and from C. Lisse (2009, private communication; see the discussion in the supplementary online material to Lisse et al. 2006 for a description of the input optical constants) for cristobalite. Absorption coefficients are calculated for silica using GRF and for cristobalite using a continuous distribution of ellipsoids (CDE). Models using silica result in higher χ² than do fits using cristobalite and fits without any SiO₂ polymorph provide yet even higher χ² values; a comparison of fits using cristobalite, silica, and neither cristobalite nor silica are shown in Figure 4. As such, we consider SiO₂ to be significantly detected in the IRS spectrum of BP Psc and conclude that annealed silica is the most likely polymorph.

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Some of the above mentioned transitions are coincident with those of polycyclic aromatic hydrocarbons (PAHs). PAHs, however, typically display strong 8.0 μm features (see, e.g., Sloan et al. 2007 and references therein). No such feature is seen in our spectrum of BP Psc, thus we conclude that PAHs do not significantly contribute to the strength of the observed solid-state features.

We briefly mention the effect of reddening on mid-infrared solid-state emission features. Highly reddened stars can exhibit depressed 10 μm features (Gielen et al. 2008). BP Psc, at a Galactic latitude of −572, is unlikely to be experiencing any significant interstellar extinction regardless of its distance. The dusty material in orbit around this star could in theory provide substantial reddening if the grains are small. In their analysis, Z08 compared low-resolution optical spectra of BP Psc to non-dusty stars of similar spectral types and showed that BP Psc is not reddened along our line of sight. Thus, reddening is unlikely to contribute to the observed strength of the 10 μm structure.

With rough grain parameters identified we proceed in a final χ² minimization fit to the spectrum. Input dust species, grain shapes, and grain sizes are restricted to those as determined from the subtraction and initial χ² fits. We allow as free parameters three independent dust continuum temperatures, three independent dust species temperatures, two dust grain sizes (∼0.1–1.0 μm and ∼2.0–4.0 μm), and five dust species—forsterite, enstatite, pyroxene, amorphous olivine, and cristobalite. The final χ² minimization routine employed herein differs slightly from that used by Gielen et al. (2008). Our routine assigns grain species into one of three distinct groups where each group is allowed its own dust temperature and temperature step size in the model grid. Amorphous materials (pyroxene and olivine) form one group which has a temperature grid step of 25 K, crystalline olivine and pyroxene form another group which has a grid step of 25 K, and silica is in its own group that has step size of 50 K. The final model fit is displayed in Figure 3. Temperatures, mass fractions, associated errors, and an estimated mass per species are reported in Table 1. Errors on these parameters are calculated as in Gielen et al. (2008): noise is added to each pixel with a value randomly chosen from within ±1σ of a Gaussian with full- width at half-maximum determined from the spectrum statistical uncertainty per pixel. In this manner 100 synthetic spectra are generated, all consistent with the data, on which we perform the same fitting procedure. The resulting slightly different fit parameters are used to derive the mean (the best-fit value) and the standard deviations. The uncertainty on the mass absorption coefficients is not taken into account in this error determination.

Table 1. Dust Component Parameters

Dust Component	Stoichiometry	Temperature	Mass Fractiona	Massb
		(K)	(%)	(Lunar Masses)
Forsterite	Mg2SiO4c	75 ± 25	59.4$\mathop {}_{-2.4}^{+2.6}$	1.2
Enstatite	MgSiO3c	75 ± 25	36.2$\mathop {}_{-2.8}^{+2.4}$	0.6
Olivine	Mg2SiO4d	150 ± 25	0.06$\mathop {}_{-0.06}^{+0.35}$	−e
Pyroxene	MgSiO3d	150 ± 25	4.0$\mathop {}_{-0.5}^{+0.3}$	6 × 10−2
Cristobalite	SiO2c	250 ± 50	0.03$\mathop {}_{-0.01}^{+0.06}$	6 × 10−4
Continuum 1	⋅⋅⋅	1000$\mathop {}_{-100}^{+50}$	⋅⋅⋅	600f
Continuum 2	⋅⋅⋅	250$\mathop {}_{-35}^{+25}$	⋅⋅⋅
Continuum 3	⋅⋅⋅	175$\mathop {}_{-30}^{+25}$	⋅⋅⋅

Notes. ^aFraction of mass in 0.1–1.0 μm, solid-state emitting grains detected in the IRS spectrum only. The reported percentage does not include the mass contained in the material responsible for the continuum emission. ^bAssuming the mass of the moon is 7.35 × 10²⁵ g and that BP Psc is a giant star 300 pc distant from the Earth (Z08). For an assumed distance of 80 pc, appropriate if BP Psc were a T Tauri star, the mass per grain species is reduced by a factor of ∼15. ^cCrystalline grains (see Section 3.2). ^dAmorphous grains (see Section 3.2). ^eWe do not consider amorphous olivine as significantly detected in the final χ² model fit. ^fThis mass is from Z08 where they computed the disk dust mass assuming half of the 880 μm detected flux toward BP Psc comes from a region of the disk having T_dust= 36 K (fits to the IRS spectrum do not require that an additional ∼36 K dust region exists; Figure 4 of Malfait et al. 1998 shows how the 33 μm forsterite feature is sensitive to cool material). If there is no 36 K dust, then the mass listed for the continuum component could be a few times smaller.

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Here we summarize some of the main results of the spectral fitting. No larger sized (∼2.0–4.0 μm) grains are required in the fit. Amorphous olivine (Mg₂SiO₄, hereafter olivine) is not necessary to obtain the minimum χ² model fit. SiO₂, however, is required despite its low mass fraction and its inclusion in the fit results in a significantly reduced final χ² (∼84 if included and ∼110 if not; see Section 7 of Gielen et al. 2008 for how we calculate χ²). From Table 1 it is clear that the crystallinity fraction of the small dust grains is high, ∼96%, with the majority of this coming from forsterite and enstatite.

The sub-micron sized dust grains orbiting BP Psc, in the case that it is a first-ascent giant star, would be radiatively blown out without a spatially coincident gas disk (this would not be the case if BP Psc were a T Tauri star). To illustrate this, we assume BP Psc has a luminosity of 100 L_☉ and a mass of 1.8 M_☉. With Equation (1) from Chen et al. (2006), and assuming grain densities of 3.3 and 2.3 g cm⁻³ for silicates and SiO₂ respectively, we estimate that grains smaller than ∼10 μm in size will be radiatively blown out of the BP Psc system in the absence of gaseous material.

3.2.1. Unmodeled Features

Classical T Tauri stars are pre-main sequence, solar-like stars that are still surrounded by substantial amounts of primordial gaseous and dusty material. The IRS indices (see Section 3.1) for these disks are consistent with flat, optically thick, active accretion disks (see e.g., Furlan et al. 2006). BP Psc's IRS indices are strongly discrepant with those for the T Tauri stars presented in Furlan et al. (2006) and Watson et al. (2009)—where the Taurus median of n_6–13, n_13–25, and n_6–25 are −0.82, −0.17, and −0.48 respectively—suggesting that the structure of BP Psc's disk is significantly different from T Tauri star disk structures (see Section 4.2).

T Tauri star dusty material shows a variety of compositional characteristics that are at odds or incompatible with what is observed for BP Psc:

• 1.  
  T Tauri stars sometimes host disks with high crystallinity fractions, but these grains are typically accompanied by significant quantities of amorphous species and are confined to within ≲10 AU separation from their host stars (Watson et al. 2009). Reasonable age and mass estimates of BP Psc as a classical T Tauri star (see Table 6 of Z08) would require its cool forsterite and enstatite grains to reside at separations ≳12 AU.
• 2.  
  If BP Psc were a young T Tauri star, its disk atmosphere would have one of the highest masses in small grains (∼0.1 lunar masses if located 80 pc from Earth; see notes to Table 1) for a star of its class (e.g., Sargent et al. 2009a, 2009b, quote a range of mass in small dust grains for the T Tauri stars they studied of ∼0.8–700 × 10⁻⁴ lunar masses).
• 3.  
  Watson et al. (2009) find in the T Tauri stars they studied an anti-correlation between the strength of the 11 μm crystalline olivine feature and the total strength of the entire 10 μm solid-state emission complex. Additionally, Watson et al. (2009) identify a positive correlation between the total strength of the 10 μm complex and the magnitude of the n_13–25 index. These correlations suggest that stronger crystalline emission features, and hence more chemically evolved grain populations, accompany disk settling in T Tauri star disks. Sargent et al. (2009a) found that chemical evolution does not necessarily imply grain growth has occurred, further suggesting that chemical evolution and sedimentation are tied (but Dullemond & Dominik 2008 show that dust sedimentation alone, without grain growth, cannot reproduce the observed correlations). BP Psc's grains, despite their nearly 100% crystallinity fraction, are still suspended in the flared disk atmosphere, apparently in contrast with the observed T Tauri star trends.

Herbig Ae/Be (HAeBe) stars are the intermediate mass counterparts of classical T Tauri stars. HAeBe stars are much hotter and more luminous (median T_eff ∼ 6000–7000 K, L ∼ 10–1000 L_☉ depending on their progress along pre-main sequence tracks; see Palla & Stahler 1993) than lower mass, solar-like T Tauri stars and hence provide a far different circumstellar environment.

BP Psc's SED is reminiscent of Meeus group I HAeBe stars (see Figure 4 in Meeus et al. 2001). The IRS indices for BP Psc, when plotted in Figure 2 of Acke et al. (2009), lie in the region of infrared excess space describing HAeBe disks having a Meeus group II disk structure (where group II sources have an outer disk which is protected against direct stellar radiation by the puffed-up inner disk rim; see Dullemond & Dominik 2004 and references therein). This behavior is peculiar, but repeated in a well-studied HAeBe star, HD 100546. This source is given as an exemplar Meeus group I source in Meeus et al. (2001). However, it too resides in the region of Figure 2 of Acke et al. (2009) describing Meeus group II disk structures. Recent interferometric work by Benisty et al. (2010) has confirmed that HD 100546 has a gap in its disk (see Section 6.2). It would seem that gapped disks can provide confusing results when relying on spectral indices alone. Nonetheless, BP Psc's SED, and hence disk structure, is consistent with those found for HAeBe stars.

The match of BP Psc's disk structure with those of HAeBe stars suggests that their inner disk morphologies are determined from the same physical effect. It is not yet clear what determines this inner radius environment, but the ubiquity of hot excess temperatures of ∼1500 K that fit the near-infrared "bumps" in HAeBe SEDs (thought to arise from puffed-up inner disk rims) suggests that dust sublimation is responsible. This is in contrast to solar mass T Tauri stars, whose inner disk morphologies are determined by magnetospheric accretion (which act on T Tauri disks at ∼7 R_*, close to sublimation temperatures; see Bouvier et al. 2007 and references therein).

Infrared Space Observatory (ISO), IRS, and ground-based mid-infrared spectroscopy of HAeBe stars indicate disks sometimes populated by PAHs and/or significantly evolved dust as evidenced by high mass fractions of larger than sub-micron size, chemically and thermally processed grains (Bouwman et al. 2001; Acke & van den Ancker 2004; van Boekel et al. 2005; Keller et al. 2008). One HAeBe star, HD 100546, shows dust emission features in its mid-infrared spectrum that are similar to those seen in the IRS spectrum of BP Psc (Figure 2). HD 100546 was shown by Malfait et al. (1998) to have strong contributions to its mid-infrared spectrum from forsterite and PAH emission. The grains orbiting HD 100546 are sub-micron sized and originate from two distinct temperature regions (Malfait et al. 1998). More discussion of HD 100546, and its relation to BP Psc, can be found in Section 6.

Three other first-ascent giant stars have well-characterized infrared excess emission. Two of these objects, HD 233517 (a K2 III star; Fekel et al. 1996; Jura 2003; Jura et al. 2006) and HD 100764 (a ∼ 4400 K, R-type carbon star; Skinner 1994; Sloan et al. 2007), also have published IRS spectra. The third, TYC 4144 329 2 (an F2-type star; Melis et al. 2009), has existing IRS spectroscopy that will be mentioned here (a more detailed description of TYC 4144 329 2's IRS spectrum will appear in C. Melis et al. 2011, in preparation). The infrared excess emission for these three objects is modeled as arising from a Keplerian disk of dusty material that orbits the central giant star. In the case of HD 100764 and TYC 4144 329 2, near-infrared excess emission is present indicating dust as hot as ∼1500 K (Skinner 1994; Melis et al. 2009). HD 233517 exhibits infrared excess emission indicating a flared, cool dust disk (T_dust ∼ 70 K) orbiting at ∼45 AU separation from the giant star (Jura 2003).

IRS spectroscopy of all three of the above mentioned giant stars indicates that they are orbited by PAHs and small, amorphous, silicate dust grains (Jura et al. 2006; Sloan et al. 2007, C. Melis et al. 2011, in preparation). It is interesting to note that all three of these giant stars host obvious PAH features while BP Psc does not (see Figure 1; although the ∼6.5 μm feature in BP Psc's IRS spectrum remains unidentified, it is unlikely to be the characteristic 6.2 μm PAH transition).

With the IRS and TIMMI2 mid-infrared spectrographs, Gielen et al. (2008) performed a comprehensive study of the circumstellar material in Keplerian orbits around post-asymptotic giant branch (post-AGB) binaries having a median stellar effective temperature of ∼6000 K and assumed luminosities in the range of ∼5000 ± 2000 L_☉. The disks around post-AGB binary systems are well modeled as passive, irradiated disks (Deroo et al. 2007a, 2007b). Some of the post-AGB binary IRS spectra presented in Gielen et al. (2008) have similar slopes as the BP Psc IRS spectrum, indicating that they could have similar structure.

Gielen et al. (2008) found that the stable disks orbiting post-AGB binaries host populations of hot and cold amorphous and crystalline grains. Grains in post-AGB binary dust disks show evidence for strong processing, both in the form of grain growth beyond sub-micron sizes and crystallization. The physical process by which disks form in post-AGB binary systems is not well understood, but it is expected that interactions between the evolved star and its companion play a necessary role (Deroo et al. 2007b).

Similar to our discussion of radiative blow out for grains orbiting BP Psc, it can be shown that post-AGB binaries must also have significant quantities of gas spatially coincident with their dusty material. Since the minimum grain size that can orbit a star scales linearly with luminosity, and since post-AGB binary systems have similar masses as first-ascent giants, we estimate that the minimum size grains that can orbit a post-AGB binary in the absence of gas would be ≳100 μm in size.

According to the Shu et al. (1979) model, material lost from binary interaction will initially be close to the host giant star and thus would be subjected to the intense giant star radiation field. Once this material passes beyond the sublimation radius it can begin to coalesce into dust grains. These dust grains should be efficiently annealed with the heat from the nearby luminous star, resulting in a high fraction of dust being crystalline. In their study of the 10 μm emission feature of HAeBe stars, Bouwman et al. (2001) found that with increasing abundances of forsterite one expects to see larger mass fractions of crystalline SiO₂. Such a result is indicative of the thermal annealing process which transforms amorphous into crystalline grains with SiO₂ as a by-product. That we see SiO₂ in the material surrounding BP Psc lends some support to a disk formation model similar to that presented by Shu et al. (1979). The orbital semi-major axis of this crystalline material will continue to expand until the disk reaches its maximum size. Thus, highly crystalline material would be transported to the cooler, outer regions of the disk where it is observed.

There are some problems with the above grain evolution scenario. One is that other first-ascent giants with dusty material thought to originate in a manner similar to BP Psc's do not show evidence for highly crystalline material. A second problem is that the polymorph of SiO₂ most likely present in BP Psc's IRS spectrum, cristobalite, must be cooled very quickly after being annealed or it will revert to lower temperature polymorphs that do not exhibit the characteristic 16 μm emission feature (Sargent et al. 2009b). It is difficult to imagine that the disk excretion could be slow enough to efficiently anneal SiO₂ into a cristobalite polymorph and at the same time rapid enough to transport this cristobalite to cooler regions before it can revert. More detailed modeling and simulations of disk formation through engulfment could further explore these issues.

It seems unlikely that the composition of the dust orbiting BP Psc is linked to its disk formation mechanism due to the problems discussed above. Instead, the dust mineralogy could be the result of evolutionary processes which occur in protoplanetary disks and are understood to be the precursors to (or indicators of) planet/planetesimal formation. Under such an assumption the IRS results could provide insight into whether or not new planetesimal formation is occurring in BP Psc's disk. As discussed above, the presence of cristobalite would require an event that heated the disk to temperatures of ∼1000 K and then allowed it to cool rapidly. Such an event likely took place in BP Psc's outer disk where the disk equilibrium temperature is sufficiently low to prevent the cristobalite from reverting (Sargent et al. 2009b). As discussed in Sargent et al. (2009b), disk-lightning or nebular shock scenarios can explain the presence of cool, highly crystalline material (especially cristobalite). However, they do not explain why so much of this material would be in BP Psc's flared disk atmosphere (lightning and shocks are expected to mainly act in the disk interior; Pilipp et al. 1998; Harker & Desch 2002), especially when one considers that grain processing should be linked with grain growth and sedimentation (e.g., Natta et al. 2007; Watson et al. 2009 and references therein).

Potential solutions to these problems come from comparing BP Psc to HD 100546. Bouwman et al. (2003) suggest that HD 100546—which has an SED (Figure 2) and crystalline silicate emission similar to those of BP Psc (with the exception of the presence of SiO₂)—has a proto-gas giant planet carving a gap within its disk. Such a gap naturally explains the enhanced mid- to far-infrared excess emission relative to the near-infrared excess emission in HD 100546 when compared to other HAeBe stars as the far side of the gap would be directly irradiated by the star. This direct stellar irradiation would produce a vertically extended wall in the disk, allowing it to intercept a large fraction of stellar light which would then be reradiated as blackbody emission having the characteristic temperature for the disk gap location (∼200 K for HD 100546; see Figure 2). Interferometric observations of HD 100546 by Benisty et al. (2010) confirm that HD 100546 does indeed have a gap within its disk. Recent optical and ultraviolet spectroscopic studies of HD 100546 further support the interpretation that this star has a giant planet orbiting within the gap in its disk (Grady et al. 2005; Acke & van den Ancker 2006). BP Psc and HD 100546 have similar SEDs (Figure 2) and thus could potentially have similar disk structure (it is noted that BP Psc's disk inclination angle ∼75° is closer to edge-on than HD 100546's ∼51° and that edge-on disks without gaps around young solar-mass stars are known to have "double-hump" SEDs; Grady et al. 2001; Wood et al. 2002). If this were the case, it would be reasonable to surmise that the same mechanism responsible for HD 100546's disk structure (a gap-opening giant planet) operates also in BP Psc's disk. Interferometric observations of BP Psc as well as detailed modeling of its resolved disk images and SED are necessary to confirm such a gapped disk model. Any such giant planet orbiting BP Psc would have an orbital semi-major axis of ∼4 AU (assuming BP Psc has a luminosity of ∼100 L_☉). We note that theoretical works predict that any such object have a mass that is <10 M_Jup as more massive bodies would restrict the flow of material toward the star resulting in a depleted inner disk (Lubow et al. 1999). Such depletion would not be compatible with observations that indicate large quantities of gaseous and dusty material in BP Psc's inner disk (Z08). It is not clear whether any such giant planet would be from BP Psc's original planetary system or if it would be a protoplanet forming from the material in BP Psc's giant star disk.

Two mechanisms to explain the observed dust mineralogy are discussed in the following subsections. Both rely on the existence of a giant planet opening a gap within BP Psc's disk.

6.2.1. Colliding Planetesimals

6.2.2. Giant Planet Disk Shocking