THE LIFETIME OF PROTOPLANETARY DISKS IN A LOW-METALLICITY ENVIRONMENT^*

We show the disk fractions of the Cloud 2 clusters, as well as of the derived disk fraction of seven embedded clusters in the solar neighborhood, in the disk fraction-age diagram (Figure 5; see Section 5). The disk fractions of the Cloud 2-N and 2-S clusters are significantly lower than nearby embedded clusters of similar age. As discussed in Section 4, the contamination from the foreground objects and the possible unidentified cluster members have only a small effect on the estimated disk fraction. Although the difference between the filter system for our data (MKO) and the data in the literature might cause some systematic offset for the disk fraction value, we confirmed that the disk fraction does not depend on the choice of the filter system by confirming that the disk fraction of a good reference cluster (NGC 2024 cluster) is identical for both CIT and MKO systems (see the Appendix).

Given the importance of the age of the clusters to the above conclusion, here we discuss the uncertainties of the age and the age spread of the clusters. Considering the IMF derived from K-band luminosity function (KLF), the age of the Cloud 2 clusters should be less than 2 Myr: the KLF fitting shows an unrealistic top-heavy IMF with the age of 2 Myr (Yasui et al. 2006, 2008). Therefore, we conservatively estimate that the age upper limit of the Cloud 2 clusters is 1 Myr. Moreover, the suggested supernovae triggered star formation of the Cloud 2 clusters (Kobayashi et al. 2008) suggests the age of 0.4 Myr, which strongly supports the above estimate from the KLF. Because there is no spectroscopic study of the cluster members, there is no observed age-spread information as for the nearby clusters as in, e.g., Palla & Stahler (2000). Because the mean age of this cluster is estimated at ∼0.5 Myr, the age spread should be smaller down to ±0.5 Myr as assumed in the young cluster model of Muench et al. (2000). Muench et al. (2002) estimated the age of the Trapezium cluster at 0.8 ± 0.6 Myr. Palla & Stahler (2000) actually obtained a smaller age spread for the youngest embedded clusters (rho Oph, ONC). Moreover, in the above triggered star formation picture (Kobayashi et al. 2008), the age spread of the Cloud 2 clusters should be small because of the single triggering mechanism at a certain time. Therefore, we conclude that the most likely age of the clusters is 0.5 Myr and no more than 1 Myr. Even if we consider the possible age range, the estimated disk fractions are still quite low compared with those in the solar neighborhood.

Although the Cloud 2 clusters appear to be quite close on the sky, they are totally independent clusters with a projected distance of ∼25 pc at the heliocentric distance of D ≃ 12 kpc (Yasui et al. 2008). If they were located at the same heliocentric distance as the Orion dark cloud (D ≃ 400 pc), the angular separation between the clusters becomes 35, which is larger than 25 between two independent clusters, e.g., NGC 2024 and NGC 2071 clusters, listed in the previous study of JHK disk fraction (Lada 1999). Because the measured disk fractions for two independent clusters were similarly low, the disk fractions of embedded clusters in the low-metallicity environment are inferred to be universally low, at least in the EOG. In combination with the fact that there are no very young (⩽1 Myr) embedded clusters of solar metallicity whose disk fractions are this low, our results strongly suggest that disk fraction depends strongly on metallicity.

The most simple interpretations of the low disk fraction are that the disk is optically thin either because of the collisional agglomeration of dust grains in the disk (Andrews & Williams 2005) or because of the low dust-to-gas ratio due to the low metallicity. However, the former is unlikely because the probability of dust collision, which is proportional to the square of dust density, should be rather low in the low-metallicity environment. The latter is also unlikely because the inner disk should be optically thick even with a metallicity of −1 dex: opacity of the disk with the wavelength of 2 μm (ν ≃ 1.5 × 10¹⁴ [Hz]) at 0.1 AU is estimated to be ∼10⁵, assuming a minimum mass solar nebula (surface gas density of ≃5 × 10⁴ g cm⁻² at 0.1 AU; Hayashi 1981) and a standard power-law opacity coefficient κ_ν (≃15; κ_ν = 0.1(ν/10¹² [Hz]) cm² g⁻¹; Beckwith et al. 1990), and considering the dust-to-gas ratio of 0.001 (Ruffle et al. 2007), which is 1/10 smaller than that in the solar metallicity. If we assume that the typical disk-to-star mass ratio (0.01; e.g., Andrews & Williams 2005; Natta et al. 2006), we would expect the total disk mass of 10⁻³ M_☉ for the lowest-mass stars in our sample (M_* ∼ 0.1 M_☉). Because this is roughly one-tenth that of the minimum mass solar nebulae (0.01–0.02 M_☉), we still expect a very large optical thickness of ∼10⁴ at K band, assuming that the disk mass measured in the submillimeter correlates directly with surface density in the inner regions. This assumption is used for disks in the solar metallicity environment (e.g., Andrews & Williams 2005). Even if we assume the lowest observed disk-to-star mass ratio in the nearby star-forming regions (∼10⁻⁴; Andrews & Williams 2005), the expected optical thickness is still ∼10². Model spectral energy distributions with various disk mass do not show a significantly different H–K color excess (less than 0.05 mag) even if the amount of dust disks decreased to 1/10 (Wood et al. 2002), which correspond to the dust-to-gas ratio of ∼0.001 in the EOG. Therefore, we conclude that the small disk fraction implies that the inner region of the disk is cleared out.

Note that optical thickness does not necessarily mean the existence of observable H–K excess for lowest-mass stars with low effective temperature (∼3000 K) and with very low disk mass of 10⁻³ to 10⁻⁸ M_☉ (e.g., Ercolano et al. 2009). Because the lowest-mass stars of our samples (∼0.1 M_☉) are M6-type stars with an effective temperature (T_eff) of ∼3000 K (see, e.g., bottom figure in Figure 7 of Lada & Lada 2003), it may be inevitable that some lowest-mass stars in our sample do not have detectable H–K excess simply because of the less dust content under low metallicity, thus contributing to the low disk fraction artificially. To investigate this effect, we made a plot of the disk fraction of the Cloud 2 clusters for all sources brighter than certain K-band magnitudes (Figure 6). It is clearly seen that the disk fractions stay almost flat at the low level and do not decrease even including the M stars of the faintest magnitudes (K ∼ 20) that may lower the disk fraction described above. Therefore, we conclude that the disk fraction is genuinely low for all sources down to the mass detection limit due to clearing out of the inner region of the disk. For the above arguments, we note two related studies. One is the detailed disk fraction study of the Trapezium cluster by Lada et al. (2004), who show that even for the latest M-type stars (e.g., M9-type stars, ∼0.02 M_☉, T_eff ∼ 2600 K at 1 Myr) have a detectable H–K excess and the JHK disk fraction does not change even including the stars of this low mass. In view of the youth of the Cloud 2 clusters (∼0.5 Myr) that is similar to the Trapezium cluster, we would naively expect a similar detectable K-band excess even for the lowest-mass stars in our sample (∼0.1 M_☉, M6-type stars) with T_eff ∼ 3000 K even with the low metallicity. Also, in the simulation by Wood et al. (2002), a detectable H–K excess is seen even with very small disk mass of 10⁻⁶ M_☉ under solar metallicity (which corresponds to 10⁻⁵ M_☉ with the metallicity of Cloud 2), assuming a central source with 0.6 M_☉ and T_eff = 4000 K.

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Why does the inner region of the disk become cleared out effectively with lower metallicity? There are two well-known mechanisms that can clear the inner disk: dust sublimation (Millan-Gabet et al. 2007) and the X-wind model (Shu et al. 1994). In the following, we discuss if these mechanisms can effectively work with lower metallicity.

• 1.  
  Dust sublimation. Since dust sublimation typically occurs around 1500 K, the very inner part of the disk with T> 1500 K becomes dust-free. The dust sublimation radius, R_s, is described approximately as (L_*/4πT⁴_rimσ)^1/2, where L_* is the stellar luminosity, T_rim (∼1500 K) is the disk temperature at inner disk radius (R_s), and σ is the Stefan–Boltzmann constant (Dullemond et al. 2007). However, because the inner disk is expected to be optically thick even with the low metallicity of −1 dex, the temperature distribution inside the disk for −1 dex should not differ from that for the solar metallicity (0 dex). Therefore, R_s is not expected to be significantly larger in the lower metallicity environment.
• 2.  
  X-wind model. Due to the interaction between the stellar magnetic field and the accretion disk, the gas disk is thought to be truncated at an inner radius of $R_{\rm x} = \Phi _{\rm dx}^{-4/7} (\mu _*^4 / G M_* \dot{M_D^2})^{1/7}$ (Shu et al. 2000), where M_* is the star's mass, $\dot{M_D}$ is the disk accretion rate, μ_* is the magnetic dipole moment, Φ_dx is a dimensionless number of order unity, and G is the gravitational constant. Among these parameters determining R_x, only the disk accretion rate, $\dot{M_D}$, depends on metallicity. The magnetorotational instability (MRI), which is the most likely cause for disk accretion (Hartmann 2009), largely depends on the ionization of the gas disk by Galactic cosmic rays (Gammie 1996), X-rays from the central young star (Igea & Glassgold 1999), and thermal ionization (Sano et al. 2000). In a low-metallicity environment, we can expect that the ionization fraction increases and the dead zone, which is the MRI inactive region of the disk (Gammie 1996), shrinks because the recombination on grain surfaces is reduced. As a result, $\dot{M_D}$ increases and R_x decreases. In fact, Sano et al. (2000) suggested that the dead zone shrinks when the dust sedimentation of dust grain proceeds, which mimics the case in the low metallicity. On the other hand, low metallicity also means fewer molecular ions, which would reduce the ionization fraction (e.g., Sano et al. 2000), and thus would reduce $\dot{M_D}$. Which process dominates in the low-metallicity environment has not been determined conclusively since the combination of many physical processes determines the size of the dead zone (e.g., Fromang et al. 2002). However, the former process, thus larger $\dot{M_D}$, may dominate (T. Sano, T. Suzuki, & F. Shu, et al. 2009, private communication).

Although further theoretical studies are necessary to have a firm conclusion, we would naively expect that R_x is not significantly larger in a lower metallicity environment, and it appears that there is no theoretical reason to suspect that lower metallicity would make disks less detectable through the H–K excess. The lower dust level would still result in an optically thick inner edge and the size of the cleared out inner region should not change significantly with the metallicity. Therefore, our observations can simply be interpreted that the inner disk (gas and dust) is mostly absent in Cloud 2-N and 2-S.

The above arguments lead to the suggestion that the initial disk fraction (age = 0 in Figure 5) in the low-metallicity environment of our targets is expected to be as high as that for the solar metallicity case, assuming that the distribution of initial disk properties is exactly the same regardless of metallicity. Although this assumption is not obvious and more detailed observations of the disks in the extreme outer Galaxy are needed, it is not an unreasonable assumption because the star formation process from gas to stars does not seem to significantly change for the metallicity of the Cloud 2 clusters, for example, in view of the universal IMF throughout various physical/chemical environments (e.g., Elmegreen et al. 2008; see Omukai 2000 for theoretical study). Therefore, we suggest that the significant decrease of the disk fraction in Figure 5 is a result of the much shorter lifetime (∼1 Myr) of the inner disk in the low-metallicity environment compared with that in the solar metallicity environment, 5–6 Myr from JHK disk fraction (Section 5; Lada 1999). This can be expressed with the rapid decrease of the disk fraction as shown with the red thick line in Figure 5.

We know that the entire circumstellar disk, both the inner and outer disks, dissipates almost simultaneously in the solar metallicity environment because the submillimeter detection fraction and the fraction of objects with an NIR excess are identical (Andrews & Williams 2005), and also because the observed fraction of transition objects, between the Class II and Class III states, is very low (Duvert et al. 2000). Therefore, we suggest that the entire disk dispersal is also rapid in the low-metallicity environment. The distributions of (H–K) excess in the Cloud 2 clusters, which are consistent with those of more evolved (∼5 Myr) embedded clusters with solar metallicity, also support the above idea, though other mechanisms might cause the formation of the similar (H–K) distributions. We constructed intrinsic H–K color distributions (Figure 7) for the Cloud 2 clusters and nearby embedded clusters (Table 1). The intrinsic (H–K) colors of each star were estimated by dereddening along the reddening vector to the young star locus in the color–color diagram (see Figure 4). For convenience the young star locus was approximated by the extension of the classical T Tauri star (CTTS) locus (gray lines in Figure 4), and only stars that are above the CTTS locus were used. For the Cloud 2 clusters (Figure 7, top), the CTTS locus in the MKO system (Yasui et al. 2008) was used, while for the nearby clusters (Figure 7, bottom), the original CTTS locus in the CIT system (Meyer et al. 1997) was used. To make the figure clearer, we show the color distributions only for NGC 2024 (Haisch et al. 2000), Taurus (Kenyon & Hartmann 1995), and IC 348 (Haisch et al. 2001b), which have significantly different disk fractions. It is clearly seen that the distribution becomes bluer and sharper with lower disk fractions. The distributions of the Cloud 2 clusters resemble that of IC 348, whose disk fraction is as low as the Cloud 2 clusters (∼20%).

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As the mechanism of disk dispersal, two possibilities are known: (1) disk accretion (Hartmann et al. 1998); and (2) photoevaporation of the surface layer of the gas disk due to extreme-ultraviolet (EUV) radiation from the central star and/or the external radiation field (Hollenbach et al. 2000). In the low-metallicity environment, both possibilities may work effectively. First, the disk accretion rate may increase in the low metallicity as discussed in Section 6.2, if the increase of the ionization fraction due to less dust is larger than the decrease of the ionization fraction due to few molecular ions. This could be the reason for the rapid disk dispersal. Second, the photoevaporation process may also work effectively to shorten the disk lifetime. Because the EUV photoevaporation is solely based on the Strömgren condition of the hydrogen gas, metallicity (or dust-to-gas ratio) should not affect the rate of the photoevaporation mass loss. However, the recent theoretical work (Gorti & Hollenbach 2009) shows that far-ultraviolet (FUV) or X-ray radiation is more effective than EUV to photoevaporate the disk. Because FUV penetration strongly depends on the amount of dust in the disk, Gorti & Hollenbach (2009) found that the disk lifetime decreases with the dust opacity. Although the dust opacity dependence of the disk lifetime is not strong (a factor of ∼2 changes with the dust opacity change of 10), they noted that the results are still in a preliminary stage and further detailed modeling is awaited. Therefore, this could also be the reason for the rapid disk dispersal in low metallicity. In addition, something specific to the EOG environment might be the reason (see, e.g., Haywood 2008), but obviously more studies are necessary to pin down the physics of this phenomenon.

If the lifetimes of disks at the solar metallicity ([O/H] ∼ 0) and the low metallicity ([O/H] ∼ −0.7) are approximated as 5 Myr and 1 Myr, respectively, our results suggest that the disk lifetime strongly depends on the metallicity (Z ≡ [M/H]) with a ∼10^Z dependence. Because the disk lifetime (τ_disk) is directly connected to the planet formation probability (P_pl), the strong metallicity dependence of τ_disk may create a similarly strong metallicity dependence of P_pl. Therefore, the disk dispersal could be one of the major driving mechanisms for the planet–metallicity correlation, which shows a strong sharp (∼10^2Z) metallicity dependence (Fischer et al. 2005). In the current standard core nucleated accretion model of the giant planet formation (e.g., see a review by Lissauer & Stevenson 2007), the planet formation timescale is determined by both the core growth time and the gas accretion time onto the core. Since the first study by Safronov (1969), the core growth time in the giant planet zone has been thought to be far longer than the observed τ_disk. But, after the discovery that τ_disk is less than 10 Myr, it is widely accepted that giant planet cores must form via rapid runaway growth (Wetherill & Stewart 1989) and oligarchic growth (Kokubo & Ida 1998), which can grow the cores for the giant planet (5–10 M_⊕) at the outer disk (5 AU) in a reasonable time, e.g, 10 Myr. Because this growth time is comparable with τ_disk, the variation of τ_disk due to the metallicity around this timescale may cause a strong metallicity dependence of the planet formation probability, P_pl, thus contributing to the planet–metallicity correlation.

As far as we know, a deterministic model based on the core-accretion model by Ida & Lin (2004) is the only study that quantitatively estimates the effect of τ_disk variation on P_pl. They show that the planet formation probability decreases with decreasing τ_disk (see their Figure 2(b)). However, the amount of decrease is only a factor of 2–4 with a factor of 10 change in the disk lifetime: the dependence is more like P_pl ∼ τ^0.5_disk and is not a strong function of τ_disk. If this is the case, our suggestion that τ_disk ∼ 10^Z means the disk dispersal can contribute to the planet–metallicity correlation by a factor of 10^0.5Z. Ida & Lin (2004) not only show that the core-accretion model can qualitatively explain the planet–metallicity relation, but also note that the suggested metallicity dependence is not as strong as the observed relation: it is more like ∼10^Z dependence judging from their Figure 2(b). Therefore, by adding the contribution from the disk dispersal (∼10^0.5Z), most of the observed metallicity dependence of the planet formation probability (10^2Z) can be reasonably explained. However, a quantitative argument is difficult at this stage because there are ambiguities and complexities in the planet formation models, and thus the planet-formation timescale. Note that other groups are trying to reproduce the steep metallicity dependence by introducing a critical solid mass (Wyatt et al. 2007; Matsuo et al. 2007) for the core-accretion model.

While the planet–metallicity correlation appears to be clear in Fischer's systematic work (Fischer et al. 2005), Udry & Santos suggest that the correlation in a low-metallicity range ([Fe/H] <0) may be relatively weak (Udry & Santos 2007). Santos suggests that the planet formation mechanism could be different for the two metallicity ranges: core accretion for the high-metallicity range and disk instability for the low-metallicity range (Santos 2008). Because our results seem to qualitatively explain a significant part of the 10^2Z dependence of the planet–metallicity relation, we assume that the dependence also holds true in the low-metallicity range ([Fe/H] < 0), where we made our observations. However, the core-accretion model may not be able to explain the existence of planets around the low-metallicity stars with such short disk lifetime.