Chapter 2 UV Photoevaporation of PPDs: Metallicity Dependence 26
2.3 Results
2.3.2 Different Metallicities Disks
Chapter 2 UV Photoevaporation of PPDs: Metallicity Dependence 42
Fig. 2.4 Same as Figure 3 except that it examines heavy elements along a different ray at θ = 69◦. In the bottom panel, Θ1, Θ2, and Θ3 represent the shielding factors against CO dissociating photons by CO (self-shielding), H2, and dust (see also Appendix 2.2.4 for full details for these shielding factors).
is located at z ≃20 au withR = 50 au in our simulation, whilez ∼15 au at R ≃50 au in Woitke et al.(2009). Hydrodynamics does not strongly influence the chemical structure of CO molecules as that of H2molecules in our model.
43 2.3 Results
Fig. 2.5 Structure of the photoevaporating disk at t = 8 tc with different metallicities:
Z = 100.5Z⊙ (top panel),Z = 10−0.5Z⊙(middle panel), and Z = 10−4Z⊙ (bottom panel).
The disk structure is visualized in the same manner as in Figure 2.1.
105–107cm−3withZ = 10−0.5Z⊙. It is found that the base density of the neutral photoevaporative flows approximately scales with∝Z−1 in our simulations. The results of the simulations suggest that at least a subsolar metallicity ofZ ≳10−0.5Z⊙is required to drive the neutral photoevaporative flows by FUV heating, and if excited, the density is higher for lower metallicity disks.
The optical depth for FUV photons is determined by the column density of dust grains along with a ray. The visual extinctionAV effectively provides an optical depth for FUV photons in our simulations. Since the amount of grains proportionally decreases with decreasing metallicity, the visual extinction also decreases asAV∝NHZ. The formula describes that a lower-metallicity disk
Chapter 2 UV Photoevaporation of PPDs: Metallicity Dependence 44 medium has a smaller optical thickness when it compared at the same column NH. Thus, FUV reaches a denser region of a PPD with low metallicities FUV photons can heat the denser region of the disk with low metallicity, and the higher-density photoevaporative flows excited from the Z = 10−0.5Z⊙ disk (Figure 2.5). It is concluded that the decrease of the dust amount is the cause for the higher-density neutral flows in the lower-metallicity disks.
The neutral flows are only weakly driven for even lower-metallicities ofZ ≲10−0.5Z⊙ and almost cease at the low-metallicity extent Z = 10−4Z⊙. FUV heats the gas by ejecting thermalizing electrons from dust grains, and thus the relative amount of dust grains to gas matters to determine the efficiency of FUV heating. We assume the dust-to-gas mass ratio proportional to metallicity.
The relative amount decreases with decreasing metallicity, which indicates the decline of the specific FUV heating rate in low-metallicity disks. Moreover, the electron abundance of the neutral region is set by the abundance of ionized carbon under our chemistry model. The neutral region is electron-poor in low-metallicity disks, and it makes the recombination timescale of charged grains longer at a fixed gas density. Dust grains are easy to be positively charged. Thermalizing electrons are hard to be ejected owing to the deepened Coulomb potential of the grains. The photoelectric effect efficiency (cf. Eq.(2.23)) is lowered, and hence the heating efficiency of the photoelectric heating is reduced.
This explains the low heating rate in the low-density neutral region close to the ionization front of HII.
Similarly, the specific cooling rates of metal elements of dust decrease with decreasing metallicity.
The second row of Figure 2.6 directly shows this behavior; O I cooling, H2 cooling, and dust-gas collisional cooling rates are the largest in the neutral region for Z ≥100.5Z⊙, and decrease with decreasing metallicity. Adiabatic cooling is dominant in both the HIIand HIregions in the lowest-metallicity disk (Z = 10−4Z⊙). In HII regions, EUV heating and adiabatic cooling dominate at any metallicity, and the rates are largely independent of metallicity.
The decrease in the amounts of dust and metal elements reduces the specific heating/cooling rates of FUV heating, OIcooling, and dust-gas collisional cooling. These heating and cooling contribute to determine Figure 2.6 shows a clear decline in the temperatures of the neutral regions, implying that the contribution of coolants is more effective than FUV heating.
In the neutral region dominated by OIcooling and H2 cooling, the specific FUV heating rate is decreased by the smaller amount of grains and the reduced photoelectric efficiency, as metallicity declines. In contrast, the specific O I cooling rate is decreased owing to the reduced amount of OI, and metallicity does not explicitly affect the H2 cooling rate. Thus, FUV heating is decreased more efficiently as metallicity lowers, compared with these coolants. In the high-density regions dominated by dust-gas collisional cooling, FUV heating and dust-gas collisional cooling set the temperatures. Since the hydrogen nuclei density and the electron abundance approximately scale with∼Z−1 and Z, respectively, in this region, the photoelectric efficiency hardly varies according to metallicity. Hence, the specific FUV heating rate is almost purely proportional to the amount of grains, i.e. metallicity. By contrast, the specific dust-gas collisional cooling rate is proportional to both Z and nH, and is also dependent on dust temperature. Dust temperatures are set by the balance between the absorption of irradiating photons and (re-)emission by dust grains. Both the absorption and (re-)emission are proportional to the opacities, and the opacities scale with Z.
Thus, the distribution of dust temperatures are similar at any metallicity, other than the optically-thick regions are embedded in high-gas-density regions for lower-metallicity disks. Regarding the base gas density, it is inversely proportional to metallicity, so that the specific rate of dust-gas collisional cooling is almost independent of metallicity in the region. The decrease of the dust-gas collisional cooling rate is slower than that of the FUV heating rate, and thus the cooling becomes
45 2.3 Results
Fig. 2.6 Meridional distributions of various physical quantities atr≃80 au in the disks with various metallicities: Z = 100.5Z⊙ (left column), 10−0.5Z⊙ (middle column), and 10−4Z⊙ (right column). The snapshots are taken att= 8tc. In each column, the profiles are shown in the same manner as in Figure 2.2. We note that, in the second panel forZ = 10−4Z⊙, some heating and cooling rates are missing because their values are too small to be plotted.
more efficient compared to FUV heating in lower-metallicity disks. To summarize, as metallicity decreases, OIcooling, H2cooling, and dust-gas collisional cooling dominantly contribute to thermal balance in the neutral region compared to FUV heating. This results in the lower temperatures of the neutral regions. The reduced FUV heating is ineffective to provide a sufficient energy to the neutral gas for escape from the gravitational binding. For this reason, the neutral photoevaporative flows are even hardly driven in the lowest-metallicity range ofZ ≲10−2Z⊙.
2.3.2.2 Hydrogen-Bering Species Distribution
The balance of photodissociation, the photoevaporative advection of H2, and H2formation on grains determines the chemical structures of H2 and H I, As discussed in Section 2.3.1, the chemical structures of H2 and H I is determined by the H2 advection driven by FUV, H2 formation on
Chapter 2 UV Photoevaporation of PPDs: Metallicity Dependence 46 grains, and photodissociation. The self-shielding effect of hydrogen molecules are effective to protect themselves from the photodissociating FUV at any metallicity (Figure 2.7).
Fig. 2.7 (Top): radial profile of the abundances for the H-bearing species. (Bottom): the shielding factors. These quantities are shown for various metallicity disks withZ = 100.5Z⊙ (left column), 10−0.5Z⊙ (middle column), and Z = 10−4Z⊙ (right column). We take the snapshots att = 8 tc. The profiles are presented along a different ray at θ = 76◦ forZ = 10−4Z⊙. The panels in each column are shown in the same manner as Figure 2.3.
The balance between H2 advection and unshielded photodissociation determines the position of the photodissociation front. A sufficient H2 flows are necessary to be driven to form the photodis-sociation front in the flow regions. In high-metallicity disks, FUV heating is efficient to yield high gas temperatures in the neutral regions and drives H2 flows from an inner region of a disk. The FUV-driven H2 flows have a small density owing to the large dust attenuation at the disk surface.
(See also Section 2.3.4 for quantitative discussions.) Therefore, for high metallicity, the efficient FUV heating drives low-density H2flows from an inner region, forming the photodissociation front in a low-density region.
The density at the ionization front is determined by the balance of photoionization and recombi-nation. These processes are independent of metallicity. By contrast, the photodissociation front is located in a small-density region for higher metallicities. Hence, the density at the photodissociation front becomes close to that at the ionization front with high metallicity. This forms a geometrically thin HIregion in the photoevaporative flows (Figure 2.5).
2.3.2.3 Metal Species Distribution
As the dust amount decreases, dust shielding becomes inefficient to protect CO molecules against the dissociating FUV. Figure 2.8 demonstrates that the dominant shielding source is replaced by H2 molecules in low-metallicity disks; the dust extinction factor Θ3(AV) is the most important with Z = 100.5Z⊙ and Z = 10−0.5Z⊙, whereas the H2 shielding factor Θ2(NH2) controls the total shielding effect with Z = 10−4Z⊙. Dust dominantly attenuates CO-dissociating FUV in high-metallicity disks, but the dominant shielding source is switched to molecular hydrogen in
low-47 2.3 Results
Fig. 2.8 Same as Figure 2.7 but heavy elements are examined (also see Figure 2.4). Note that we show the profiles along the different rays: θ = 69◦ forZ = 100.5Z⊙ (left column), θ= 66◦forZ= 10−0.5Z⊙(middle column), andθ= 76◦forZ= 10−4Z⊙(right column).
metallicity disks. Note that hydrogen molecules abundantly exist with any metallicities. The CO photodissociation front is embedded in high-density regions of the disks with all metallicities. This result is similar to that for the solar-metallicity disk in Section 2.3.1.