Chapter IV: Constraining Gas Masses of CO-Depleted Disks with Mul-
4.3 Constraining the Gas Mass of J160900-190852
We carry out a computational study of the sensitivity of disk gas tracers N2H+, HCO+, and C18O to changes in the total disk gas mass, CO/H2 abundance, and cosmic-ray ionization rate. We aim to determine what constraints can be placed on the H2 gas mass of J160900-190852 based on this set of tracers. A 2-D thermo-chemical disk model is used based on the framework of Du and Bergin (2014) and setup of Anderson et al. (2019). Initial disk parameters are listed in Table 4.2 and initial abundances are those from Anderson et al.
(2019) with the exception of CO. The total disk gas mass, CO abundance, and H2 cosmic-ray ionization rate are varied in order of magnitude steps over the ranges provided in Table 4.2. The dust mass in unaltered, resulting in gas-to-dust ratios of 0.1–100 for the gas masses tested. CO abundances start at the interstellar level of ∼10−4 and decrease by factors of up to 1000×. Current observations of protoplanetary disks suggest that CO abundances may be up to 100×below interstellar (Favre et al. 2013; McClure et al. 2016). The range of H2cosmic-ray ionization rates corresponds to one order of magnitude above the interstellar level down to two orders of magnitude below, which is the upper limit estimated based on molecular ion observations for TW Hya (Cleeves et al. 2016). Variations in modeled fluxes over the tested parameter ranges are shown in Figure 4.2.
Table 4.2: Fiducial Model Input Parameters.
Fixed Parameters Stellar Properties:
M∗ 0.65 M
R∗ 1.25 R
T∗ 3890 K
Source of stellar spectrum TW Hya
LX−ray 1.6(30) erg s−1
Disk Properties:
Disk dust mass 4(-5) M
Inner radius 1 au
Outer radius 100 au
Scale height at radius of 80 au 10 au Power index: surface density 1.0 Power index: scale height 1.0
vs. radius
Total run time 106 yrs
Turbulent viscosity α = 0.01 Varied Parameters
Disk gas mass 4(-6)–4(-3) M
Initial CO abundance (per H) 1.4(-7)–1.4(-4) H2 cosmic-ray ionization rate 1.36(-17) s−1
— 1.36(-14) & 1.36(-19) s−1
Note: a(b) indicates a×10b
CO is expected to be the dominant carbon carrier throughout most of the disk. Emission from the dominant isotopologue often becomes optically thick in disks because of the high abundance of CO combined with its self-shielding properties. Consequently, observations of less abundant CO isotopologues, such as C18O, are used to probe deeper regions of the disk gas and provide flux measurements that are more reflective of the total CO gas column. As a result, C18O emission is dependent on both the CO/H2 abundance in the disk as well as the H2 gas mass. Decreasing either will cause a reduction in the observed C18O flux as seen in Fig. 4.2.
HCO+is formed mainly through the protonation of CO via H+3, which is preva- lent in ionized H2 gas. The amount of HCO+ will therefore be largely tied to the CO abundance of the disk in addition to the bulk H2 mass and the H2
ionization rate. As expected, modeled HCO+ fluxes follow similar trends as
C18O with decreasing CO abundance and H2 mass (Fig. 4.2).
Analogous to HCO+, N2H+ is formed mainly through the protonation of N2
via H+3. N2 is expected to be the dominant nitrogen carrier throughout most of the disk and has similar volatility to CO. As a non-carbon-bearing species, the formation of N2H+ tracks N2 content and is independent of the amount of CO in the disk. However, the N2H+ abundance is still related to the CO abundance. CO has a higher proton affinity than N2 resulting in destruction of N2H+ forming HCO+ where CO is abundant. The relationship between N2H+ and CO may result in emission originating in distinct regions of the disk for these species depending on the disk structure (Aikawa et al. 2015; van ’t Hoff et al. 2017). This could complicate estimates of N2/CO ratios for specific disk locations based on this analysis where the the emission is not spatially resolved. However, the modeled fluxes do indicate that the total fluxes derived from the disk for N2H+ and C18O remain sensitive to the bulk properties of the disk. Because high CO abundances result in the destruction of N2H+, the modeled N2H+ fluxes increase with decreasing CO abundance (Fig. 4.2). This represents a distinct trend relative to the C18O and HCO+ tracers, providing additional information that may break the degeneracy between CO abundance and H2 mass.
Comparing two optically thin gas tracers provides a flux ratio that is not very sensitive to the disk mass. This is the case for the N2H+/C18O flux ratio, which is strongly dependent on the CO abundance but relatively less sensitive to the disk gas mass (Fig. 4.2). The N2H+/HCO+ flux ratio shows some sensitivity to both parameters suggesting that HCO+ fluxes respond less to changes in the disk mass and may be more optically thick than the other two tracers. Perhaps the use of HCO+ isotopologues, such as DCO+, would be more appropriate for CO abundance estimates.
The N2H+/C18O and HCO+/C18O flux ratios depend on the level of ionization in the disk. As cosmic-ray ionization rates increase the fluxes of molecular ions N2H+ and HCO+ increase as well, whereas C18O fluxes decrease (Fig. 4.2).
The N2H+/HCO+ flux ratio should have a lower dependence on the level of ionization in the disk because both species are molecular ions. However, the model results show that N2H+ fluxes are more sensitive to changes in the cosmic-ray ionization rate than HCO+ fluxes creating a similar dependence on the ionization level. This also means that the HCO+/C18O flux ratio is only
6
10 10
5
10
43
10
Di sk M as s [ M ]
10
710
610
510
4CO/
H Ab
2und anc e 10
310
110
110
3N
2H
+Flux [mJy]
6
10 10
5
10
4
10
3
Di sk M as s [ M ]
10
1910
1710
16Cos mic- ray ion iza tion ra te [
1
s
]
6
10 10
5
10
43
10
Di sk M as s [ M ]
10
710
610
510
410
310
110
110
3HC O
+Flux [mJy]
6
10 10
5
10
4
10
3
Di sk M as s [ M ]
10
1910
1710
166
10 10
5
10
43
10
Di sk M as s [ M ]
10
710
610
510
410
310
110
110
3C
18O Flux [mJy]
6
10 10
5
10
4
10
3
Di sk M as s [ M ]
10
1910
1710
166
10 10
5
10
43
10
Di sk M as s [ M ]
10
710
610
510
410
310
110
110
3N
2H
+/C
18O Fluxes
6
10 10
5
10
4
10
3
Di sk M as s [ M ]
10
1910
1710
166
10 10
5
10
43
10
Di sk M as s [ M ]
10
710
610
510
410
310
110
110
3HC O
+/C
18O Fluxes
6
10 10
5
10
4
10
3
Di sk M as s [ M ]
10
1910
1710
166
10 10
5
10
43
10
Di sk M as s [ M ]
10
710
610
510
410
310
110
110
3N
2H
+/H CO
+Fluxes
6
10 10
5
10
4
10
3
Di sk M as s [ M ]
10
1910
1710
16 Figure4.2:ModeledN2H+ ,HCO+ ,andC18 OfluxesinadditiontoN2H+ /C18 O,HCO+ /C18 O,andN2H+ /HCO+ fluxratios. VariationsinmodelparametersspanCOabundancesfromtheinterstellarvalueto1000×belowandgas-to-dustmassratiosof 0.1to100foraninterstellarH2cosmic-rayionizationrateof3×10−17 s−1 (toppanels)andH2cosmic-rayionizationratesfrom 3×10−19 –3×10−16 s−1 foraninterstellarCO/H2abundanceof∼10−4 (bottompanels).Modeledfluxesandfluxratiosaretobe comparedwithobservationsinordertoconstraintheunderlyingdiskparameters,namelyCOabundance,cosmic-rayionization rate,andtotalgasmass.weakly dependent on the cosmic-ray ionization rate relative to the N2H+/C18O flux ratio. Therefore, disk ionization remains a confounding factor for the flux ratios in this analysis. Further investigations into additional sources of ionization are also needed. For example, Cleeves et al. (2015) find that a hardened stellar X-ray spectrum is a key component of their best-fit model to the N2H+ and HCO+ observations of TW Hya.
From this analysis, we can use the N2H+/C18O flux ratio to constrain the CO abundance for a given cosmic-ray ionization rate (Fig. 4.2). For an interstellar ionization rate, CO depletion by two orders of magnitude is required to re- produce the observed N2H+/C18O flux ratio of 1.9. The level of CO depletion required decreases with increasing disk ionization and vice versa. Combining this information with the individual gas tracer fluxes, we can attempt to place some constraints on the total disk gas mass. The current model does not provide a satisfactory fit to the fluxes of all three tracers in J160900-190852 and requires further testing of potential sources of ionization and the parame- ters describing the disk structure in this model. However, certain patterns do emerge from the current model grid. The observed C18O flux can be repro- duced by CO abundances 10–100× below the interstellar value or gas-to-dust ratios of 0.1–10 depending on the cosmic-ray ionization rate. The observed HCO+ flux requires a high mass and high CO abundance to be reproduced by this model grid. In the case of N2H+, low masses are unable to reproduce the observed flux. The N2H+ observations require a disk gas mass of &4×10−3 M and CO depletion of .100× below interstellar for an interstellar ioniza- tion rate. For a 10× higher ionization rate, the N2H+ observations require a disk mass of &4×10−4 M for a similar level of CO depletion or &4×10−3 Mfor interstellar CO abundances. The low ionization rate of 3×10−19s−1is incapable of reproducing the molecular ion fluxes. Overall, at least interstellar levels of disk ionization and gas-to-dust ratios of 10–100 are needed to explain the observed N2H+ and HCO+ fluxes.