Strong Isotope-dependent Photodissociation Branching Ratios of N₂ and Their Potential Implications for the ¹⁴N/¹⁵N Isotope Fractionation in Titan's Atmosphere

In the VUV photon energy range below 14.523 eV (the threshold for the channel N(²D)+N(²D)), N₂ has the following three energetically available dissociation channels:

$$\begin{eqnarray}&&\begin{array}{l}{{\rm{N}}}_{2}({X}^{1}{{\rm{\Sigma }}}_{{\rm{g}}}^{+})+{\rm{h}}{v}_{\mathrm{VUV}}\to {\rm{N}}{(}^{4}{\rm{S}})+{\rm{N}}{(}^{4}{\rm{S}})\\ \ \ \,{\rm{h}}{v}_{\mathrm{VUV}}\geqslant 9.754\,\mathrm{eV}=127.1\,\mathrm{nm}\end{array}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&\to {\rm{N}}{(}^{4}{\rm{S}})+{\rm{N}}{(}^{2}{\rm{D}})\,{\rm{h}}{v}_{\mathrm{VUV}}\geqslant 12.138\,\mathrm{eV}=102.2\,\mathrm{nm}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&\to {\rm{N}}{(}^{4}{\rm{S}})+{\rm{N}}{(}^{2}{\rm{P}})\,{\rm{h}}{v}_{\mathrm{VUV}}\geqslant 13.330\,\mathrm{eV}=93.02\,\mathrm{nm}.\end{eqnarray} \tag{ 3 }$$

N(⁴S) is the ground state of the N atom, N(²D) and N(²P) are the first and second excited states, which are 2.384 and 3.576 eV higher than the ground state, respectively. In Figures 1(e), (f), (g), and (h), two typical VMI images and their corresponding TKER spectra for the b '¹ ${{{\boldsymbol{\Sigma }}}_{u}}^{+}$(ν' = 9) and b '¹ ${{\boldsymbol{\Sigma }}}_{u}^{+}$(ν' = 16) vibronic states of ¹⁴N¹⁵N are presented.

Zoom In Zoom Out Reset image size

Similar to the photodissociation of the main isotopologue ¹⁴N₂ (Song et al. 2016), no signal into the ground channel N(⁴S)+N(⁴S) (Reaction 1) is detected for all the states of ¹⁴N¹⁵Nobserved in the current study. Two rings of different radii are seen in Figures 1(e) and (g), where the ring of larger size corresponds to the channel N(⁴S)+N(²D) with a higher velocity, and the ring of smaller size corresponds to the channel N(⁴S)+N(²P) with a lower velocity, due to the fact that N(²P) has a higher internal energy than N(²D). The images are integrated and converted to the TKER spectra as shown in Figures 1(f) and (h), respectively. The underneath areas of the two peaks are calculated, which are proportional to the relative branching ratios of the corresponding channels. By comparing Figures 1(e) and (f) with Figures 1(g) and (h), it can be seen that the branching ratios strongly depend on the quantum states of ¹⁴N¹⁵N that are excited. The b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (ν' = 9) state predominantly forms N(⁴S)+N(²D), while the b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (ν' = 16) state mainly dissociates into the channel N(⁴S)+N(²P). For the purpose of following discussion, all the states that dissociate with substantial amounts into the channel N(⁴S)+N(²P) (>5%) are listed in Table 1. A full list of all the branching ratio measurements in this study can be found in Tables A1 and A2 in the Appendix, and plots of the branching ratios of the channel N(⁴S)+N(²P) versus the VUV photon energy are presented in Figure 2 (red) for all different types of vibronic states, i.e., valence${}^{{\bf{1}}}{{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ and ¹ Π _u states (dots), Rydberg ${}^{{\bf{1}}}{{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ and ¹ Π _u states (triangles).

Zoom In Zoom Out Reset image size

Table 1. Band Origins, Branching Ratios, and Kinetic Energy Releases of ¹⁴N and ¹⁵N Produced in the Channel N(⁴S)+N(²P) for Several Relevant Absorption States of ¹⁴N₂ and ¹⁴N¹⁵N

Upper State	14N15N					14N2
	νo (eV)	νo (cm−1)	N(2P) (%) a	14N (eV)	15N (eV)	νo (eV)	νo (cm−1) b	N(2P) (%) c	14N (eV)
b'1Σu +(v' = 9)	13.6517	110,110.9	5.7 ± 0.2 d	0.166	0.155	13.6623	110,196.7	30.7 ± 0.4	0.166
c4'1Σu +(v' = 3)	13.7081	110,565.8	3.8 ± 0.6	0.196	0.183	13.7194	110,656.7	5.7	0.195
b'1Σu +(v' = 12)	13.9004	112,116.7	16.2 ± 0.9	0.295	0.275	13.9155	112,238.5	21.0 ± 1.5	0.293
c4'1Σu +(v' = 4)	13.9670	112,654.3	25.8 ± 0.2	0.329	0.308	13.9811	112,768.1	57.4 ± 3.7	0.326
b'1Σu +(v' = 13)	13.9811	112,767.7	96.2 ± 1.0	0.337	0.314	13.9984	112,907.6	81.8 ± 1.6	0.334
b1Πu (v' = 17)	14.0061	112,969.4	83.9 ± 0.6	0.350	0.326	14.0256	113,127.0	88.1 ± 0.9	0.348
b'1Σu +(v' = 14)	14.0594	113,399.1	89.0 ± 1.0	0.377	0.352	14.0767	113,539.2	94.3 ± 1.9	0.373
b1Πu (v' = 18)	14.0778	113,547.9	56.9 ± 0.8	0.387	0.361	14.0975	113,707.0	78.6 ± 0.9	0.384
b'1Σu +(v' = 15)	14.1367	114,022.8	93.1 ± 0.7	0.417	0.389	14.1549	114,169.6	83.8 ± 1.0	0.412
b1Πu (v' = 19)	14.1458	114,096.6	0.4 ± 0.4	0.422	0.394	14.1655	114,255.0	10.4 ± 2.3	0.418
b'1Σu +(v' = 16)	14.2109	114,621.0	90.0 ± 0.8	0.456	0.425	14.2274	114,754.2	1.3 ± 0.1	0.449
c4'1Σu +(v' = 5)	14.2154	114,657.5	74.7 ± 2.2	0.458	0.427	14.2371	114,833.0 e	22.6 ± 2.4 f	0.454
o3 1Πu (v' = 5)	14.2719	115,113.1	33.2 ± 0.4	0.487	0.455	14.2899	115,258.8 e	13.4 ± 0.7	0.480
b'1Σu +(v' = 17)	14.2847	115,216.8	96.6 ± 0.3	0.494	0.461	14.3036	115,369.3	46.8 ± 0.7	0.487
c4 1Πu (v' = 0)	14.3282	115,567.1	5.6 ± 0.6	0.516	0.482	14.3280	115,565.8	1.7 ± 2.1	0.499
c5'1Σu +(v' = 0)	14.3488	115,733.4	93.0 ± 0.2	0.527	0.492	14.3632	115,849.8	63.3 ± 0.2	0.517
b'1Σu +(v' = 18)	14.3937	116,095.6	61.3 ± 2.2	0.550	0.514	14.4074	116,206.6	79.3 ± 2.8	0.539
b'1Σu +(v' = 19)	14.4453	116,511.6	96.6 ± 1.7	0.577	0.538	14.4664	116,682.3	94.7 ± 0.4	0.568
c4'1Σu +(v' = 6)	14.4618	116,645.0	87.9 ± 4.0	0.585	0.546	14.4819	116,806.8	27.5 ± 2.8	0.576
b'1Σu +(v' = 20)	14.5105	117,037.8	73.2 ± 1.4	0.611	0.570	14.5312	117,204.6	92.5 ± 0.5	0.601

Notes.

^a For each absorption band, the value measured at the R(0) transition line is used for representing the branching ratio of the whole band. ^b Band origins (ν_o) of ¹⁴N₂ are from the Harvard CfA N₂ database: https://lweb.cfa.harvard.edu/amp/ampdata/N2ARCHIVE/n2term.html. ^c The branching ratios for ¹⁴N₂ are adopted from Song et al. (2016). ^d The statistical uncertainties are the standard deviations of three to five independent measurements. ^e Band origins (ν_o) of ¹⁴N₂ are from Heays et al. (2009). ^f For the absorption band ${{\boldsymbol{c}}}_{{\bf{4}}}{{\prime} }^{{\bf{1}}}{{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (v' = 5) of ¹⁴N₂, the branching ratio measured at the P(1) transition is used as adopted from Song et al. (2016).

Download table as:  ASCIITypeset image

The isotope-dependent photodissociation mechanism of N₂ has been the subject of numerous experimental and theoretical studies, due to its prime importance in understanding the N isotope fractionation process among different solar system objects and planetary atmospheres (Lewis et al. 2005; Liang et al. 2007; Muskatel et al. 2011; Chakraborty et al. 2014; Heays et al. 2014; Ajay et al. 2018). Isotope substitution has been shown to alter the photoabsorption peak positions, oscillator strengths, and photodissociation rates of ¹⁴N₂, ¹⁴N¹⁵N, and ¹⁵N₂ (Lewis et al. 2005; Muskatel et al. 2011), while how the branching ratios into different dissociation channels of ¹⁴N¹⁵N and ¹⁵N₂ are different from those of ¹⁴N₂ has never been studied before. Our previous studies have shown that for CO, which is isoelectronic to N₂ (Lefebvre-Brion & Lewis 2007), isotope substitution strongly alters its photodissociation branching ratios (Jiang et al. 2019; Guan et al. 2020; Chi et al. 2020a, 2020b). To demonstrate the strong isotope effect of the photodissociation branching ratios for N₂, we present the VMI images and their corresponding TKER spectra for the b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (ν' = 9) and b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (ν' = 16) vibronic states of ¹⁴N₂ in Figures 1(a), (b) and (c), (d), respectively. For the b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (ν' = 9) state, a previous study by Song et al. (2016) observed substantial photodissociation into the channel N(⁴S)+N(²P) (∼30%) for ¹⁴N₂. Our own data as shown in Figures 1(a) and (b) are consistent with Song et al. (2016). For ¹⁴N¹⁵N, the branching ratio into the channel N(⁴S)+N(²P) is much smaller (∼6%), as shown in Figures 1(e) and (f). For the b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (ν' = 16) state, the branching ratio of the main isotopologue ¹⁴N₂ into the channel N(⁴S)+N(²P) measured in the present study is ∼2% as shown in Figures 1(c) and (d), which is in accordance with the study of Song et al. (2016); in the case of ¹⁴N¹⁵N, the channel N(⁴S)+N(²P) completely dominates the photodissociation process with a branching ratio of ∼90%, as shown in Figures 1(g) and (h). Thus, a strong and quantum state selective isotope effect on the photodissociation branching ratio similar to that of CO has been observed for N₂ for the first time.

To compare how differently the photodissociation branching ratio depends on the VUV photon energy (or quantum state) between ¹⁴N₂ and ¹⁴N¹⁵N, the branching ratios of the channel N(⁴S)+N(²P) for ¹⁴N₂ as obtained by Song et al. (2016) are also plotted in Figure 2 in blue. Similar to CO (Jiang et al. 2019; Guan et al. 2020; Chi et al. 2020a, 2020b), isotope substitution changes the absolute values of the branching ratios for many common upper states of ¹⁴N₂ and ¹⁴N¹⁵N, as shown in Figures 1 and 2, and in Table 1. Isotope substitution shifts the relative energy positions of the mutually interacting quantum states, and thus can change the coupling strengths between the directly excited singlet states and the ³ Π _u states correlating to each of the dissociation limits. This finally determines the relative quantum yields for each of the channels (Muskatel et al. 2011; Jiang et al. 2019).

Despite the changes of the absolute values of branching ratios due to isotope substitution, the dependences of the branching ratios on the VUV photoexcitation energy for ¹⁴N₂ and ¹⁴N¹⁵N show many similarities below the threshold of the channel N(²D)+N(²D), as shown in Figure 2. For ¹⁴N₂, although the asymptotic limit of the channel N(⁴S)+N(²P) is located at ∼107,510 cm⁻¹, prominent dissociation into this channel does not occur until a distinct onset at ∼112,000 cm⁻¹ is reached. This is caused by the potential barrier in the adiabatic C '³ Π _u state correlating to the N(⁴S)+N(²P) channel, which is formed through an avoided crossing with the higher III³ Π _u state (Walter et al. 1993; Song et al. 2016). Below this onset, only the b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (ν' = 9) state at ∼110,200 cm⁻¹ dissociates substantially into the channel N(⁴S)+N(²P). This has been attributed to the sudden crossing between the C '³ Π _u state and the 2⁵ Π _u state, which is a repulsive quintet state correlating to the N(⁴S)+N(²P) channel (Song et al. 2016). For ¹⁴N¹⁵N, the onset at ∼112,000 cm⁻¹ has also been observed as shown by the red curves in Figure 2; and also, only the b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (ν' = 9) state dissociates substantially into the channel N(⁴S)+N(²P) below the onset with a branching ratio of ∼6%, which is much smaller than that of ¹⁴N₂ (∼30%). This might indicate that the coupling strength of the b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (ν' = 9) level to the C '³ Π _u state, and finally to the 2⁵ Π _u state, is much weaker for ¹⁴N¹⁵N than that for ¹⁴N₂.

The most prominent difference between ¹⁴N₂ and ¹⁴N¹⁵N occurs at photon energies above the aforementioned onset. For ¹⁴N₂, previous studies by Song et al. (2016) and Helm & Cosby (1989; Walter et al. 1993) revealed two peaks centered at ∼113,550 and ∼116,700 cm⁻¹, where formation of the channel N(⁴S)+N(²P) dominates the photodissociation process, as shown by the blue curves in Figures 2(a) and (b). In between the two peaks is a prominent valley centered at ∼114,800 cm⁻¹, where the ¹⁴N₂ molecules predominantly dissociate into the N(⁴S)+N(²D) channel. For ¹⁴N¹⁵N, the N(⁴S)+N(²P) channel dominates the photodissociation process from the aforementioned onset all the way up to the threshold of the N(²D)+N(²D) channel, and no obvious valley structure can be noticed, especially for the valence and Rydberg ${}^{{\bf{1}}}{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}^{+}$ states, as shown by the red curves in Figures 2(a) and (b). This may imply very different photodissociation mechanisms between ¹⁴N₂ and ¹⁴N¹⁵N in this energy range.

Since no singlet states correlate with N(⁴S)+N(²D) and N(⁴S)+N(²P), the branching ratios into the above two channels are mainly determined by the potential curves of valence ³ Π _u states (Walter et al. 1993; Lewis et al. 2005; Song et al. 2016). The peak at ∼113,550 cm⁻¹ is caused by the avoided crossing between the C '³ Π _u and III³ Π _u states, which has been mentioned above (Walter et al. 1993; Song et al. 2016). The mechanism for the peak at ∼116,700 cm⁻¹ is still not clear. Song et al. ascribed this to the higher excitation efficiency to the Rydberg c '¹ ${{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}^{+}$ state in this energy range, which subsequently couples to the C '³ Π _u state to form the N(⁴S)+N(²P) channel (Song et al. 2016). However, the coupling between the c '^'1 ${{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}^{+}$ and C '³ Π _u state should mainly occur in the Franck–Condon region (inner part of the C '³ Π _u potential curve), then the avoided crossing between the C '³ Π _u state and the lower C ³ Π _u state will be reached first, which leads N₂ to the N(⁴S)+N(²D) channel (Lewis et al. 2005), before it can reach the avoided crossing between the C '³ Π _u and III³ Π _u states at a larger internuclear distance. Here, we propose a more plausible mechanism, which relies on the coupling to the III³ Π _u state. The III³ Π _u state has an equilibrium bond length close to that of the b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ state (Guberman 2012; Song et al. 2016), and thus the vibrational integrals between them may be large at the high vibrational levels of the b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ state, and the III³ Π _u state could couple with the C '³ Π _u state through their avoided crossing to go into the N(⁴S)+N(²P) channel. The highest barrier in the III³ Π _u state caused by the avoided crossing with a higher ³ Π _u state locates in the range between ∼115,800 and ∼117,000 cm⁻¹, which is coincident with the peak position at ∼116,700 cm⁻¹ (Guberman 2012; Song et al. 2016). This process has also been previously pointed out by Helm et al. as a possible mechanism for the sudden increase of the N(²P) quantum yield at ∼115,500 cm⁻¹ (Helm & Cosby 1989).

Since both ¹⁴N₂ and ¹⁴N¹⁵N photodissociate predominantly into the N(⁴S)+N(²P) channel in the two peak areas of ¹⁴N₂ (Figure 2(a)), they should share similar mechanisms as discussed above. However, in contrast to ¹⁴N₂ with deep valley (dominated by N(⁴S)+N(²D) channel) at ∼114,800 cm⁻¹, ¹⁴N¹⁵N still photodissociates predominantly into the N(⁴S)+N(²P) channel between the two peaks. This cannot be explained by the avoided crossings among the various ³ Π _u states. One possible reason for this could be due to the crossing of the 2⁵ Π _u state with the III³ Π _u state, which should locate in between the two peak positions (see Figure 4 in Song et al. 2016), leading the ¹⁴N¹⁵N molecules in the b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (ν' = 16, 17) levels to predominantly dissociate into the N(⁴S)+N(²P) channel. This mechanism can be strongly isotope dependent, similar to the case of the b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (ν' = 9) level as discussed above. Detailed theoretical calculations on the accurate potential curve of the III³ Π _u state and the couplings with nearby states are needed to quantitatively explain all the similarities and dissimilarities between ¹⁴N₂ and ¹⁴N¹⁵N as observed in the current study.

Proper considerations of all the N isotope fractionation mechanisms are crucial for reconstructing the average initial ¹⁴N/¹⁵N ratio of Titan's building blocks, and thus for determining the specific reservoir(s) out of which Titan's N₂ originated. In this study, we have systematically measured the branching ratios into the channels of producing N(²D) and N(²P) for ¹⁴N¹⁵N, below the energy threshold of the N(²D)+N(²D) channel. The most important finding is that a strong and state-selective isotope effect on photodissociation branching ratios exists between ¹⁴N₂ and ¹⁴N¹⁵N, and most of the absorption states of ¹⁴N¹⁵N above the onset at ∼112,000 cm⁻¹ predominantly dissociate into the N(⁴S)+N(²P) channel, especially for the valence and Rydberg ${}^{{\bf{1}}}{{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ states, as shown in Figures 2(a) and (b). Since N(²P) is 1.192 eV higher in internal energy than N(²D), the N atoms generated from the N(⁴S)+N(²P) channel have much lower kinetic energies than that of the N(⁴S)+N(²D) channel. The finding in this study can have a profound effect on the VUV photodissociation induced N escape process in the upper atmosphere of Titan.

We have calculated the kinetic energies of ¹⁴N and ¹⁵N from the N(⁴S)+N(²P) channel for the absorption states of both ¹⁴N₂ and ¹⁴N¹⁵N, as listed in Table 1. The escape energy of ¹⁴N at Titan's exobase (above which the collision effect is negligible, thus atoms and molecules can escape if they have enough kinetic energies) is ∼0.314 eV, and that for ¹⁵N is ∼0.336 eV (Lammer et al. 2000). As seen in Table 1, the kinetic energies of ¹⁴N and ¹⁵N are in the range of 0.15–0.62 eV, which is close to the escape energy to have a significant impact on the N fractionation process in Titan's atmosphere (Lammer et al. 2000). The absorption states in Table 1 can be divided into three categories based on their kinetic energy releases.

The first category refers to absorption states that produce both ¹⁴N and ¹⁵N atoms with kinetic energies lower than their corresponding escape energies for the N(⁴S)+N(²P) channel, while all N atoms generated in the N(⁴S)+N(²D) channel have enough kinetic energies to escape from Titan. Therefore, which isotope is enriched is determined by the relative branching ratios of the N(⁴S)+N(²P) channel between ¹⁴N₂ and ¹⁴N¹⁵N. The following three states, b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (v' = 9), ${{\boldsymbol{c}}}_{{\bf{4}}}{{\prime} }^{{\bf{1}}}{{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (v' = 3), and b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (v' = 12) belong to this category. The branching ratios into the N(⁴S)+N(²P) channel of the above three states for ¹⁴N¹⁵N are 5.7%, 3.8%, and 16.2%, respectively; while those for ¹⁴N₂ are 30.7%, 5.7%, and 21.0%, respectively, which are all larger than the corresponding values of ¹⁴N¹⁵N, as shown in Table 1. This means all these three states preferentially retain ¹⁴N in Titan's atmosphere, because ¹⁴N₂ generates proportionally more ¹⁴N atoms in the N(⁴S)+N(²P) channel, which stay in Titan's atmosphere, than ¹⁴N¹⁵N does, if the same photodissociation cross sections are assumed for the two N₂ isotopologues.

The second category refers to all absorption states that produce ¹⁴N atoms with enough kinetic energies to escape from Titan's exobase, while producing ¹⁵N atoms without enough kinetic energies to escape, for the N(⁴S)+N(²P) channel. The absorption states ${{\boldsymbol{c}}}_{4}{{\prime} }^{{\bf{1}}}{{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (v' = 4), b '¹ ${{{\boldsymbol{\Sigma }}}_{{\boldsymbol{u}}}}^{+}$ (v' = 13), and b ¹ Π _u (v' = 17) belong to this category. If ¹⁴N¹⁵N dissociates into the N(⁴S)+N(²P) channel, they produce ¹⁴N atoms with kinetic energies of 0.329 eV, 0.337 eV, and 0.350 eV, respectively, all higher than the escape energy of 0.314 eV for ¹⁴N, and thus can escape from Titan's exobase; on the other hand, the corresponding kinetic energies of ¹⁵N atoms are 0.308 eV, 0.314 eV, and 0.326 eV, respectively, all lower than the escape energy of 0.336 eV for ¹⁵N, and thus cannot escape from Titan's exobase. The ¹⁴N atoms generated from the above three states of ¹⁴N₂ in the N(⁴S)+N(²P) channel all have enough kinetic energies to escape. This is similar to the dissociative recombination process of the ¹⁴N¹⁵N⁺ ions in Mars' atmosphere (Fox & Hać 1997), thus the above three states will enrich the heavier ¹⁵N isotope in the atmosphere of Titan.

The third category refers to all absorption states that produce both ¹⁴N and ¹⁵N atoms with high enough kinetic energies to escape from Titan's exobase. All the rest of the states listed in Table 1 belong to this category, except for the six states discussed above. As shown in Table 1, the initial kinetic energy obtained by the ¹⁵N isotope is always slightly smaller than that obtained by ¹⁴N, and furthermore the ¹⁵N isotope has a higher escape energy than that of ¹⁴N, thus all the absorption states of the third category prefer the enrichment of the heavier ¹⁵N isotopes, consistent with Lammer et al. (2000). Lammer et al. (Lammer et al. 2000) further argued that ¹⁵N isotopes need fewer collisions to go below the corresponding escape energy than ¹⁴N does, and thus has a larger chance to stay in Titan. This is because the kinetic energy of N atoms from photodissociation is higher than the average kinetic energy of Brownian motion of Titan's atmospheric molecules; therefore, collisions between the two would tend to reduce the kinetic energy of the N fragments of photodissociation.

It is obvious that the enrichment of ¹⁵N would be further enhanced if ¹⁴N¹⁵N has a larger branching ratio into the N(⁴S)+N(²P) channel than ¹⁴N₂ does, because the N(⁴S)+N(²P) channel has much smaller kinetic energy release than that of N(⁴S)+N(²D); however, if ¹⁴N¹⁵N has a smaller branching ratio into the N(⁴S)+N(²P) channel than ¹⁴N₂ does, the ¹⁵N enrichment effect would be diminished or even reversed, that is, the ¹⁴N is enriched. Which isotope is enriched is determined by the relative photodissociation cross sections and branching ratios between ¹⁴N₂ and ¹⁴N¹⁵N.

The atomic N escape induced by the solar VUV photodissociation of N₂ is an important process in the upper atmosphere of Titan (Shematovich 1999; Shematovich et al. 2003). To the best of our knowledge, the potentially important N isotope fractionation effect corresponding to photodissociation with associated kinetic energies and branching ratios into N(⁴S)+N(²P) has not been included yet in any models for predicting the initial ¹⁴N/¹⁵N ratio of Titan's atmosphere. The above N isotope fractionation mechanism does not rely on the presence of CH₄ in Titan's atmosphere, as the photochemical effect did (Erkaev et al. 2020), thus they can fractionate the N isotopes continuously for the entire lifetime of Titan's atmosphere. More importantly, the solar VUV photon flux was up to several hundred times the present value in the early solar system (Mandt et al. 2009; Tu et al. 2015; Erkaev et al. 2020), thus the photodissociation rate of N₂ should be much higher, consequently the fractionation mechanism as found in this study could be more efficient in the early history of Titan than that at the present, if the exobase level remained unchanged during the Titan's lifetime. Future modeling work would need to consider such an effect and its contribution to the ¹⁴N/¹⁵N evolution in Titan's atmosphere. The exobase level could be higher in the past due to the higher solar flux (Erkaev et al. 2020), which could decrease the escape velocities of ¹⁴N and ¹⁵N, and thus will diminish the fractionation effect as found in this study. Such an effect should also be considered in future modeling work.

Besides the VUV energy range as described in the current study, there are two other ranges that could also contribute to the above N isotope fractionation mechanism. The first one is at ∼103,000 cm⁻¹, where only the N(⁴S)+N(²D) channel is available. There is not enough energy to dissociate into the N(⁴S)+N(²P) channel at 103,000 cm⁻¹, as the threshold of this channel is at ∼107,500 cm⁻¹. The absorption states in this energy range also produce N atoms with kinetic energies close to the escape energy. For example, the band origins of the b ¹ Π _u (v' = 3, 4) states of ¹⁴N¹⁵N were measured by Heays et al. to be at 102,841 cm⁻¹ (12.750 eV) and 10,3517 cm⁻¹ (12.834 eV), respectively (Heays et al. 2011); they dissociate to produce the ¹⁴N isotope with high enough kinetic energy to escape from Titan's exobase, while the ¹⁵N isotope does not get enough energy to escape. They are similar to the states of the second category as discussed above. The second one is the energy range higher than the threshold of the channel N(²D)+N(²D). Song et al. have shown that ¹⁴N₂ can still dissociate substantially into the channels N(⁴S)+N(²D) and N(⁴S)+N(²P) above the energy threshold of the channel N(²D)+N(²D), which produce N atoms with high enough kinetic energy to escape from Titan (Song et al. 2016); however, when N₂ dissociates into the channel N(²D)+N(²D), the N atoms produced will not get enough energy to escape. If the photodissociation branching ratios into the N(²D)+N(²D) channel are also isotope dependent in the high energy range, then it can also contribute significantly to the N isotope fractionation in Titan's atmosphere.