Chinese Journal of Chemical Physics  2020, Vol. 33 Issue (1): 107-113

The article information

Xia Zhang, Donghui Quan, Jarken Esimbek
张霞, 全冬晖, 加尔肯·叶生别克
Gas-Grain Modeling of Interstellar O$ _\textbf{2} $
星际氧气分子的气相-尘埃模型研究
Chinese Journal of Chemical Physics, 2020, 33(1): 107-113
化学物理学报, 2020, 33(1): 107-113
http://dx.doi.org/10.1063/1674-0068/cjcp1911206

Article history

Received on: November 16, 2019
Accepted on: December 3, 2019
Gas-Grain Modeling of Interstellar O$ _\textbf{2} $
Xia Zhanga,b , Donghui Quana,c , Jarken Esimbeka,d     
Dated: Received on November 16, 2019; Accepted on December 3, 2019
a. Xinjiang Astronomical Observatory, Chinese Academy of Sciences, Urumqi 830011, China;
b. University of Chinese Academy of Sciences, Beijing 100049, China;
c. Department of Chemistry, Eastern Kentucky University, Richmond, KY 40475, USA;
d. Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, Urumqi 830011, China
Abstract: Molecular oxygen (O$ _2 $) is essential to human beings on the earth. Although elemental oxygen is rather abundant, O$ _2 $ is rare in the interstellar medium. It was only detected in two galactic and one extra-galactic region. The inconsistency between observations and theoretical studies is a big challenge for astrochemical models. Here we report a two-phase modeling research of molecular oxygen, using the Nautilus gas-grain code. We apply the isothermal cold dense models in the interstellar medium with two typical sets of initial elemental abundances, as well as the warm-up models with various physical conditions. Under cold dense conditions, we find that the timescales for gas-phase CO, O$ _2 $ and H$ _2 $O to reach peak values are dependent on the hydrogen density and are shortened when hydrogen density increases. In warm-up models, O$ _2 $ abundances are in good agreement with observations at temperatures rising after 10$ ^5 $ yr. In both isothermal and warm-up models, the steady-state O$ _2 $ fractional abundance is independent of the hydrogen density, as long as the temperature is high enough ($ > $30 K), at which O$ _2 $ is prevented from significant depleting onto grain surface. In addition, low density is preferable for the formation of O$ _2 $, whether molecular oxygen is under cold conditions or in warm regions.
Key words: Astrochemistry    Models    Interstellar medium    Molecules    Abundances    
Ⅰ. INTRODUCTION

Elemental oxygen is abundant in the universe and molecular oxygen is essential for life on the earth. Searches for interstellar molecular oxygen in galactic and extragalactic sources have a long history [1-8]. However, molecular oxygen has only been detected in two galactic sources: $ \rho $ Oph A [5, 8] and Orion [6], with the Odin and Herschel space telescopes, respectively. Recently, molecular oxygen has also been firstly detected toward the nearest extra-galactic QSO Mrk 231 with the ground telescopes IRAM 30 m and NOEMA (NOrthern Extended Millimeter Array) [9]. Besides, Wang et al. (in preparation) estimated the statistical average observational upper limit of O$ _2 $ abundance in 17 of the 20 studied giant molecular cores in Goldsmith et al. [10].

The dominant O$ _2 $ formation pathway at the standard cold core temperature of 10 K in the gas phase is the reaction of O+OH$ \rightarrow $O$ _2 $+H [11]. The reaction rate is a key parameter for astrochemical models at low temperatures. Davidsson & Stenholm [12] calculated the rate relation in the temperature range from 10 K to 300 K using the extended Langevin method. Smith & Stewart [13] explored the rate constants for this reaction down to 158 K by experiment. Later, Carty et al. [14] measured the rates down to the temperature of 39 K. Therefore the value of the reaction rate at low temperatures used in the present astrochemical model is highly uncertain. Quan et al. [15] has explored the uncertainties of the rate coefficient for the reaction using gas-phase models and determined that an age of cold core can be at early time by comparing calculated O$ _2 $ abundance with observations for O-rich abundances. Meanwhile, late-time solutions can also be possible for C-rich abundances. In astrochemical models, OH is one of the most important reactants for O$ _2 $ formation in the gas phase, which is mainly formed by the reaction between H$ _3 $O$ ^+ $ and electron. However the reaction has multiple product channels:

$ \begin{eqnarray} \rm{H}_3 \rm{O}^+ + \rm{e}^- &\rightarrow& \rm{H}_2 \rm{O} + \rm{H} \end{eqnarray} $ (1)
$ \begin{eqnarray} &\rightarrow& \rm{OH} + \rm{H}_2 \end{eqnarray} $ (2)
$ \begin{eqnarray} &\rightarrow & \rm{OH} + 2 \rm{H} \end{eqnarray} $ (3)
$ \begin{eqnarray} & \rightarrow& \rm{O} + \rm{H} + \rm{H}_2 \end{eqnarray} $ (4)

Therefore the branching ratio for OH of the above reactions is also important for O$ _2 $ formation. However, experimental studies have found four different branching ratios and the ratio sum of the above two OH production channels are suggested to be 0.65, 0.66, 0.74 and 0.78 [16-19].

Up to date, there are many astrochemical models to simulate the O$ _2 $ chemistry [15, 20-25]. However, the observational abundances for O$ _2 $ in dense clouds are two to three orders of magnitude smaller than what is predicted by astrochemical models. Theoretical researches have been conducted to explain this inconsistency. Viti et al. [26] explored the possibility that chemical models can display bistabilities [27, 28] and considered initial oxygen elemental abundance smaller than 1.6$ \times $10$ ^{-4} $ to reproduce the low abundance of molecular oxygen observed in dark clouds at all times. Wakelam et al. [29] predicted that O$ _2 $ abundance can be below 10$ ^{-8} $ by taking into account the full history of the evolution of the physical conditions from the diffuse medium to the cold cores. He et al. [30] used the higher binding energy of atomic oxygen (1660 K) and found this can decrease the O$ _2 $ abundance in the photodissociation region (PDR) models. Lu et al. [31] also found the higher binding energy of atomic oxygen can make the abundance of surface O$ _2 $ about two orders of magnitude lower. Further astrochemical modeling studies are still needed to explore molecular oxygen chemical processes and appropriate physical models.

In this study, we firstly use the gas-grain code Nautilus to set up dark clouds models for O$ _2 $ and choose two types of initial elemental abundance for L134N and TMC-1. Then, we simulate O$ _2 $, CO, and H$ _2 $O abundances with a variety of hydrogen densities and temperatures for the O-rich initial abundances. We also simulate the O$ _2 $ in warm-up models. Finally, we discuss the results of our chemical models by comparing with the observations.

Ⅱ. CHEMICAL MODEL

In this section, we describe chemical models using the two-phase gas-grain code Nautilus. The code was presented in detail by Reboussin et al. [32] and Ruaud et al. [33]. We have set up several physical models to simulate different astronomical sources.

In the first set, we used constant physical parameters throughout the models for the cold dense regions, with the hydrogen density $ n_ \rm{H} $ = 2$ \times $10$ ^4 $ cm$ ^{-3} $, the visual extinction $ A_\nu $ = 10 mag, the cosmic-ray ionization parameter $ \xi $ = 1.3$ \times $10$ ^{-17} $ s$ ^{-1} $, the temperature $ T $ = 10 K, a dust-to-gas mass ratio d/g = 0.01, the UV factor is 1, and the initial elemental abundances are listed in Table Ⅰ. The elemental C/O ratios are 0.4 and 1.2, respectively. In addition, since the gas-phase elemental oxygen is mainly in the form of CO, O$ _2 $ and H$ _2 $O under cold dense conditions, we simulated these molecules with different hydrogen densities and temperatures, and the settings are listed in Table Ⅱ. For these four models, we used the initial O-rich abundance, as listed in Table Ⅰ.

Table Ⅰ Initial nonzero fractional abundances
Table Ⅱ Physical parameters of hydrogen densities and temperatures in cold dense models

Secondly, we performed calculations using the warm-up models, with $ n_ \rm{H} $ = 2$ \times $10$ ^4 $ cm$ ^{-3} $ for T30-100N4, 2$ \times $10$ ^5 $ cm$ ^{-3} $ for T30-100N5 and 2$ \times $10$ ^6 $ cm$ ^{-3} $ for T30-100N6, and O-rich initial abundance as those in the L134N model. Other physical parameters are similar to those for the cold dense regions, with $ n_ \rm{H} $ = 2$ \times $10$ ^4 $ cm$ ^{-3} $, $ A_\nu $ = 10 mag, $ \xi $ = 1.3$ \times $10$ ^{-17} $ s$ ^{-1} $, $ T $ = 30$ - $100 K, and the UV factor is 1. The dust to gas mass ratio is an important input physical parameter of astrochemical models. Leroy et al. suggested that in our Galaxy, this ratio is not constant and may vary between 0.01 and 0.02 [34]. So we increase the dust to gas mass ratio from 0.01 to 0.02 in warm-up models to study the effect of this parameter. After the initial cold phase of 1$ \times $10$ ^5 $ yr where $ T $ is kept unchanged at 10 K, the gas and dust temperatures increase to the maximum temperatures of $ T_{ \rm{max}} $ = 30 K, 50 K, and 100 K within 3$ \times $10$ ^5 $ yr, as shown in FIG. 1. After reaching the maximum, the temperature remains unchanged at the constant high value.

FIG. 1 Warm-up models' temperature profiles
Ⅲ. RESULTS A. Results from the cold dense models

In FIG. 2, we compare the calculated O$ _2 $ abundance from our models with observations in two cold clouds L134N and TMC-1. These upper limits set by observational groups with respect to H$ _2 $ are 1.7$ \times $10$ ^{-7} $ in L134N and 7.7$ \times $10$ ^{-8} $ in TMC-1 [35]. It can be seen that the O$ _2 $ fractional abundance from both models quickly increases within the time range of 3$ \times $10$ ^2 $$ - $(2$ - $3)$ \times $10$ ^5 $ yr. The main formation reaction of O$ _2 $ is O+OH$ \rightarrow $H+O$ _2 $. Meanwhile, the main destruction reaction of O$ _2 $ is C+O$ _2 $$ \rightarrow $CO+O. Till a time near 2$ \times $10$ ^6 $ yr, the steady state is eventually reached, and the timescale agrees with the theoretical results from the pure gas-phase models by Quan et al. [15]. Our modeling results within the full time range for TMC-1 are below the upper limit of observation. For L134N, the results show that the O$ _2 $ abundances are below the upper limit at times before 10$ ^5 $ yr. Therefore, it can be speculated that the age of L134N is younger than 10$ ^5 $ yr. This agrees with the suggestions by Smith et al. [36] and Wakelam et al. [25]. If the cold cloud's age was between 10$ ^5 $ and 10$ ^6 $ yr, the peak abundance of gaseous O$ _2 $ would reach above 10$ ^{-6} $. On the grain surface, molecular oxygen barely desorbs to gas phase at such low temperature. Furthermore, the adsorbed O$ _2 $ molecule is depleted by successive hydrogenation reactions to form O$ _2 $H and HOOH, which finally form H$ _2 $O ice on grain surface.

FIG. 2 Fractional abundance of O$ _2 $ with respect to H$ _2 $ is plotted as a function of time for cold dense models. Both O-rich and C-rich results are shown. The observational upper limits are depicted as dotted horizontal lines

In cold dense models, the gas-phase elemental oxygen is mainly in the form of CO, O$ _2 $ and H$ _2 $O. So we research the variation of these three oxygen reservoirs as a function of time with different hydrogen densities and temperatures using O-rich initial abundance, as shown in Table Ⅱ. The calculated abundances are shown in FIG. 3 in comparison with observational abundance/upper limits. The upper panels of FIG. 3 show how fractional abundances of O$ _2 $, CO and H$ _2 $O change as a function of time at the temperature of 10 K for cold dense models (T10N3-T10N6) with four different hydrogen densities. The lower panel of FIG. 3 shows results with temperatures remaining unchanged at 10, 20, 30, 40, and 50 K (Models T10-50N4) and the hydrogen density $ n_ \rm{H} $ of 2$ \times $10$ ^4 $ cm$ ^{-3} $. To compare with the observational values in L134N, we adopt the fractional abundance of 8$ \times $10$ ^{-5} $ by Ohishi et al. [37] for CO, and the upper limits of $ \leq $1.7$ \times $10$ ^{-7} $ [35] and $ \leq $3.0$ \times $10$ ^{-7} $ [38] for O$ _2 $ and H$ _2 $O, respectively.

FIG. 3 Fractional abundances of O$ _2 $, CO and H$ _2 $O with respect to H$ _2 $ are plotted as a function of time for cold dense models. Upper panels: results from four different hydrogen densities at the temperature 10 K; lower panels: five different temperatures at the hydrogen density $ n_ \rm{H} $ = 2$ \times $10$ ^4 $ cm$ ^{-3} $. The observational upper limits or abundances are depicted as dotted horizontal lines or solid horizontal lines, respectively

From the results of Models T10N3-T10N6, the peak abundances of CO, O$ _2 $ and H$ _2 $O all decrease with the hydrogen densities rising. The peak abundance of O$ _2 $ is more sensitive than those of CO and H$ _2 $O to the variation of hydrogen density. O$ _2 $ peak abundance is changed by three orders of magnitude from Model T10N3 to Model T10N6, while CO and H$ _2 $O peak abundances are only slightly changed. The reason is that one of O$ _2 $'s main reactant OH is more susceptible to the change of hydrogen density. CO is mainly formed by the reaction C$ _2 $+O$ \rightarrow $C+CO in the gas phase. Atomic O is depleted mainly by this reaction before 4$ \times $10$ ^3 $ yr, and O$ _2 $ and H$ _2 $O could not be efficiently produced before this time due to low abundance of O. Thus CO is produced at an early time compared with O$ _2 $ and H$ _2 $O. When most elemental carbon goes into CO, CO reaches its peak abundance. After that, CO abundance begins to decrease. Meanwhile, O$ _2 $ abundance increases quickly to its maximum. This can be explained by the competition to gain atomic oxygen as O is the major reactant to form O$ _2 $ and CO. The upper panels of FIG. 3 show that the timescales for gas-phase CO, O$ _2 $ and H$ _2 $O to reach their abundance peaks are dependent on the hydrogen density and are shortened with hydrogen density increasing.

From lower panels of FIG. 3, it can be seen that the abundances of O$ _2 $, CO, and H$ _2 $O increase as temperatures increase up to 50 K at the hydrogen density $ n_ \rm{H} $ = 2$ \times $10$ ^4 $ cm$ ^{-3} $. The laboratory experiments show that these three molecules desorb from the surface of dust grain analogs at $ \sim $30 K [39], $ \sim $26.5 K [40] and $ \sim $160 K [39], respectively. When temperature reaches 30$ - $50 K, the abundances of these three molecules do not increase much when temperature rises further. For O$ _2 $ and CO, they have reached their desorption temperature when the $ T $ is above 30 K. The steady state is reached after 10$ ^5 $ yr and 10$ ^6 $ yr for CO and O$ _2 $, respectively. On the other hand, these temperatures are too low compared with the H$ _2 $O's desorption temperature. As a result, H$ _2 $O hardly reaches its steady state at such low temperatures. On grain phase, oxygen atom mainly converts into H$ _2 $O, CO and H$ _2 $CO molecules with abundances of $ \sim $10$ ^{-4} $, $ \sim $10$ ^{-5} $ and $ \sim $10$ ^{-5} $, respectively. These abundances imply that a large portion of oxygen exists in the form of H$ _2 $O ice on grain surface. Therefore, a reasonable explanation for low abundance of gas-phase molecular oxygen is as the following: atomic oxygen accretes onto grain surface in cold clouds, and is successively hydrogenated to form water ice and remains in the form before dust temperature rises to $ \sim $100 K [22, 41].

Our modeling results also show that in cold dense models at $ T $ = 10 K, high cosmic-ray ($ \xi $$ \geq $3$ \xi_0 $) that forms high H$ _3 $O$ ^+ $ abundance can produce high O$ _2 $ abundance ($ \geq $10$ ^{-5} $), because H$ _3 $O$ ^+ $ can easily produce OH radicals, and OH reacting with O is a major formation route of O$ _2 $ in the gas phase.

B. Results from the warm-up models

FIG. 4 shows the results of fractional abundances of O$ _2 $ as a function of time for warm-up models (T30-100N4$ - $T30-100N6). The observed abundance of O$ _2 $ accords to Goldsmith et al. [6]. In warm-up models, O$ _2 $ is still mainly formed by the reaction between OH and H in gas phase. All warm-up models can yield sufficient O$ _2 $ abundance compared with the observed value during the warm up to maximum temperatures of 30 K, 50 K and 100 K. But when the temperature reaches its maxima, the calculated O$ _2 $ abundances are far too large, therefore the optimized temperatures for agreement are in the time range of 1$ \times $10$ ^5 $$ - $3$ \times $10$ ^5 $ yr at $ n_ \rm{H} $ = 2$ \times $10$ ^4 $ cm$ ^{-3} $ (N30-100N4 models), at $ n_ \rm{H} $ = 2$ \times $10$ ^5 $ cm$ ^{-3} $ (N30-100N5 models) and $ n_ \rm{H} $ = 2$ \times $10$ ^6 $ cm$ ^{-3} $ (N30-100N6 models), the time ranges are 3$ \times $10$ ^5 $$ - $10$ \times $10$ ^5 $ yr (as shown in the upper panels of FIG. 4). At a time near 2$ \times $10$ ^6 $ yr, the abundance of O$ _2 $ can reach $ \sim $10$ ^{-5} $ for T30-100N4, T50-100N5 and T50-100N6 models. At the maximum temperature 30 K, the model at hydrogen density 2$ \times $10$ ^4 $ cm$ ^{-3} $ is preferable for the formation O$ _2 $ (as shown in the lower panels of FIG. 4). In addition, the steady-state O$ _2 $ fractional abundances are independent of the hydrogen density, as long as the temperature is sufficiently high ($ > $30 K) to prevent a significant amount of O$ _2 $ from accreting onto grain surface. That is in agreement with the calculated result from Goldsmith et al. [6]. In Wang et al. [9], the O$ _2 $ emission region is located at about 10 kpc away from the central AGN. In this region, with the low temperature of 20 K to 50 K and the density of 10$ ^2 $ to 10$ ^5 $ cm$ ^{-3} $, our calculated results agree with the observed value of $ > $2$ \times $10$ ^{-5} $ for warm-up models of T30-50N4 and T50N5.

FIG. 4 Fractional abundances of O$ _2 $ with respect to H$ _2 $ are plotted as a function of time for the warm-up models. Results from three different hydrogen densities and maximum temperatures of $ T_{ \rm{max}} $ = 30 K, 50 K, 100 K are shown. Purple area is used to demonstrate the observed abundance of O$ _2 $ $ \pm $a factor of 3 uncertainty in Orion. Dashed lines represent temperatures profiles

FIG. 5 shows the effect of dust to gas mass ratio on the O$ _2 $ abundance versus time. The mass ratio of dust to gas are set to be 0.01 and 0.02 for assorted models, respectively. The figure has three panels, each containing the results of a simulation with a different temperature profile and with three different density settings from warm-up models (T30-100N4$ - $T30-100N6). The comparison between these two dust to gas mass ratios shows that when the dust to gas mass ratio increases to 0.02, there are less effects on O$ _2 $ abundance for models T50-100N4, T50-T100N5, and T30-100N6. But for models T30N4 and T30N5, the differences between the results from two dust to gas mass ratios are around an order of magnitude. Overall, when the dust to gas mass ratio increases from 0.01 to 0.02, O$ _2 $ abundances decrease in all warm-up models. The reason is that with the higher dust to gas mass ratio, more oxygen atoms are hydrogenated to finally form H$ _2 $O ice on grain surface.

FIG. 5 Fractional abundances of O$ _2 $ with respect to H$ _2 $ are plotted as a function of time for the warm-up models. Results from three different hydrogen densities and maximum temperatures of $ T_{ \rm{max}} $ = 30 K, 50 K, 100 K are shown. Purple area is used to demonstrate the observed abundance of O$ _2 $ $ \pm $a factor of 3 uncertainty in Orion. Dashed lines and solid lines represent the dust to gas mass ratio 0.01 and 0.02, respectively
Ⅳ. SUMMARY

We compared the calculated O$ _2 $ abundance from our models with observations in two cold clouds, L134N and TMC-1. The age of L134N may be younger than 10$ ^5 $ yr by our inference. Under cold dense conditions, if the cold cloud age is between 10$ ^5 $ and 10$ ^6 $ yr, the peak abundance of gaseous O$ _2 $ can be above 10$ ^{-6} $ from calculated results. The steady state is eventually reached till the time near 2$ \times $10$ ^6 $ yr. Besides, high cosmic-ray ionization rate gives a possibility to yield high O$ _2 $ abundance in the gas phase under cold dense conditions.

By investigating the oxygen reservoirs CO, O$ _2 $ and H$ _2 $O at different hydrogen densities and temperatures, we found that the peak abundances of CO, O$ _2 $ and H$ _2 $O all decrease with the hydrogen densities rising. But the peak abundance of O$ _2 $ is more sensitive than the other two to the variation of hydrogen density. As atomic O is depleted mainly by the reaction of C$ _2 $+O$ \rightarrow $C+CO in the gas phase before 4$ \times $10$ ^3 $ yr, CO is produced in early time compared with O$ _2 $ and H$ _2 $O in our models. After that time, CO abundance begins to decrease and O$ _2 $ abundance begins to increase quickly until it reaches the peak. The timescales of CO, O$ _2 $ and H$ _2 $O to reach peaks in gas-phase are dependent on the hydrogen density.

The warm-up models yield molecular oxygen abundances that are in good agreement with observations after 10$ ^5 $ yr when the temperatures rise. The hydrogen density significantly influences the molecular oxygen abundance at low temperature ($ \sim $30 K). Models with relatively low hydrogen density of 2$ \times $10$ ^4 $ cm$ ^{-3} $ show preferable results for the formation O$ _2 $ at 30 K. The steady-state O$ _2 $ fractional abundances are independent of the hydrogen density, as long as the temperature is sufficiently high ($ > $30 K). Higher dust to gas mass ratio (0.02) introduces deduction of gas phase O$ _2 $ abundance for certain models.

Whether molecular oxygen is under cold conditions or in warm regions, low density is preferable for the formation of O$ _2 $. But the age of cloud is also an important factor for detection of O$ _2 $ in space.

Ⅴ. Acknowledgments

This work was supported by the National Natural Science Foundation of China (No.11973075 and No.11433008).

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星际氧气分子的气相-尘埃模型研究
张霞a,b , 全冬晖a,c , 加尔肯·叶生别克a,d     
a. 中国科学院新疆天文台,乌鲁木齐 830011;
b. 中国科学院大学,北京 100049;
c. 美国东肯塔基大学化学系,里士满 KY 40475;
d. 中国科学院射电重点实验室,乌鲁木齐 830011
摘要: 本文采用气相-尘埃模型Nautilus研究了星际氧气的演化过程,使用了两种典型初始丰度值下的恒温模型和变化物理条件下的加热模型进行模拟计算. 结果表明,在冷致密云的条件下,CO、O$_2$和H$_2$O达到峰值的时间依赖于氢核密度的多少,其随氢核密度的增大而减小. 在加热模型中,在温度升高后的10$^5$年后,氧气的丰度值与观测结果符合较好. 在温度大于30 K后,氧气的稳态丰度值将不再随氢核密度而变化,且大于此温度可以阻止氧气大量的沉降到尘埃表面. 此外,无论在恒温模型还是在加热模型中,低氢核密度更有利于O$_2$的生成.
关键词: 天体化学    模型    星际介质    分子    丰度