Destruction of molecular hydrogen ice and Implications for 1I/2017 U1 (`Oumuamua)

The first interstellar object observed in our solar system, 1I/2017 U1 (`Oumuamua), exhibited a number of peculiar properties, including extreme elongation, tumbling, and acceleration excess. Recently, Seligman \&Laughlin (2020) proposed that the object was made out of molecular hydrogen (H$_{2}$) ice. The question is whether H$_2$ objects could survive their travel from the birth sites to the solar system. Here we study destruction processes of icy H$_2$ objects through their journey from giant molecular clouds (GMCs) to the interstellar medium (ISM) and the solar system, owing to interstellar radiation, gas and dust, and cosmic rays. We find that thermal sublimation due to heating by starlight can destroy `Oumuamua-size objects in less than 10 Myr. Thermal sublimation by collisional heating in GMCs could destroy H$_2$ objects before their escape into the ISM. Most importantly, the formation of icy grains rich in H$_2$ is unlikely to occur in dense environments because collisional heating raises the temperature of the icy grains, so that thermal sublimation rapidly destroys the H$_2$ mantle before grain growth.


INTRODUCTION
The detection of the first interstellar object, 1I/2017 U1 ('Oumuamua) by the Pan-STARRS survey (Bacci et al. 2017) implies an abundant population of similar interstellar objects (Meech et al. 2017;Do et al. 2018). The extreme axial ratio of 5 : 1 implied by 'Oumuamua's lightcurve is mysterious (Fraser et al. (2018); see also Jewitt et al. 2017 andGaidos et al. 2017). Bannister et al. (2017) and Gaidos (2017) suggested that 'Oumuamua is a contact binary, while others speculated that the bizarre shape might be the result of violent processes, such as collisions during planet formation. Domokos et al. (2017) suggested that the elongated shape might arise from ablation induced by interstellar dust, and Hoang et al. (2018) suggested that it could originate from rotational disruption of the original body by mechanical torques. Sugiura et al. (2019) suggested that the extreme elongation might arise from planetesimal collisions. The latest proposal involved tidal disruption of a larger parent object close to a dwarf star (Zhang & Lin 2020), but this mechanism is challenged by the preference for a disk-like shape implied by 'Oumuamua's lightcurve (Mashchenko 2019).
Another peculiarity is the detection of nongravitational acceleration in the trajectory of 'Oumuamua (Micheli et al. 2018). Interestingly, no cometary activity of carbon-based molecules was found by deep observations with the Spitzer space telescope (Trilling et al. 2018). Bialy & Loeb (2018) explained the acceleration anomaly by means of radiation pressure acting on a thin lightsail, and Moro-Martin (2019) and Sekanina (2019) suggested a porous object. Fitzsimmons et al. (2018) proposed that an icy object of unusual composition might survive its interstellar journey.
Most recently, Seligman & Laughlin (2020) suggested hydrogen ice to explain 'Oumuamua's excess acceleration and unusual shape. Their modeling implied that the object is ∼ 100 Myr old. Assuming a speed of 30 km s −1 , they suggested that the object was produced in a Giant Molecular Cloud (GMC) at a distance of ∼ 5 kpc. However, their study did not consider the destruction of H 2 ice in the interstellar medium (ISM), but only through evaporation by sunlight. Here, we explore the evolution of H 2 ices from their potential GMC birth sites to the diffuse ISM and eventually the solar system.
Assuming H 2 objects could be formed in GMCs, we quantify their destruction and determine the minimum size of an H 2 object that can reach the solar system. We assume that the H 2 objects are ejected from GMCs into the ISM by some dynamical mechanism such as tidal disruption of bigger objects or collisions (see Raymond et al. 2018;Rice & Laughlin 2019). The evolution of H 2 objects in the ISM has additional implications for baryonic dark matter (White 1996;Carr & Sakellariadou 1999).
The structure of the paper is as follows. In Sections 2-4, we calculate the destruction timescales from various processes for H 2 objects. In Section 5, we compare the destruction times with the travel time for different object sizes. In Section 6, we explore the formation of H 2 -rich objects in dense GMCs and the implications for baryonic dark matter. We conclude with a summary of our main findings in Section 7.

DESTRUCTION OF H 2 ICE BY INTERSTELLAR RADIATION
Let us first assume that H 2 objects could form in dense GMCs and get ejected into the ISM and examine several mechanisms for H 2 ice destruction. The formation of H 2 ice is likely to occur on an H 2 O ice mantle. The binding energy of H 2 to the H 2 O surface is E b /k ∼ 100 K (Sandford & Allamandola 1993), equivalent to E b (H 2 ) ≈ 0.01 eV . For simplicity, we assume a spherical object shape in our derivations, but the results can be easily generalized to other shapes.

Thermal sublimation
Heating by starlight raises the surface temperature of H 2 ice. We assume that the local radiation field has the same spectrum as the interstellar radiation field (ISRF) in the solar neighborhood (Mathis et al. 1983) with a total radiation energy density of u MMP ≈ 8.64 × 10 −13 erg cm −3 . We calibrate the strength of the local radiation field by the dimensionless parameter, U , so that the local energy density is u rad = U u MMP .
The characteristic timescale for the evaporation of an H 2 molecule from a surface of temperature T ice is where ν 0 is the characteristic oscillation frequency of the H 2 lattice (Watson & Salpeter 1972). We adopt ν 0 = 10 12 s −1 for H 2 ice (Hegyi & Olive 1986;Sandford & Allamandola 1993).
Assuming that the H 2 ice has a layered structure, the sublimation rate for an H 2 object of radius R is given by, where n ice ≈ 3×10 22 cm −3 is the molecular number density of H 2 ice with a mass density of ρ ice = 0.1 g cm −3 . The sublimation time is then, where dR/dt was substituted from Equation (2). Plugging the numerical parameters into the above equation, we obtain, for H 2 ice. At the minimum temperature of the presentday Cosmic Microwave Background (CMB) radiation, T obj = 2.725 K, the sublimation time is t sub ≈ 0.85 Gyr for R = 1 km. The heating rate due to absorption of isotropic interstellar radiation is given by, where is the surface emissivity averaged over the starlight radiation spectrum.
The cooling rate by thermal emission is given by, is the bolometric emissivity, integrated over all radiation frequencies, ν.
The energy balance between radiative heating and cooling yields the surface equilibrium temperature, At this temperature, the sublimation time is short, less than 272 yr, according to Equation (4). However, to access the actual temperature of the ice, we need to take account of evaporative cooling (Watson & Salpeter 1972;Hoang et al. 2015). The cooling rate by evaporation of H 2 is given by, where dN mol /dt is the evaporation rate, namely, the number of molecules evaporating per unit time, and N s = 4πR 2 /r 2 s is the number of surface sites with r s = 10Å being the average size of the H 2 surface site (Sandford & Allamandola 1993).
The ratio of evaporative to radiative cooling rates is given by, implying that the evaporative cooling dominates over radiative cooling for T ice > 3 K. Therefore, the H 2 surface temperature is maintained at T ice ∼ 3 K.
For an H 2 object moving at a speed, v obj , through the ISM, the heating rate by gas collisions is given by, where µ is the mean molecular weight of the ISM and m H is the mass of a hydrogen atom. For the cosmic He abundance, µ = 1.4. The ratio of collisional heating to radiative heating is given by, GMCs, collisional heating is important and can destroy H 2 objects rapidly (see Section 5). For the diffuse ISM, collisional heating is negligible.
CMB photons also warm up icy objects. The CMB temperature at a redshift z is T CMB = 2.73(1 + z). At present, heating by the CMB is less important than by starlight, and H 2 -ice reaches T ice ≈ 3 K from the standard ISRF.

Photodesorption
Next we estimate the lifetime of an icy H 2 object to UV photodesorption. Let Y pd be the photodesorption yield, defined as the number of molecules ejected over the total number of incident UV photons. The rate of mass loss due to UV photodesorption is wherem is the mean mass of ejected molecules, and F UV is the flux of UV photons. This yields wherem = 2m H , Y pd = hν/E b = 10 3 for hν = 10 eV , and F UV = 10 7 cm −2 s −1 for the ISRF. We define G = F UV /F UV,MMP to calibrate the strength of background UV radiation, where F UV,MMP = 10 7 cm −2 s −1 is the UV flux of the standard ISRF. The photodesorption time for an object of radius R is, An enhancement of the local UV radiation near an OB association can increase the photodesorption rate by a factor of G.

DESTRUCTION BY COSMIC RAYS
The stopping power of a relativistic proton in H 2 ice is, dE/dx ∼ −10 6 eV cm −1 at an energy E ∼ 1 GeV (Hoang et al. 2015;Hoang et al. 2017). The corresponding penetration length is R p = −E/(dE/dx) ∼ 10 3 cm = 10 m.
The ice volume evaporated by a cosmic ray (CR) proton is determined by the heat transfer from the CR to the ice volume that reaches an evaporation temperature T evap ∼ E b /3k (i.e., thermal energy per H 2 comparable to the binding energy). Since the object radius is much larger than the above penetration length, the volume of ice evaporated by a CR proton, δV , is given by, Because the penetration length is much shorter than the 'Oumuamua's estimated size, CRs would gradually erode the object. The fraction of the object volume eroded by CRs per unit of time is.
The timescale required to eliminate the object is, where F CR = 1 cm −2 s −1 is the flux of proton CRs of E = 1 GeV. The above result is comparable to the estimate by White (1996). The contribution of heavy ion CRs is less important than proton CRs because their flux is lower; for iron ions, the abundance ratio is F Fe /F p = 1.63 × 10 −4 (see Leger et al. 1985 which is short only in GMCs and unimportant for the diffuse ISM.

Impulsive collisional heating and transient evaporation
Collisions of H 2 ice with the ambient gas at high speeds can heat the frontal area to a temperature T evap , resulting in transient evaporation. The volume of ice evaporated by a single collision, δV , can be given by where the impact kinetic energy is assumed to to be fully converted into heating. The evaporation rate by gas collisions is given by, The evaporation time by gas collisions is then, somewhat shorter than the sputtering time given in Equation (18). Similarly, dust grains of mass m gr deposit a kinetic energy of E gr = m gr v 2 obj /2 upon impact, resulting in transient evaporation. The evaporation rate by dust collisions is given by yielding a dust evaporation time, Assuming that all grains have the same size, a, and using the dust-to-gas mass ratio M d/g = n gr 4πa 3 ρ gr /(3µm H n H ), one obtains the grain number density, where ρ gr = 3 g cm −3 is assumed. Substituting n gr into Equation (23) yields, t evap,d 6.5 × 10 11 R 1 km The destruction by dust is less efficient than by gas due to a lower dust mass.

Destruction by bow shocks
For a cold GMC of temperature T gas ∼ 3 K, the thermal gas velocity is v th ∼ 0.2(T gas /3 K) 1/2 km s −1 .
The mean free path for atomic collisions is λ mfp ∼ 1/(n H vσ H ) ∼ 0.5(10 6 cm −3 /n H )(0.2 km s −1 /v th )(10 −15 cm −2 /σ H ) km. Thus, for objects larger than R = 1 km, bow shocks are formed if the gas density n H 10 6 cm −3 . The post-shock gas has a high temperature and can be efficient in thermal sputtering. However, bow shocks are not expected to form for objects of R < 1 km and n H < 10 6 cm −3 .

Destruction in the ISM
Assuming that H 2 objects of various sizes are produced in a nearby GMC, we estimate the minimum size of objects that could reach the Earth. The closest GMC, W51, is located at a distance of 5.2 kpc. Thus, at a speed of 30 km s −1 , it takes t trav ∼ 1.6 × 10 8 yr for objects to reach the solar system. Figure 1 compares the various destruction times with t trav for different object radii at a typical speed. We find that only very large objects of radius R > 5 km could survive thermal sublimation and reach the solar system.

Destruction on the way from the center of GMCs to the ISM
The total gas column density toward the densest GMC amounts to extinction of A V ∼ 200 (see e.g., Mathis et al. 1983), which corresponds to a hydrogen column density of N H ∼ 3 × 10 23 cm −2 based on the scaling N H /A V ∼ 10 21 cm −2 /mag (Draine 2011). Assuming a mean GMC density n H = 10 4 cm −3 and a GMC radius R GMC ∼ 10 pc, the travel time is t trav = R GMC /v obj ≈ 3.2 × 10 5 (R GMC /10 pc)(30 km s −1 /v obj ) yr.
As shown in Section 2, collisional heating is important in GMCs because of their high density, n H 10 3 cm −3 . Assuming that a fraction η of the impinging proton's energy is converted into surface heating to a temperature below T evap , collisional heating raises the temperature of the frontal surface to: The resulting destruction time is much shorter than the travel time t trav . We conclude that H 2 objects cannot survive their journey from their GMC birthplace to the ISM.
Seligman & Laughlin (2020) suggested that H 2 ice objects can form in the densest region of a GMC where the gas density is n H ∼ 10 5 cm −3 and temperature is T gas ∼ 3 K. Below, we show that H 2 -rich grains cannot form in the GMC due to destruction by collisional heating, preventing the formation of H 2 objects.
At low temperatures, the accretion of H 2 molecules from the gas phase onto a grain core is a main process enabling the formation of an H 2 mantle. The characteristic timescale for forming an icy grain of radius a is given by, where the thermal velocity v th = (8kT gas /πm H ) 1/2 , and the sticking coefficient s H = 1 is assumed. The timescale to form H 2 ice from collisions between two icy grains of equal sizes a and relative velocity v gg is given by, amounting to ∼ 10 4 yr for a density of n H ∼ 10 6 cm −3 , a sticking coefficient, s gr = 1, and the grain number density, n gr , is given by Equation (24). In conclusion, the timescale to form micron-sized grains by coagulation is much longer than the formation time by gas accretion, in agreement with the estimate by Seligman & Laughlin (2020). However, Seligman & Laughlin (2020) did not consider the destructive effect of icy H 2 grains by collisional heating by gas. Greenberg & de Jong (1969) noted that, at a density of n H > 10 5 cm −3 , collisional heating might prevent the formation of H 2 ice. We calculate the grain temperature heated by gas with a minimum temperature T gas = T CMB = 2.725 K as follows: where Q abs T ≈ 1.1×10 −4 (a/1 µm)(T /3 K) 2 for silicate grains (Draine 2011).
Substituting this typical temperature and the grain size a = 1 µm into Equation (3) yields, much shorter than the accretion time t acc given in Equation (28). We therefore conclude that micron-sized H 2 grains cannot form in dense GMCs due to collisional heating. Figure 2 shows the accretion time and sublimation time as functions of gas density for different emissivities Q abs T . In the densest region where the gas temperature could be very low, collisional heating becomes important. On the other hand, in lower density regions, accretion is faster, but the heating by CRs and interstellar radiation could still be important to sublimate H 2 ice. 6.2. Implications: Could 'Oumuamua made of H 2 ice survive the journey from the birth site to the solar system?
Assuming that H 2 objects could somehow form in the densest regions of GMCs, we found that sublimation by collisional heating inside the GMC would destroy the objects before their escape into the ISM. We also studied various destruction mechanisms of H 2 ice in the ISM. In particular, we found that H 2 objects are heated by the average interstellar radiation to the sublimation temperatures, so that they cannot survive beyond a sublimation time of t sub ∼ 10 Myr for R = 300 m (see Figure  1). Only H 2 objects larger than 5 km could survive.

Implications for H 2 ice as baryonic dark matter
Primordial snowballs were suggested as baryonic dark matter (White 1996). Previous studies considered collisions between snowballs as a destructive mechanism (Hegyi & Olive 1986;Carr & Sakellariadou 1999). Hegyi & Olive (1986) studied destruction of H 2 ice by the CMB and found that at redshift (1 + z) = 3.5, sublimation would rapidly destroy H 2 ice. Later, White (1996) argued that the treatment of sublimation by Hegyi & Olive (1986) was inadequate because evaporative cooling was not taken into account. In this work, we have shown that the evaporative cooling is only important for T 3 K. Even when evaporative cooling is taken into account, thermal sublimation by starlight still plays an important role in the destruction of H 2 objects. The present CMB temperature T CMB is not high enough to rapidly sublimate H 2 ice. However, at redshifts z > 1, the CMB temperatures of T CMB > 5 K, can rapidly destroy H 2 objects of R ∼ 1 km within t sub ∼ 48 yr, based on Equation (4).
More importantly, we found that the formation of H 2 objects cannot occur in dense GMCs because collisional heating raises the temperature of dust grains, resulting in rapid sublimation of H 2 ice mantles. Thus, we find that large objects rich in H 2 ice are unlikely to form in dense clouds, in agreement with the conclusions of Greenberg & de Jong (1969).

SUMMARY
We have studied the destruction of H 2 ice objects during their journey from their potential birth sites to the solar system. Our main findings are as follows: 1. Destruction of H 2 ice-rich objects by thermal sublimation due to starlight is important, whereas destruction by CRs and interstellar matter is less important.
2. The minimum radius of H 2 objects is required to be R min ∼ 5 km for survival from the nearest GMC.
3. H 2 objects could be destroyed on the way from the GMC to the ISM due to thermal sublimation induced by collisional heating.
4. Formation of H 2 ice-rich grains in dense GMCs is unlikely to occur due to rapid sublimation induced by collisional heating. This makes the formation of H 2 -rich objects improbable.
T.H. acknowledges the support by the National Research Foundation of Korea (NRF) grants funded by the Korea government (MSIT) through the Mid-career Research Program (2019R1A2C1087045). A.L. was supported in part by a grant from the Breakthrough Prize Foundation.