Destruction of Molecular Hydrogen Ice and Implications for 1I/2017 U1 ('Oumuamua) - IOPscience
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The Astrophysical Journal Letters, 899:L23 (7pp), 2020 August 20 https://doi.org/10.3847/2041-8213/abab0c
© 2020. The Author(s). Published by the American Astronomical Society.
Destruction of Molecular Hydrogen Ice and Implications for 1I/2017 U1 (‘Oumuamua)
Thiem Hoang1,2 and Abraham Loeb3
1
Korea Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea; thiemhoang@kasi.re.kr
2
Korea University of Science and Technology, Daejeon 34113, Republic of Korea
3
Astronomy Department, Harvard University, 60 Garden Street, Cambridge, MA, USA; aloeb@cfa.harvard.edu
Received 2020 June 14; revised 2020 July 13; accepted 2020 July 31; published 2020 August 17
Abstract
The first interstellar object observed in our solar system, 1I/2017 U1 (‘Oumuamua), exhibited a number of peculiar
properties, including extreme elongation and acceleration excess. Recently, Seligman & Laughlin proposed that the
object was made out of molecular hydrogen (H2) ice. The question is whether H2 objects could survive their travel
from the birth sites to the solar system. Here we study destruction processes of icy H2 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
H2 objects of ‘Oumuamua-size before their escape into the ISM. Most importantly, the formation of icy grains rich
in H2 is unlikely to occur in dense environments because collisional heating raises the temperature of the icy grains,
so that thermal sublimation rapidly destroys the H2 mantle before grain growth.
Unified Astronomy Thesaurus concepts: A stars (5); Amor group (36); Interstellar dynamics (839); Dense
interstellar clouds (371); Astrosphere interstellar medium interactions (106); Comets (280); Aperiodic comets (52);
Asteroids (72)
1. Introduction acceleration anomaly by means of radiation pressure acting on
a thin lightsail, and Moro-Martin (2019) and Sekanina (2019)
The detection of the first interstellar object, 1I/2017 U1
suggested a porous object. Fitzsimmons et al. (2018) proposed
(‘Oumuamua) by the Pan-STARRS survey (Bacci et al. 2017)
that an icy object of unusual composition might survive its
implies an abundant population of similar interstellar objects
interstellar journey. Previously, Füglistaler & Pfenniger (2018)
(Meech et al. 2017; Do et al. 2018). An elongated shape of
suggested that ‘Oumuamua might be composed of H2.
semi-axes ~230 m ´ 35 m is estimated from light-curve
However, Rafikov (2018) argued that the level of outgassing
modeling (Jewitt et al. 2017). The extreme axial ratio of
needed to produce the acceleration excess would rapidly
5: 1 implied by ‘Oumuamua’s light curve is mysterious
change the rotation period of ‘Oumuamua, in conflict with the
(Gaidos et al. 2017; Fraser et al. 2018).
Bannister et al. (2017) and Gaidos (2017) suggested that observational data.
Most recently, Seligman & Laughlin (2020) suggested
‘Oumuamua is a contact binary, while others speculated that
hydrogen ice to explain ‘Oumuamua’s excess acceleration
the bizarre shape might be the result of violent processes, such
as collisions during planet formation. Domokos et al. (2017) and unusual shape. Their modeling implied that the object is
suggested that the elongated shape might arise from ablation ∼100 Myr old. Assuming a speed of 30 km s−1, they suggested
induced by interstellar dust, and Hoang et al. (2018) suggested that the object was produced in a giant molecular cloud (GMC)
that it could originate from rotational disruption of the original at a distance of ∼5 kpc. However, their study did not consider
body by mechanical torques. Sugiura et al. (2019) suggested the destruction of H2 ice in the interstellar medium (ISM), but
that the extreme elongation might arise from planetesimal only through evaporation by sunlight. Here, we explore the
collisions. The latest proposal involved tidal disruption of a evolution of H2 ices from their potential GMC birth sites to the
larger parent object close to a dwarf star (Zhang & Lin 1919), diffuse ISM and eventually the solar system.
but this mechanism is challenged by the preference for a disk- Assuming that H2 objects could be formed in GMCs by
like shape implied by ‘Oumuamua’s light curve some mechanisms (Füglistaler & Pfenniger 2016; Füglistaler &
(Mashchenko 2019). Pfenniger 2018; Seligman & Laughlin 2020), we quantify their
Another peculiarity is the detection of non-gravitational destruction and determine the minimum size of an H2 object
acceleration in the trajectory of ‘Oumuamua (Micheli et al. that can reach the solar system. We assume that the H2 objects
2018). The authors suggested that cometary activity such as are ejected from GMCs into the ISM by some dynamical
outgassing of volatiles could explain the acceleration excess. mechanism such as tidal disruption of bigger objects or
Interestingly, no cometary activity of carbon-based molecules collisions (see Raymond et al. 2018; Rice & Laughlin 2019).
was found by deep observations with the Spitzer space The evolution of H2 objects in the ISM has additional
telescope (Trilling et al. 2018) and Gemini North telescope implications for baryonic dark matter (White 1996; Carr &
(Drahus et al. 2018). Bialy & Loeb (2018) explained the Sakellariadou 1999).
The structure of this Letter is as follows. In Sections 2–4, we
calculate the destruction timescales from various processes for
Original content from this work may be used under the terms
of the Creative Commons Attribution 4.0 licence. Any further H2 objects. In Section 5, we compare the destruction times with
distribution of this work must maintain attribution to the author(s) and the title the travel time for different object sizes. In Section 6, we
of the work, journal citation and DOI. explore the formation of H2-rich objects in dense GMCs and
1The Astrophysical Journal Letters, 899:L23 (7pp), 2020 August 20 Hoang & Loeb
the implications for baryonic dark matter. We conclude with a The heating rate due to absorption of isotropic interstellar
summary of our main findings in Section 7. radiation and CMB photons is given by
2. Destruction of H2 Ice by Interstellar Radiation dEabs
= pR 2c (UuMMP + u CMB) , (5 )
Let us first assume that H2 objects could form in dense dt
GMCs and get ejected into the ISM and examine several
mechanisms for H2 ice destruction. The binding energy of H2 where is the surface emissivity averaged over the back-
in the hydrogen ice is Eb k ~ 100 K (Sandford & Allaman- ground radiation spectrum.
dola 1993), equivalent to Eb (H2) » 0.01 eV . For simplicity, The cooling rate by thermal emission is given by
we assume a spherical object shape in our derivations, but the
results can be easily generalized to other shapes. dEemiss
= 4pR 2 T sT 4, (6 )
dt
2.1. Thermal Sublimation
where T = ò dn (n ) Bn (T ) ò dnBn (T ) is the bolometric
Heating by starlight and cosmic microwave background
emissivity, integrated over all radiation frequencies, ν.
(CMB) radiation raises the surface temperature of H2 ice. We
The energy balance between radiative heating and cooling
assume that the local interstellar radiation field (ISRF) has the
yields the surface equilibrium temperature
same spectrum as the ISRF in the solar neighborhood (Mathis
et al. 1983) with a total radiation energy density of
uMMP » 8.64 ´ 10-13 erg cm-3. We calibrate the strength of ⎛ c (UuMMP + u CMB) ⎞1 4 ⎛ ⎞1 4
Tice = ⎜ ⎟ ⎜ ⎟
the local radiation field by the dimensionless parameter, U, so ⎝ 4s ⎠ ⎝T ⎠
that the local energy density is u rad = UuMMP . The CMB
⎛ ⎞1 4
radiation is blackbody with a temperature 3.59 (U + [1 + z]3 )1 4 ⎜ ⎟ K. (7 )
TCMB = 2.725 (1 + z ) K at a redshift z, and the radiation ⎝T ⎠
energy density is uCMB=ò 4pBn (TCMB) dν/c=4
sTCMB
4
c » 4.17 ´ 10-13(1 + z )4 erg cm-3. At present, At this temperature, the sublimation time is short, less than
heating by the CMB is less important than by starlight. ~1 ´ 10 5 yr, according to Equation (4).
The characteristic timescale for the evaporation of an H2 However, to access the actual temperature of the ice, we
molecule from a surface of temperature Tice is need to take account of evaporative cooling (Watson &
Salpeter 1972; Hoang et al. 2015). The cooling rate by
⎛ Eb ⎞
tsub = n -
0 exp ⎜
1
⎟, (1 ) evaporation of H2 is given by
⎝ kTice ⎠
dEevap Eb dNmol Eb Ns
where n0 is the characteristic oscillation frequency of the H2 = = , (8 )
lattice (Watson & Salpeter 1972). We adopt n0 = 1012 s-1 for dt dt tsub (Tice)
H2 ice (Hegyi & Olive 1986; Sandford & Allamandola 1993).
where dNmol dt is the evaporation rate, namely, the number of
Assuming that the H2 ice has a layered structure, the
sublimation rate for an H2 object of radius R is given by molecules evaporating per unit time, and Ns = 4pR2 rs2 is the
number of surface sites with rs = 10 Å being the average size
dR n ⎛ E ⎞
= - 10 3 exp ⎜ - b ⎟ , (2 ) of the H2 surface site (Sandford & Allamandola 1993).
dt n ice ⎝ kTice ⎠ The ratio of evaporative to radiative cooling rates is given by
where n ice » 3 ´ 10 22 cm-3 is the molecular number density dEevap dt Eb n 0 exp ( - Eb kTice)
of H2 ice with a mass density of rice = 0.1 g cm-3. =
The sublimation time is then dEemiss dt T sTice
4 2
rs
⎛ 1.1 ⎞ ⎛ 3 K ⎞4 ⎛ ⎡ 1 1 ⎤⎞
1 3
Rn ice ⎛ E ⎞ ⎜ ⎟⎜ ⎟ exp ⎜100 K ⎢ -
tsub (Tice) = -
R
= exp ⎜ b ⎟ , (3 ) ⎥⎟
⎝ kTice ⎠ ⎝ T ⎠ ⎝ Tice ⎠ ⎝ ⎣ Tice 3 K ⎦⎠
dR dt n0
⎞ ⎛ 10 Å ⎞
2
where dR/dt was substituted from Equation (2). ⎛ Eb
´⎜ ⎟⎜ ⎟ , (9 )
Plugging the numerical parameters into the above equation, ⎝ 0.01 eV ⎠ ⎝ rs ⎠
we obtain
⎛ R ⎞ implying that the evaporative cooling dominates over radiative
tsub (Tice) 2.95 ´ 107 ⎜ ⎟
cooling for Tice 3 K .
⎝ 1 km ⎠
For an H2 object moving at a speed,vobj, through the ISM, the
⎛ ⎡ 1 1 ⎤⎞ heating rate by gas collisions is given by
´ exp ⎜100 K ⎢ - ⎥ ⎟ yr (4 )
⎝ ⎣ Tice 3 K ⎦⎠
dEcoll 1
for H2 ice, and the ice temperature is normalized to Tice = 3 K = pR 2nH mm H vobj
3
, (10)
dt 2
expecting that starlight raises the surface temperature above
TCMB. At the minimum temperature of the present-day CMB where μ is the mean molecular weight of the ISM and mH is the
radiation, Tobj = 2.725 K, the sublimation time is mass of a hydrogen atom. For the cosmic He abun-
tsub » 0.85 Gyr for R = 1 km . dance, μ=1.4.
2The Astrophysical Journal Letters, 899:L23 (7pp), 2020 August 20 Hoang & Loeb
The ratio of collisional heating to radiative heating by 3. Destruction by Cosmic Rays
starlight is given by
The stopping power of a relativistic proton in H2 ice is
(nH mm H vobj
3
2) dE dx ~ -106 eV cm-1 at an energy E ~ 1 GeV (Hoang
dEcoll
= et al. 2015; Hoang et al. 2017). The corresponding penetration
dEabs cUuMMP length is Rp = -E (dE dx ) ~ 10 3 cm = 10 m.
⎛ n ⎞⎛ vobj ⎞3 ⎛ U ⎞ The ice volume evaporated by a cosmic ray (CR) proton is
1.2 ⎜ 3 H -3 ⎟ ⎜ ⎟ ⎜ ⎟, (11) determined by the heat transfer from the CR to the ice volume
⎝ 10 cm ⎠ ⎝ 30 km s-1 ⎠ ⎝ ⎠
that reaches an evaporation temperature Tevap ~ Eb 3k (i.e.,
implying dominance of collisional heating if thermal energy per H2 comparable to the binding energy).
nH cUuMMP (mmH vobj 3
2) 825U (30 km s-1 vobj)3 cm-3, Because the object radius is much larger than the above
penetration length, the volume of ice evaporated by a CR
assuming = 1. Thus, in GMCs, collisional heating is
proton, dV , is given by
important and can destroy H2 objects rapidly (see Section 5).
For the diffuse ISM, collisional heating is negligible. n ice dVEb = E CR. (16)
The final energy balance equation reads Because the penetration length is much shorter than the
dEevap ‘Oumuamua’s estimated size, CRs would gradually erode the
dEabs dEcoll dEemiss
+ = + . (12) object. The fraction of the object volume eroded by CRs per
dt dt dt dt unit of time is
We numerically solve the above equation for the equilibrium 1 dV 4pR 2FCR dV 3F E
temperature, and obtain Tice = 2.996 » 3 K , assuming U=1, =- = - CR CR , (17)
the present CMB, and nH = 10 cm-3. At this temperature, V dt V Rn ice Eb
Equation (4) implies the sublimation time of ∼30 Myr for where V = 4pR3 3 is the object’s volume.
R=1 km. Passing near a region with enhanced radiation The timescale required to eliminate the object is
fields, e.g., near a star, would reduce the sublimation time
significantly. V Rn ice Eb
tCR = - =
dV dt 3FCR E CR
2.2. Photodesorption ⎛ R ⎟⎞ ⎜⎛ Eb ⎟⎞ ⎛ 109 eV ⎞
3.2 ´ 108 ⎜ ⎜ ⎟
Next we estimate the lifetime of an icy H2 object to ⎝ 1 km ⎠ ⎝ 0.01 eV ⎠ ⎝ E CR ⎠
ultraviolet (UV) photodesorption. Let Ypd be the photodesorp-
⎛ 1 cm-2 s-1 ⎞
tion yield, defined as the number of molecules ejected over the ´⎜ ⎟ yr, (18)
total number of incident UV photons. The rate of mass loss due ⎝ FCR ⎠
to UV photodesorption is
where FCR = 1 cm-2 s-1 is the flux of proton CRs of
dm 4pR 2r ice dR E=1 GeV. The above result is comparable to the estimate
= = - mY
¯ pd FUV pa2 , (13)
dt dt by White (1996).
The contribution of heavy-ion CRs is less important than
where m̄ is the mean mass of ejected molecules, and FUV is the proton CRs because their flux is lower; for iron ions, the
flux of UV photons. This yields abundance ratio is FFe Fp = 1.63 ´ 10-4 (see Leger et al.
1985).
dR mY
¯ pd FUV
=-
dt 4r ice 4. Destruction by Interstellar Matter
⎛ F ⎞ ⎛ Ypd ⎞ ⎛ 0.1 g cm-3 ⎞ 4.1. Nonthermal Sputtering
- 262 ⎜ 7 UV ⎟⎜ ⎟⎜ ⎟ Å yr-1,
⎝ 10 cm s ⎠ ⎝ 10 3 ⎠ ⎝
- 2 - 1 r ice ⎠ At a characteristic speed of vobj ~ 30 km s-1, each ISM
(14) proton delivers an energy of Ep = mH vobj2
2 » 4.66 eV to the
impact location. Thus, protons can eject H2 out of the ice
where m¯ = 2mH , Ypd = hn Eb = 10 3 for hn = 10 eV , and surface with a sputtering yield of Ysp ~ Ep Eb ~ 460.
FUV = 107 cm-2 s-1 for the ISRF. The destruction time of H2 ice by sputtering is given by
We define G = FUV FUV,MMP to calibrate the strength of
background UV radiation, where FUV,MMP = 107 cm-2 s-1 is R 4r ice R
tsp = - =
the UV flux of the standard ISRF. The photodesorption time for dR dt nH m H vobj Ysp
an object of radius R is ⎛ 0.1 g cm-3 ⎞ ⎛ R ⎞ ⎛ 10 cm-3 ⎞
2.6 ´ 1010 ⎜ ⎟⎜ ⎟⎜ ⎟
tpd = -
R ⎝ r ice ⎠ ⎝ 1 km ⎠ ⎝ nH ⎠
dR dt ⎛ 30 km s-1 ⎞ ⎛ 10 3 ⎞
7.5 ´ 1010 ⎛⎜ R ⎞⎟ ⎛ 10 3 ⎞ ⎛ 107 cm-2 s-1 ⎞ ´⎜ ⎟⎜ ⎟ yr, (19)
⎜ ⎟⎜ ⎟ yr. (15) ⎝ vobj ⎠ ⎝ Ysp ⎠
G ⎝ 1 km ⎠ ⎝ Ypd ⎠ ⎝ FUV,MMP ⎠
which is short only in GMCs and unimportant for the diffuse
An enhancement of the local UV radiation near an OB ISM. Moreover, most of proton’s energy may go into forming a
association can increase the photodesorption rate by a factor deep track instead of surface heating, reducing the sputtering
of G. effect.
3The Astrophysical Journal Letters, 899:L23 (7pp), 2020 August 20 Hoang & Loeb
4.2. Impulsive Collisional Heating and Transient Evaporation
Collisions of H2 ice with the ambient gas at high speeds can
heat the frontal area to a temperature Tevap , resulting in transient
evaporation. The volume of ice evaporated by a single
collision, dV , can be given by
1
n ice dVEb = mm H vobj
2
, (20)
2
where the impact kinetic energy is assumed to to be fully
converted into heating.
The evaporation rate by gas collisions is given by
1 dV pR 2nH vobj dV 3nH mm H vobj
3
=- =- . (21)
V dt V 8Rn ice Eb
The evaporation time by gas collisions is then
V 8Rn ice Eb Figure 1. Comparison of various destruction timescales (slanted colored lines)
tevap,gas = - = as a function of the object radius (in meters) to the travel time from a GMC at a
dV dt 3 n H mm H v 3
distance of 5.2 kpc, assuming a characteristic speed of 30 km s−1 (horizontal
⎛ R ⎞ ⎛ 30 km s-1 ⎞
3
black line).
6.5 ´ 109 ⎜ ⎟⎜ ⎟
⎝ 1 km ⎠ ⎝ vobj ⎠
4.3. Destruction by Bow Shocks
⎛ nH ⎞-1⎛ Eb ⎞
´⎜ ⎟ ⎜ ⎟ yr, (22) For a cold GMC of temperature Tgas ~ 3 K , the thermal
⎝ 10 cm-3 ⎠ ⎝ 0.01 eV ⎠ velocity of the gas is
v T = (3kTgas mH )1 2 ~ 0.27 (Tgas 3 K)1 2 km s-1. Objects
which is somewhat shorter than the sputtering time given in
moving rapidly through the gas with vobj ~ 30 km s-1 vT ,
Equation (19).
will produce a bow shock if their radius is larger than the mean
Similarly, dust grains of mass mgr deposit a kinetic energy of
free path of gas molecules (Landau & Lifshitz 1959). The mean
Egr = mgr vobj
2
2 upon impact, resulting in transient evapora-
free path for molecular collisions is
tion. The evaporation rate by dust collisions is given by
lmfp ~ 1 (nH sH2 ) = 10 4 (106 cm-3 nH )(10-15 cm-2 sH2 ) km
1 dV pR 2ngr vobj dV 3
3ngr mgr vobj with sH2 being the H2 cross-section. Thus, for objects larger
=- =- , (23) than R = 10 4 km, bow shocks are formed if the gas density
V dt V 8Rn ice Eb nH 106 cm-3. The post-shock gas has a high temperature and
yielding a dust evaporation time, can be efficient in thermal sputtering. However, bow shocks are
not expected to form for objects of R < 10 4 km
V 8Rn ice Eb and nH < 106 cm-3.
tevap,d = - = 3
. (24)
dV dt 3ngr mgr vobj
5. Numerical Results
Assuming that all grains have the same size, a, and using the 5.1. Destruction in the ISM
dust-to-gas mass ratio Md g = ngr 4pa3rgr (3mmH nH ), one
obtains the grain number density Assuming that H2 objects of various sizes are produced in a
nearby GMC, we estimate the minimum size of objects that
Md g (3mm H nH) could reach the Earth. The closest GMC, W51, is located at a
ngr =
4pa 3rgr distance of DGMC = 5.2 kpc. Thus, at a speed of 30 km s-1, it
takes ttrav » 1.6 ´ 108 yr for objects to reach the solar system.
⎛ Md g ⎞ ⎛ nH ⎞
» 1.85 ´ 10-11⎜ ⎟⎜ ⎟ Figure 1 compares the various destruction times with ttrav for
⎝ 100 ⎠ ⎝ 10 cm-3 ⎠ different object radii at a typical speed. The sublimation time is
⎛ 0.1 m m ⎞3 -3 obtained using the equilibrium temperature
´⎜ ⎟ cm , (25) Tice = 2.9939 » 3 K (see Section 2). We find that only very
⎝ a ⎠
large objects of radius R > 5 km could survive thermal
where rgr = 3 g cm-3 is assumed. sublimation and reach the solar system. The minimum size of
Substituting ngr into Equation (24) yields the objects that can survive is obtained by setting
tsub = ttrav, ISM , yielding
⎛ R ⎞ ⎛ 30 km s-1 ⎞
3
tevap,d 6.5 ´ 1011⎜ ⎟⎜ ⎟ ⎛ D ⎞ ⎛ 30 km s-1 ⎞
⎝ 1 km ⎠ ⎝ vobj ⎠ Rmin, ISM = 5.4 ⎜ GMC ⎟ ⎜ ⎟
⎝ 5.2 kpc ⎠ ⎝ vobj ⎠
⎛ nH ⎞ ⎛ Eb ⎞
´⎜ ⎟⎜ ⎟ yr. (26) ⎛ ⎡ 1 1 ⎤⎞
⎝ 10 cm-3 ⎠ ⎝ 0.01 eV ⎠ ´ exp ⎜100 K ⎢ - ⎥ ⎟ km. (27)
⎝ ⎣ Tice 3 K ⎦⎠
The destruction by dust is less efficient than by gas due to a
lower dust mass.
4The Astrophysical Journal Letters, 899:L23 (7pp), 2020 August 20 Hoang & Loeb
5.2. Destruction on the Way from the Center of GMCs to sublimation times are shorter than the travel time of
the ISM ttrav = 0.5 au vobj = 14.42 days. The sputtering by the solar
wind is less important than thermal sublimation.
The total gas column density toward the densest GMC
amounts to extinction of AV ~ 200 (see e.g., Mathis et al.
6. Discussion
1983), which corresponds to a hydrogen column density of
NH ~ 3.74 ´ 10 23 cm-2 based on the scaling 6.1. Can H2-rich Grains form in Dense Clouds?
NH AV » (5.8 ´ 10 21 RV ) cm-2 mag with RV = 3.1
Seligman & Laughlin (2020) suggested that H2 ice objects
(Draine 2011). Assuming a mean GMC density
can form by means of accretion and coagulation of dust grains
nH = 10 4 cm-3 and a GMC radius RGMC » 12 pc, the travel
in the densest region of a GMC where the gas density is
time
nH ~ 10 5 cm-3 and temperature is Tgas ~ 3 K . Below, we
is ttrav,GMC = RGMC vobj . show that H2-rich grains cannot form in the GMC due to
» 3.91 ´ 10 5(RGMC 12 pc)(30 km s-1 vobj) yr destruction by collisional heating, preventing the formation of
Equation (22) implies a destruction time by gas collisions of H2 objects.
tevap,gas ~ 9 ´ 106 (R 1 km)(nH 10 4 cm-3) yr , which is longer At low temperatures, the accretion of H2 molecules from the
than the travel time. gas phase onto a grain core is a main process enabling the
As shown in Section 2, collisional heating is important in formation of an H2 mantle. The characteristic timescale for
GMCs because of their high density, nH 10 3 cm-3. Assum- forming an icy grain of radius a is given by
ing that a fraction η of the impinging proton’s energy is mgr 4r ice a
converted into surface heating to a temperature below Tevap , tacc = =
collisional heating raises the temperature of the surface to 1.05sH nH m H vth pa2 3.15sH nH m H vth
⎛ a ⎞⎛ nH ⎞-1⎛ Tgas ⎞1 2
⎛ hnH 1.4m H v 3 2 ⎞1 4
102 ⎜ ⎟ ⎜ 5 -3 ⎟ ⎜ ⎟
Tice = ⎜⎜
obj
⎟⎟ ⎝ 1 m m ⎠ ⎝ 10 cm ⎠ ⎝ TCMB ⎠
⎝ 4s T ⎠ ⎛ r ice ⎞
⎛ ⎞1 4 ⎛ h ⎞1 4 ⎛ vobj ⎞3 4 ´⎜ ⎟ yr, (31)
n
6.1 ⎜ 4 H -3 ⎟ ⎜ ⎟ ⎜ ⎟ K, (28) ⎝ 0.1 g cm-3 ⎠
⎝ 10 cm ⎠ ⎝ T ⎠ ⎝ 30 km s-1 ⎠
where the thermal velocity vth = (8kTgas pmH )1 2 , the factor
which implies effective cooling by evaporation (see 1.05 accounts for n (He) nH = 0.1, and the sticking coefficient
Equation (9)). sH = 1 is assumed.
To find the actual equilibrium temperature, we solve The timescale to form H2 ice from collisions between two
Equation (12) and obtain Tice » 3.26 K for nH = 10 4 cm-3, icy grains of equal sizes a and relative velocity vgg is given by
assuming h = T = 1. Substituting this typical temperature
into Equation (3) yields 1 4argr
tcoag = =
⎛ R ⎞ ngr vgg pa 2 3Md g mm H nH vgg sgr
tsub (Tice) 2.1 ´ 10 6 ⎜ ⎟
⎛
⎝ 1 km ⎠ 2.5 ´ 10 5 a ⎞ ⎛ 10 5 cm-3 ⎞
⎜ ⎟⎜ ⎟
⎛ ⎡ 1 1 ⎤⎞ sgr ⎝ 1 mm ⎠ ⎝ nH ⎠
´ exp ⎜100 K ⎢ - ⎥ ⎟ yr. (29)
⎝ ⎣ Tice 3.26 K ⎦ ⎠ ⎛ 0.1 km s-1 ⎞ ⎛ 0.01 ⎞
´⎜ ⎟⎜ ⎟ yr, (32)
The minimum size of the objects that can survive is obtained ⎝ vgg ⎠ ⎝ Md g ⎠
by setting tsub = ttrav, GMC , yielding
amounting to ~10 4 yr for a density of nH ~ 106 cm-3, a
⎛R ⎞ ⎛ 30 km s-1 ⎞ sticking coefficient, sgr = 1, and the grain number density, ngr ,
Rmin, GMC » 186 ⎜ GMC ⎟ ⎜ ⎟
is given by Equation (25). In conclusion, the timescale to form
⎝ 12 pc ⎠ ⎝ vobj ⎠
micron-sized grains by coagulation is much longer than the
⎛ ⎡ 1 1 ⎤⎞
´ exp ⎜100 K ⎢ - ⎥ ⎟ m. (30) formation time by gas accretion, in agreement with the estimate
⎝ ⎣ Tice 3.26 K ⎦ ⎠ by Seligman & Laughlin (2020).
However, Seligman & Laughlin (2020) did not consider the
We conclude that H2 objects cannot survive their journey destructive effect of icy H2 grains by collisional heating by gas.
from their GMC birthplace to the ISM if their radius is below Greenberg & de Jong (1969) noted that, at a density of
Rmin, GMC . The actual value Rmin, GMC would be larger because nH > 10 5 cm-3, collisional heating might prevent the forma-
the surface temperature is higher when objects are moving tion of H2 ice. We calculate the grain temperature heated by gas
through the core of GMCs with higher gas density. with a minimum temperature Tgas = TCMB = 2.725 K as
follows:
5.3. Destruction in the Solar System
When ‘Oumuamua entered the solar system, solar radiation ⎛ 1.05nH vth ´ pa2 ´ 2kTgas ⎞1 4
Tgr = ⎜ ⎟
heated the frontal surface to an equilibrium. We numerically ⎝ 4pa2s áQabsñT ⎠
solve Equation (12) and obtain the equilibrium temperatures
⎞1 4 ⎛ Tgas ⎞3 8 ⎛ 10-4 ⎞
1 4
Tice = 7.94 and 7.15 K at heliodistances D=0.25 and 0.5 au . ⎛ n
3.02 ⎜ 5 H -3 ⎟ ⎜ ⎟ ⎜ ⎟ K, (33)
Substituting these temperatures into Equation (4), one obtains ⎝ 10 cm ⎠ ⎝ TCMB ⎠ ⎝ áQabsñT ⎠
tsub = 3.18 and 12.72 days, assuming R = 300 m . These
5The Astrophysical Journal Letters, 899:L23 (7pp), 2020 August 20 Hoang & Loeb
6.3. Implications for H2 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 H2 ice by the CMB and found that at
redshift (1+z)=3.5, sublimation would rapidly destroy H2
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 Tice 3 K . Even when evaporative cooling is taken into
account, thermal sublimation by starlight still plays an
important role in the destruction of H2 objects. The present
CMB temperature TCMB is not high enough to rapidly sublimate
H2 ice. However, at redshifts z > 1, the CMB temperatures of
TCMB > 5 K, can rapidly destroy H2 objects of R ~ 1 km
Figure 2. Comparison of accretion timescale (red line) with the sublimation within tsub ~ 48 yr , based on Equation (4).
time (blue lines) by collisional heating for different emissivities áQabsñT , More importantly, we found that the formation of H2 objects
assuming Tgas = TCMB and the grain size of a = 1 m m . The typical emissivity cannot occur in dense GMCs because collisional heating raises
at low temperatures is áQabsñT = 10-4 . the temperature of dust grains, resulting in rapid sublimation of
H2 ice mantles. Thus, we find that large objects rich in H2 ice
are unlikely to form in dense clouds, in agreement with the
conclusions of Greenberg & de Jong (1969).
where 2kTgas is the mean kinetic energy of thermal particles Lastly, if H2 objects form via a phase transition, as proposed
colliding with the grain, and by Füglistaler & Pfenniger (2018), they must be larger than
áQabsñT » 1.1 ´ 10-4 (a 1 m m)(T 3 K)2 for silicate grains ∼5 km to survive the journey from the GMC to the solar
(Draine 2011). Gas collisions eventually lead to thermal system.
equilibrium at Tgr = Tgas.
Substituting this typical temperature and the grain size 7. Summary
a = 1 m m into Equation (3) yields We have studied the destruction of H2 ice objects during
their journey from their potential birth sites to the solar system.
⎛ a ⎞ ⎛ ⎡1 1 ⎤⎞ Our main findings are as follows.
tsub (Tgr ) 0.85 ⎜ ⎟ exp ⎜⎜100 K ⎢ - ⎥ ⎟⎟ yr, (34)
⎝ 1 mm ⎠ ⎝ ⎣ Tgr TCMB ⎦ ⎠ 1. Destruction of H2 ice-rich objects by thermal sublimation
due to starlight is important, whereas destruction by CRs
which is much shorter than the accretion time tacc given in and interstellar matter is less important.
Equation (31). The gas temperature in realistic GMCs is larger 2. The minimum radius of H2 objects is required to be
Rmin ~ 5 km for survival in the ISM from the near-
than TCMB due to CR heating, resulting in a much shorter
est GMC.
sublimation time. We therefore conclude that micron-sized H2 3. H2 objects of radius R < 200 m could be destroyed on
grains cannot form in dense GMCs due to collisional heating. the way from the GMC to the ISM due to thermal
Figure 2 shows the accretion time and sublimation time as sublimation induced by collisional heating.
functions of gas density for different emissivities áQabsñT . For 4. Formation of H2 ice-rich grains in dense GMCs is
the typical value of áQabsñ ~ 10-4 , sublimation is faster than unlikely to occur due to rapid sublimation induced by
accretion for nH > 2 ´ 10 4 cm-3. On the other hand, in lower collisional heating. This makes the formation of H2-rich
density regions, accretion is faster than sublimation, but heating objects improbable.
by CRs and interstellar radiation could still be important for
heating the gas above TCMB and increase sublimation of H2 ice. We thank the anonymous referee for a constructive report, as
well as Ed Turner, Ludmilla Kolokolova, Alex Lazarian, and
Shu-ichiro Inutsuka for useful comments. T.H. acknowledges
6.2. Implications: Could ‘Oumuamua made of H2 Ice Survive the support by the National Research Foundation of Korea
the Journey from the Birth Site to the Solar System? (NRF) grants funded by the Korea government (MSIT) through
the Mid-career Research Program (2019R1A2C1087045). A.L.
Assuming that H2 objects could somehow form in the
densest regions of GMCs, we found that sublimation by was supported in part by a grant from the Breakthrough Prize
Foundation.
collisional heating inside the GMC would destroy the objects
before their escape into the ISM. We also studied various
ORCID iDs
destruction mechanisms of H2 ice in the ISM. In particular, we
found that H2 objects are heated by the average interstellar Thiem Hoang https://orcid.org/0000-0003-2017-0982
radiation, so that they cannot survive beyond a sublimation Abraham Loeb https://orcid.org/0000-0003-4330-287X
time of tsub ~ 10 Myr for R=300 m (see Figure 1). Only H2
objects larger than 5 km could survive.
6The Astrophysical Journal Letters, 899:L23 (7pp), 2020 August 20 Hoang & Loeb
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