Photophoresis in the circumjovian disk and its impact on the orbital configuration of the Galilean satellites

Sota Arakawa; Yuhito Shibaike

REVIEW 3 major objections 5 minor 16 references

Photophoresis in the circumjovian disk and its impact on the orbital configuration of the Galilean satellites

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper argues that photophoresis in the circumjovian disk creates a surface-density bump near Io's orbit, halting Io's inward migration and enabling the 4:2:1 resonance of the Galilean satellites.

desk verdict A plausible, clearly presented new mechanism for halting Io's migration, but the surface-density bump is assumed via a viscosity jump rather than derived from photophoresis; worth refereeing as a proof of concept. read the letter →

arxiv 1908.03128 v1 pith:NGRHWW75 submitted 2019-08-08 astro-ph.EP astro-ph.SR

Sota Arakawa , Yuhito Shibaike This is my paper · ORCID

classification astro-ph.EPastro-ph.SR

keywords photophoresiscircumjoviandiskGalileansatellitesmeanmotionresonancelightbarriermagnetorotationalinstabilitydustmigrationsatelliteformation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to solve a specific puzzle: what stopped Io's inward migration so that Europa and Ganymede could be trapped into the observed 4:2:1 resonance. The proposed answer is photophoresis, the force that radiation from young Jupiter exerts on dust grains that are warmer on their illuminated side. In the outer circumjovian disk this force is weaker than gas drag, but near a few Jupiter radii it balances drag, creating a 'light barrier' where dust accumulates instead of drifting inward. The dust-depleted inner disk ionizes more easily and therefore becomes more turbulent, and the jump in turbulence at the barrier produces a bump in gas surface density. A sympathetic reader would care because this offers a formation path for the Galilean system without requiring an anomalously large or slowly spinning young Jupiter, and it places the bump at roughly Io's current orbit.

What carries the argument

The load-bearing object is the light barrier, defined as the radius at which the outward photophoretic force on a dust grain equals the inward force of gas drag (the residual gravity from the disk's pressure support). The paper uses analytic expressions for both forces: the free-molecular photophoretic force from standard kinetic theory and the gas-drag term, both scaling as $a^3$, so the barrier location is independent of dust radius for small grains. The barrier does two jobs: it sets where dust is removed, and it fixes the radius where the disk's turbulent viscosity jumps. That viscosity jump is what actually creates the pressure maximum and surface-density bump; the paper shows in an appendix that the bump forms for any outer $\alpha$ as long as the inner $\alpha$ is about ten times larger.

What would settle it

Compute the ionization fraction and turbulent stress in a circumjovian disk with the dust abundance set by photophoresis, including turbulent diffusion of dust across the light barrier; if the resulting inner-disk $\alpha$ does not exceed the outer-disk $\alpha$ by roughly a factor of ten, the surface-density bump disappears and the proposed Io parking mechanism fails. A measurement that young Jupiter's luminosity or the disk accretion rate during satellite formation was outside the ranges considered ($L\sim 10^{-6}{-}10^{-5}\,L_\odot$, $\dot{M}\lesssim 10^{-7}\,M_J\,{\rm yr}^{-1}$) would also move the predicted barrier away from Io's orbit.

Watch

Extended reading notes

Core claim

The central discovery is that the photophoretic force in a circumjovian accretion disk can balance the inward gas drag on micron-sized dust at a radius near Io's present orbit, so the region inside that radius becomes depleted of dust. Because dust grains remove free charges, the dust-poor inner disk has a higher ionization fraction and supports stronger magnetorotational-instability-driven accretion stress; the paper models this as a jump from $\alpha = 10^{-3}$ in the outer disk to $\alpha = 10^{-2}$ in the inner disk. In a steady-state viscous disk, a change in $\alpha$ at a fixed radius changes the slope of the surface density profile, producing a local pressure maximum and a bump in $\Sigma$ at the barrier. The paper computes the barrier location for mass accretion rates $\dot{M} = 10^{-7}$, $10^{-8}$, and $10^{-9}\,M_J\,{\rm yr}^{-1}$, finding $r_{\rm lb} = 6.9\,R_J$, $6.1\,R_J$, and $4.2\,R_J$ respectively, and argues that the resulting bump halts Io's migration and lets Europa and Ganymede be captured into 2:1 resonances.

Load-bearing premise

The whole bump rests on the assumption that removing dust raises the MRI-driven viscosity of the inner disk by about an order of magnitude (from $\alpha=10^{-3}$ to $10^{-2}$); if dust depletion does not produce that viscosity contrast, no surface-density bump forms and Io's migration is not halted.

Editorial extensions

If this is right

Io's orbit becomes a natural parking radius: the light barrier sits at $6.1\,R_J$ for $\dot{M}=10^{-8}\,M_J\,{\rm yr}^{-1}$, close to Io's current $5.9\,R_J$, so no fine-tuned inner cavity is required.
The scenario avoids the slow-spin requirement of the magnetic inner-cavity model, because the bump location is set by luminosity and accretion rate, not by Jupiter's rotation period and radius.
Icy satellites survive: for $\dot{M}\lesssim 10^{-8}\,M_J\,{\rm yr}^{-1}$, the disk temperature at Ganymede's orbit falls below the water-ice sublimation temperature, unlike the silicate-sublimation bump model.
Resonance capture works: the computed type-I migration timescale is orders of magnitude longer than the critical timescale for 2:1 resonance capture from N-body simulations, so Europa and Ganymede can be trapped after Io stalls.
The mechanism is robust to the absolute value of $\alpha$; only the contrast between inner and outer viscosity matters, as verified for outer $\alpha = 10^{-3}$, $5\times10^{-4}$, and $2.5\times10^{-4}$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural next test is a self-consistent treatment of turbulent diffusion of dust across the light barrier, which could smooth the assumed sharp jump in dust abundance and opacity and possibly weaken the viscosity contrast on which the bump depends.
The same photophoretic-barrier logic would likely apply to circumplanetary disks around Saturn and giant exoplanets, predicting pressure bumps and potential satellite- or ring-formation sites at radii set by the planet's luminosity and disk accretion rate.
Because the barrier radius is independent of dust size for small grains but photophoresis weakens for larger pebbles, the mechanism predicts a dust-size sorting across the disk: fine dust is held back while cm-sized pebbles drift inward unless their aggregates have very low thermal conductivity, a signature that dust evolution calculations could test.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The genuinely new thing here is applying the photophoretic light barrier to a circumjovian disk. The analytic force balance is straightforward, and it lands at 4–7 RJ for reasonable accretion rates, close to Io. The paper also does a service by laying out concrete problems with the two prior bump mechanisms (silicate sublimation and magnetic inner cavity), and it checks the key physical assumptions in appendices: free-molecular regime, rotation, opacity, radiation pressure. That is solid, honest work.

The soft spot is exactly what the stress-test note flags. Photophoresis is shown to deplete dust in the inner region, but the surface-density bump is not a consequence of that depletion in any self-consistent sense. The bump comes from an imposed factor-of-ten jump in alpha at the light barrier, and Appendix G admits this is 'the key to generating the bump.' The dust depletion factor fd=10^-6 is also set by hand, and turbulent diffusion of dust is neglected as a 'simplicity' choice. That last point matters because diffusion would smooth the very gradient that produces the jump. The authors acknowledge these limitations, which is good, but they leave the central mechanism as a plausible hypothesis rather than a demonstrated result.

I want to be fair: the light-barrier location is an independent calculation, and the force-ratio result is not sensitive to the alpha jump. The paper's own sensitivity test (Appendix G) shows the bump forms for a range of alpha values as long as the inner region is more turbulent. So the criticism is not that the calculation is wrong; it is that the causal chain is incomplete. The missing piece is a microphysical argument connecting dust depletion to the ionization fraction and MRI stress. Without that, the abstract's claim that photophoresis 'could be the cause' of the bump overstates what is shown.

Who is this for? Anyone working on satellite formation or circumplanetary disk evolution. It gives a concrete, observable-anchored suggestion for where a bump might form, and it lays out a testable path—compute the ionization and MRI stress with and without dust depletion, and include turbulent diffusion. The paper deserves a serious referee, and it is citable as a proposed mechanism, even if it is not established. I would send it to review and ask for the viscosity jump to be justified or at least framed as an explicit assumption whose failure would kill the mechanism.

Referee Report

3 major / 5 minor

Summary. The paper argues that photophoresis in the circumjovian disk, driven by irradiation from young Jupiter, creates a "light barrier" where the photophoretic force balances gas drag, preventing µm-sized dust from drifting into the inner disk. The resulting dust-poor inner region is assumed to have higher ionization and therefore larger MRI-driven viscosity (α = 10^-2 versus 10^-3), producing a local maximum in surface density that can halt the inward migration of Io and enable 4:2:1 resonance capture of Europa and Ganymede. The authors compute the light barrier location for a steady-state α-disk model and show it is near Io's orbit for Mdot = 10^-8 to 10^-7 MJ/yr.

Significance. The proposed mechanism is novel, combining photophoresis with MRI-driven viscosity to explain the surface density bump invoked in satellite formation models. The force-balance calculation is straightforward and carefully checked against free-molecular, opacity, rotation, and particle-size assumptions in the appendices. The paper is honest in stating the limitations of the opacity and viscosity treatments. The key weakness is that the bump itself is not a self-consistent outcome of photophoresis: it arises from an assumed order-of-magnitude jump in α. If that jump is justified by future microphysical modeling, the scenario would be a valuable complement to the sublimation and magnetic-cavity mechanisms; in its present form, the paper is better read as a proof-of-concept scenario than as a demonstrated causal chain.

major comments (3)

[Section 2.2 and Appendix G] The surface-density bump is generated by the assumed factor-of-10 jump in α at the light barrier, not by a self-consistently computed feedback between photophoretic dust depletion and MRI turbulence. In Section 2.2, α = 10^-3 (outer region) and α = 10^-2 (inner region) are imposed by hand, and Appendix G states explicitly that "the increase in α at the light barrier is the key to generating the bump." No calculation connects the assumed dust depletion fd = 10^-6 to the ionization fraction or to the actual MRI stress. Therefore the abstract's claim that photophoresis "could be the cause of the bump" is not directly supported: photophoresis is shown to create a dust-poor region, but the bump is manufactured by the assumed viscosity contrast. The authors should either derive the α jump from a microphysical ionization model or revise the claim to state that the bump forms if dust depletion raises α by an order of magnitude.
[Section 2.2] The sharp boundary in dust abundance, fd = 0.1 outside and fd = 10^-6 inside, is assumed "for simplicity" with no treatment of turbulent diffusion. This sharp boundary is exactly the feature that produces the bump. If turbulent diffusion smooths the dust gradient, the ionization fraction and hence α would vary smoothly over a finite radial width, potentially eliminating the pressure maximum and the migration trap. The paper acknowledges that diffusion may be important but does not quantify the diffusion timescale or assess the robustness of the bump to finite mixing. Since the bump is the central result, a quantitative estimate of the mixing effect (or a model with a finite transition width) is needed.
[Section 3.1] For the case Mdot = 10^-9 MJ/yr, the condition min{(FPh/FD)_n, (FPh/FD)_p} = 1 is satisfied at both r = 4.2 RJ and r = 10.9 RJ, and the paper speculates that the true light barrier lies between these radii. Because a central conclusion is that the bump is located near the current orbit of Io (5.9 RJ), the ambiguity in the barrier location should be resolved or explicitly discussed. In particular, the manuscript should clarify which of the two crossings acts as the barrier to inward-drifting dust from the outer disk, and why the inner crossing is physically relevant for the surface-density structure.

minor comments (5)

[Section 2.1] The density of dust particles is given as ρp = 2 g cm^-2; the units should be g cm^-3.
[Figure 2 / Section 3.1] For the Mdot = 10^-9 case, the double crossing of FPh/FD = 1 is not visible in the printed figure at the resolution provided; a zoom or explicit mark of the two crossing radii would help the reader follow the discussion.
[Appendix F] The analytical fit for the Planck mean gas opacity, Eq. (F.1), should specify the pressure range and temperature range over which it is valid, since Figure F.1 shows pressure dependence but the text states the dependence is small.
[Section 3.2 / Figure 4] The magnitude of the surface-density bump (fractional increase in Σ at the light barrier) is not stated; reporting this number would help evaluate whether the bump is strong enough to halt migration of an Io-mass satellite.
[Appendix I] Equation (I.2) evaluates the migration timescale at r = 9 RJ, whereas the innermost satellite is located at r = 5.9 RJ; the choice of radius should be justified, or the evaluation should be repeated at the relevant orbital radius.

Circularity Check

1 steps flagged · score 6.0 of 10

The surface-density bump is produced by an assumed factor-of-10 viscosity jump, not by a calculated consequence of photophoretic dust depletion; the central prediction is partly built into the input.

fitted input called prediction [Section 2.2, Eq. (3), and Appendix G; bump result used in Section 3.2]
"Thus, we assumed α = 10−3 for the outer region and α = 10−2 for the inner region. We note that the choice of absolute values of α does not change the results drastically; the increase in α at the light barrier is the key to generating the bump in the surface density distribution (see Appendix G)."

The bump is not a self-consistently calculated effect of photophoresis. In the steady-state solution Eq. (3) with ν = α c_s²/Ω_K, the surface density scales as Σ ∝ 1/ν at fixed radius, so imposing α_inner = 10 α_outer at r_lb directly produces a factor-of-10 jump in Σ and a pressure maximum at that radius. The paper asserts, but does not calculate, that dust depletion raises the ionization fraction and MRI stress by this amount; the cited 'could be larger' is not quantified. Appendix G confirms that the bump exists only because the inner turbulence is assumed stronger. Hence the abstract's claim that photophoresis 'could be the cause of the bump' reduces to the hand-imposed viscosity contrast; the photophoretic force only supplies the location of the discontinuity.

full rationale

The light-barrier location itself is derived from an independent force balance (FPh = FD) and is not circular: Appendix G shows that rlb depends only weakly on α, and the photophoresis formulas are taken from external laboratory/kinetic theory work. However, the central new result claimed in the abstract—the surface-density bump that halts Io's migration—is not a computed consequence of the photophoretic dust profile. The steady-state solution Eq. (3) directly converts the assumed α discontinuity (10^-3 outer, 10^-2 inner) into a Σ jump/bump at r_lb. The paper does not model the ionization fraction, electron density, or MRI stress as functions of dust abundance; it simply assumes the factor-of-10 viscosity contrast. Appendix G explicitly states that this α increase is 'the key to generating the bump.' Therefore, the existence and magnitude of the predicted bump reduce by construction to an input assumption, giving partial circularity. This is not a case of load-bearing self-citation or an imported uniqueness theorem; the same flaw would remain if all references were external. Score 6 reflects that one predicted feature is built into the input while the barrier-location part retains independent content.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The model's key outputs, especially the surface-density bump, rest on assumed jumps in dust abundance (0.1 to 1e-6) and viscosity (1e-3 to 1e-2) at the light barrier. The location of the barrier is derived from force balance with parameters taken from laboratory and evolutionary calculations, but the existence and shape of the bump are not independently derived.

free parameters (4)

fd_outer = 0.1
Dust abundance scaling factor in the outer disk. Set to one-tenth solar metallicity by hand; the paper states this value is assumed because dust settles toward the midplane.
fd_inner = 1e-6
Dust abundance in the dust-depleted inner region. Adopted as five orders of magnitude below the outer value; the transition is assumed sharp.
alpha_outer = 1e-3
Turbulent viscosity parameter in the MRI-inactive outer disk. Chosen to represent hydrodynamic instabilities.
alpha_inner = 1e-2
Turbulent viscosity parameter in the dusty-poor inner region. Assumed one order of magnitude higher because of MRI activity; this jump generates the surface-density bump.

assumptions (5)

domain assumption The circumjovian disk is a steady-state viscous accretion disk with constant mass accretion rate and gas supply at rb = 27 RJ.
Equation (3) for the surface density is a steady-state solution; if the disk is not steady, the density profile and the inferred barrier location change.
ad hoc to paper Dust abundance changes discontinuously from fd = 0.1 to fd = 1e-6 at the light barrier, with no turbulent diffusion of dust.
Section 2.2 states this sharp-boundary assumption; the size of the depletion step is not derived from the photophoresis model, and diffusion is neglected.
ad hoc to paper The effective viscosity is α = 1e-2 in the dust-poor inner region and α = 1e-3 in the outer region.
Assumed in Section 2.2; Appendix G calls the α increase 'the key to generating the bump', so this assumption largely creates the central result.
domain assumption The abundance of nm and sub-µm dust is negligibly small, so dust opacity and ionization are governed by µm-sized grains.
Section 2.2; if small grains persist, the ionization fraction and the MRI-driven viscosity jump would be smaller.
domain assumption The radiative intensity from the planet is I = L/(4πr^2) at the light barrier, and the photophoretic force formula, Eq. (1), applies.
Used in Section 3.1 to compute the force ratio; the point-source dilution may not hold across the optically thick/transitional region.

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Cite this review

Pith. "Pith review of Photophoresis in the circumjovian disk and its impact on the orbital configuration of the Galilean satellites." pith.science (2026). https://pith.science/paper/NGRHWW75

@misc{pith2026190803128,
  author       = {Pith},
  title        = {Pith review of: Photophoresis in the circumjovian disk and its impact on the orbital configuration of the Galilean satellites},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NGRHWW75}},
  note         = {Machine review of arXiv:1908.03128}
}

read the original abstract

Jupiter has four large regular satellites called the Galilean satellites: Io, Europa, Ganymede, and Callisto. The inner three of the Galilean satellites orbit in a 4:2:1 mean motion resonance; therefore their orbital configuration may originate from the stopping of the migration of Io near the bump in the surface density distribution and following resonant trapping of Europa and Ganymede. The formation mechanism of the bump near the orbit of the innermost satellite, Io, is not yet understood, however. Here, we show that photophoresis in the circumjovian disk could be the cause of the bump, using analytic calculations of steady-state accretion disks. We propose that photophoresis in the circumjovian disk could stop the inward migration of dust particles near the orbit of Io. The resulting dust depleted inner region would have a higher ionization fraction, and thus admit increased magnetorotational-instability-driven accretion stress than the outer region. The increase of the accretion stress at the photophoretic dust barrier would form a bump in the surface density distribution, halting the migration of Io.

Figures

Figures reproduced from arXiv: 1908.03128 by the authors.

**Figure 1.** Schematic of the circumplanetary disk with a dust-poor inner region formed by photophoresis. Both the pressure maximum and the bump in the surface density distribution are at the light barrier. comet 67P/Churyumov-Gerasimenko (e.g., Bentley et al. 2016) and the estimation of the radius of constituent particles called monomers in the protoplanetary disk around the young protostar HL Tau (e.g., Okuzumi et al. 2016). … view at source ↗

**Figure 2.** The force ratio FPh/FD under the assumption that I = L/(4πr 2 ). The solid lines correspond to the force ratio calculated from the normal model (fd = 10−1 and α = 10−3 ), and the dashed lines are the dustpoor model (fd = 10−6 and α = 10−2 ). The vertical lines represent the location of the light barrier. The line colors represent the mass accretion rate (M˙ = 10−7MJ yr−1 for blue, M˙ = 10−8MJ yr−1 for pink, and M˙ … view at source ↗

**Figure 4.** shows the surface density distribution. We found that the bump in the surface density distribution is formed at the light barrier when the mass accretion rate is lower than 10−7MJ yr−1 . The migration direction and speed depend on the mass of the satellite and the disk structure (e.g., Tanaka et al. 2002; Paardekooper et al. 2011; Romanova et al. 2019). Fujii et al. (2017) found that the innermost satellite is stop… view at source ↗

Figures from the paper (1 more)

**Figure 5.** Figure 5: The temperature distribution of the disk. The solid lines correspond to the temperature T calculated from the normal model, and the dashed lines are the dust-poor model. We note, however, that the disk temperature depends on the assumed opacity (e.g., Canup & Ward 200…

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Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages

[1]

1976, Progress of The oretical Physics, 56, 1756 Arakawa, S., Tanaka, H., Kataoka, A., & Nakamoto, T

Adachi, I., Hayashi, C., & Nakazawa, K. 1976, Progress of The oretical Physics, 56, 1756 Arakawa, S., Tanaka, H., Kataoka, A., & Nakamoto, T. 2017, A& A, 608, L7 Arakawa, S., Tatsuuma, M., Sakatani, N., & Nakamoto, T. 2019 , Icarus, 324, 8 Balbus, S. A. & Hawley, J. F. 1991, ApJ, 376, 214 Batygin, K. 2018, AJ, 155, 178 Bell, K. R. & Lin, D. N. C. 1994, Ap...

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[2]

2013), Msat is the mass of the satellite, and Rsat is the radius of the satellite

7 × 1010 erg g−1 is the latent heat of sublimation of H2O ice (Tanaka et al. 2013), Msat is the mass of the satellite, and Rsat is the radius of the satellite. Therefore, the evaporation timescale is shorter than the dissipation timescale of the c ircum- planetary disk (a few Myr). Moreover, the evaporation times cale is proportional to the radius Rsat an...

work page 2013
[3]

Here, we compare the photophoretic force FPh and the radiation force Frad

00 × 1010 cm s −1 is the speed of light. Here, we compare the photophoretic force FPh and the radiation force Frad. The force ratio of the radiation force to the photophoretic f orce is Frad FPh ≃ 6kthT cap ≃ 6 × 10−2 ( T 300 K ) ( a 3 µm ) −1( p 102 dyn cm−2 ) −1 . (C.2) Then, we found that the radiation force is negligibly weaker than the photophoretic ...

work page 2012
[4]

Although the current magnetic ﬁeld of Jupiter is 7.8 G, according to the observations from the Juno spacecraf t (Bolton et al

2RJ ( B 150 G ) 4/ 7( ˙M 10−8MJ yr−1 ) −2/ 7 , (B.1) where µ∼ BR3 is the dipole moment of the planet, B is the surface magnetic ﬁeld of the planet, and R = RJ is the plan- etary radius. Although the current magnetic ﬁeld of Jupiter is 7.8 G, according to the observations from the Juno spacecraf t (Bolton et al. 2017; Connerney et al. 2017), young Jupiter ...

work page 2017
[5]

submitted)

9 RJ), the orbital conﬁguration of the Galilean satellites can be r epro- duced (Ogihara & Ida 2012, Shibaike et al. submitted). If the planetary magnetic ﬁeld can be coupled e ﬀectively to the inner region of a circumplanetary accretion disk, then the disk co uld be disrupted at the radius rin (e.g., Königl 1991): rin = ( µ4 2GM ˙M2 ) 1/ 7 ≃

work page 2012
[6]

However, there is another requirement to make an inner cav- ity in a steady-state disk

9RJ could be achieved if the ionization degree of the circumjovian disk is high enough, and the plane - tary magnetic ﬁeld is coupled to the disk. However, there is another requirement to make an inner cav- ity in a steady-state disk. To maintain its steady-state acc retion, the corotation radius rco should not be smaller than the radius of the inner cavi...

work page 1991
[7]

3RJ ( 2π/ωspin 36 hours ) 2/ 3 , (B.2) where ωspin is the angular velocity of the planetary spin. The rotation period of current Jupiter is 10 h; thus, the angular ve- locity of young Jupiter should have been about four times low er than that of current Jupiter if the inner cavity were created by the magnetic coupling between young Jupiter and the circumj...

work page 2010
[8]

(B.3) Then, the planetary radius of young Jupiter would be as large as twice that of current Jupiter if we assumed conservation o f spin angular momentum

21MR2ωspin. (B.3) Then, the planetary radius of young Jupiter would be as large as twice that of current Jupiter if we assumed conservation o f spin angular momentum. Evolutionary calculations of the pl ane- tary interior demonstrated, however, that the planetary ra dius of young Jupiter should have been about 1.5 times the current ra - dius at 1 Myr afte...

work page 2010

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[9]

Appendix C: Radiation pressure The radiation pressure is caused by the direct momentum tran s- fer of photons

25RJ); however, subsequent N-body sim- ulations by Ogihara & Ida (2012) revealed that the positions of the cavity and the innermost satellite must have been the sam e. Appendix C: Radiation pressure The radiation pressure is caused by the direct momentum tran s- fer of photons...

2012
[10]

In contrast to FPh, the residual gravity caused by gas drag FD is independent of a/ lm (Weidenschilling 1977): FD = − 4πa3 3 ρp ρg dp dr

5 ( lm a ) 2 , (D.3) and FPh decreases with increasing of a. In contrast to FPh, the residual gravity caused by gas drag FD is independent of a/ lm (Weidenschilling 1977): FD = − 4πa3 3 ρp ρg dp dr . (D.4) Therefore, FPh/ FD is independent of a for the case of a < lm, while FP...

1977
[11]

(E.1) The heat conduction timescale within a dust particle, τcond, is (Krauss & Wurm 2005; Loesche & Wurm

4 × 10−2 ( a 3 µm ) 5/ 2( T 300 K ) −1/ 2 s. (E.1) The heat conduction timescale within a dust particle, τcond, is (Krauss & Wurm 2005; Loesche & Wurm

2005
[12]

0 × 10−5 ( a 3 µm ) 2 s, (E.2) 10-5 10-4 10-3 10-2 10-1 100 101 102 102 103 κP, g [cm2 g-1] Temperature T [K] p = 100 dyn cm-2 p = 102 dyn cm-2 p = 104 dyn cm-2 p = 106 dyn cm-2 fitting 10-5 10-4 10-3 10-2 10-1 100 101 102 102 103 Fig. F .1. The Planck mean opacity of gas κP, ...

2014
[13]

The contribution of gas to the Rosseland mean opacity of a disk with solar metallicity, κR, g, is given by Freedman et al

4κR, d (Nakamoto & Nakagawa 1994). The contribution of gas to the Rosseland mean opacity of a disk with solar metallicity, κR, g, is given by Freedman et al. (2014), and we use their analytical ﬁt of κR, g for the so- lar metallicity gas. We also evaluated κP, g, using Table 3...

2014
[14]

8] −1 cm2 g−1

15(T/ 100 K)0. 8] −1 cm2 g−1. (F.1) Within the temperature range of 100–2000 K, the pressure de- pendence of κP, g is small. Thus, we assume κP, g is only the func- tion of the temperature (see Figure F.1). We note that the dominant contributions to the Rosseland mean opacity ...

2000
[15]

Figure G.2 shows the surface density distribution of the dis k for various viscosity parameters

9RJ by choosing appropriate val- ues of the luminosity L and mass accretion rate ˙M. Figure G.2 shows the surface density distribution of the dis k for various viscosity parameters. We conﬁrmed that a bump in the surface density distribution forms at the light barrier in all c...

2013
[16]

The migration timescale τmig is given by (e.g., Paardekooper et al

9 × 1025 g is the mass of Io and Minner is the mass of the inner satellite. The migration timescale τmig is given by (e.g., Paardekooper et al. 2011; Fujii et al

2011

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

1976, Progress of The oretical Physics, 56, 1756 Arakawa, S., Tanaka, H., Kataoka, A., & Nakamoto, T

Adachi, I., Hayashi, C., & Nakazawa, K. 1976, Progress of The oretical Physics, 56, 1756 Arakawa, S., Tanaka, H., Kataoka, A., & Nakamoto, T. 2017, A& A, 608, L7 Arakawa, S., Tatsuuma, M., Sakatani, N., & Nakamoto, T. 2019 , Icarus, 324, 8 Balbus, S. A. & Hawley, J. F. 1991, ApJ, 376, 214 Batygin, K. 2018, AJ, 155, 178 Bell, K. R. & Lin, D. N. C. 1994, Ap...

work page 1976

[2] [2]

2013), Msat is the mass of the satellite, and Rsat is the radius of the satellite

7 × 1010 erg g−1 is the latent heat of sublimation of H2O ice (Tanaka et al. 2013), Msat is the mass of the satellite, and Rsat is the radius of the satellite. Therefore, the evaporation timescale is shorter than the dissipation timescale of the c ircum- planetary disk (a few Myr). Moreover, the evaporation times cale is proportional to the radius Rsat an...

work page 2013

[3] [3]

Here, we compare the photophoretic force FPh and the radiation force Frad

00 × 1010 cm s −1 is the speed of light. Here, we compare the photophoretic force FPh and the radiation force Frad. The force ratio of the radiation force to the photophoretic f orce is Frad FPh ≃ 6kthT cap ≃ 6 × 10−2 ( T 300 K ) ( a 3 µm ) −1( p 102 dyn cm−2 ) −1 . (C.2) Then, we found that the radiation force is negligibly weaker than the photophoretic ...

work page 2012

[4] [4]

Although the current magnetic ﬁeld of Jupiter is 7.8 G, according to the observations from the Juno spacecraf t (Bolton et al

2RJ ( B 150 G ) 4/ 7( ˙M 10−8MJ yr−1 ) −2/ 7 , (B.1) where µ∼ BR3 is the dipole moment of the planet, B is the surface magnetic ﬁeld of the planet, and R = RJ is the plan- etary radius. Although the current magnetic ﬁeld of Jupiter is 7.8 G, according to the observations from the Juno spacecraf t (Bolton et al. 2017; Connerney et al. 2017), young Jupiter ...

work page 2017

[5] [5]

submitted)

9 RJ), the orbital conﬁguration of the Galilean satellites can be r epro- duced (Ogihara & Ida 2012, Shibaike et al. submitted). If the planetary magnetic ﬁeld can be coupled e ﬀectively to the inner region of a circumplanetary accretion disk, then the disk co uld be disrupted at the radius rin (e.g., Königl 1991): rin = ( µ4 2GM ˙M2 ) 1/ 7 ≃

work page 2012

[6] [6]

However, there is another requirement to make an inner cav- ity in a steady-state disk

9RJ could be achieved if the ionization degree of the circumjovian disk is high enough, and the plane - tary magnetic ﬁeld is coupled to the disk. However, there is another requirement to make an inner cav- ity in a steady-state disk. To maintain its steady-state acc retion, the corotation radius rco should not be smaller than the radius of the inner cavi...

work page 1991

[7] [7]

3RJ ( 2π/ωspin 36 hours ) 2/ 3 , (B.2) where ωspin is the angular velocity of the planetary spin. The rotation period of current Jupiter is 10 h; thus, the angular ve- locity of young Jupiter should have been about four times low er than that of current Jupiter if the inner cavity were created by the magnetic coupling between young Jupiter and the circumj...

work page 2010

[8] [8]

(B.3) Then, the planetary radius of young Jupiter would be as large as twice that of current Jupiter if we assumed conservation o f spin angular momentum

21MR2ωspin. (B.3) Then, the planetary radius of young Jupiter would be as large as twice that of current Jupiter if we assumed conservation o f spin angular momentum. Evolutionary calculations of the pl ane- tary interior demonstrated, however, that the planetary ra dius of young Jupiter should have been about 1.5 times the current ra - dius at 1 Myr afte...

work page 2010