Edward W. Thommes

Gas Disks to Gas Giants: Simulating the Birth of Planetary Systems

The ensemble of now more than 250 discovered planetary systems displays a wide range of masses, orbits and, in multiple systems, dynamical interactions. These represent the end point of a complex sequence of events, wherein an entire protostellar disk converts itself into a small number of planetary bodies. Here, we present self-consistent numerical simulations of this process, which produce results in agreement with some of the key trends observed in the properties of the exoplanets. Analogs to our own solar system do not appear to be common, originating from disks near the boundary between barren and (giant) planet-forming.

Modeling the Formation of Giant Planet Cores. I. Evaluating Key Processes

One of the most challenging problems we face in our understanding of planet formation is how Jupiter and Saturn could have formed before the solar nebula dispersed. The most popular model of giant planet formation is the so-called core accretion model. In this model a large planetary embryo formed first, mainly by two-body accretion. This is then followed by a period of inflow of nebular gas directly onto the growing planet. The core accretion model has an Achilles heel, namely the very first step. We have undertaken the most comprehensive study of this process to date. In this study, we numerically integrate the orbits of a number of planetary embryos embedded in a swarm of planetesimals. In these experiments, we have included a large number of physical processes that might enhance accretion. In particular, we have included (1) aerodynamic gas drag, (2) collisional damping between planetesimals, (3) enhanced embryo cross sections due to their atmospheres, (4) planetesimal fragmentation, and (5) planetesimal-driven migration. We find that the gravitational interaction between the embryos and the planetesimals leads to the wholesale redistribution of material—regions are cleared of material and gaps open near the embryos. Indeed, in 90% of our simulations without fragmentation, the region near those embryos is cleared of planetesimals before much growth can occur. Thus, the widely used assumption that the surface density distribution of planetesimals is smooth can lead to misleading results. In the remaining 10% of our simulations, the embryos undergo a burst of outward migration that significantly increases growth. On timescales of ~105 years, the outer embryo can migrate ~6 AU and grow to roughly 30 M ⊕. This represents a largely unexplored mode of core formation. We also find that the inclusion of planetesimal fragmentation tends to inhibit growth except for a narrow range of fragment migration rates.

Saving Planetary Systems: Dead Zones and Planetary Migration

The tidal interaction between a disk and a planet leading to a planets migration is widely believed to be the mechanism that explains the variety of orbital radii of extrasolar planets. A long-standing question is what stops the migration before planets plunge into their central stars. We propose a new, simple mechanism to significantly slow down planet migration and test it using a hybrid numerical integrator to simulate disk-planet interaction. Key to this scenario are the low-viscosity regions in protostellar disks known as dead zones. Low viscosity affects planetary migration in two ways. First, it allows a smaller mass planet to open a gap, and hence trade the faster type I migration (pre-gap-opening migration) for the slower type II migration (post-gap-opening migration). Second, low viscosity slows down type II migration itself, because type II migration varies directly with viscosity. We present numerical simulations of planetary migration in disks using a hybrid symplectic integrator-gas dynamics code. Assuming that the disk viscosity parameter inside the dead zone is α = 10-4 to 10-5, we find that, when a low-mass planet (1-10 M⊕) migrates from outside the dead zone, it is stopped by mass accumulation inside the dead zone. When a low-mass planet migrates from inside the dead zone, it opens a gap, slowing its migration. A massive planet like Jupiter, in contrast, opens a gap and slows down inside the dead zone, independent of its initial orbital radius. The final orbital radius of a Jupiter-mass planet depends on the dead zones viscosity. For the range of α-values noted above, this can vary from 7 AU to an orbital radius of 0.1 AU, which is characteristic of the hot Jupiters.

From Mean Motion Resonances to Scattered Planets: Producing the Solar System, Eccentric Exoplanets, and Late Heavy Bombardments

We show that interaction with a gas disk may produce young planetary systems with closely spaced orbits, stabilized by mean motion resonances between neighbors. On longer timescales, after the gas is gone, interaction with a remnant planetesimal disk tends to pull these configurations apart, eventually inducing dynamical instability. We find that this can lead to a variety of outcomes; some cases resemble the solar system, while others end up with high-eccentricity orbits reminiscent of the observed exoplanets. A similar mechanism has been previously suggested as the cause of the lunar late heavy bombardment. Thus, it may be that a large-scale dynamical instability, with more or less cataclysmic results, is an evolutionary step common to many planetary systems, including our own.

UNSTABLE PLANETARY SYSTEMS EMERGING OUT OF GAS DISKS

One of the most surprising properties of extrasolar planets is the eccentricity of their orbits, which vary from nearly circular (e ∼ 0) to highly eccentric ones (up to e ∼ 0.9). Planet-planet scattering with no gas disk has successfully reproduced the observed eccentricity distribution. However, this scenario alone cannot explain the distribution of planetary semi-major axes if giant planets form outside of ∼ 1 AU. Taking into account the effects of a residual gas disk after planet formation, we investigate the onset of dynamical instability in young planetary systems. Using a hybrid symplectic integrator + gas dynamics code, we demonstrate how planet-disk interactions along with planet-planet dynamical interactions could explain both the observed semi-major axis and eccentricity distributions of extrasolar planets.

The Growth and Migration of Jovian Planets in Evolving Protostellar Disks with Dead Zones

The growth of Jovian mass planets during migration in their protoplanetary disks is one of the most important problems that needs to be solved in light of observations of the small orbital radii of exosolar planets. Studies of the migration of planets in standard gas disk models routinely show that the migration speeds are too high to form Jovian planets, and that such migrating planetary cores generally plunge into their central stars in less than a million years. In previous work, we have shown that a poorly ionized, less viscous region in a protoplanetary disk called a dead zone slows down the migration of fixed-mass planets. In this paper, we extend our numerical calculations to include dead zone evolution along with the disk, as well as planet formation via accretion of rocky and gaseous materials. Using our symplectic integrator-gas dynamics code, we find that dead zones, even in evolving disks wherein planets grow by accretion as they migrate, still play a fundamental role in saving planetary systems. We demonstrate that Jovian planets form within 2.5 Myr for disks that are 10 times more massive than a minimum-mass solar nebula (MMSN) with an opacity reduction and without slowing down migration artificially. Our simulations indicate that protoplanetary disks with an initial mass comparable to the MMSN only produce Neptunian mass planets. We also find that planet migration does not help core accretion as much in the oligarchic planetesimal-accretion scenario as was expected in the runaway planetesimal-accretion scenario. Therefore, we expect that an opacity reduction (or some other mechanisms) is needed to solve the formation timescale problem even for migrating protoplanets, as long as we consider the oligarchic growth. We also point out a possible role of a dead zone in explaining long-lived, strongly accreting gas disks.

PLANETARY MIGRATION AND ECCENTRICITY AND INCLINATION RESONANCES IN EXTRASOLAR PLANETARY SYSTEMS

The differential migration of two planets due to planet-disk interaction can result in capture into the 2:1 eccentricity-type mean-motion resonances. Both the sequence of 2:1 eccentricity resonances that the system is driven through by continued migration and the possibility of a subsequent capture into the 4:2 inclination resonances are sensitive to the migration rate within the range expected for type II migration due to planet-disk interaction. If the migration rate is fast, the resonant pair can evolve into a family of 2:1 eccentricity resonances different from those found by Lee. This new family has outer orbital eccentricity e 2 0.4-0.5, asymmetric librations of both eccentricity resonance variables, and orbits that intersect if they are exactly coplanar. Although this family exists for an inner-to-outer planet mass ratio m 1/m 2 0.2, it is possible to evolve into this family by fast migration only for m 1/m 2 2. Thommes and Lissauer have found that a capture into the 4:2 inclination resonances is possible only for m 1/m 2 2. We show that this capture is also possible for m 1/m 2 2 if the migration rate is slightly slower than that adopted by Thommes and Lissauer. There is significant theoretical uncertainty in both the sign and the magnitude of the net effect of planet-disk interaction on the orbital eccentricity of a planet. If the eccentricity is damped on a timescale comparable to or shorter than the migration timescale, e 2 may not be able to reach the values needed to enter either the new 2:1 eccentricity resonances or the 4:2 inclination resonances. Thus, if future observations of extrasolar planetary systems were to reveal certain combinations of mass ratio and resonant configuration, they would place a constraint on the strength of eccentricity damping during migration, as well as on the rate of the migration itself.

Natural attack rate of influenza in unvaccinated children and adults: a meta-regression analysis

BackgroundThe natural (i.e. unvaccinated population) attack rate of an infectious disease is an important parameter required for understanding disease transmission. As such, it is an input parameter in infectious disease mathematical models. Influenza is an infectious disease that poses a major health concern worldwide and the natural attack rate of this disease is crucial in determining the effectiveness and cost-effectiveness of public health interventions and informing surveillance program design. We estimated age-stratified, strain-specific natural attack rates of laboratory-confirmed influenza in unvaccinated individuals.MethodsUtilizing an existing systematic review, we calculated the attack rates in the trial placebo arms using a random effects model and a meta-regression analysis (GSK study identifier: 117102).ResultsThis post-hoc analysis included 34 RCTs (Randomized Control Trials) contributing to 47 influenza seasons from 1970 to 2009. Meta-regression analyses showed that age and type of influenza were important covariates. The attack rates (95% CI (Confidence Interval)) in adults for all influenza, type A and type B were 3.50% (2.30%, 4.60%), 2.32% (1.47%, 3.17%) and 0.59% (0.28%, 0.91%) respectively. For children, they were 15.20% (11.40%, 18.90%), 12.27% (8.56%, 15.97%) and 5.50% (3.49%, 7.51%) respectively.ConclusionsThis analysis demonstrated that unvaccinated children have considerably higher exposure risk than adults and influenza A can cause more disease than influenza B. Moreover, a higher ratio of influenza B:A in children than adults was observed. This study provides a new, stratified and up to-date natural attack rates that can be used in influenza infectious disease models and are consistent with previous published work in the field.

RESONANCE TRAPPING IN PROTOPLANETARY DISKS. I. COPLANAR SYSTEMS

Mean-motion resonances (MMRs) are likely to play an important role both during and after the lifetime of a protostellar gas disk. We study the dynamical evolution and stability of planetary systems containing two giant planets on circular orbits near a 2:1 resonance and closer. We find that by having the outer planet migrate inward, the two planets can capture into either the 2:1, 5:3, or 3:2 MMR. We use direct numerical integrations of ~1000 systems in which the planets are initially locked into one of these resonances and allowed to evolve for up to ~107 yr. We find that the final eccentricity distribution in systems which ultimately become unstable gives a good fit to observed exoplanets. Next, we integrate ~500 two-planet systems in which the outer planet is driven to continuously migrate inward, resonantly capturing the inner planet; the systems are evolved until either instability sets in or the planets reach the star. We find that although the 5:3 resonance rapidly becomes unstable under migration, the 2:1 and 3:2 are very stable. Thus the lack of observed exoplanets in resonances closer than 2:1, if it continues to hold up, may be a primordial signature of the planet formation process.

Relative Vaccine Effectiveness of High-Dose versus Standard-Dose Influenza Vaccines among Veterans Health Administration Patients

Background We examined whether a high-dose inactivated influenza vaccine was more efficacious in preventing hospitalizations than a standard-dose vaccine in the Veterans Health Administration (VHA) senior population. Methods This study estimated the relative vaccine effectiveness (rVE) of high dose versus standard dose using a retrospective cohort of VHA patients 65 years of age or older in the 2015-2016 influenza season. To adjust for measured confounders, we matched each high-dose recipient with up to 4 standard-dose recipients vaccinated at the same location within a 2-week period and having 2 or more pre-existing medical comorbidities. We used the previous event rate ratio method (PERR), a type of difference-in-differences analysis, to adjust for unmeasured confounders. Results We evaluated 104965 standard-dose and 125776 high-dose recipients; matching decreased the population to 49091 standard-dose and 24682 high-dose recipients. The matched, PERR-adjusted rVE was 25% (95% confidence interval [CI], 2%-43%) against influenza- or pneumonia-associated hospitalization, 7% (95% CI, -2% to 14%) against all-cause hospitalization, 14% (95% CI, -8% to 32%) against influenza- or pneumonia-associated outpatient visit, 5% (95% CI, 2%-8%) against all-cause outpatient visit, and 38% (95% CI, -5% to 65%) against laboratory-confirmed influenza. Conclusions In protecting senior VHA patients against influenza- or pneumonia-associated hospitalization, a high-dose influenza vaccine is more effective than a standard-dose vaccine.