Planet formation with different gas depletion timescales : Comparing with observations

This paper mainly focus on the influence of N-body interaction in the later stage of planets formation, especially the gas depleted timescale. We want to interpret the distribution of eccentricity comparing with observations.

1. INTRODUCTION Ida & Lin (2004a, 2004b, 2005and 2008) use the core accretion model to reproduce the distribution of a-M of planets successfully.Due to the core accretion model, some planets growth to gas giants fast, and the interaction between planets become important to influence their final configuration.The eccentricities of planets can also be excited by gravitation via resonance.
In this paper, we mainly focus on the eccentricities of planets, as well as the influences of different gas depletion timescale.In Section 2, we will describe the protoplanetary disk model and oue main results.Finally we will make conclusions and further discussions.

DISK MODEL AND RESULTS
Here we derive a modified minimum mass solar nebular (MMSN) according to Pringle 1981: and give a gas surface density profile as following: To understand the influence of gas depletion timescale, we use a uniform distribution of log disk with a range of 5 × 10 5 ∼ 5 × 10 6 yr, which is indicated by Haisch et al. (2001).To highlight this influence, we fix some other parameters: the typical mass of a host star M * = 1M ; the gas enhancement factory f g = 1.0 = 280 g/cm −2 corresponding to the mean total gas disk mass of a Taurus-Auriga a e-mail: zhoujl@nju.edu.cnThis is an Open Access article distributed under the terms of the Creative Commons Attribution-Noncommercial License 3.0, which permits unrestricted use, distribution, and reproduction in any noncommercial medium, provided the original work is properly cited.The main results are shown as following Figure 2 give the correlation between the mean ecc of planets in each system e mean and disk .Figure 3 comparing our results and observations in statistics.
The timescale disk will influence the e mean by two ways: (1) damp the eccentricity via tidal damp; (2) excite the eccentricity via scattering.The tidal damp is effective before gas depletion.After gas depletion, there is no way to damp the eccentricity, so smaller disk lead to larger e mean .In contrast, the planets experience a sufficient migration inward.The initial embryos will be compacted spatially and then scattered with large eccentricities.This effect will enhance e maen at large disk .As seen in Figure 2 e mean is decreasing with disk but there is a slight increase when disk > 2 Myr.

Research, Science and Technology of Brown Dwarfs and Exoplanets
For the diagram of a − N, the same with observations, there is an accumulation at 0.05AU, the inner boundary of gas disk.A few small planets were scattered into 0.05 AU.Another accumulation appears near 0.2 AU, which isn't detected by observations.Due to the type I migration model we adopted in Section 2.1, i.e. the MRI effect, small planets may halt at a crit , we can evaluate a crit ∼0.2 AU.Because type I migration only affects the small planets.Most planets locate from 1 AU to 8 AU while the observation indicates a range about 1∼5 AU.Most of them are massive, and experienced type II migration.Due to the braking phase, they can't migrate too close to the star, hence they halted out of 1 AU and located at different location because of their different masses and initial locations.Some small planets, about tens of Earth's mass, appear in this range.Most of these small planets were scattered from inner region.

CONCLUSIONS AND DISCUSSION
Our results show a correlation between the mean e and disk .We also interpret observations and may guide the further observations.The accumulations around 0.2 AU are predicted in our simulations which can be verified in the future.
There are some uncertainties in our model.The migration rates as well as the boundary between type I and type II migrations are still debated.Different type I migration rate will influence the locations of planets directly.The uncertain initial conditions of embryos still affect our results.

Figure 1 .
Figure1.A sketch map of the initial conditions in our simulations, mars-size planets extend from 0.5 2.4 AU, while earth-size planets extend to 10 AU.

Figure 2 .
Figure 2. The influences of disk for e mean .e mean is decreasing with disk before disk = 2 Myr, then a slight increase.The error bars are the standard error of mean.