Gap formation in a self-gravitating disk and the associated migration of the embedded giant planet

We present the results of our recent study on the interactions between a giant planet and a self-gravitating gas disk. We investigate how the disk's self-gravity affects the gap formation process and the migration of the giant planet. Two series of 1-D and 2-D hydrodynamic simulations are performed. We select several surface densities and focus on the gravitationally stable region. To obtain more reliable gravity torques exerted on the planet, a refined treatment of disk's gravity is adopted in the vicinity of the planet. Our results indicate that the net effect of the disk's self-gravity on the gap formation process depends on the surface density of the disk. We notice that there are two critical values, \Sigma_I and \Sigma_II. When the surface density of the disk is lower than the first one, \Sigma_0 < \Sigma_I, the effect of self-gravity suppresses the formation of a gap. When \Sigma_0 > \Sigma_I, the self-gravity of the gas tends to benefit the gap formation process and enlarge the width/depth of the gap. According to our 1-D and 2-D simulations, we estimate the first critical surface density \Sigma_I \approx 0.8MMSN. This effect increases until the surface density reaches the second critical value \Sigma_II. When \Sigma_0 > \Sigma_II, the gravitational turbulence in the disk becomes dominant and the gap formation process is suppressed again. Our 2-D simulations show that this critical surface density is around 3.5MMSN. We also study the associated orbital evolution of a giant planet. Under the effect of the disk's self-gravity, the migration rate of the giant planet increases when the disk is dominated by gravitational turbulence. We show that the migration timescale associates with the effective viscosity and can be up to 10^4 yr.Comment: 24 pages, 13 figures, accepted by RA

Twitter analysis for depression on social networks based on sentiment and stress

Detecting words that express negativity in a social media message is one step towards detecting depressive moods. To understand if a Twitter user could exhibit depression over a period of time, we applied techniques in stages to discover words that are negative in expression. Existing methods either use a single step or a data subset, whereas we applied a multi-step approach which allowed us to identify potential users and then discover the words that expressed negativity by these users. We address some Twitter specific characteristics in our research. One of which is that Twitter data can be very large, hence our desire to be able to process the data efficiently. The other is that due to its enforced character limitation, the style of writing makes interpreting and obtaining the semantic meaning of the words more challenging. Results show that the sentiment of these words can be obtained and scored efficiently as the computation on these dataset were narrowed to only these selected users. We also obtained the stress scores which correlated well with negative sentiment expressed in the content. This work shows that by first identifying users and then using methods to discover words can be a very effective technique