An Interpretation Of The Anomalously Low Mass Of Mars

The origin of the solar system is one of the basic problems in modern science. It plays an important role in understanding the whole process from the origin of the Universe to the origin of life. So far, more than 500 extrasolar planets around solar-type stars have been detected. The study on the origin of the solar system can also help us to understand the origin of these planetary systems. The earliest systematic theory to explain the origin of the solar system is the nebula theory proposed by Laplace. This theory has been successful in accounting for the orbital properties of planets, but it has its own difficulties. From late 20th century, great progress has been made in the study on the origin of the solar system. At present, the widely accepted theory is the modern solar nebula theory. According to this theory, the solar nebula is a gas disk surrounding the protosun. Planets are thought to form in such a disk through the following processes. The small-size solids in the nebula accumulate and grow to large-size ones through many complicated processes. If these solid bodies are massive enough during any of these processes, they will accrete the surrounding gas in the nebula and eventually form giant planets. The less massive ones will form terrestrial planets.The solar nebula theory provides a framework of understanding the origin of the solar system but it is still need a lot of work to solve many problems. According to observations of the solar system, the mass of Mars is only one tenth of the mass of Earth. If Mercury which is the innermost planet and Pluto which is the outermost one are excluded, the mass of Mars is far less massive than those of other planets. No widely accepted theory can give a solution to this problem. In this work, we have studied it and give a natural interpretation.In the 1970's, according to the composition of planets in the solar system, researchers developed a minimum mass solar nebula model. The approximate surface density distribution is (?), where R is the heliocentric distance. To give an interpretation of the anomalously low mass of Mars with this nebula model, other physical processes are needed to take mass out of the Mars region preferentially. It is suggested that planetesimals from the Jupiter region can enter into orbits with large eccentricity due to interaction with Jupiter. When they pass through the Mars region or asteroid belt region, they collide with planetesimals already formed there. The collision is intensive and the materials there are depleted. This leads to the low mass of Mars. Alternatively, it seems to solve this problem through studying the chaotic growth of terrestrial planet formation with N-body simulation. The results show that Mars is a leftover protoplanet without experiencing the chaotic growth. However, the simple monotonic surface density distribution of the nebula is used in these interpretations and it can not fit the mass distribution of planets in the solar system.In order to solve the problem of the anomalously low mass of Mars, we construct a new nebula model to study the evolution of the solar nebula. The results show that the surface density distribution is not monotonic and there is a minimum around Mars region. This is significantly different from the traditional model where the surface density is monotonic. The surface density in our model naturally fits the mass distribution of planets in our solar system.The appearance of minimum in the surface density distribution is caused by using the widely accepted nonuniform viscosity mechanism in our nebula model. According to the recent study of viscosity mechanism, the magnetohydrodynamic (MHD) turbulence caused by magnetorotational instability (MRI) is one of the dominant angular momentum transport mechanisms. We have considered the nonuniform (both space and time) viscosity caused by MRI. Since this mechanism is based on the interaction between nebular material and magnetic field, MRI can survive only if there is enough ionization. According to if MRI can survive, the nebula can be divided into three regions. The one where the heliocentric distance is small is the inner region of the nebula. The temperature there is high enough for thermal ionization. MRI can survive in this region and the viscosity is high. The region where the heliocentric distance is large is the outer region of the nebula. The temperature is too low for thermal ionization. But the surface density in this region is low enough for cosmic ray penetration which can give enough ionization. Thus MRI can survive in this region and the viscosity is high. The region between the inner region and outer region is the intermediate region. The temperature is not high enough for thermal ionization and the surface density is not low enough for cosmic ray ionization. So MRI can not survive in this region and the viscosity is low. During the nebula evolution, since the viscosity is difference between the inner region and intermediate region, thermal instability appears.Our numerical calculations show that there is a minimum in the surface density around Mars region. There are two kinds of minimum. One is a sustained minimum (SM) which almost does not change during the nebula evolution. The other is a temporary minimum (TM) which is at the boundary between the inner region and the intermediate region. In the inner region, the viscosity and accretion rate are high because MRI can survive. However, in the intermediate region, the viscosity and accretion rate are low. The materials at the boundary between them are rapidly depleted and a minimum appears, i.e. TM. During the nebula evolution, the TM moves back and forth around the Mars region. We point out that this is caused by thermal instability. With the movement of TM, materials in this region are continually depleted and a low surface density with SM near Mars region forms.According to the standard terrestrial planet formation model, we point out that the minimum (both SM and TM) in the surface density can interpret the anomalously low mass of Mars through three aspects. First, the low surface density in the Mars region provides low mass supply for Mars formation. The mass in this region is limited. Second, the low surface density results in low formation rate of planetesimal and then low surface density of planetesimal in Mars region. Third, the low surface density makes a protoplanet in this region tend to not gain mass during the chaotic growth, i.e. a protoplanet tends to be a leftover.