The story of our work starts in 2016. My advisor Prof. Ji-Lin Zhou asked Dr. Ming Yang and me to investigate observation data and pertinent literature on  planetary systems around white dwarfs. Because planet systems around white dwarfs provide keys to understanding the structure and the fate of planet systems around main sequence stars with masses less than about eight solar mass, including the Solar System. 

Two observation phenomena, dusty disks and metal pollution of single white dwarfs are thought to be associated with the accretion of remnant planetary systems, similar to asteroids in our Solar System. However, the dynamical evolution of the two phenomena are still unclear yet. The physical mechanisms causing the difference between the occurrence rates of disk-possessing white dwarfs (1%-4%) and metal-polluted ones (25%-50%) were not well understood, either. Therefore, we focused on these problems.

We consider a simplified solar system remnant as a fiducial model, which consists of a central white dwarf, an asteroid belt and a Jupiter-mass planet. Through N-body simulations, we record the flux of the asteroids dynamically falling into the Roche limit of the white dwarf. With a few simulation tests, Professor Zhou believed that the dynamically falling flux would follow a power decay with time. He explained to me the physics, “For the restricted three-body problem, the number of escaping asteroids decays with the evolution time in a power law”. Then we investigated a lot more cases by varying various parameters in a large range. Indeed, the falling flux always fits well with a power decay as expected. 

Asteroids falling into the Roche limit would be torn apart to dust due to gravitational tides and mutual collisions. In the subsequent evolution, dust will drop onto the white dwarf atmosphere mainly due to the Poynting–Robertson  drag. Based on previous works, we derived the accretion rate of PR drag in theory, which is also a power law decay of time. 

Then we want to test our model with observation data. However, I was not familiar with observation data at that time. Luckily, Dr. Si-Yi Xu of the Gemini Observatory in Hawaii visited our school in Dec. 2017. I asked her many questions on observation data. She was very nice and gave me many useful suggestions. Based on her suggestions, Dr. Ji-Wei Xie and me collected an observational sample of metal-polluted white dwarfs. Then we calculated the mass accretion rates and cooling ages of all white dwarfs in our sample. During the calculation, I also sent a few emails to Dr. Detlev Koester of Universität Kiel to ask some questions on the evolutionary models of white dwarfs and received nice replies and useful answers.

After that, Dr. Xie and me performed a uniform analysis of the sample. He told me that statistical analysis is an essential and powerful tool for scientific research, especially for astronomy. Statistics reveals the science hidden in the observation data. From the data, we found that the metal accretion rate was best fitted with a broken power law of time. Excitingly, the observational best fit is almost identical to our derived theoretical accretion rate due to the Poynting–Robertson effect at early stage and matches well with the asteroid dynamically falling rate at the late stage. The above match between observation and theory motivates us to outline an evolution scenario. The presence of dusty disk is mainly at the early stage (~ 0.1− 0.7 Gyr) of the whole process of metal pollution, which is detectable until ~8 Gyr, naturally explaining the fraction (~2–16%) of metal-polluted white dwarfs with dusty disks quantitatively. The success of this scenario also implies that the configuration of an asteroid belt with an outer gas giant might be common around stars of several solar masses.

Because this is my first work, I did not know how to answer the reviewers’ comments at the first time and sometimes I misunderstood their comments. Dr. Xie helped me a lot in the revision process. He told me this is a process to “fight” with reviewers and a precious opportunity to learn from them and upgrade myself. “Be passionful and enjoy this process”, he said to me. Now, after about two year work, our paper is published, and I feel that I have been upgrade to a higher level.