Dr. Zhicheng He (何志成)
13/03/2023
Doing a PhD is like gambling (In Chinese, these two words have the same pronunciation). The differences in experiences and outcomes between different people can be very significant, filled with randomness and chance. If lucky enough to come across a suitable topic, or have a moment of inspiration, doing a PhD can be very smooth.
Speaking for myself, my core achievement came from a moment of inspiration. Sharing this might be helpful for PhD students currently studying. One key problem I had to solve during my PhD was how to measure the recombination time scale (or gas density) of ionized gas by the accretion disk of black holes in galaxies, through the absorption lines in spectra.
At that time, there was already a "standard" method for measuring the density of absorbing gas, which is to use the line ratio between the ground state and the excited state generated by the absorption line. This line ratio is very sensitive to density, so different line ratios correspond to different densities. However, this method requires the excited state and the ground state to be very close to each other to be compared accurately, and the two lines generated at this time are also very close to each other. The absorbing gas velocity dispersion I was studying was very large (called broad absorption lines, with a velocity dispersion of more than 10,000 km/s), and the ground state and excited state were often mixed together and could not be separated. For this reason, the study of the outflow of broad absorption line gas progressed slowly in the past 20 years. I got involved in this problem when I was doing my PhD. I had a faint feeling that the current spectral survey data was so rich that there must be a way to solve this problem. Because of this problem, I wracked my brains all day long, lying in bed without thinking about food or drink, and meditating. This state lasted for half a year.
Until one day, the turning point came. One morning, I woke up and found that the light bulb outside the dormitory was flickering due to poor contact. Lying there thinking, I stared at the light bulb. If the frequency at which the bulb flashes gradually exceeds a certain frequency, people will no longer be able to see the flashing light. I suddenly realized that the problem I had been trying to solve was similar to this light bulb: if the observation interval is less than the recombination time of the gas, the change in ionization degree of the gas cannot be seen either. So I came up with a question: if there is a group of people, each of whom has a limit frequency at which they can see the light flashing, how can we control a light bulb to measure the distribution of the group's limit frequencies? Soon, I came up with an answer. Let a group of people stand in front of the light bulb. At the beginning, the frequency at which the bulb flashes is high enough that no one can see it. At this time, the proportion of people who can see the flashing light is p=0%. As the bulb flashes slower and slower, more and more people can see it, and p gradually increases. When the bulb flashes slowly enough, p=100%. Therefore, p is monotonically increasing and is a function of frequency. Obviously, the derivative of p with respect to frequency can be used to obtain the frequency distribution of the group.
So, I applied the above method in my research and immediately obtained the distribution of physical parameters of ionized gas outflows in over a thousand active galactic nuclei. There was a small incident during this process. After I finished the calculation and wrote an article, I only expressed the idea in words without providing mathematical formulas. I submitted the article to The Astrophysical Journal and after two rounds of review, the reviewers couldn't understand what I wrote and only thought that I was "ambitious". I also felt that I didn't write clearly, so I withdrew the submission and decided to calm down and reorganize my thoughts. My advisor suggested that I express the idea with mathematical equations. After much deliberation, I successfully wrote the formula.
Nowadays, this formula seems very simple, but it was not easy to figure out at the time. This work was later published in Nature Astronomy: https://www.nature.com/articles/s41550-018-0669-8. I am very satisfied with this work, and if I have to choose an epitaph in the future, I might carve this formula on it.
As a graduate student, when faced with difficulties, one should have the determination to not give up until the problem is solved and to not accept defeat easily. Under this kind of continuous brainstorming, inspiration might suddenly come up at any time. However, one should not be overly obsessed with one problem and get stuck. It is best to have at least two research projects, so if one does not work out, one can try another. After all, graduation is very important for students.