The Influence of Self Interacting Dark Matter on Galactic Formation and the Last Parsec Problem

Student: Jihao Yu
Table: MATH1705
Experimentation location: Home
Regulated Research (Form 1c): No
Project continuation (Form 7): No

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The canonical cold dark matter paradigm has been shown to have significant phenomenological flaws leading to the "core-cusp" problem. It has been noticed that allowing the dark matter to self interact resolves this problem. In this paper we explore other consequences of the Self Interacting Dark Matter (SIDM) model. In particular, we investigate the effects of self interaction on the dynamical friction force incurred upon an object traversing dark matter halos. We show that SIDM has
the added benefit of helping resolve "last parsec problem" allowing super massive black holes to go through binary inspirals within the Hubble time. This scenario can be tested by measuring SMBH inspiral rates at space based gravitational wave
detectors such as LISA.


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Research Plan:

The “Last Parsec Problem”, that Super Massive Blackholes(SMB) ceases to merge at the distance of several parsecs, may be partially solved by the assumption of Self Interacting Dark Matter(SIDM). In this research, we attempted to prove that introducing the SIDM to matter component may help to solve the problem by the dynamical friction effect during stellar merger. We referenced previous researches that discussed Self Interacting Matter, especially baryonic particles, and dynamical friction. By application the conditions for baryonic matter to SIDM and adjusting for applicable conditions, we figured out the effect of SIDM on galactic formation and whether SIDM is helpful to solve the “Last Parsec Problem”

Questions and Answers

1. What was the major objective of your project and what was your plan to achieve it? 

       a. Was that goal the result of any specific situation, experience, or problem you encountered?  

       b. Were you trying to solve a problem, answer a question, or test a hypothesis?

I conducted the research out of my interest in the Astrophysics field, and I tried to solve a problem. The research aimed at the possible solution to the Last Parsec Problem. During the merger of two Super Massive Black Holes, each of them will cease to approach when they are still a few parsecs from each other. But the increase in dynamical friction will decrease their seperation.

2. What were the major tasks you had to perform in order to complete your project?

       a. For teams, describe what each member worked on.

The major task was to understand how the conditions of baryonic particles described in citation papers could be adapted on dark matter. It took effort to research the mass limits of dark matter and understand their relationships, as what is finally shown in my results and conclusion.

3. What is new or novel about your project?

       a. Is there some aspect of your project's objective, or how you achieved it that you haven't done before?

       b. Is your project's objective, or the way you implemented it, different from anything you have seen?

       c. If you believe your work to be unique in some way, what research have you done to confirm that it is?

I started the idea that Self Interacting Dark Matter may affect the dynamical friction greatly and therefore affect the dynamical friction timescale and possibly solve the Last Parsec Problem. The research indeed made progress on solving the Last Parsec Problem and lowered the merging time a few magnitudes for different dark matter particle compositions.

4. What was the most challenging part of completing your project?

      a. What problems did you encounter, and how did you overcome them?

      b. What did you learn from overcoming these problems?

The most challenging part was choosing the specific topic and research direction of the project. Although I decided to do research on the merger of two black holes, I was limited by my math skills in linear algebra and little knowledge in general relativity. I finally found this specific topic on the Last Parsec Problem using almost an entire month, but the decision of furthering my research in this field was very meaningful to me. 

5. If you were going to do this project again, are there any things you would you do differently the next time?

Yes, I would definitely look for the special relativity effect of dark matter particles, since during the Last Parsecs of the merger process particles would be accelerated to high velocity and the possible relativity effect will start to be important.

6. Did working on this project give you any ideas for other projects? 

Absolutely. This research project informed me that unsolved problems such as the Last Parsec Problem could have a lot of factors affecting it and any other factors could be researched on in further steps. One possible direction was looking for the possible effect of the viscosity of dark matter on dynamical friction.

7. How did COVID-19 affect the completion of your project?

COVID-19 limited the accessibility for me to go to labs and libraries to collect supporting data, but fortunately, I was able to manage the research project virtual and online.