Amanda Newton

Welcome to my website for the research I conducted in the CIERA REU program. I'm Amanda Newton (she/her), an undergraduate Physics and Math major at Loyola University Chicago. This summer I worked at Northwestern University's Center for Interdisciplinary Research in Astrophysics (CIERA). I worked in Dr. Fred Rasio's stellar dynamics group with Dr. Sanaea Rose on simulating BH-star collisions in a Galactic nucleus like the Milky Way's, expanding on Dr. Rose's work of BH mass change in these collisions to include BH spin change in the simulation.

Current as of 8/16/24

SMBH in Center of M87 Galaxy: Event Horizon Telescope collaboration et al. https://jpl.nasa.gov/edu/news/2019/4/19/how-scientists-captured-the-first-image-of-a-black-hole/

Abstract

Authors: Amanda Newton^1,2, Sanaea Rose¹, Fulya Kiroglu^1,, Frederic Rasio¹

Affiliations:

¹Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, IL 60201, USA,

²Loyola University Chicago, 6460 N Kenmore Ave, Chicago, IL 60660,USA

Abstract:

In galatic nuclei, black holes (BHs) collide often with stars due to the high density and velocity dispersion in this environment. In these collisions, BHs accrete mass from the stars. Because of the frequent collisions, BHs may accrete large amount of mass, and grow in mass above 500 M_⊙. This is significant because these intermediate mass black holes (IMBHs) are larger than BHs formed through star death along, so they must be formed through collisions or other physics. BHs have two characteristics, mass and spin. We study how spin changes in these collisions. We use the Volonteri et al 2005, 2013 spin model to simulate spin change in BH-star collisions in galactic nuclei. Hughes & Blandford 2003 shows it's expected that spin will tend towards zero after a number of collisions. We find he results from our simulation support this theory. This is impactful in studying stellar dynamics in galactic nuclei, as understanding the relationship between mass change and spin change in collisions can allow us to indirectly observe mass change through observed spin change. This provides insight into the formation of IMBHs through collisions in galactic nuclei.

See below for the poster for this work

A cartoon depiction of a GN. The maps symbol represents the SMBH, and the circle orbiting the SMBH is a BH, with an orbit with semi-major axis r. The density of stars in this picture represents the higher density closer to the SMBH than further.

Background

Our Galactic nucleus (GN) is comprised of a supermassive black hole (SMBH) of mass 4×10⁶ M_⊙. For our study, we consider a GN like our own, comprised of a 4×10⁶ M_⊙ SMBH, 1 M_⊙ stars, and 10 M_⊙ stellar mass black holes (BHs). Density and velocity dispersion in the GN vary with distance r from the SMBH. The density and velocity dispersion of the GN affect BH-star collisions; specifically, shortening the collision timescale, making collisions more likely in GN. When BHs and stars collide, the BH may gain mass due to accretion from the star.

In addition to BHs growing in mass because of collisions, BH spin also changes. It's useful to study BH collision spin change because BH spin can be observed indirectly using observational astronomy. Connecting spin change to mass growth allows us to more easily observe BH mass growth.

The top right image is a cartoon depiction of a BH-star collision. Image credit: Sanaea Rose sites.google.com/wellesley.edu/srose/home . As the BH gets close to the star, it gains some of the star's material depending on the BH's collision radius and grows in mass according to the material it accreted from the star. The top left image shows how the rotation of the accretion disk (prograde or retrograde) impacts ''spin up'' or ''spin down'' cases. The bottom image is a plot describing the relationship between mass growth and change in spin. It shows how final spin after a collision, χ_f , is dependent on the percent change of mass accreted in that collision. The blue line represents the initial spin χ_i . The three cases plotted here are χ_i = 0.1, 0.5, and 0.9. The two red lines represent the resulting χ_f in the case of ''spin up,'' for the top red line, and ''spin down,'' for the bottom red line.

Methods

Using the conditions for a GN stated in ''Background,'' we choose a sample of 500 BHs for this simulation with a duration of 10 billion years. We use the collision timescale to determine when collisions occur and the model for mass growth due to accretion from Rose et al 2022. We use the model of BH spin change proposed in Volonteri et al 2005, 2013. The figure to the left shows how this spin model works. Spin χ is always calculated assuming equatorial orbit. χ is a normalized dimensionless parameter with units J/M^2, and takes values -1 to 1. When the BH accretes mass in the direction of its initial spin χ_i, called prograde, this is called ''spin up,'' and the magnitude of spin increases. When the BH accretes in the opposite direction to χ_i, called retrograde, this is called ''spin down.'' The sign of the spin represents the orientation of angular with respect to an arbitrary z-axis.

We show the final spins and change in mass of 500 BHs after the described simulation for 1 billion years, each dot representing one of the black holes, and the histogram to the left represents the frequency of black holes that have final spin in each bin. We see a trend towards lower final spins for black holes with higher change in mass.

Results

We find the BHs that are more massive after successive collisions have spins closer to zero. This supports the findings from Hughes & Blandford 2003, that higher mass BHs have lower spins after a merger. Our simulation extends this theory to collisions in galactic nuclei, as well.

This result is also unsurprising given the results from the model test in Figure 2. While the choice of ''spin down'' or ''spin up'' is chosen randomly, we find that, for the same change in mass, the change in magnitude of BH spin is greater in the ''spin down'' case than ''spin up,'' using the Volonteri et al 2005, 2013 model. This can be seen in how the ''spin down'' curve is steeper than ''spin up.'' Therefore, over each collision the spin changes, but it changes with greater magnitude if the BH ''spun down.''

This can be pictured as a random walk, with each collision as a timestep, and the Volonteri et al 2005, 2013 model determining the spin step. At the final time, we then expect to see BHs that have undergone more collisions and are more massive to have spins with lesser magnitudes. Figure 3 shows this.

The spin calculations used in this simulation can be applied to any dynamical timescales, including dynamical friction, mass segregation, and two-body relaxation. Future work includes tracking BH spin in the GN in a simulation with more comprehensive timescales including additional physics.

References

1. Davies, M. B., Blackwell, R., Bailey, V. C., & Sigurdsson, S. 1998, Monthly Notices of the Royal Astronomical Society, 301, 745.

2. Event Horizon Telescope collaboration et al. https://jpl.nasa.gov/edu/news/2019/4/19/how-scientists-captured-the-first-image-of-a-black-hole/

3. Ford, E. B., Joshi, K. J., Rasio, F. A., & Zbarsky, B. 2000, The Astrophysical Journal, 528, 336.

4. Gammie, C. F., Shapiro, S. L., & McKinney, J. C. 2004, ApJ, 602, 312

5. Genzel, R., Eisenhauer, F., & Gillessen, S. 2010, Rev. Mod. Phys., 82, 3121.

6. Ghez, A. M., Salim, S., Hornstein, S. D., et al. 2005, The Astrophysical Journal, 620, 744.

7. Heger, A., Fryer, C. L., Woosley, S. E., Langer, N., & Hartmann, D. H. 2003, The Astrophysical Journal, 591, 288.

8. Hughes, S. A., & Blandford, R. D. 2003, ApJL, 585, L101

9. Li, Z., & Bambi, C. 2014, Journal of Cosmology and Astroparticle Physics, 2014, 041–041.

10. Rees, M. J. 1978, Nature, 275, 516

11. Rose, S. C., Naoz, S., Sari, R., & Linial, I. 2022, ApJL, 929, L22

12. Rose, Sanaea C., ''Home,'' Accessed 2024, sites.google.com/wellesley.edu/srose/home.

13. Stolovy, Susan et al., NASA, JPL-Caltech, SSC/Caltech, https://science.nasa.gov/resource/revealing-the-milky-ways-center/

14. Volonteri, M., Madau, P., Quataert, E., & Rees, M. J. 2005,ApJ, 620, 69

15. Volonteri, M., Sikora, M., Lasota, J.-P., & Merloni, A. 2013, The Astrophysical Journal, 775, 94.

16. ESO/WFI (Optical); MPIfR/ESO/APEX/A.Weiss et al. (Submillimetre); NASA/CXC/CfA/R.Kraft et al. (X-ray) - http://www.eso.org/public/images/eso0903a/, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=5821706

Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No. AST2149425, a Research Experiences for Undergraduates (REU) grant awarded to CIERA at Northwestern University. Any opinions, findings, and conclusions or recommendation expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This research was supported in part through the computational resources and staff contributions provided for the Quest high performance computing facility at Northwestern University which is jointly supported by the Office of the Provost, the Office for Research, and Northwestern University Information Technology.

Amanda Newton thanks CIERA for the opportunity and resources that made this research possible, and to the program mentors, Aaron Geller and Chase Kimball, whose support were invaluable. Thanks to Fred Rasio for his expertise and the opportunity to conduct research in his group, and thanks to Sanaea Rose, whose mentorship greatly contributed to the development of this work. Additional thanks to the CIERA REU 2024 cohort for their camaraderie.

Spins of Intermediate Mass Black Holes in Galactic Nuclei - Amanda Newton