A Monte Carlo Density Distribution Model Study to Analyze Galaxy Structure, Mass Distribution, and Dark Matter Phenomena

Budiman Nasution; Ruben Cornelius  Siagian; Winsyahputra Ritonga; Lulut Alfaris; Aldi Cahya Muhammad; Arip Nurahman

doi:10.12928/irip.v6i1.8240

Authors

Budiman Nasution Medan State University https://orcid.org/0000-0003-1129-3593
Ruben Cornelius Siagian Medan State University
Winsyahputra Ritonga Medan State University https://orcid.org/0000-0003-1688-8481
Lulut Alfaris Politeknik Kelautan dan Perikanan Pangandaran https://orcid.org/0000-0002-1040-1727
Aldi Cahya Muhammad Islamic University of Technology
Arip Nurahman Indonesian Institute of Education https://orcid.org/0000-0002-6930-7903

DOI:

https://doi.org/10.12928/irip.v6i1.8240

Keywords:

Monte carlo density distribution model, Galaxy structure, Mass distribution of galaxies, Dark matter phenomenon, Mathematical model

Abstract

This research uses the Monte Carlo density distribution model to study the structure and mass distribution of galaxies and the dark matter phenomenon. Through computer simulations, the research developed a mathematical model with parameters such as rho0, rc, beta, and others, to describe the structure and mass distribution of galaxies. The results show that the model can reproduce various galaxy structures, including groups, clusters and filaments, and influence the behavior and characteristics of individual galaxies. This research provides a deeper understanding of dark matter and its impact on the evolution of the universe. It has implications for improving our understanding of dark matter and the use of Monte Carlo density distribution models to study galaxies. This study provides new insights into the evolution of galaxies and their relationship with dark matter in cosmology. Using both physics and mathematical concepts, this research helps to understand the phenomenon of dark matter and the structure of galaxies, and provides a basis for further research on dark matter and galaxy evolution.

Author Biographies

Budiman Nasution, Medan State University

Departemen of Physics, Faculty of Mathematic and Natural Science, Medan State University, Indonesia

Ruben Cornelius Siagian , Medan State University

Departemen of Physics, Faculty of Mathematics and Natural Science, Medan State University

Winsyahputra Ritonga, Medan State University

Departemen of Physics, Faculty of Mathematic and Natural Science, Medan State University, Indonesia

Lulut Alfaris, Politeknik Kelautan dan Perikanan Pangandaran

Department of Marine Technology, Politeknik Kelautan dan Perikanan Pangandaran, Indonesia

Aldi Cahya Muhammad, Islamic University of Technology

Department of Electrical and Electronics Engineering, Islamic University of Technology, Bangladesh

Arip Nurahman, Indonesian Institute of Education

Department of Physics Education, Indonesian Institute of Education, West Java, Indonesia

References

J. Billard et al., “Direct detection of dark matter—APPEC committee report,” Reports Prog. Phys., vol. 85, no. 5, p. 056201, May 2022, https://doi.org/10.1088/1361-6633/ac5754.

R. C. Siagian, L. Alfaris, and G. H. D. Sinaga, “Review for Understanding Dark Matter in The Universe as Negative Energy,” in Conference on Religion, Science and Education, 2023, pp. 679–685, [Online]. Available: https://sunankalijaga.org/prosiding/index.php/icrse/article/view/980.

R. C. Siagian, P. Pribadi, G. H. D. Sinaga, A. Nurahman, and B. Nasution, “Statistical Data Retrieval Technique in Astronomy Computational Physics,” JATISI (Jurnal Tek. Inform. dan Sist. Informasi), vol. 10, no. 1, pp. 1045–1054, Mar. 2023, https://doi.org/10.35957/jatisi.v10i1.4712.

J. Jaeckel and S. Schenk, “Challenging the Stability of Light Millicharged Dark Matter,” Phys. Rev. D, vol. 103, no. 10, p. 103523, May 2021, https://doi.org/10.1103/PhysRevD.103.103523.

L. Alfaris, R. C. Siagian, and E. P. Sumarto, “Study Review of the Speed of Light in Space-Time for STEM Student,” J. Penelit. Pendidik. IPA, vol. 9, no. 2, pp. 509–519, Feb. 2023, https://doi.org/10.29303/jppipa.v9i2.2757.

V. S. Netchitailo, “Decisive Role of Dark Matter in Cosmology,” J. High Energy Physics, Gravit. Cosmol., vol. 08, no. 01, pp. 115–142, 2022, https://doi.org/10.4236/jhepgc.2022.81009.

G. H. D. Sinaga, M. B. Panjaitan, R. C. Siagian, and K. W. A. Siahaan, Memahami Indahnya Semesta dengan Dasar Teori Kosmologi dan Astronomi Fisika Serta Sejarahnya. Bandung: Widina Bhakti Persada, 2022.

M. Jacquart, “Dark Matter and Dark Energy,” in The Routledge Companion to Philosophy of Physics, New York: Routledge, 2021, pp. 731–743.

B. Nasution, R. C. Siagian, A. Nurahman, and L. Alfaris, “Exploring the Interconnectedness of Cosmological Parameters and Observations: Insights Into the Properties and Evolution of the Universe,” Spektra J. Fis. dan Apl., vol. 8, no. 1, pp. 25–42, Apr. 2023, https://doi.org/10.21009/SPEKTRA.081.03.

R. C. Siagian et al., Pengantar Matematika Geometri Lubang Hitam. Banyumas: Wawasan Ilmu, 2023.

C. Prescod-Weinstein, “Enter the Axion: A New Fundamental Particle Could Solve A Major Puzzle in Particle Physics--and Also Explain the Nature of the Dark Matter that Permeates the Universe,” Am. Sci., vol. 109, no. 3, pp. 158–166, 2021, https://doi.org/10.1511/2021.109.3.158.

Y. A. El-Neaj et al., “AEDGE: Atomic Experiment for Dark Matter and Gravity Exploration in Space,” EPJ Quantum Technol., vol. 7, no. 1, p. 6, Dec. 2020, https://doi.org/10.1140/epjqt/s40507-020-0080-0.

R. C. Siagian, “Filsafat Fisika dalam Konteks Teori Relativitas.” 2022, [Online]. Available: https://www.researchgate.net/profile/Ruben-Siagian/publication/368106109_Philosophy_and_Historical_Physics_Theory_of_Relativity/links/6456bb48809a535021522be3/Philosophy-and-Historical-Physics-Theory-of-Relativity.pdf.

D. Baxter et al., “Recommended Conventions for Reporting Results from Direct Dark Matter Searches,” Eur. Phys. J. C, vol. 81, no. 10, p. 907, Oct. 2021, https://doi.org/10.1140/epjc/s10052-021-09655-y.

A. Amon et al., “Dark Energy Survey Year 3 results: Cosmology from cosmic shear and robustness to data calibration,” Phys. Rev. D, vol. 105, no. 2, p. 023514, Jan. 2022, https://doi.org/ 10.1103/PhysRevD.105.023514.

J. Andrade and J. Duggan, “A Bayesian Approach to Calibrate System Dynamics Models using Hamiltonian Monte Carlo,” Syst. Dyn. Rev., vol. 37, no. 4, pp. 283–309, Oct. 2021, https://doi.org/10.1002/sdr.1693.

M. Milgrom, “Does Dark Matter Really Exist?,” Sci. Am., vol. 287, no. 2, pp. 42–52, Aug. 2002, https://doi.org/10.1038/scientificamerican0802-42.

R. C. Siagian, L. Alfaris, A. C. Muhammad, U. I. Nyuswantoro, and G. T. Rancak, “The Orbital Properties of Black Holes: Exploring the Relationship between Orbital Velocity and Distance,” J. Phys. Its Appl., vol. 5, no. 2, pp. 35–42, Jun. 2023, https://doi.org/10.14710/jpa.v5i2.17860.

A. Brilianza, M. Jannah, and A. M. Hamdan, Lubang Hitam: Sebuah Pengantar Populer. Malang: Pustaka Learning Center, 2020.

R. C. Siagian, L. Alfaris, A. Nurahman, and E. P. Sumarto, “Termodinamika Lubang Hitam: Hukum Pertama dan Kedua Serta Persamaan Entropi,” J. Kumparan Fis., vol. 6, no. 1, pp. 1–10, 2023, https://doi.org/10.33369/jkf.6.1.1-10.

L. Sadeghian, F. Ferrer, and C. M. Will, “Dark-Matter Distributions Around Massive Black Holes: A General Relativistic Analysis,” Phys. Rev. D, vol. 88, no. 6, p. 063522, Sep. 2013, https://doi.org/10.1103/PhysRevD.88.063522.

S. T. Lumbangaol, Y. O. Purba, M. K. W. A. Siahaan, and R. C. Siagian, Teori Relativitas, 1st ed. Tasikmalaya: Rumah Cemerlang Indonesia, 2023.

E. A. Bender, An Introduction to Mathematical Modeling. New York: John Wiley & Sons, 1978.

Misbah et al., Persamaan Diferensial Matematika Fisika. Cipedes Tasikmalaya: Rumah Cemerlang Indonesia, 2022.

G. Bertone and D. Hooper, “History of Dark Matter,” Rev. Mod. Phys., vol. 90, no. 4, p. 045002, Oct. 2018, https://doi.org/10.1103/RevModPhys.90.045002.

S. Ghigna, B. Moore, F. Governato, G. Lake, T. Quinn, and J. Stadel, “Density Profiles and Substructure of Dark Matter Halos: Converging Results at Ultra‐High Numerical Resolution,” Astrophys. J., vol. 544, no. 2, pp. 616–628, Dec. 2000, https://doi.org/10.1086/317221.

K. C. Zekser et al., “Mass Modeling of Abell 1689 Advanced Camera for Surveys Observations with a Perturbed Navarro‐Frenk‐White Model,” Astrophys. J., vol. 640, no. 2, pp. 639–661, Apr. 2006, https://doi.org/10.1086/500285.

S. Setiawan, Gempita Tarian Kosmos. Yogyakart: Andi Offset, 1994.

A. A. Antonov, “Universes Being Invisible on Earth Outside the Portals Are Visible in Portals,” Nat. Sci., vol. 12, no. 08, pp. 569–587, 2020, https://doi.org/10.4236/ns.2020.128044.

R. Aris, Mathematical Modelling Techniques. New York: Dover Publication, 1994.

V. Gammaldi et al., “Dark Matter Search in Dwarf Irregular Galaxies with the Fermi Large Area Telescope,” Phys. Rev. D, vol. 104, no. 8, p. 083026, Oct. 2021, https://doi.org/10.1103/PhysRevD.104.083026.

E. R. Coughlin and C. J. Nixon, “On the Impact of Relativistic Gravity on the Rate of Tidal Disruption Events,” Astrophys. J., vol. 936, no. 1, p. 70, Sep. 2022, https://doi.org/10.3847/1538-4357/ac85b3.

M. Roshan and B. Mashhoon, “Characteristics of Effective Dark Matter in Nonlocal Gravity,” Astrophys. J., vol. 934, no. 1, p. 9, Jul. 2022, https://doi.org/10.3847/1538-4357/ac75d6.

Z. Prudil et al., “Milky Way Archaeology using RR Lyrae and Type II Cepheids,” Astron. Astrophys., vol. 664, p. A148, Aug. 2022, https://doi.org/10.1051/0004-6361/202142251.

H. Fan, L. Lu, J. Luo, and J. Wang, “Mass Function and Density Profile of Dark Matter Halos in Illustris-TNG,” J. Phys. Conf. Ser., vol. 2441, no. 1, p. 012026, Mar. 2023, https://doi.org/10.1088/1742-6596/2441/1/012026.

Y. Shi et al., “A Cuspy Dark Matter Halo,” Astrophys. J., vol. 909, no. 1, p. 20, Mar. 2021, https://doi.org/10.3847/1538-4357/abd777.

M. Crăciun and T. Harko, “Testing Bose–Einstein Condensate Dark Matter Models with the SPARC Galactic Rotation Curves Data,” Eur. Phys. J. C, vol. 80, no. 8, p. 735, Aug. 2020, https://doi.org/10.1140/epjc/s10052-020-8272-4.

R. García, E. Rozo, M. R. Becker, and S. More, “A Redefinition of the Halo Boundary Leads to A Simple Yet Accurate Halo Model of Large-Scale Structure,” Mon. Not. R. Astron. Soc., vol. 505, no. 1, pp. 1195–1205, Jun. 2021, https://doi.org/10.1093/mnras/stab1317.

K. Zhu, S. Lu, M. Cappellari, R. Li, S. Mao, and L. Gao, “MaNGA DynPop – I. Quality-Assessed Stellar Dynamical Modelling from Integral-Field Spectroscopy of 10K Nearby Galaxies: A Catalogue of Masses, Mass-to-light Ratios, Density Profiles, and Dark Matter,” Mon. Not. R. Astron. Soc., vol. 522, no. 4, pp. 6326–6353, May 2023, https://doi.org/10.1093/mnras/stad1299.

S. Yuan, B. Hadzhiyska, S. Bose, D. J. Eisenstein, and H. Guo, “Evidence for Galaxy Assembly Bias in BOSS CMASS Redshift-Space Galaxy Correlation Function,” Mon. Not. R. Astron. Soc., vol. 502, no. 3, pp. 3582–3598, Feb. 2021, https://doi.org/10.1093/mnras/stab235.

X. Ou, A.-C. Eilers, L. Necib, and A. Frebel, “The Dark Matter Profile of the Milky Way Inferred from Its Circular Velocity Curve,” Mar. 2023, [Online]. Available: http://arxiv.org/abs/2303.12838.

E. Papastergis, A. Cattaneo, S. Huang, R. Giovanelli, and M. P. Haynes, “A Direct Measurement of The Baryonic Mass Function of Galaxies and Implications for the Galactic Baryon Fraction,” Astrophys. J., vol. 759, no. 2, p. 138, Nov. 2012, https://doi.org/10.1088/0004-637X/759/2/138.

M. Eingorn, A. E. Yükselci, and A. Zhuk, “Effect of the Spatial Curvature of The Universe on the form of the Gravitational Potential,” Eur. Phys. J. C, vol. 79, no. 8, p. 655, Aug. 2019, https://doi.org/10.1140/epjc/s10052-019-7169-6.

R. R. Lefever, A. A. C. Sander, T. Shenar, L. G. Poniatowski, K. Dsilva, and H. Todt, “Exploring the Influence of Different Velocity Fields on Wolf–Rayet Star Spectra,” Mon. Not. R. Astron. Soc., vol. 521, no. 1, pp. 1374–1392, Mar. 2023, https://doi.org/10.1093/mnras/stad625.

C. Chang, P. Scott, T. E. Gonzalo, F. Kahlhoefer, A. Kvellestad, and M. White, “Global Fits of Simplified Models for Dark Matter with GAMBIT,” Eur. Phys. J. C, vol. 83, no. 3, p. 249, Mar. 2023, https://doi.org/10.1140/epjc/s10052-023-11399-w.

C. Wolf, K. Meisenheimer, H.-W. Rix, A. Borch, S. Dye, and M. Kleinheinrich, “The COMBO-17 Survey: Evolution of the Galaxy Luminosity Function from 25 000 Galaxies with Z,” Astron. Astrophys., vol. 401, no. 1, pp. 73–98, Apr. 2003, https://doi.org/10.1051/0004-6361:20021513.

P. R. Shapiro, I. T. Iliev, and A. C. Raga, “A Model for the Post-Collapse Equilibrium of Cosmological Structure: Truncated Isothermal Spheres from Top-Hat Density Perturbations,” Mon. Not. R. Astron. Soc., vol. 307, no. 1, pp. 203–224, Jul. 1999, https://doi.org/10.1046/j.1365-8711.1999.02609.x.

P. Gondolo and J. Silk, “Dark Matter Annihilation at the Galactic Center,” Phys. Rev. Lett., vol. 83, no. 9, pp. 1719–1722, Aug. 1999, https://doi.org/10.1103/PhysRevLett.83.1719.

A. Papapetrou, “Einstein’s Theory of Gravitation and Flat Space,” Proc. R. Irish Acad. Sect. A Math. Phys. Sci., vol. 52, pp. 11–23, 1948, [Online]. Available: https://www.jstor.org/stable/20488488.

V. Berezinsky, V. Dokuchaev, and Y. Eroshenko, “Small-Scale Clumps in the Galactic Halo and Dark Matter Annihilation,” Phys. Rev. D, vol. 68, no. 10, p. 103003, Nov. 2003, https://doi.org/10.1103/PhysRevD.68.103003.

G. Parady, D. Ory, and J. Walker, “The Overreliance on Statistical Goodness-Of-Fit and Under-Reliance on Model Validation in Discrete Choice Models: A Review of Validation Practices in the Transportation Academic Literature,” J. Choice Model., vol. 38, p. 100257, Mar. 2021, https://doi.org/10.1016/j.jocm.2020.100257.

A. Zeimbekakis, “On Misuses of the Kolmogorov–Smirnov Test for One-Sample Goodness-of-Fit,” University of Connecticut, 2022.

T. M. C. Abbott et al., “Dark Energy Survey Year 3 Results: Constraints on Extensions to ΛCDM with Weak Lensing and Galaxy Clustering,” Phys. Rev. D, vol. 107, no. 8, p. 083504, Apr. 2023, https://doi.org/10.1103/PhysRevD.107.083504.

J. Hainmueller, “Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies,” Polit. Anal., vol. 20, no. 1, pp. 25–46, Jan. 2012, https://doi.org/10.1093/pan/mpr025.

J. S. Mathis, W. Rumpl, and K. H. Nordsieck, “The Size Distribution of Interstellar Grains,” Astrophys. J., vol. 217, p. 425, Oct. 1977, https://doi.org/10.1086/155591.

S. LO, H. MA, and S. LO, “Quantifying and Reducing Uncertainty in Life Cycle Assessment Using the Bayesian Monte Carlo Method,” Sci. Total Environ., vol. 340, no. 1–3, pp. 23–33, Mar. 2005, https://doi.org/10.1016/j.scitotenv.2004.08.020.

J. A. Vrugt, C. J. F. ter Braak, M. P. Clark, J. M. Hyman, and B. A. Robinson, “Treatment of Input Uncertainty in Hydrologic Modeling: Doing Hydrology Backward with Markov Chain Monte Carlo Simulation,” Water Resour. Res., vol. 44, no. 12, pp. 1–15, Dec. 2008, https://doi.org/10.1029/2007WR006720.

S. J. Phillips et al., “Sample Selection Bias and Presence-only Distribution Models: Implications for Background and Pseudo-Absence Data,” Ecol. Appl., vol. 19, no. 1, pp. 181–197, Jan. 2009, https://doi.org/10.1890/07-2153.1.

C. Wang, Q. Duan, W. Gong, A. Ye, Z. Di, and C. Miao, “An Evaluation of Adaptive Surrogate Modeling Based Optimization with Two Benchmark Problems,” Environ. Model. Softw., vol. 60, pp. 167–179, Oct. 2014, https://doi.org/10.1016/j.envsoft.2014.05.026.

D. Abercrombie et al., “Dark Matter Benchmark Models for Early LHC Run-2 Searches: Report of the ATLAS/CMS Dark Matter Forum,” Phys. Dark Universe, vol. 27, p. 100371, Jan. 2020, https://doi.org/10.1016/j.dark.2019.100371.