Dark Matter Reconstructions from Stellar Orbits in the Galactic Centre
Background
In the centre of our galaxy there resides a massive compact object – very likely a black hole – of about 4.3 million solar masses. We know this from different observations, such as the recent imaging of its shadow [1] or the tracing of orbiting stars and heated blobs of gas, called flares [2, 3, 4, 5].
How black holes can become so massive is one of the big unanswered questions of astrophysics. Certain theories predict that black holes can grow continuously by accreting Dark Matter – which there are good reasons to believe accounts for 85% of all matter in the universe, but the physical nature of which is still not understood [6]. These scenarios, known as adiabatic growth models, predict the Dark Matter to accumulate around a massive black hole in a density spike [7, 8]. A star orbiting a black hole through such a spike distribution will feel a continuously changing gravitational pull from the Dark Matter altering its trajectory (Figure 1). Conversely, by precisely measuring its trajectory, we can infer the distribution. Current studies applying this method to constrain the amount of possibly present Dark Matter in the innermost Galactic Centre are, however, based on assumptions made for the principal shape of its distribution [9, 10]. Hence, these results are only valid if the Dark Matter is distributed as assumed. Our project aims to eliminate this assumption.
Project overview
We take inspiration from [11], where the authors applied a machine learning approach to the spacecraft geodesy of asteroids and comets, based on so-called geodesyNets which learns accurate density models of irregular bodies using minimal prior information. Inferring the Dark Matter distribution in the Galactic Centre from stellar observations poses an analogous inversion problem. For this we design models for distributed matter which are able to attain a wide range of physically reasonable density profiles.
We then approximated continuous spherically symmetric distributions by a series of concentric mass shells. For this we picked both cusp and core distributions. With a series of analyses of mock data (on sky astrometry and line of sight velocity) we then probed the potential utility of our model to discriminate between various Dark Matter candidate models, with current and future observations of the star S2 in the Galactic Centre.
Key results
We performed a proof of principle that, given astrometric and spectroscopic observations of sufficient precision, a fit of our model is able to find an underlying ground truth Dark Matter distribution with high enough accuracy to discriminate between various physical models and compositions. Unlike with conventional models based on certain functional forms for the density distribution, no a priori assumption about the principal profile of the ground truth is made.
Using the spherical shell model our results indicate that with the measurement uncertainty of current and next generation instruments it will not be possible to achieve unbiased constraints on the radial profile of an underlying matter distribution.
We however showed that future observations can yield unbiased constraints on the overall amount of enclosed mass within apocentre, though such constraints require observations over multiple orbital periods. We interpreted these results from the theoretical perspective of secular versus nonsecular orbital dynamics, where a capturing of the former is required for good constraints on the overall amount of mass within apocentre, but in addition a capturing of the latter is required to yield unambiguous constraints on the radial profile.
References
[1] Event Horizon Telescope Collaboration 2022. First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way. ApJL 930 L12. https://doi.org/10.3847/2041-8213/ac6674
[2] The Nobel Committee for Physics 2020. Scientific Background on the Nobel Prize in Physics 2020 – Theoretical Foundation for Black Holes and the Supermassive Compact Object at the Galactic Centre. https://www.nobelprize.org/uploads/2020/10/advanced-physicsprize2020.pdf
[3] Genzel R. 2022. Nobel Lecture: A forty-year journey. Rev. Mod. Phys. 94 020501. https://doi.org/10.1103/RevModPhys.94.020501
[4] GRAVITY collaboration et al. 2018b. Detection of orbital motions near the last stable circular orbit of the massive black hole SgrA*. A&A 618 L10. https://doi.org/10.1051/0004-6361/201834294
[5]Wielgus et al. 2022. Orbital motion near Sagittarius A∗ – Constraints from polarimetric ALMA observations. A&A 665 L6. https://doi.org/10.1051/0004-6361/202244493
[6] Planck Collaboration 2014. Planck 2013 results. I. Overview of products and scientific results. A&A 571 A1. https://doi.org/10.1051/0004-6361/201321529
[7] Gondolo P. & Silk J. 1999. Dark Matter Annihilation at the Galactic Center. Phys. Rev. Lett. 83 1719. https://doi.org/10.1103/PhysRevLett.83.1719
[8] Gnedin O. Y. & Primack J. R. 2004. Dark Matter Profile in the Galactic Center. Phys. Rev. Lett. 93 061302. https://doi.org/10.1103/PhysRevLett.93.061302
[9] Heißel, G. et al. 2022. The dark mass signature in the orbit of S2. A&A 660 A13. https://doi.org/10.1051/0004-6361/202142114
[10] GRAVITY collaboration et al. 2022. Mass distribution in the Galactic Center based on interferometric astrometry of multiple stellar orbits. A&A 657 L12. https://doi.org/10.1051/0004-6361/202142465
[11]Izzo, D., Gómez, P. Geodesy of irregular small bodies via neural density fields. Commun Eng 1, 48 (2022). https://doi.org/10.1038/s44172-022-00050-3
[12] Lechien T., Heißel G., Grover J., Izzo D. 2022. https://doi.org/10.48550/arXiv.2308.09170