Direct Accelerated Estimation of Dark Matter
Directly Measuring Dark Matter Density with the Direct Acceleration Method.
Article by Pratyush Singh, a member of the Astronomy Club, IIT BHU.
Introduction
Since the discovery of dark matter(DM), a big challenge arose to perfectly evaluate the dark matter density distribution(ρDM) around the Milky Way(MW) halos, subhalos, and disk by observing the rotational speeds of stars, gas clouds, the gravitational lensing dilemma of bullet clusters, etc.
History
The conventional method of finding ρDM using the rotational and centripetal curves of the nearby stars(inside the galactic disc) is excessively error-prone because of many approximations in it, such as:
● It is assumed that dark matter has a spherically symmetrical distribution around the Milky Way. This assumption leads to dynamic equilibrium and neglects the actual shape of dark matter halos and the presence of dark matter subhalos, the MW galactic disc, and the dwarf satellite galaxies(the Large Magellanic Cloud, the Small Magellanic Cloud, etc).
● The determination of the rotational dynamics of the MW to calculate ρDM is indirect and inaccurate due to the non-Gaussian probability distribution of the star’s position, velocity, etc.
● While measuring the velocities of stars, understanding and estimating the underlying effects of companion planets and stars along with noise emitter gases, ions, and radiations is difficult to handle.
● Interstellar noise(due to interstellar dust, cosmic rays, etc) also adds to the error.
The Direct Acceleration Method
Due to these assumptions and approximations, ρDM of the Solar system’s neighbourhood is indefinite. Since all stars rotate around the galactic centre, they experience a centripetal acceleration(aᵣ). Aᵣ can be found using Newton’s second law by evaluating the change in velocity in a particular direction(Precision radial velocity (Rᵥ)) due to the aᵣ. Hence, aᵣ can be used to assess the net density(ρ_total) of our neighbouring region using Gauss law for gravitation(i.e., 4πGρ = −∇ · aᵣ ). So, ρDM could be precisely evaluated with sufficient information on ρ_total, ρ_disk, and the effects of satellite galaxies. This method is called the direct acceleration method of ρDM estimation. The effects of ρdisk contents should be nullified for higher accuracy by choosing the sample space of stars above(or below) the galactic plane.
Historical Use in Star and Exoplanet Systems
This method was previously used to determine the properties of multiple star and exoplanet systems. Its use was not possible earlier because, at the galactic scale, even though stars in our neighbourhood revolve with very high velocities due to tremendously large radial distances from GC, the net ar is too low. Hence, the change in RV due to aᵣ is also significantly less.
Measurement of such small stellar values requires careful calibration of the spectrograph to get significant changes in Rᵥ over decade-long observations. The ideal tool for this task is a specialized laser frequency comb, known as Astro-combs, referenced to GPS-disciplined atomic clocks. These spectrograph wavelength solutions have become trustworthy over a decade. Even measurements from multiple comb-calibrated observatories can be combined into a single data set if all observatories use the same reference clock for the Astro-combs. Also, the effect of the sky, which creates perspective acceleration due to the motion of the stars, has to be removed.
All these calibrations in some recent observatory projects, like the Gaia satellite project by ESA, designed to measure star positions, distances, and motions with unprecedented precision, were done. The first time through DR2, the data received from Gaia from 25 July 2014 to 23 May 2016, an opportunity was discovered to use the vertical velocity and number density distributions of different populations of stars that trace the gravitational potential for precisely determining the total matter density, including baryons and dark matter.
Data Analysis and Results
More than 90,000 G and K-type dwarf stars were selected from the cross-matched sample of LAMOST DR5 and Gaia DR2 for our analysis. It measured the local ρDM in a heliocentric cylinder of radius R = 150 pc and half-height z = 200 pc.
Under a Gaussian prior on the total stellar surface density, the local dark matter density inferred from Markov Chain Monte Carlo simulations is 0.0133 Msun/ pc³.
Challenges in Direct Acceleration Estimation
It is still a difficult and decade-long observation project. The main challenge is to extract the Rᵥ from v_total:
v_total (t) = v_accel (t) + v_comp (t) + v_plan (t) + v_noise (t)
where,
v_accel (t) is velocity due to radial acceleration change.
v_comp (t) is sinusoidal due to rotation about COM of the star system.
v_plan (t) is sinusoidal due to rotation about COM of planets star system.
v_noise (t) is noise in signal(already removed).
Conclusion
Direct Acceleration Estimations using Rᵥs have proved to be a pioneer in estimating dark matter distribution and measuring galactic potential due to their exact and accurate results.
Developing precise spectroscopic measurements has accelerated our knowledge of exoplanets and DM distribution around the halo and the disk!
In conclusion, the direct acceleration method of estimating dark matter density is a promising approach that overcomes the limitations of conventional methods. Researchers have made significant strides in understanding the distribution of dark matter around the Milky Way by measuring centripetal acceleration and employing precise spectroscopic tools like astrocombs. Despite the challenges posed by various velocity components, this method has provided exact and accurate results, contributing to our knowledge of both exoplanets and dark matter in the galactic halo and disk. As technology continues to advance, we can expect even more precise measurements and further insights into these intriguing cosmic phenomena.
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