Elsevier

New Astronomy

Volume 84, April 2021, 101521
New Astronomy

Alternative way to detect and measure parameters of compact dark matter object as a component of a binary system

https://doi.org/10.1016/j.newast.2020.101521Get rights and content

Highlights

  • New method for detecting and measuring parameters of compact dark matter objects (CDOs).

  • CDO and a star represent a binary system.

  • The star has a planet.

  • The mass of the CDO and its distance from the star can be deduced from the parameters of the planetary orbit.

Abstract

Various compact dark matter objects (CDOs) were discussed in the literature. Typically parameters of CDOs, such as the mass and the distance, were evaluated by using the gravitational microlensing effect. However, this method has limitations. We propose an alternative method for detecting and measuring parameters of CDOs. It is based on the scenario where there is a star having one planet, such that the orbital plane of the planet does not contain the star. This indicates the presence of a gravitating object located far away at the axis directed from the star to the planetary orbital plane. If in this direction there is no visible star, this could mean that the distant gravitating object is a CDO. We derived analytical expressions for determining the unknown mass of the CDO and its unknown distance from the star based on the parameters of the planetary orbit. We believe that this method could help obtaining additional observational data on the CDOs in particular and therefore on dark matter in general.

Introduction

Various compact dark matter objects (CDOs) were discussed in the literature – see, e.g., papers by Liao et al. (2020), Horowitz et al. (2020), Dvali et al. (2020), Raidal et al. (2018), Hadjimichef et al. (2017), Errehymy et al. (2017), and references therein. Typically parameters of CDOs, such as the mass and the distance, were evaluated by using the gravitational microlensing effect. However, this method has limitations – see, e.g., papers by Hawkins (2015), Griest et al. (2013), and Gilster (2006). First, the needed alignment has to be precise and this makes detections both rare and unpredictable. Second, there are competing background events that have to be taken into account, thus making the task very difficult.

In the present paper we propose an alternative method for detecting and measuring parameters of CDOs. The method is based on the results of papers by Oks (2015) and by Kryukov & Oks (2017), as explained below.

Oks (2015) demonstrated analytically a possibility of a circumbinary planet, whose trajectory is a helix on the surface of a frustum of a cone, the axis of the cone coinciding with the interstellar axis. In this conic-helical state, the planet, while spiraling on the surface of the cone, oscillates between two end-circles which result from cutting the cone by two parallel planes perpendicular to its axis – see Fig. 1. The two stars rotate about their center of mass, but if their rotation is slow compared to the fast motion of the planet, then the conic-helical orbit of the planet would follow the rotation of the interstellar axis.

Later Kryukov and Oks (2017) showed analytically that if the planetary orbit is much closer to the star of the smaller mass and the ratio of the stellar masses is greater or of the order of 10, then the planetary orbit will remain stable for a very long time despite the rotation of the stars. In the latter case, both the distance (denoted as z) of planetary orbital plane from the star of the smaller mass and the radius (denoted as ρ) of the planetary orbit undergo only small oscillations around the corresponding equilibrium values z0 and ρ0, respectively.

In the present paper we consider the following scenario. Let us visualize a star of mass m having one planet, such that the orbital plane of the planet does not contain the star, i.e., there is a distance z0 between the star and the equilibrium position of the planetary orbital plane (the origin being chosen at the star and the positive direction of the z-axis being from the star towards the planetary orbital plane). This means that there is a relatively distant gravitating object located at the z-axis at some yet unknown distance R from the star, such that R >> z0, the object and the star forming a binary system. However, if in the positive direction of the z-axis there is no visible star, this could mean that the star companion in this binary system is a CDO.

In the next section we show that it is possible to determine analytically the unknown mass M of the CDO and its unknown distance R from the star by using the following input data: z0, ρ0, m (the star mass), and the orbital frequency F (or the orbital period T) of the planet.

Section snippets

Results

As in Oks paper (2015), we introduce the following scaled, dimensionless notations (here and below G is the gravitational constant):w=z0/R,v=ρ0/R,b=M/m,f=FR3/2/(Gm)1/2

(we remind that F is the orbital frequency of the planet). According to Oks paper (2015), the scaled, dimensionless orbital frequency f of the planet can be expressed through w and v as follows:f=(1w)1/2(w2+v2)3/4.

By expressing F = f(Gm)1/2/R3/2 (from the definition of f in Eq. (1)) and using Eq. (2) together with the

Conclusions

We suggested an alternative method for detecting and measuring parameters of CDOs. It is based on the scenario where there is a star having one planet, such that the orbital plane of the planet does not contain the star. This indicated the presence of a gravitating object located far away at the axis directed from the star to the planetary orbital plane. If in this direction there is no visible star, this could mean that the distant gravitating object is a CDO. We derived analytical expressions

Declaration of Competing Interest

The author declares that he has no conflict of interest.

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