A Conjecture on the Possible Another Supermassive Black Hole in the Bar of Our Milky Way

1. Introduction

The Milky Way is with a super gigantic scale. It only can be well observed with modern technology. Therefore, the outline of the galaxy only can have been known in recent time and a long time was spent in knowing the whole image of it. First, in 1958, it was observed by Oort et al. [1] that the hydrogen clouds are in pure circular rotation about the galactic center. Second, in 1976, it was observed by Georgelin & Georgelin[2] that the galaxy is with four spiral arms. Third, it was known a line about the galactic bar by Oort & Rougoor[3,4] in 1959 and in 1960; and the bar was further confirmed by de Vaucouleurs[5] in 1964; and, it was observed that there are two red clumps in the bar, and, the bar is with peanut shape and a boxy core or “x-shaped structure”.[6,7,8,9,10] Fourth, it was observed[11] that a supermassive black hole, the Sgr A*, is at the center of the galaxy. Firth, it is currently thought that the radius of the Milky Way is almost 105 lightyears, the thickness at the center of the galaxy is almost 104 lightyears; the mass of the Milky Way is almost 5.8×10¹¹ M_sun. The observed image of the Milky Way is known as that in the Figure 1. The shape and structure of the Milky Way was generally known while the reason for the galactic bar and spiral arms is unknown.[12]

On another line, for detecting gravitational waves, the supermassive black hole binaries was generally observed and studied. [13,14,15,16,17,18,19,20,21,22,23] It was presented that there is a pair of supermassive black holes with a separation less than 1 pc at the active galactic nuclei in a single galaxy or less than 30 kpc in an interacting system. Therefore, it is not impossible that there are two supermassive black holes in one single galaxy. (We think, only a little fraction of the supermassive black hole binaries can merge.) And, abundance of “x-shaped radio” galaxies were observed.[14,15] It was pointed out that the “x-shaped radio” may be a signposts of the supermassive black hole binaries.[13]

In this work, from the peanut shape and the “x-shaped structure” or boxy core of the bar[6,7,8,9,10] and the studying about the supermassive black hole binaries,[13,14,15,16,17,18,19,20,21,22,23] we present that there should be another supermassive black hole in the bar of our milky way.

2. The Peanut Shape with the “x-Shaped Structure” or Boxy Core of the Bar: the Possible Another Supermassive Black Hole in the Bar of the Milky Way

2.1. The Possible Structure of the Bar of the Milky Way

As shown in Figure 2, if there should be two supermassive black holes Sgr A* and B, there should be a lots of stars orbit around Sgr A* while another lots of stars around the B. The peanut shape with “x-shaped structure” or boxy core is formed by the two orbits. And, other a lots of stars orbit around both A* and B which formed the bar. The orbits around a pair of supermassive black holes is analogous to the orbits of the planets around the triple stars in [24]. And, from [24] we know, the black hole B should be orbiting around A*. The shape and structure of the bar cannot be changed by the orbit of B.

The boxy core or “x-shaped structure”. The boxy core in the bar was discussed.[7,25,26,27,28] But, as shown in Figure 2, a box could be formed from the three orbits in green and red. In the box, there is no other orbit. The observed image of the boxy core is determined with the direction of observation and the distance between the two black holes. Vertical to the line A*B, the observed image is a box; while along an angle from A*B, the two green orbits appear a “x-shaped structure”, as it is noted that the orbits of stars around one black hole forms a sphere. And, the box can be longer as the distance between two black holes is longer and the “x-shaped structure” disappears.

The complicated orbits in the bar. Figure 2 shows, because of the two black holes, the orbits of the stars in the bar is very complicated. It is accordant with current observations. Now, in the bar, it was observed: 1) the pure cylindrical rotation,[32,33] 2) the orbits in different components in the bar correspondent to different distinct orbital families,[9,10] and 3) the circular velocity curve in the bar is very complicated.[29,30,31] Maybe, there is neither a single bar pattern speed, nor a single circular velocity curve in the bar, just as the orbits of the planets around the triple stars in [24].

The possible two inner bars. From that the bar is with a thickness of almost 10,000 ly, it could be concluded that the orbits around A* or B form a sphere and around both A* and B form a spheroid, rather than a disk or a plane. It is analogous to the orbits of the moons around the Jupiter or to the orbits of the S-stars around the Sgr A*.[34,35,36,37,38,39] Therefore, the stars orbiting one of the black hole could form an inner bar in the primary bar, it is noted that one inner bar was observed in [40]. Under the condition of Figure 2, there should be two inner bars in the primary bar of our galaxy, which could be correspondent with the two red clumps.[6,7,8,9,10] Therefore, the orbits in the bar is very complicated. It is very difficult to observe the speed of the orbit around one of or both of the two black holes. And, the boxy core is factually a cylinder space. But, from [24] we know, the speed of the orbit of the black hole B around the Sgr A* could be observed. And, the mass of Sgr A* can be accurately and precisely known from this speed.

Strong and weak bar. It is observed that 44% of the spiral galaxies are with a bar which is with different strength. [41] Here, we present, the strength of a bar is determined with these factors: 1) the ratio of ${\displaystyle \frac{M_B}{M_{A*}}}$, where $M_{A*}$ and $M_B$ are the mass of the black hole A* and B, $0<{\displaystyle \frac{M_B}{M_{A*}}}<1$. As ${\displaystyle \frac{M_B}{M_{A*}}}$ is larger, the bar is stronger; as ${\displaystyle \frac{M_B}{M_{A*}}}$ is less, the bar is weaker; as ${\displaystyle \frac{M_B}{M_{A*}}}$ is very little, B shall become a satellite of A*, the bar is vanished. 2) The distance d between B and A*. As d is very large, no star can orbit both A* and B. Therefore, the necessary condition to form a bar is that the orbit of the stars is affected by both of the two black holes in the same way. 3) As d is very little, no star can orbit around B while many stars orbit around both A* and B. It is a strong bar.

Multi black holes of a bar. There should be more than two supermassive black holes in a bar and a lots of stars have the orbits around all of the black holes, just as the orbits of the planets around three stars in [24].

There were many observations and different discussions about the galactic bar.[12,41,42,43,44,45] However, we think, as 44% of the observed 4378 disc galaxies are with a bar,[41] these bars should be formed by dynamics or kinematics, rather than by accidental event, such as a collision of two galaxies (galaxy-galaxy interaction or cluster-cluster interaction).

2.2. The Galactic Spiral Arms and Hill Sphere

The galactic spiral arms could be understood with the Hill sphere. For two celestial bodies, as the body with less mass is in the Hill radius of the larger one, it can have a stable orbit around the larger one. Or, the less one can move away from the larger one. Therefore, as two stars are orbiting around the Sgr A* with orbit ab and a’b’ as shown in Figure 3, if the distance between ab and a’b’ is less than the Hill radius of the two stars, the two orbits shall merge into one single orbit. Therefore, the condition for the two orbits ab and a’b’ is that the distance between two orbits is larger than the Hill radius of the two stars.

From $r=d\sqrt{m/3M}$ we know, for one same stars, the Hill radius of a star is determined with the distance d between the star and the center mass which the star is orbiting around. In the Figure 3, because the distance d for the star at point b is larger than that at a, the Hill radius of the same star at point b is larger than that at point a. As the Hill radius of the star at point b is $r=d\sqrt{m/3M}=bb\prime$, then, only the orbit with the distance L ≥ bb′ can be remained. It makes the spiral arm produced.

There were different understandings about the reason for the galactic spiral arms.[12,41,42,43,44,45,46] Here, we presented that the reason need be accordant with celestial dynamics or kinematics. As the reason is not accordant with dynamics or kinematics, the orbit should be broken off.

It is noted that, in the solar system, although the distance between the orbits of two neighboring planets is affected by the Hill sphere, the factual distance is much larger than the Hill radius of the planets. And, the factual distance of the neighboring orbits can be described with the Titius-Bode law. So, it could be concluded that the distance between two neighboring arms in a galaxy is much larger than that obtained from the Hill sphere.

2.3. The Mass and Position of the Black Hole B

From [24] we know, the black hole B is orbiting around Sgr A*. The Hill radius of B is $r=d\sqrt{m_B/3M_{SgrA*}}$. It is known that the length of the bar of our Milky Way is almost 20,000 lightyears and the largest thickness is almost 10,000 lightyears. It is noted that the thickness is determined with the orbits around both the black holes Sgr A* and B. Therefore, it is a ratio, k, to the radius of the orbits of the stars around the Sgr A* or B. In Figure 3, it could be known that the distance between Sgr A* and a’ is almost 5,000 lightyears. For the same reason, the distance between B and b’ can be approximately known. Here, for convenience, first, for the possible maximum mass of B, assuming Bb’=2,500 ly, then, the distance between B and Sgr A* should be almost d~20,000 − 5,000 − 2,500 =12,500 ly. Under the assumption k=0.6, the radius of the orbits of the stars around the black hole B should be 2500k=1500 ly, it could be concluded that $m_B~{\displaystyle \frac{1}{30}}{M}_{SgrA*}$. Second, for the possible minimum mass of B, assuming Bb’=250ly, it could be concluded that $m_B~{\displaystyle \frac{1}{\mathrm{72,000}}}{M}_{SgrA*}$. From these assumptions, according to Figure 1 and the observation about the distance between two red clumps,[6] it could be concluded that the distance between the two black holes is almost 10,000 ly and the mass of B should be in the range of 10⁻²~10⁻⁵M_SgrA∗. This is only a concluding based on the assumed condition. To accurately know the mass and position of B, the radius of the orbits around B or Sgr A* need be accurately measured. Of course, the position and mass of black hole B could be directly measured if the B had been observed.

3. Discussions

3.1. The Complicated Orbits in the Bar: The Strong Evidence for the Possible Another Supermassive Black Hole

It is generally agreed that the boxy core of the bar was observed while it is questioned whether there is the “x-shaped structure”,[7,25,26,27], even the two red clumps;[27] while several observations [6,8,9,10,25,26] think they was observed. However, it is clear, the boxy core certainly showed that the Srg A* is not at the center of the bar, under the condition that the boxy core is the core of the bar.[6,7,8,9,10,25,26,27] Therefore, as shown in Figure 2, there are two stellar clumps positioned in the different side of the boxy core, no matter what are the kinds of the stars that form the stellar clumps. So, the two red clumps [6,7,8,9,10,25,26,27] is fundamental to the structure of the bar. The “x-shaped structure” or boxy core is only formed by the orbits in the two red (stellar) clumps (or possible inner bars). And, if the Sgr A* is in one side of the boxy core, systematically, there should be another correspondent black hole in the opposite side.

As the orbits in the red clumps is noted, it shall be clearly known that the boxy core or two red clumps [6,7,8,9,10] shows the very complicated orbits in the bar. It is emphasized that the complicated orbits in the bar [9,10,29,30,31,32,33] could be the strong evidences for the possible two supermassive black holes with the two inner bars. If there is only one black hole, the orbits in the bar should be much simpler. Now, besides the assumption of two black holes with two inner bars, the complicated orbits in the bar cannot be explained with other condition.

Now, the position of the Sgr A* in the galaxy [11] and the orbits of the S-stars around it were observed.[34,35,36,37,38,39] Here, it is emphasized that, from the orbits around the Sgr A*, the structure of the bar can be certainly known. The orbits in the bar were observed from different aspects.[9,10,25,26,27,28,29,30,31,32,33,45] However, all of the orbits in the bar have not been completely known. And, it is too early to have a conclusion about the structure of the bar before the orbits in the bar have been completely known. To observe the orbits that is different from the orbits around the Sgr A*, such as the pure cylindrical rotation [6,32,33] and the orbits in different components in the bar correspondent to different orbital families,[9,10] is important to know whether there is another supermassive black hole. If the numbers of the orbits that are not around the Sgr A* is a large ratio to that around Sgr A*, it could be concluded that there is another black hole with a very large mass.

On another hand, the possible another black hole can be certainly observed from the orbits around it. It is clear that the stars in the different sides of the boxy core cannot have the same orbits around the Sgr A*. Thus, it is a problem that what is the center mass that the stars in opposite side of the boxy core orbit around? So, the boxy core strongly implies that another supermassive black hole is needed for the orbits of the stars (red clumps) in opposite side. It means that a pair of supermassive black holes is needed to make the stars in both of the sides of the boxy core can have stable orbits.

It is very important, as we select these observations: two red clumps,[6] “x-shaped structure”,[6,7,8,9,10] boxy core [7,8,9,10,22,23,24] and inner bar,[38] we can arrive at Figure 2. And, if Figure 2 should be valid, the orbits around the Sgr A* in the inner bar can appear as pure cylindrical rotation.[32,33] So, our conclusion that there should be two supermassive black holes in the bar is supported by observations.

3.2. The Supermassive Black Holes Binaries in a Galaxy

Currently, only the supermassive black hole binaries that should merge was focused on.[13,14,15,16,17,18,19,20,21,22,23] The orbits about the pair of black holes are varying. While, in our work, it is assumed that the orbits in a galaxy are stable. We think, in a galaxy, only a little fraction of the black hole binaries can merge. Therefore, the numbers of the exist pair of black holes is much larger than the observed merged ones and cannot be estimated with the merged ones.

3.3. The Newtonian Theory of Orbit and the Galactic Dynamics

It is emphasized that, in the Newtonian theory of orbit, only the black hole with the larger mass is the center of the galaxy. The black hole with the less mass is orbiting around the larger one while the larger one can be treated as that it is at rest, just analogous to the orbits in [24]. If the two black holes were orbiting around the center of mass of them as usually thought, it should result in that, relative to the stars orbiting around them, the distribution and the center of the mass of the two black holes are varying. It should further result in that the orbits of the stars around the two black holes is unstable. This case can be known as soon as a real orbit is considered. Therefore, only the larger one is at the center. It can be called the center black hole. Any other celestial bodies, including other supermassive black holes, are orbiting around the center black hole. And, the Circular Velocity Curve of the Milky Way is only determined with the mass of the center black hole.[29,30,31]

If the mass of B is larger than that of Sgr A* which is with the mass of ~4.3 × 10⁶ M_Sun,[11] from the Hill sphere, it could be concluded that B is the center black hole with the mass of ~1 × 10¹¹ M_Sun. And, the distance between the two black holes is ~10,000 ly.

In the stellar system, the stability of the orbit can be described with the Hill sphere, such as the orbits in the triple stars system in [24]. The orbit in the Hill radius is stable. We clearly know, the orbit in a galaxy is stable. The observation for the galaxy rotation curve and the recent observation about Circular Velocity Curve of the Milky Way showed that the orbits in a galaxy are stable and obey the theory of orbit, such as the Keplerian law.[29,30,31] Therefore, the Hill sphere is valid to describe the stability of the orbit in a galaxy. While, the Hill sphere is little used to study the orbit in a galaxy, although no evidence shows that the Hill sphere is invalid to the orbit in a galaxy. In this work, the Hill sphere is directly used to understand the orbits of stars around the supermassive black hole and to predict the possible supermassive black hole. It should be a necessary way to make galactic dynamics more completed.

4. Conclusion

The peanut shape with the “x-shaped structure” or boxy core of the bar very strongly implies that there should be a pair of supermassive black holes in the bar of our Milky Way. The complicated orbits in the bar [9,10,29,30,31,32,33] should be strong evidence for the implication. It is emphasized that the boxy core or “x-shaped structure” can be well understood as there should be a pair of supermassive black holes in the bar.

The two red (stellar) clumps [6,7,8,9,10,25,26,27] should be another evidence for the two possible supermassive black holes. And, it is an important line to detect the possible black hole: at the center of one of the stellar clumps, there should be a supermassive black hole. It is well known that one black hole can be certainly detected through the orbits of the stars around it; which can be distinguished from the orbits around another black hole under the condition that there are two black holes. In addition, the pair of supermassive black holes could be more easily detected in the weak bar with a large distance between the two black holes.

If there should be a pair of supermassive black holes in the bar, the origin and orbital motion of the bar and the arms, even the structure and motion of the whole galaxy, can be well understood. Therefore, to test the possible another supermassive black hole is significant to well understand our Milky Way.