How to tell an accreting boson star from a black hole
Radio-astronomical observations of the supermassive black-hole candidate in the galactic center will soon offer the possibility to study gravity in its strongest regimes and to test different models for these compact objects. Studies based on semi-analytic models and strong-field images of stationary plasma configurations around boson stars have stressed the difficulty to distinguish them from black holes. We here report on the first general-relativistic magnetohydrodynamic simulations of accretion onto a nonrotating boson star and employ general-relativistic radiative-transfer calculations to revisit the appearance of an accreting boson star. We find that the absence of an event horizon in a boson star leads to important differences in the dynamics of the accretion and results in both the formation of a small torus in the interior of the boson star and in the absence of an evacuated high-magnetization funnel in the polar regions. Synthetic reconstructed images considering realistic astronomical observing conditions show that differences in the appearance of the two compact object are large enough to be detectable. These results, which also apply to other horizonless compact objects, strengthen confidence in the ability to determine the presence of an event horizon via radio observations and highlight the importance of self-consistent multidimensional simulations to study the compact object at the galactic center.
pacs:04.50.Kd 04.40.Dg, 95.30.Sf, 97.10.Gz
Introduction. Observations of the galactic center have confirmed the existence of a supermassive compact object at the radio source Sgr A*. Stellar motions have constrained its mass to (Boehle et al., 2016; Ghez et al., 2008; ?; ?) and its density to (Ghez et al., 2008), favoring the hypothesis of a single massive object. Moreover, its low luminosity combined with its estimated accretion rate indicates the absence of an emitting hard surface Marrone et al. (2007); ?. All of these features are consistent with a supermassive black hole (SMBH) as those believed to exist at the centers of most galaxies.
International efforts from the Event Horizon Telescope Collaboration (EHTC) (Doeleman et al., 2008; ?; ?) and BlackHoleCam Goddi et al. (2017) aim to use very-long-baseline interferometry (VLBI) techniques in a joint effort to image the galactic center, achieving, for the first time, a resolution comparable to the size of the event horizon. The outcome of such observations is expected to be a “crescent” or ring-like feature, consisting of a dark region (the shadow of the black hole) obscuring the lensed image of a bright accretion disk (Cunningham and Bardeen, 1973; ?; ?). The shape of this shadow can be exploited either to determine the properties of the black hole or to perform tests of general relativity (Abdujabbarov et al., 2015; ?; ?; ?), a possibility assessed by Mizuno et al. (2018) in a realistic scenario for the 2017 EHTC campaign and for near-future observations.
However, because all of the expectations above rely on the assumption
that Sgr A* is a black hole, it is natural to wonder whether this
conjecture could blind us to other plausible alternatives,
thus missing out on new insights in fundamental physics.
In fact, black holes are not the only objects allowed
by general relativity which fulfill the constraints of: (1) being able to
grow to millions of solar masses, (2) being extremely compact and (3)
lacking a hard surface
Boson stars, compact objects formed from scalar fields, are a very interesting case due to the ubiquity of the latter in cosmology (Linde, 1982; ?; Preskill et al., 1983; ?; ?), string theory (Arvanitaki et al., 2010) and extensions to general relativity such as scalar-tensor theories (Fujii and ichi Maeda, 2003). Several authors have explored the possibility that supermassive boson stars could exist at the centers of galaxies or act as black-hole mimickers (see, e.g., Vincent et al., 2016; Schunck and Liddle, 1997; Schunck and Torres, 2000; Torres et al., 2000; ?; ?; ?). Consequently, a number of studies have explored the signatures of such objects, which include the dynamics of accreted particles Schunck and Torres (2000), the gravitational redshift Schunck and Liddle (1997) and lensing Dabrowski and Schunck (2000); ?; ? of radiation emitted within the boson star, and the stellar orbits around them (Grould et al., 2017). Guzmán (2006, 2011) studied spectra of alpha–discs (Shakura and Sunyaev, 1973) around boson stars, reporting the lack of a clear signature distinguishing them from black holes. Motivated by the forthcoming observations of the EHTC, Vincent et al. (2016) reached similar conclusions by comparing strong-field images of stationary tori around black holes and boson stars. However, the robustness of these considerations is limited by the fact that such configurations do not allow matter to freely explore the interior of the boson star, as would happen in a realistic accretion scenario.
Subsequently, Meliani et al. (2016) simulated non-magnetized accretion onto boson stars and black holes, finding a significantly different behaviour caused by the absence of an event horizon, specifically, a polar outflow produced by the collision of matter infalling on the equatorial plane. However, this study did not include a systematic investigation of the discernability of the emission from the two compact objects via ray-traced images. Moreover, considering the ubiquity of magnetic fields in astrophysical compact objects and their importance for accretion processes as a means for angular momentum transport and jet production, it is essential to extend the study to produce ray-traced images of fully dynamical accretion in the presence of magnetic fields.
We here revisit this question and challenge the notion that accreting boson stars and black holes cannot be distinguished. To this end, we extend the work of Vincent et al. (2016) on strong-field images of stationary tori around boson stars, by performing the first general-relativistic ideal-magnetohydrodynamic (GRMHD) simulations of the accretion flow onto a nonrotating boson star. Using these simulations, we perform general-relativistic radiative-transfer (GRRT) calculations and produce synthetic images accounting for realistic EHTC observations. We compare the dynamics of the accretion flow with those in the case of a Kerr black hole, and contrast the images obtained in each case. As we will highlight in what follows, when considering magnetized accretion and realistic observational corrections of the ray-traced images, we can conclude that it is possible to discriminate between an accreting black hole and a boson star.
Physical scenario. We simulate numerically and in three dimensions (3D) the accretion from a magnetized torus onto a Kerr black hole with total angular momentum and a nonrotating boson star with the same mass . While the Kerr black hole has a dimensionless spin parameter (we use units with ), the boson star is chosen to be nonrotating. There are two reasons for this choice. Firstly, astrophysical boson stars cannot be rapid rotators, becoming dynamically unstable for (Cardoso et al., 2008). Secondly, the absence of a surface or a capture cross section permits stable circular orbits down to the center of the boson star Guzmán (2011). Therefore, the ray-traced image of a rapidly-rotating black hole, for which the innermost stable circular orbit (ISCO) is near to the event horizon, is closer to that of a boson star in terms of intrinsic source size and represents a worst-case scenario for distinguishing between the two objects.
The boson star spacetime is a solution of the Einstein-Klein-Gordon system in spherical symmetry for the potential of a mini boson star (Kaup, 1968). The method for computing these configurations is presented in a number of works (see, e.g., Kaup, 1968; Ruffini and Bonazzola, 1969; ?; Olivares and et al., 2019). More specifically, the boson star considered here has an oscillation frequency and a scalar particle mass of , where is the Planck mass. For the mass of Sgr A* ( (Boehle et al., 2016)), this corresponds to , which is within the range allowed by astronomical observations Amaro-Seoane et al. (2010).
To simulate the accretion flow we used BHAC Porth et al. (2017); ?, which solves the equations of GRMHD in arbitrary stationary spacetimes using state-of-the art numerical methods. The plasma was assumed to follow the equation of state of an ideal fluid with an adiabatic index Rezzolla and Zanotti (2013). The simulations were performed on a logarithmically spaced radial grid in spherical polar coordinates, with three refinement levels, to give an effective resolution of , and with the outer boundary placed at . The accretion torus was perturbed to trigger the magneto-rotational instability (MRI), causing turbulent transport of angular momentum and driving the accretion (Balbus and Hawley, 1991). Since the mass of the accretion disk is negligible compared to that of the compact object (test-fluid approximation), the spacetime can be considered fixed. Except for gravitation, the scalar field has no interaction with the fluid or the electromagnetic fields.
Numerical results. After the initial growth and saturation of the MRI at , the accretion flow for both objects becomes quasi-stationary for . This is illustrated in Fig. 1, which reports in arbitrary units the evolution of the mass-accretion rate (panel a) and of the accreted magnetic flux threading the outer horizon in the case of the black hole, or a spherical surface at coordinate in the case of the boson star (panel b). Comparing the behaviour of these two quantities it is possible to appreciate that while the black hole has always a positive , the boson star can also record negative values. This is allowed at all radii due to the absence of an event horizon.
As we will discuss below, this outflow is due to oscillations of a stalled-accretion torus produced close to the steep centrifugal barrier that develops inside the boson star. A magnification of during the quasi-stationary stage of the accretion is shown in the inset of Fig. 1, highlighting the quasi-periodic inflows and outflows of matter in the simulations involving a boson star. When comparing the typical frequency associated with the quasi-periodic oscillations in , we have found them to be very close to the value of the epicyclic frequency at the location of the rest-mass density maximum. This is unsurprising since matter accumulates at this location and small perturbations there will induce large excursions, both positive and negative, in the accretion rate.
Figure 1 shows a snapshot at and on the meridional plane, of rest-mass density (panels c and d) and plasma magnetization (panels e and f), where is the magnitude of the magnetic field in the fluid frame. In each panel we contrast the behavior of these quantities in the case of the Kerr black hole (panels c and e) with that of a boson star (panels d and f). As expected, differences in the dynamics of accretion onto the two objects arise mainly from the presence or absence of an event horizon within which matter can disappear, and which causally disconnects its interior from its exterior. In contrast to a black hole, matter in the interior of a boson star continues to influence its exterior. As a result, an evacuated funnel in the polar regions – such as the one produced by the black hole – is absent in the case of the boson star, where this region is instead filled with material slowly flowing out from the hotter and denser interior.
As anticipated above, a peculiar feature of the accretion onto the boson star is the formation of a smaller torus, which is most clearly visible in the right inset of panel (d) of Fig. 1. This small torus, which effectively represents a stalled portion of the accretion flow, is produced by a steep centrifugal barrier and by the suppression of the MRI. In fact, as a result of the reduced curvature in the boson-star interior, the radial distribution of angular momentum in the accretion disc reverses at small radii, violating the MRI stability criterion Balbus and Hawley (1991); Olivares and et al. (2019). Since all regular axially symmetric, asymptotically flat spacetimes need to be flat at their centers, we expect the same phenomenology for all horizonless, surfaceless accreting objects non-interacting with the plasma and the electromagnetic field. Without the principal mechanism for angular momentum transport, the plasma cannot penetrate the centrifugal barrier except by diffusion (see also Torres (2002)). Unable to access the core of the boson star, a portion of the infalling matter escapes as a slowly moving wind, i.e., with Lorentz factors , which propagates in the polar directions. As a comparison, the polar outflow in the Kerr simulation can reach . Note that this slow wind from the boson star is fundamentally different from the mass ejection discussed in (Meliani et al., 2016), which is caused by the pressure increase at the stellar center due to matter accreted radially without magnetic fields or angular momentum. For such shocked matter with no centrifugal support, the polar regions represent the only direction where escape is possible.
Ray-traced and synthetic images. We next discuss how to use the results of the GRMHD simulations to produce ray-traced and synthetic images at the EHTC observing frequency of , assuming a population of thermal electrons which emit synchrotron radiation and are also self-absorbed. Several parameters need to be fixed when converting the dimensionless quantities evolved numerically to produce physical images. We fix the mass and the distance from the observer to (Boehle et al., 2016). This sets the length and time scalings of the radiative-transfer calculations (see, e.g., Younsi et al. (2012); Mizuno et al. (2018)) and yields the appropriate flux scaling. Finally, the ion-to-electron temperature ratio (Mościbrodzka et al., 2009), the observer inclination angle , and the compact object mass-accretion rate are chosen such that, at a resolution of pixels, the total integrated flux of the image reproduces Sgr A*’s observed flux of at (Marrone et al., 2006). In this way, using the radiative-transfer code BHOSS Younsi and et al. (2019), we produce images at several observing angles, and present here those at , consistent with observational constraints (Psaltis et al., 2015b).
For both compact objects, we consider the interval , which for Sgr A* corresponds to an observing time of . At these times, both of the GRMHD simulations are well within the quasi-stationary state (cf. Fig. 1). The leftmost panels of Fig. 2 show the median of the ray-traced images and can be used to draw some general considerations regarding the features that make the two objects distinguishable. First, the boson star exhibits a smaller source size as a result of the emission from the small torus in its interior and thus at radii comparable or smaller than the black-hole horizon. Second, the boson star yields a more symmetric image due to the absence of frame-dragging, which significantly reduces Doppler boosting and consequently the sharp contrast in emission between fluid approaching and receding from the observer. Finally, although less likely to be noticed by observations, the boson-star image lacks a sharp transition between the middle dark region and its bright surroundings, which is a fundamental property of a black-hole shadow and the narrow photon ring. In fact, due to the absence of a photon-capture cross section, the central dark region in the boson star case is simply a lensed image of the central low-density region.
From these ray-traced images, we finally generate synthetic radio images using the EHTIm software package (Chael et al., 2016). We select as an observing array the configuration of the EHTC 2017 observing campaign, consisting of eight radio telescopes in the US, Europe, South America and the South Pole. To mimic realistic radio images, we follow closely the 2017 observing schedule, using an integration time of , an on-source scan length of calibration and pointing gaps between the on-source scans and a bandwidth of . Within these constraints we perform the synthetic observations of the galactic centre on April 8th 2017 from 08:30 to 14:30 UT. The visibilities are computed by Fourier-transforming the GRRT images and sampling them with projected baselines of the array (Chael et al., 2016). During this calculation, we include thermal noise and gain variations as well as interstellar scattering by a refracting screen (Johnson and Gwinn, 2015). We reconstruct the final images using a maximum entropy method (MEM), provided with EHTIm. In addition to the calculation of the synthetic images, we convolve the GRRT images with 50% of the EHTC beam (second column in Fig. 2). These images can be used to examine the influence of the sparse sampling of the Fourier space and interstellar scattering on the reconstructed images (third column in Fig. 2).
A visual inspection of the reconstructed images (third column in Fig. 2) shows a clear difference between the two compact objects, both in size and structure, with the black-hole image exhibiting a “crescent” structure. A more quantitative statement can be made by computing the image-comparison metrics, such as the structural dissimilarity index (DSSIM) (Wang et al., 2004). The DSSIM is computed between the convolved GRRT images and the reconstructed ones and, to guarantee that we compare similar structures within both images, we perform an image alignment prior to its calculation. Comparing the convolved Kerr image with the reconstructed image leads to a DSSIM of 0.13 and in the case of the Boson star we obtain a DSSIM of 0.06. The inter-model comparison, i.e., Kerr–Boson star and Boson star–Kerr, reveals DSSIMs of 0.20 and 0.12, respectively. Given these values, we conclude that both models are distinguishable by current EHTC observations. An additional tool to discriminate between the two objects can come from the variability of the emission. Given the qualitative differences in the accretion rate, we expect different spectral-energy properties and different closure-phase variabilities for the two objects, especially for large antenna triangles, which probe the innermost regions currently accessible by the EHTC.
Conclusions. We combined the first 3D GRMHD simulations of accretion onto a boson star with GRRT calculations, with the goal of determining whether, under realistic observing conditions such as those of the EHTC, an accreting boson star can be distinguished from a Kerr black hole. By comparing the images produced for the two compact objects using very similar setups, we found important differences, both in the plasma dynamics and in the GRRT images, which permit to distinguish the two objects. For the boson star case, the dynamical differences include the formation of a small torus in its interior and the absence of an evacuated high-magnetization funnel in the polar regions, while its images show a smaller source size and a more symmetric emission structure, in contrast to the characteristic crescent of Kerr-black-hole accretion. While these results have been obtained for a nonrotating boson star, we believe they also apply qualitatively in the case of rotation as well as for other surfaceless and horizonless compact objects. Finally, we note that ongoing pulsar searches around Sgr A* Kramer et al. (2004), when successful, could provide additional important information to the experiment outlined here. A suitable pulsar orbiting a rotating boson star, would enable a precise determination of its spin and possibly even its quadrupole moment, providing valuable input for interpretation of the image and complementary tests Wex and Kopeikin (1999); Liu et al. (2012); Psaltis et al. (2016). Details on this will be part of future work. Overall, our results and the ability to distinguish between these compact objects underline the potential of EHTC observations to extend our understanding of gravity in its strongest regimes and to potentially probe the existence of self-gravitating scalar fields in astrophysical scenarios.
Acknowledgements.Acknowledgements. We thank Jordy Davelaar, Thomas Bronzwaer, David Kling, Jonas Köhler, Elias Most, Alejandro Cruz-Osorio, Arne Grenzebach, Hung-Yi Pu, Norbert Wex and Lijing Shao for useful input. Support comes from the ERC Synergy Grant “BlackHoleCam - Imaging the Event Horizon of Black Holes” (Grant 610058), the COST Action CA16214 “PHAROS”, the LOEWE-Program in HIC for FAIR, the European Union’s Horizon 2020 Research and Innovation Programme (Grant 671698) (call FETHPC-1-2014, project ExaHyPE). HO is supported in part by a CONACYT-DAAD scholarship. ZY is supported by a Leverhulme Trust Early Career Fellowship and an Alexander von Humboldt Fellowship. The simulations were performed on the SuperMUC cluster at the LRZ in Garching, and on the LOEWE and Iboga clusters in Frankfurt. This research has made use of NASA’s Astrophysics Data System.
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