Optical Appearances of Accreting Ellis-Bronnikov Wormholes Observed from Both Sides of Throats

Technical Summary: Optical Appearances of Accreting Ellis-Bronnikov Wormholes Observed from Both Sides of Throats

Problem Statement
Following the Event Horizon Telescope's (EHT) imaging of black holes, distinguishing between black holes and alternative compact objects, such as traversable wormholes, has become a critical objective in gravitational physics. While previous studies have examined wormhole shadows and optical appearances, gaps remain regarding the Ellis-Bronnikov (EB) wormhole. Specifically, prior works have either neglected optically thick accretion scenarios or failed to consider observations made from the side of the throat opposite to the accretion disk. This study addresses these gaps by investigating the optical appearance of an EB wormhole under both optically thick and thin accretion conditions, analyzing the system from both asymptotic regions ($R^+$ and $R^-$) connected by the wormhole throat.

Methodology
The authors employ a theoretical framework based on the original metric of the Ellis-Bronnikov wormhole. The study proceeds through the following steps:

1. Geodesic Analysis: The authors solve the geodesic equations for both null (photons) and timelike (massive particles) trajectories. They derive the relationship between the impact parameter ($b$) and the aiming distance ($d^*$), demonstrating that these quantities are not equal when the observer and the accretion disk are on opposite sides of the throat.
2. Accretion Disk Modeling:
   • Optically Thick: The accretion disk is modeled as a geometrically thin, optically thick structure. The authors utilize the ray-tracing method (based on Luminet's approach) to simulate direct and secondary images. They calculate the observed radiative flux by incorporating gravitational redshift and Doppler effects.
   • Optically Thin: The study adopts the emission model proposed by Gralla et al., classifying light rays by their orbital number (direct image, lensing ring, and photon ring). Two emission functions ($I_{em1}$ and $I_{em2}$) are tested to simulate different radiative decay profiles.
3. Simulation: Numerical ray-tracing is performed using a backward ray-tracing code. The simulations generate optical images and intensity profiles for observers located in the $R^+$ region (same side as the disk) and the $R^-$ region (opposite side of the throat).

Key Contributions and Results

• Geometric Asymmetry: The study establishes that for an EB wormhole, the relationship between the impact parameter and the aiming distance depends on the observer's location relative to the throat. Specifically, $b = \lim_{r\to\pm\infty} (d^*/f(r))$, leading to a fixed ratio between aiming distances in $R^+$ and $R^-$ spacetimes.
• Accretion Disk Location: Analysis of timelike geodesics reveals that stable circular orbits for massive particles only exist in the $R^+$ spacetime. Consequently, the accretion disk is confined to the $R^+$ side, while the $R^-$ side is devoid of such matter.
• Optically Thick Accretion:
  • $R^+$ Observer: The wormhole image resembles a black hole but is dimmer. As the parameter $n$ increases, the apparent size of the wormhole image grows, while its brightness decreases.
  • $R^-$ Observer: The image morphology changes significantly. The direct image appears larger and dimmer as $n$ increases. Crucially, the inner region of the accretion disk (closer to the throat) appears at the outer edge of the image, creating an "inside-out" inversion compared to the $R^+$ view.
• Optically Thin Accretion:
  • Unlike the optically thick case, the direct image does not obscure higher-order images (lensing and photon rings), allowing radiation from regions closer to the throat to reach the observer.
  • For an observer in $R^-$, the radial intensity profile is inverted relative to the $R^+$ observer. For instance, with emission function $I_{em1}$, the flux in the $R^-$ direct image increases from the center outward, whereas it decreases from the center outward in the $R^+$ view.
• Comparison with Black Holes: When the observer is in $R^+$, EB wormholes with small values of $n$ produce images that mimic EHT black hole observations to some extent. However, wormholes with large $n$ or those observed from the $R^-$ side produce images that are distinct enough to be ruled out as black hole candidates based on current EHT data.

Significance and Claims
The paper claims that the optical appearance of an EB wormhole is highly dependent on the observer's position relative to the throat and the optical depth of the accretion flow. The most significant finding is the "counterintuitive brightness profile" observed when the observer is on the opposite side of the accretion disk ($R^-$). In this configuration, the image exhibits an internal-external inversion where the inner parts of the image correspond to the outer parts of the accretion disk.

The authors conclude that this distinctive brightness signature, particularly the inversion of intensity profiles in optically thin flows, could serve as a potential observational fingerprint for identifying wormholes. They assert that while small-$n$ wormholes in $R^+$ might mimic black holes, the specific morphological and brightness characteristics of large-$n$ wormholes or $R^-$ observers are inconsistent with current EHT images of M87* and Sgr A*, allowing these specific configurations to be excluded. The study emphasizes that future observations by the next-generation EHT, with improved resolution and frequency coverage, could further constrain the optical depth structure of accretion flows and help clarify the physical nature of these compact objects.