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Resolved magnetic-field structure and variability near the event horizon of Sagittarius A*

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Science  04 Dec 2015:
Vol. 350, Issue 6265, pp. 1242-1245
DOI: 10.1126/science.aac7087

Magnetic fields near the event horizon

Astronomers have long sought to examine a black hole's event horizon—the boundary around the black hole within which nothing can escape. Johnson et al. used sophisticated interferometry techniques to combine data from millimeter-wavelength telescopes around the world. They measured polarization just outside the event horizon of Sgr A*, the supermassive black hole at the center of our galaxy, the Milky Way. The polarization is a signature of ordered magnetic fields generated in the accretion disk around the black hole. The results help to explain how black holes accrete gas and launch jets of material into their surroundings.

Science, this issue p. 1242

Abstract

Near a black hole, differential rotation of a magnetized accretion disk is thought to produce an instability that amplifies weak magnetic fields, driving accretion and outflow. These magnetic fields would naturally give rise to the observed synchrotron emission in galaxy cores and to the formation of relativistic jets, but no observations to date have been able to resolve the expected horizon-scale magnetic-field structure. We report interferometric observations at 1.3-millimeter wavelength that spatially resolve the linearly polarized emission from the Galactic Center supermassive black hole, Sagittarius A*. We have found evidence for partially ordered magnetic fields near the event horizon, on scales of ~6 Schwarzschild radii, and we have detected and localized the intrahour variability associated with these fields.

Sagittarius A* (Sgr A*) emits most of its ~1036 erg/s luminosity at wavelengths just short of 1 mm, resulting in a distinctive “submillimeter bump” in its spectrum (1). A diversity of models attribute this emission to synchrotron radiation from a population of relativistic thermal electrons in the innermost accretion flow (24). Such emission is expected to be strongly linearly polarized, ~70% in the optically thin limit for a highly ordered magnetic field configuration (5), with its direction tracing the underlying magnetic field. At 1.3-mm wavelength, models of magnetized accretion flows predict linear polarization fractions >~30% (69), yet connected-element interferometers measure only a 5 to 10% polarization fraction for Sgr A* (10, 11), which is typical for galaxy cores (12). However, the highest resolutions of these instruments, ~0.1 to 1″, are insufficient to resolve the millimeter emission region, and linear polarization is not detected from Sgr A* at the longer wavelengths at which facility very-long-baseline interferometry (VLBI) instruments offer higher resolution (13). Thus, these low-polarization fractions could indicate any combination of low intrinsic polarization, depolarization from Faraday rotation or opacity, disordered magnetic fields within the turbulent emitting plasma, or ordered magnetic fields with unresolved structure, leading to a low beam-averaged polarization. The higher polarization seen during some near-infrared flares may support the last possibility (14, 15), but the origin and nature of these flares is poorly understood and may probe a different emitting electron population than is responsible for the energetically dominant submillimeter emission.

To definitively study this environment, we are assembling the Event Horizon Telescope (EHT), a global VLBI array operating at 1.3-mm wavelength. Initial studies with the EHT have spatially resolved the ~40 micro–arc sec emission region of Sgr A* (16, 17), suggesting the potential for polarimetric VLBI with the EHT to resolve its magnetic field structure. For comparison, Sgr A* has a mass of ~4.3 × 106 M (M, solar mass) and lies at a distance of ~8 kpc, so its Schwarzschild radius (RSch = 2GM/c2) is 1.3 × 1012 cm and subtends 10 micro–arc sec (18, 19). In March 2013, the EHT observed Sgr A* for five nights using sites in California, Arizona, and Hawaii. In California, we phased together eight antennas from the Combined Array for Research in Millimeter-wave Astronomy (CARMA) to act as a single dual-polarization station, and we separately recorded dual-polarization data from an additional 10.4-m antenna. We also conducted normal observations with CARMA in parallel with the VLBI observations. In Arizona, the 10-m Submillimeter Telescope (SMT) recorded dual polarizations. In Hawaii, seven 6-m dishes of the Submillimeter Array (SMA) were combined into a single-polarization phased array, while the nearby 15-m James Clerk Maxwell Telescope (JCMT) recorded the opposite polarization, forming a single effective dual-polarization station. Each station, except for the CARMA reference antenna, recorded two 512-MHz bands, centered on 229.089 and 229.601 GHz, and circular polarizations.

A linearly polarized signal manifests itself in the cross-hand correlations between stations, Embedded Image and Embedded Image, where Li denotes left circular polarization and Ri denotes right circular polarization at site i, and the asterisk denotes complex conjugation. These correlations are typically much weaker than their parallel-hand counterparts, Embedded Image and Embedded Image, which measure the total flux. After calibrating for the spurious polarization introduced by instrumental cross-talk (20), quotients of the cross-hand to parallel-hand correlations on each baseline u joining a pair of stations are sensitive to the fractional linear polarization in the visibility domain: Embedded Image. Here, ℐ, Embedded Image, and Embedded Image are Stokes parameters, and the tilde denotes a spatial Fourier transform relating their sky brightness distributions to interferometric visibilities in accordance with the Van Cittert-Zernike Theorem. Embedded Image provides robust phase information and is insensitive to station gain fluctuations and to scatter-broadening in the interstellar medium (20, 21). On baselines that are too short to resolve the source, Embedded Image gives the fractional image-averaged polarization. On longer baselines, Embedded Image mixes information about the spatial distribution of polarization with information about the strength and direction of polarization and must be interpreted with care. For instance, one difference from its image-domain analog m = (Embedded Image + iEmbedded Image)/ℐ is that Embedded Image can be arbitrarily large. Nevertheless, Embedded Image readily provides secure inferences about the intrinsic polarization properties of Sgr A*.

Our measurements on long baselines robustly detect linearly polarized structures in Sgr A* on ~6 RSch scales (Fig. 1). The high (up to ~70%) and smoothly varying polarization fractions are an order of magnitude larger than those seen on shorter baselines (Fig. 2), suggesting that we are resolving highly polarized structure within the compact emission region. Measurements on shorter baselines show variations that are tightly correlated with those seen in simultaneous CARMA-only measurements (figs. S4 and S8). This agreement demonstrates that there is negligible contribution to either the polarized or total flux on scales exceeding ~30 RSch, conclusively eliminating dust or other diffuse emission as an important factor (20). Because CARMA does not resolve polarization structure in Sgr A*, these variations definitively reflect intrahour intrinsic variability associated with compact structures near the black hole.

Fig. 1 Interferometric fractional polarization measurements for Sgr A*.

Interferometric fractional polarization measurements, Embedded Image, for Sgr A* in our two observing bands during one day of EHT observations in 2013 (day 80). The color and direction of the ticks indicate the (noise-debiased) amplitude and direction of the measured polarization, respectively. For visual clarity, we omit CARMA-only measurements, show only long scans, show only low-band measurements for the SMT-CARMA baseline, and exclude points with a parallel-hand signal-to-noise below 6.5. The fractional polarization is expected to change smoothly as the baseline orientation changes with the rotation of the Earth, and the polarization of Sgr A* is also highly variable in time (fig. S8). The pronounced asymmetry in Embedded Image indicates variation in the polarization direction throughout the emission region.

Fig. 2 Signatures of spatially resolved fields from 1.3-mm VLBI.

Long-baseline measurements of interferometric fractional polarization, Embedded Image, are plotted against the “deblurred” and normalized total-flux visibilities (20, 35); errors are ±1σ (details of the error analysis are provided in the supplementary materials). The black dashed line and gray shaded region show the average and SD of the CARMA measurements of fractional polarization, respectively. The sharp increase in the polarization fraction and variability on long baselines demonstrates that we are resolving the compact and polarized emission structure on scales of ~6 to 8 RSch. The marked difference in the two polarization products, Embedded Image and Embedded Image, on equal baselines indicates changes in the polarization direction on these scales (Fig. 1).

We emphasize that Embedded Image does not imply correspondingly high image polarizations or that we are measuring polarization near a theoretical maximum. Because polarization can have small-scale structure via changes in its direction, disordered polarization throughout a comparatively smooth total emission region will result in long baselines resolving the total flux more heavily than the polarization (20). As a result, Embedded Image can be arbitrarily large, especially in locations near a visibility “null,” where Embedded Image is close to zero. Although our highest measured polarization fractions occur where Embedded Image falls to only 5 to 10% of the zero-baseline flux (Fig. 2), the rise is slower than expected for completely unresolved polarization structure, showing that the long baselines are partially resolving coherent polarized structures on the scale of ~6 RSch (Fig. 3). Because interferometric baselines only resolve structure along their direction and our long baselines are predominantly east-west, these conclusions describe the relative coherence of the polarization field in the east-west direction.

Fig. 3 Strength and order of the polarization field from 1.3-mm VLBI.

(A, B, and C) Example realizations from three models with Gaussian distributions of intensity. Color indicates total flux on a linear scale; ticks indicate polarization amplitude and direction. Each model has a constant polarization fraction but stochastically varying polarization direction with prescribed coherence lengths (0.64, 0.29, and 0.11 times the Gaussian full width at half maximum). The polarization fractions are determined by matching the ensemble-average zero-baseline polarization to the averaged CARMA measurements. (D) A sample image from a general relativistic magnetohydrodynamic simulation with polarimetric radiative transfer (9). The image-averaged polarization fraction, weighted by brightness, is 26%. (E) Points with errors (±1σ) show the average of VLBI measurements from Fig. 2 after grouping in bins of width 0.05. Dashed orange lines indicate two limiting cases: a uniform polarization field and a highly disordered (unresolved) polarization field. Each is set equal to 5.2% when the normalized visibility is unity so that the zero-baseline polarization matches the average of all CARMA-only measurements. Our data differ from model (A) at a significance exceeding 4σ, differ from model (C) by 3.4σ, and are compatible with model (B) (20). The GRMHD simulation (E) also exhibits a balance between order and variation in the polarization field that is compatible with our observations.

The current data, although too sparse for imaging, provide rich geometrical insights. For instance, if the fractional polarization is constant across the source image, then it will also be constant in the visibility domain. Furthermore, even if the polarization amplitude varies arbitrarily throughout the image, if its direction is constant then the amplitude of the interferometric polarization fraction will be equal for conjugate baselines (20). Our measurements (Fig. 1) eliminate both of these possibilities and thus detect variation in the polarization direction on event-horizon scales. These arguments also allow us to assess the spatial extent of the polarized emission because the detected polarization variation cannot arise from a region that is much smaller than the diffraction limit of our interferometer. The polarized emission must therefore span an extent comparable with that of the total flux (20).

The phase of Embedded Image likewise constrains the emission morphology. For example, on a short baseline, the leading-order geometrical contribution to the interferometric phase comes from the image centroid (21). Thus, just as a decrease in correlated flux with baseline length provides a characteristic angular extent of the emission, a linear change in the phase of Embedded Image with baseline length provides a characteristic angular separation of the polarized and total flux. The close agreement in phase between the two measurements on the short SMT-CARMA baseline establishes that the polarized and unpolarized flux are closely aligned—to within ~10 micro–arc sec when the polarization angle of Sgr A* is relatively steady (fig. S8). However, when variability is dominant, we measure much larger offsets, up to ~100 micro–arc sec, implicating dynamical activity near the black hole. For comparison, the apparent diameter of the innermost stable circular orbit is Embedded Image ≈ 73 micro–arc sec if the black hole of Sgr A* is not spinning. The tight spatial association of this linear polarization with the 1.3-mm emission region then cements low-accretion models for Sgr A* (11), which combined with the measured spectrum in the submillimeter bump and in the near-infrared imply a magnetic field of tens of gauss throughout the emitting plasma (3, 4, 7).

Even amid magnetically driven instabilities and a turbulent accretion environment, several effects can produce ordered fields near the event horizon. For example, as the orbits of the accreting material around the black hole become circular, magnetic fields will be azimuthally sheared by the differential rotation, resulting in a predominantly toroidal configuration (22). The high image-averaged polarization associated with the emission region necessitates that such a flow be viewed at high inclination because circular symmetry would cancel the polarization of a disk viewed face-on. The striking difference between the stability of compact structures in the total flux (17) relative to the rapid changes in the polarized structures on similar scales is then most naturally explained via dynamical magnetic field activity through coupled actions of disk rotation and turbulence driven by the magnetorotational instability (MRI) (23).

Alternatively, accumulation of sufficient magnetic flux near the event horizon may have led to a stable, magnetically dominated inner region, suppressing the disk rotation and the MRI (2426). Emission from a magnetically dominant region provides an attractive explanation for the long-term stability of the circular polarization handedness and the linear polarization direction of Sgr A* (27, 28), and it has recently received observational support in describing the cores of active galaxies with prominent jets (2931). However, the close alignment of the polarized and total emission (20) severely constrains multicomponent emission models for the quiescent flux, such as a bipolar jet (32) or a coupled jet-disk system (33). If a jet is present, then this constraint suggests substantial differences between the emitting electron populations in the jet and the accretion flow to ensure the dominance of a single component at 1.3 mm (26, 34).

With the advent of polarimetric VLBI at 1.3-mm wavelength, we are now resolving the magnetized core of our galaxy’s central engine. Our measurements provide direct evidence of ordered magnetic fields in the immediate vicinity of Sgr A*, firmly grounding decades of theoretical work. Despite the extreme compactness of the emission region, we have unambiguously localized the linear polarization to the same region and identified spatial variations in the polarization direction. We also detected intrahour variability and spatially resolved its associated offsets. In the next few years, expansion of the EHT will enable imaging of these magnetic structures and variability studies on the 20-s gravitational time scale (GM/c3) of Sgr A*.

Supplementary Materials

www.sciencemag.org/content/350/6265/1242/suppl/DC1

Supplementary Text

Figs. S1 to S8

Tables S1 to S3

References (3661)

Data Files S1 and S2

References and Notes

  1. Materials and methods are available as supplementary materials on Science Online.
  2. Acknowledgments: EHT research is funded by multiple grants from NSF, by NASA, and by the Gordon and Betty Moore Foundation through a grant to S.D. The SMA is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics. The Arizona Radio Observatory is partially supported through the NSF University Radio Observatories program. The James Clerk Maxwell Telescope was operated by the Joint Astronomy Centre on behalf of the Science and Technology Facilities Council of the UK, the Netherlands Organisation for Scientific Research, and the National Research Council of Canada. Funding for CARMA development and operations was supported by NSF and the CARMA partner universities. We thank Xilinx for equipment donations. A.E.B. receives financial support from the Perimeter Institute for Theoretical Physics and the Natural Sciences and Engineering Research Council of Canada through a Discovery Grant. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. J.D. receives support from a Sofja Kovalevskaja award from the Alexander von Humboldt Foundation. M.H. was supported by a Japan Society for the Promotion of Science Grant-in-aid. R.P.J.T. receives support from Netherlands Organisation for Scientific Research. Data used in this paper are available in the supplementary materials.
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