1.3 mm WAVELENGTH VLBI OF SAGITTARIUS A*: DETECTION OF TIME-VARIABLE EMISSION ON EVENT HORIZON SCALES

The case for linking Sgr A*, the radio source at the center of the Milky Way, with a supermassive black hole is very strong. Mass estimates inferred from stellar orbits, proper motion studies that indicate Sgr A* is nearly motionless, very long baseline interferometry (VLBI) observations that reveal it is ultracompact, and short-timescale variability from radio to X-rays all point toward Sgr A*'s association with a ∼4 × 10⁶ M_☉ black hole (see Reid 2009, and references therein). At a distance of ∼8 kpc, the Schwarzschild radius of this black hole subtends R_Sch ∼ 10 μas, making the apparent size of its event horizon the largest that we know of. VLBI at (sub)millimeter wavelengths is ideally suited to observing Sgr A* on these angular scales. Previous 1.3 mm VLBI detections of Sgr A* on a Hawaii–Arizona baseline established the existence of coherent structures on scales of a few R_Sch (Doeleman et al. 2008).

VLBI observations at 1.3 mm can address two issues concerning the fundamental nature of Sgr A*. The first is whether signatures of strong field gravitational lensing can be directly detected near the event horizon. Current 1.3 mm VLBI observations can be fit to geometric models similar in shape to the "shadow" feature predicted to be produced when emission from Sgr A* is preferentially lensed onto the last photon orbit (Falcke et al. 2000). This effect results in a relatively dim central region encircled by a brighter annulus, which can be properly imaged as the number of (sub)millimeter VLBI sites increases. A second question is whether the flaring behavior exhibited by Sgr A* arises near the event horizon. Broadband flares on timescales ranging from minutes to hours are well documented (Marrone et al. 2008; Yusef-Zadeh et al. 2009; Dodds-Eden et al. 2009) and imply time-variable structures in the innermost accretion region. If small-scale variable structures are present, 1.3 mm VLBI can sensitively monitor the changing morphology of Sgr A* using non-imaging techniques with time resolutions of tens of seconds (Doeleman et al. 2009; Fish et al. 2009b).

We report on new 1.3 mm VLBI observations of Sgr A* using a four-telescope array. These observations confirm event horizon scale structure within Sgr A*, impose new constraints on accretion models for Sgr A*, and reveal time-dependent variability on scales of a few R_Sch.

Sgr A* and several calibrator sources were observed with four telescopes at three observatories: the James Clerk Maxwell Telescope (JCMT; henceforth also J) on Mauna Kea in Hawaii, the Arizona Radio Observatory's Submillimeter Telescope (ARO/SMT; S) in Arizona, and two telescopes of the Combined Array for Research in Millimeter-wave Astronomy (CARMA; C and D, located ∼60 m apart) in California. On Mauna Kea, the Submillimeter Array (SMA) housed the VLBI recording system and synthesized the hydrogen maser based VLBI reference used at the JCMT. Masers at all sites were checked against ultra-stable crystals; combined losses due to maser instabilities and local oscillator decoherence are estimated to be ≲5%. Observations occurred over three nights: 2009 April 5–7 (days 95–97). Sources were observed in left circular polarization in two 480 MHz bandwidths centered at 229.089 and 229.601 GHz (low and high bands). Data recorded at all sites were shipped to MIT Haystack Observatory in Westford, Massachusetts for processing on the Mark4 VLBI correlator. Once correlated, data for each scan (typically 10–15 minutes) were corrected for coherence losses due to atmospheric turbulence and searched for detections using methods detailed in Doeleman et al. (2001, 2008). Atmospheric coherence times ranged from a few to ∼20 s, depending on weather conditions at each telescope.

The VLBI correlation coefficient for each baseline was multiplied by the geometric mean of the System Equivalent Flux Density (SEFD) of both antennas. The SEFD is a product of antenna gain (Jy K^–1) and the opacity-corrected system temperature, which was measured prior to each VLBI scan using a vane calibration technique that corrects for the atmosphere. For the JCMT and ARO/SMT, antenna gains, determined from planet observations at several points during the multiple-day campaign, were observed to be stable. Relative gains for the two CARMA dishes were estimated using observations taken by CARMA in interferometric array mode before each VLBI scan, and the gains were then set to a common flux scale using planet scans at the end of each night.

The flux densities of all VLBI targets (Sgr A*, 1924−292, M87, 3C273, 3C345, 1733−130, 3C279, 0854 + 201) were measured with the CARMA interferometer. For Sgr A*, interferometric data with baselines shorter than 20 kλ (fringe spacing 10'') were discarded to filter out extended emission in the Galactic center. The measured flux densities of all sources increased from day 95 to day 96 and from day 96 to day 97. We attribute this systematic trend to errors in the planet calibrations made shortly after sunrise, when antenna focus, pointing offsets, and atmospheric coherence typically change. The flux density measured for the calibrator 1924−292 was 9.95, 10.21, and 10.75 Jy on days 95, 96, and 97, respectively. To correct for this effect in the Sgr A* data, we normalized the CARMA gains on each individual day to set the flux density of 1924−292 (observed over the same time range and elevation) to a constant value of 10.25 Jy. When this is done, the measured flux densities for Sgr A* are 3.03, 3.16, and 3.61 Jy on days 95, 96, and 97, respectively, with the result that Sgr A* exhibits an increase in flux density after this correction. We adopt these fluxes for all subsequent analysis.

As shown in the upper panels of Figures 1 and 2, there are still noticeable variations in the correlated flux densities even after renormalizing the day-to-day flux scales. These residual calibration errors and amplitude variation can be corrected for by making three simplifying assumptions that allow us to use standard "self-calibration" techniques. First, the flux densities of detections in the low and high bands, which differ by only 0.2% in frequency, are assumed to be equal in each scan. Second, flux densities on the SC and SD baselines are assumed to be equal. While one could in principle require that JC and JD flux densities be equal as well, the signal-to-noise ratio (S/N) is generally much lower on the JC and JD baselines than on the shorter VLBI baselines (SC and SD), since both 1924−292 and Sgr A* are more resolved on longer baselines. Third, CARMA antenna gains are adjusted to make the correlated flux density on the VLBI CD baseline (which was correlated and processed in the same manner as the other VLBI baselines) equal to the flux density measured on baselines longer than 20 kλ each night by the CARMA interferometric array. This final constraint enforces a constant source flux density over the duration of each night of observation. While some of the observed variations in Sgr A* over the course of a night may be due to intrinsic variability, the 1924−292 data exhibit similar scatter, suggesting that calibration errors may dominate over source variability. Combined, these assumptions result in a closed-form solution for gain-correction coefficients for telescopes C, D, and S in each band. Henceforth, we will use the term "gain-corrected" to refer to flux densities that have been multiplied by these gain-correction coefficients. We note that if the total flux density (CD) is varied, the SJ flux densities are unchanged while other flux densities vary as the square root of the factor.

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The quasar 1924−292 was easily detected on all baselines (Table 1). On each scan, low-band and high-band fluxes after a priori calibration track each other consistently (Figure 1). After gain correction assuming a total flux density of 10.25 Jy, the data from all three days are highly consistent with one another. The SC and SD baselines show repeatable variation in the correlated flux density each day. The long-baseline detections (SJ, JC, and JD) also show day-to-day repeatable behavior, indicating detection of stable source structure presumably associated with a jet (Shen 1997). The consistency of these data demonstrates the validity of the gain-correction technique and suggests that the source structure in 1924−292 is stable over the three nights of observation. This permits a further cross-check on data consistency by comparing subsets of the gain-corrected data that are each independent estimates of the same sky visibility (e.g., low- and high-band JC and JD data from the same scan time on the three consecutive nights). Based on the statistics of these subsets of the 1924−292 data and on the assumption that the errors in the gain-corrected data are dominated by residual gain errors, the systematic errors are estimated to be ∼5%. Hence, a 5% error has been added in quadrature to the random errors determined from the S/N of each detection.

We report the first 1.3 mm VLBI detections of Sgr A* on Hawaii–California baselines with correlated flux densities for several scans of ≳400 mJy on the JC and JD baselines during day 96 (Figure 2). Nondetections on the JC and JD baselines on day 95 are attributable to the higher opacity at the JCMT on that day. The robust detections on the long (Hawaii–Arizona and Hawaii–California) baselines confirm the detection of event horizon scale structure reported in Doeleman et al. (2008).

Because Sgr A* was detected on baselines between all three sites, we are able to measure closure phase: the sum of interferometric phase around a closed triangle of baselines. Closure phase, which is relatively immune to calibration errors, measures asymmetry on VLBI scales and provides important constraints on source structure. On the CARMA-ARO/SMT-JCMT triangle, baseline phases on Sgr A* for days 96 and 97 (eight independent measurements) were segmented at the atmospheric coherence time, closed, and averaged over scans as described in Rogers et al. (1995). Sgr A* closure phases are consistent with a value of zero to within ±40°.

4.1. Variability

4.2. Geometrical Models of the Structure of Sgr A*

Though our data are better calibrated than in the previous epoch (Doeleman et al. 2008), the structure of Sgr A* is poorly constrained because millimeter VLBI detections of Sgr A* remain limited in terms of baseline length and orientation. As a result, many models can be made to fit the data: extended double sources, large rings, combinations of large- and small-scale components, etc.

Nevertheless, with the caveat that this small data set should not be overinterpreted, it is instructive to investigate the two classes of models originally considered by Doeleman et al. (2008) to fit the 1.3 mm VLBI data obtained in 2007: circular Gaussians and rings. All of the 2007 data points could be fitted by a single Gaussian component. In contrast, we note a loss of ∼1 Jy of correlated flux density between the connected-element (CD) and SC/SD baselines (i.e., between the red dashed line and dark blue points in the bottom panels of Figure 3). In the context of Gaussian models of emission on R_Sch scales, this suggests the existence of additional variable structure on scales between those probed by the SC/SD (a few hundred microarcseconds) and the CD (a few arcseconds) baselines.

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We adopt this assumption to estimate the size of the inner accretion flow in Sgr A*. Effectively, this reduces to fitting all of the VLBI data excluding the CD data points. For the Gaussian model, the best fits imply a flux density of 2.07^+0.14_−0.15 Jy and a size of 41.3^+5.4_−4.3 μas (FWHM; errors are 3σ) on day 95 and 2.07^+0.19_−0.19 Jy and 44.4^+3.0_−3.0 μas on day 96 (Figure 3 and Table 2). These values are consistent with the single compact component Gaussian fit of Doeleman et al. (2008), who estimated a flux density of 2.4 ± 0.5 Jy and a size of 43⁺¹⁴₋₈ μas (before deconvolution of the expected interstellar scattering; 37 μas unscattered) for the 230 GHz emission. On day 97, the best-fit model has a much higher flux density of 2.85^+0.29_−0.28 Jy but a similar FWHM of 42.6^+3.1_−2.9 μas. Despite the increase in flux density observed on day 97, the diameter of the fitted compact component in Sgr A* on that day is identical (to within the errors) to the values for the size obtained on days 95 and 96.

Table 2. Model Fits to Sgr A* Data

Model	Day	Compact	Inner	Outer	χ2	Degrees of
	Number	Flux Density	Size	Size		Freedom
		(Jy)	(μas)	(μas)
Gaussian	95	2.07	41	...	11	10
	96	2.07	44	...	39	17
	97	2.85	43	...	13	18
Ring	95	2.07	53	60	11	9
	96	2.07	37	92	26	16
	97	3.17	48	106	15	17

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Ring models with three parameters (inner radius, outer radius, and flux density) can also fit the VLBI data (Figure 3 and Table 2). However, no single set of ring model parameters consistently fits the data on all three days, which would suggest that the size and structure of Sgr A* are variable within the context of ring models. This stands in contrast with the Gaussian model, for which all epochs of data are consistent with a uniform size despite differences in the flux density. Longer-wavelength VLBI observations are inconclusive as to whether a significant correlation exists between the flux density and size of the emission in Sgr A* (Bower et al. 2004; Lu et al. 2011). However, the size of the emission at these wavelengths is dominated by interstellar scattering effects.

Future 1.3 mm VLBI observations with higher sensitivity, sufficient to robustly measure the closure phase, will be an important discriminant between these and other models. For example, an elliptical Gaussian distribution will result in zero closure phase on any triangle of baselines, while a ring model can result in closure phases of 180° depending on the orientation and length of the array baselines. The ring models shown in Figure 3 all have closure phases of zero on the CARMA-ARO/SMT-JCMT triangle of baselines, consistent with the measured closure phases (Section 4). However, a ring model with a null near 3.4 Gλ between the CARMA-JCMT and ARO/SMT-JCMT baselines, would produce a closure phase of 180°, which is strongly ruled out by the 2009 April data. Measurement on an intermediate baseline in the 1–2 Gλ range would provide a powerful discriminant between large classes of geometrical models.

5.1. Implications for Accretion and Flare Models

5.2. Physical Models of the Structure of Sgr A*

VLBI observations of Sgr A* at 1.3 mm wavelength in 2009 have robustly confirmed the detection of Schwarzschild radius scale structures reported in Doeleman et al. (2008). On the third of three days of observations, the total flux density of Sgr A* was observed to have increased by ∼17%, indicating an episode of variability similar to those described in multiwavelength monitoring campaigns (e.g., Marrone et al. 2008; Yusef-Zadeh et al. 2009). The VLBI data support a picture in which this flux density increase is due to a brightening of structure on scales of only a few R_Sch. Having achieved the dual technical milestones of successfully detecting closure phase and developing robust methods of amplitude calibration, it is clear that future (sub)millimeter VLBI observations with higher sensitivity and many more baselines will be able to powerfully constrain models of Sgr A* on event horizon scales.

High-frequency VLBI work at MIT Haystack Observatory is supported by grants from the National Science Foundation (NSF). ARO receives partial support from the NSF ATI program. The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academia Sinica. Funding for ongoing CARMA development and operations is supported by the NSF and the CARMA partner universities. D.E.B. acknowledges support from the NSF Research Experiences for Undergraduates program.

Facilities: CARMA - Combined Array for Research in Millimeter-Wave Astronomy (), HHT - Heinrich Hertz Submillimeter Telescope (), JCMT - James Clerk Maxwell Telescope (), SMA - SubMillimeter Array (), CSO - Caltech Submillimeter Observatory ()