The First Accurate Parallax Distance to a Black Hole

Stellar-mass black holes in accreting X-ray binary systems provide unique probes of the physical properties and formation mechanism of black holes, as well as the physics of accretion and associated outflow. However, our understanding of black hole systems is hampered by the fact that distances to X-ray binaries are relatively poorly known, typically uncertain by 50% or more (Jonker & Nelemans, 2004). Standard spectroscopic estimates are handicapped by the distortions induced in the secondary by its compact partner, contamination by emission from the accretion disc (Reynolds et al., 2008), and uncertainties in estimates of interstellar absorption.

Since these distance uncertainties are systematic rather than random, they cannot be reduced by making more observations. According to Jonker & Nelemans (2004), these systematic uncertainties can artificially enlarge the difference between the quiescent X-ray luminosities of black hole and neutron star systems. If true this would undermine the claimed evidence for an event horizon (Narayan et al., 1997; Menou et al., 1999; Garcia et al., 2001). Accurate distances are also required to interpret the measured proper motions of black hole X-ray binaries, by converting a measured proper motion into a physical speed, from which we can derive the peculiar velocity of the source (e.g., Mirabel et al., 2001, 2002; Mirabel & Rodrigues, 2003; Dhawan et al., 2007; Miller-Jones et al., 2009). This can be used to place constraints on any velocity kick the black hole might have received in its natal supernova, and hence on the formation mechanism of the black hole (Brandt et al., 1995; Willems et al., 2005; Fragos et al., 2009).

The only direct, model-independent method of measuring distances is via trigonometric parallax, which has hitherto been impossible for black hole X-ray binary systems, since they lie at distances of several kpc, and hence require sub-milliarcsecond astrometry to measure their parallaxes. Very Long Baseline Interferometry (VLBI) at radio wavelengths is currently the only technique available for such high-precision astrometric measurements. However, black hole X-ray binaries spend the majority of their time in a faint quiescent state, where they are often not detected in the radio band at current sensitivities. They become bright enough to be detected during outbursts, but such outbursts are typically not sufficiently long or frequent and do not sample the Earth’s orbit well enough to make a parallax measurement feasible. During outbursts, the radio emission is often resolved at the high angular resolutions required for precision astrometry, making it difficult to determine the true location of the binary system from epoch to epoch. Lastly, many black hole X-ray binaries are located in or close to the Galactic Plane, such that the scatter-broadening along the line of sight makes high-precision astrometry impossible in the centimeter waveband where current VLBI arrays have the highest sensitivity.

Here we present High Sensitivity Array (HSA) observations of V404 Cyg, the most luminous known black hole X-ray binary in quiescence. With a mass function of $6.08\pm 0.06M_{\odot}$ (Casares & Charles, 1994), the compact object is a dynamically-confirmed black hole, accreting matter from a K0 subgiant companion star (Casares et al., 1993). The system has a quiescent radio flux density of 0.3 mJy, with a flat spectrum indicative of a self-absorbed compact jet (Gallo et al., 2005), although the jets are not resolved at the angular resolution of the HSA (Miller-Jones et al., 2008). The persistent, unresolved radio emission makes this source a good target for astrometric observations to measure its parallax.

We observed V404 Cyg every 3 months over the course of one year, using the HSA. Two of the observations were made at the times of maximum parallactic displacement in Right Ascension (R.A.), since the R.A. signal is larger, and, owing to the greater size of the array in the east-west dimension, has smaller error bars than that in Declination. We observed at a frequency of 8.4 GHz, in dual circular polarization, with an observing bandwidth of 64 MHz per polarization. To these four HSA observations we added three archival datasets, two of which have already been reported (Miller-Jones et al., 2008, 2009), and one in which the source was previously not significantly detected (Mioduszewski et al., 2008), but knowing the astrometric parameters of the source, we were able to detect it at the $5\sigma$ level. A fourth archival epoch did not detect the source to a $3\sigma$ limit of 0.36 mJy beam^-1. A summary of the observations is listed in Table 1, and shows the extent of the source variability. In only one of the epochs was the source brighter than the $3\sigma$ upper limit of this archival dataset (in which none of the large dishes of the HSA were available), making the non-detection consistent with the expected source flux density.

In all cases, the observations were phase-referenced to a bright, nearby calibrator from the International Celestial Reference Frame (ICRF) source list, J 2025+3343 (Ma et al., 1998), located only 16.6^′ from the target source. This implies that our systematic errors, which scale with distance from the phase reference source, should be relatively small ($\sim 30$ $\mu$as; see below). We observed in 3-min cycles, spending 1 min on the phase reference source and 2 min on the target in each cycle. To maximize astrometric accuracy, all data below $23^{\circ}$ elevation were discarded. We also discarded data taken during the short timescale flares seen in a number of the observations (e.g., Miller-Jones et al., 2008), in case the assumed variations in the jet power responsible for the flaring events translated into positional offsets. To enable us to estimate the systematic errors affecting the astrometry, we substituted every seventh scan on the target source with an observation of a check source, the ICRF calibrator J2023+3153, located $1^{\circ}.87$ away from the phase reference source. Data were reduced according to standard procedures within AIPS (Greisen, 2003), and the source position at each epoch was determined by fitting an elliptical Gaussian to the source. In no case did the source appear to be resolved. Since the first epoch of archival data assumed a different position for the phase reference source, we corrected all epochs to a common calibrator position of $20^{\rm h}25^{\rm m}10^{\rm s}.8421056$, $33^{\circ}43^{\prime}00^{\prime\prime}.2144316$ (J 2000) before fitting for the proper motion and parallax of V404 Cyg. The measured positions are shown in Figure 1, together with the best-fit parallax and proper motion.

Pradel et al. (2006) used simulations to derive an approximate formula for the systematic errors affecting various VLBI arrays. For our calibrator-target separation and source declination, the estimated systematic errors (for a mean value of the wet zenith path delay) are 26 $\mu$as in R.A. and 30 $\mu$as in Dec. The fitted positions of the check source show an rms scatter of 13 $\mu$as in R.A. and 31 $\mu$as in Dec. Since the check source is seven times further away from the phase reference source than the target, this provides a rigorous upper limit on the systematic errors in position. As seen from Table 1, our astrometric accuracy is limited by signal-to-noise rather than systematic errors. Nevertheless, the systematic errors estimated from Pradel et al. (2006) were added to the statistical errors in quadrature before using the singular value decomposition (SVD) method (as detailed in Loinard et al., 2007) to fit for a reference position and proper motion in R.A. and Dec., and for the source parallax. The best-fitting astrometric parameters, taking the mid-point of the observations, MJD 54322, as the reference date, were:

The fitted parallax signal, with the best-fitting proper motion removed, is shown in Figure 2. The reduced-$\chi^{2}$ value of the fit is 3.2, which, with 9 degrees of freedom, implies a $>95$%-confidence result. A bootstrap data-stripping analysis, as detailed by Chatterjee et al. (2009), confirmed the validity of these results, giving median values differing by less than $1\sigma$ from those found by the SVD fit, albeit with slightly larger error bars owing to the data stripping. Our fitted parallax corresponds to a source distance of $2.39\pm 0.14$ kpc.

We have used HSA observations to measure the most accurate distance to a black hole to date, via the method of trigonometric parallax. The distance of V404 Cyg is $2.39\pm 0.14$ kpc, significantly lower than the previous best estimate of the source distance, and demonstrating that uncertainties in the interstellar extinction can introduce significant errors into distance estimates. With the new distance, we can determine that V404 Cyg did not exceed its Eddington luminosity during the 1989 outburst, and that it is likely to have formed in a natal supernova, with the peculiar velocity being consistent with recoil from the ejected mass, and any asymmetric kick being small. We have further constrained the size of the quiescent jets in the source to $<1.4$ AU. These observations demonstrate the feasibility of measuring parallax distances to black hole X-ray binaries using VLBI techniques, which could, with a larger sample of systems, firm up evidence for black hole event horizons, and provide new insights into black hole spins, the mechanism of black hole formation, and the nature of ULXs.