Galactic Center Supermassive Black Hole Research Articles

Prospects of Detecting a Jet in Sagittarius A* with Very-long-baseline Interferometry

Event Horizon Telescope (EHT) images of the horizon-scale emission around the Galactic center supermassive black hole Sagittarius A* (Sgr A*) favor accretion flow models with a jet component. However, this jet has not been conclusively detected. Using the “best-bet” models of Sgr A* from the EHT Collaboration, we assess whether this nondetection is expected for current facilities and explore the prospects of detecting a jet with very-long-baseline interferometry (VLBI) at four frequencies: 86, 115, 230, and 345 GHz. We produce synthetic image reconstructions for current and next-generation VLBI arrays at these frequencies that include the effects of interstellar scattering, optical depth, and time variability. We find that no existing VLBI arrays are expected to detect the jet in these best-bet models, consistent with observations to date. We show that next-generation VLBI arrays at 86 and 115 GHz—in particular, the EHT after upgrades through the ngEHT program and the ngVLA—successfully capture the jet in our tests due to improvements in instrument sensitivity and (u, v) coverage at spatial scales critical to jet detection. These results highlight the potential of enhanced VLBI capabilities in the coming decade to reveal the crucial properties of Sgr A* and its interaction with the Galactic center environment.

Polarized signatures of orbiting hot spots: Special relativity impact and probe of spacetime curvature

Context. The Galactic Center supermassive black hole is well known to exhibit transient peaks of flux density on a daily basis across the spectrum. Recent infrared and millimeter observations have strengthened the case for the association between these flares and circular orbital motion in the vicinity of the event horizon. The strongly polarized synchrotron radiation associated with these events leads to specific observables called QU loops, that is, looping motion in the Stokes QU plane of linear polarization. These patterns have been observed by the Submillimeter Array, VLTI/GRAVITY, and ALMA. Aims. We want to deepen the understanding of the QU loops associated with orbiting hot spots. To this end, we computed such loops in Minkowski and Schwarzschild spacetimes in order to determine which aspects of the observed patterns are due to special- or general-relativistic phenomena. Methods. We considered a parcel of energized plasma in circular motion in Minkowski spacetime and in Keplerian orbit in the Schwarzschild spacetime. We computed, using the GYOTO ray-tracing code, the polarized radiative transfer associated with this orbiting hot spot and derived the evolution of the flux density, astrometry, and Stokes Q and U parameters. Results. We show that QU loops in Minkowski spacetime at low or moderate inclination i ≲ 45° (where i = 0° is a face-on view) share all the qualitative features of Schwarzschild QU loops. There exist QU loops for all setups considered (including for the face-on view and vertical magnetic field), there may be one or two QU loops per orbital period for a vertical magnetic field configuration, and there are always two QU loops in case of a toroidal magnetic field. The simplicity of Minkowski spacetime is a key asset for allowing us to provide analytical formulas that explain the details of this behavior. Moreover, we analyzed the flux variation of the hot spot and show that it is dictated either by the angular dependence of the radiative transfer coefficients or by relativistic beaming. In the former case, this can lead to extreme flux ratios, even at a moderate inclination. Finally, we highlight the increasing mirror asymmetry of the Schwarzschild QU track with increasing inclination and show that this behavior is a specific Schwarzschild feature caused by light bending. Conclusions. Although special-relativistic effects have not been extensively discussed in this context, they are a crucial part in generating the observed QU loops. However, general-relativistic light bending leads to a specific observable feature encoded in the asymmetry of the observed loops, and this feature might allow the spacetime curvature to be quantified.

First Sagittarius A* Event Horizon Telescope Results. VII. Polarization of the Ring

The Event Horizon Telescope observed the horizon-scale synchrotron emission region around the Galactic center supermassive black hole, Sagittarius A* (Sgr A*), in 2017. These observations revealed a bright, thick ring morphology with a diameter of 51.8 ± 2.3 μas and modest azimuthal brightness asymmetry, consistent with the expected appearance of a black hole with mass M ≈ 4 × 106 M ⊙. From these observations, we present the first resolved linear and circular polarimetric images of Sgr A*. The linear polarization images demonstrate that the emission ring is highly polarized, exhibiting a prominent spiral electric vector polarization angle pattern with a peak fractional polarization of ∼40% in the western portion of the ring. The circular polarization images feature a modestly (∼5%–10%) polarized dipole structure along the emission ring, with negative circular polarization in the western region and positive circular polarization in the eastern region, although our methods exhibit stronger disagreement than for linear polarization. We analyze the data using multiple independent imaging and modeling methods, each of which is validated using a standardized suite of synthetic data sets. While the detailed spatial distribution of the linear polarization along the ring remains uncertain owing to the intrinsic variability of the source, the spiraling polarization structure is robust to methodological choices. The degree and orientation of the linear polarization provide stringent constraints for the black hole and its surrounding magnetic fields, which we discuss in an accompanying publication.

The internal Faraday screen of Sagittarius A*

We report on 85−101 GHz light curves of the Galactic Center supermassive black hole, Sagittarius A* (Sgr A*), observed in April 2017 with the Atacama Large Millimeter/submillimeter Array (ALMA). This study of high-cadence full-Stokes data provides new measurements of the fractional linear polarization at a 1−2% level resolved in 4 s time segments, and stringent upper limits on the fractional circular polarization at 0.3%. We compare these findings to ALMA light curves of Sgr A* at 212−230 GHz observed three days later, characterizing a steep depolarization of the source at frequencies below about 150 GHz. We obtain time-dependent rotation measure (RM) values, with the mean RM at 85−101 GHz being a factor of two lower than that at 212−230 GHz. Together with the rapid temporal variability of the RM and its different statistical characteristics in both frequency bands, these results indicate that the Faraday screen in Sgr A* is largely internal, with about half of the Faraday rotation taking place inside the inner 10 gravitational radii, contrary to the common external Faraday screen assumption. We then demonstrate how this observation can be reconciled with theoretical models of radiatively inefficient accretion flows for a reasonable set of physical parameters. Comparisons with numerical general relativistic magnetohydrodynamic simulations suggest that the innermost part of the accretion flow in Sgr A* is much less variable than these models predict; in particular, the observed magnetic field structure appears to be coherent and persistent.

Near-infrared Flux Distribution of Sgr A* from 2005–2022: Evidence for an Enhanced Accretion Episode in 2019

Sgr A* is the variable electromagnetic source associated with accretion onto the Galactic center supermassive black hole. While the near-infrared (NIR) variability of Sgr A* was shown to be consistent over two decades, unprecedented activity in 2019 challenges existing statistical models. We investigate the origin of this activity by recalibrating and reanalyzing all of our Keck Observatory Sgr A* imaging observations from 2005–2022. We present light curves from 69 observation epochs using the NIRC2 imager at 2.12 μm with laser-guide star adaptive optics. These observations reveal that the mean luminosity of Sgr A* increased by a factor of ∼3 in 2019, and the 2019 light curves had higher variance than in all time periods we examined. We find that the 2020–2022 flux distribution is statistically consistent with the historical sample and model predictions, but with fewer bright measurements above 0.6 mJy at the ∼2σ level. Since 2019, we have observed a maximum K s (2.2 μm) flux of 0.9 mJy, compared to the highest pre-2019 flux of 2.0 mJy and highest 2019 flux of 5.6 mJy. Our results suggest that the 2019 activity was caused by a temporary accretion increase onto Sgr A*, possibly due to delayed accretion of tidally stripped gas from the gaseous object G2 in 2014. We also examine faint Sgr A* fluxes over a long time baseline to search for a quasi-steady quiescent state. We find that Sgr A* displays flux variations over a factor of ∼500, with no evidence for a quiescent state in the NIR.

Misaligned Jets from Sgr A* and the Origin of Fermi/eROSITA Bubbles

One of the leading explanations for the origin of Fermi Bubbles is past jet activity in the Galactic center supermassive black hole Sgr A*. The claimed jets are often assumed to be perpendicular to the Galactic plane. Motivated by the orientation of pc-scale nuclear stellar disk and gas streams, as well as a low inclination of the accretion disk around Sgr A* inferred by the Event Horizon Telescope, we perform hydrodynamical simulations of nuclear jets significantly tilted relative to the Galactic rotation axis. The observed axisymmetry and hemisymmetry (north–south symmetry) of Fermi/eROSITA bubbles (FEBs) due to quasi-steady jets in Sgr A* could be produced if the jet had a super-Eddington power (≳5 × 1044 erg s−1) for a short time (jet active period ≲6 kyr) for a reasonable jet opening angle (≲10°). Such powerful explosions are, however, incompatible with the observed O viii/O vii line ratio toward the bubbles, even after considering electron–proton temperature nonequilibrium. We argue that the only remaining options for producing FEBs are (i) a low-luminosity (≈1040.5−41 erg s−1) magnetically dominated jet or accretion wind from the Sgr A*, or (ii) a supernovae or tidal disruption event driven wind of a similar luminosity from the Galactic center.

Monitoring the Size and Flux Density of Sgr A* during the Active State in 2019 with East Asian VLBI Network

In this work, we studied the Galactic Center supermassive black hole (SMBH), Sagittarius A* (Sgr A*), with the KVN and VERA Array (KaVA)/East Asian VLBI Network (EAVN) monitoring observations. Especially in 13 May 2019, Sgr A* experienced an unprecedented bright near infra-red (NIR) flare; so, we find a possible counterpart at 43 GHz (7 mm). As a result, a large temporal variation of the flux density at the level ∼15.4%, with the highest flux density of 2.04 Jy, is found on 11 May 2019. Interestingly, the intrinsic sizes are also variable, and the area and major-axis size show marginal correlation with flux density with ≳2 σ. Thus, we interpret that the emission region at 43 GHz follows the larger-when-brighter relation in 2019. The possible origins are discussed with an emergence of a weak jet/outflow component and the position angle change of the rotation axis of the accretion disk in time.

The Swansong of the Galactic Center Source X7: An Extreme Example of Tidal Evolution near the Supermassive Black Hole

We present two decades of new high-angular-resolution near-infrared data from the W. M. Keck Observatory that reveal extreme evolution in X7, an elongated dust and gas feature, presently located half an arcsecond from the Galactic Center supermassive black hole. With both spectro-imaging observations of Br-γ line emission and Lp (3.8 μm) imaging data, we provide the first estimate of its orbital parameters and quantitative characterization of the evolution of its morphology and mass. We find that the leading edge of X7 appears to be on a mildly eccentric (e ∼ 0.3), relatively short-period (170 yr) orbit and is headed toward periapse passage, estimated to occur in ∼2036. Furthermore, our kinematic measurements rule out the earlier suggestion that X7 is associated with the stellar source S0-73 or with any other point source that has overlapped with X7 during our monitoring period. Over the course of our observations, X7 has (1) become more elongated, with a current length-to-width ratio of 9, (2) maintained a very consistent long-axis orientation (position angle of 50°), (3) inverted its radial velocity differential from tip to tail from −50 to +80 km s−1, and (4) sustained its total brightness (12.8 Lp magnitudes at the leading edge) and color temperature (425 K), which suggest a constant mass of ∼50 M Earth. We present a simple model showing that these results are compatible with the expected effect of tidal forces exerted on it by the central black hole, and we propose that X7 is the gas and dust recently ejected from a grazing collision in a binary system.

Orbital motion near Sagittarius A*

We report on the polarized light curves of the Galactic Center supermassive black hole Sagittarius A*, obtained at millimeter wavelength with the Atacama Large Millimeter/submillimeter Array (ALMA). The observations took place as a part of the Event Horizon Telescope campaign. We compare the observations taken during the low variability source state on 2017 Apr. 6 and 7 with those taken immediately after the X-ray flare on 2017 Apr. 11. For the latter case, we observe rotation of the electric vector position angle with a timescale of ∼70 min. We interpret this rotation as a signature of the equatorial clockwise orbital motion of a hot spot embedded in a magnetic field dominated by a dynamically important vertical component, observed at a low inclination ∼20°. The hot spot radiates strongly polarized synchrotron emission, briefly dominating the linear polarization measured by ALMA in the unresolved source. Our simple emission model captures the overall features of the polarized light curves remarkably well. Assuming a Keplerian orbit, we find the hot spot orbital radius to be ∼5 Schwarzschild radii. We observe hints of a positive black hole spin, that is, a prograde hot spot motion. Accounting for the rapidly varying rotation measure, we estimate the projected on-sky axis of the angular momentum of the hot spot to be ∼60° east of north, with a 180° ambiguity. These results suggest that the accretion structure in Sgr A* is a magnetically arrested disk rotating clockwise.

First Sagittarius A* Event Horizon Telescope Results. III. Imaging of the Galactic Center Supermassive Black Hole

We present the first event-horizon-scale images and spatiotemporal analysis of Sgr A* taken with the Event Horizon Telescope in 2017 April at a wavelength of 1.3 mm. Imaging of Sgr A* has been conducted through surveys over a wide range of imaging assumptions using the classical CLEAN algorithm, regularized maximum likelihood methods, and a Bayesian posterior sampling method. Different prescriptions have been used to account for scattering effects by the interstellar medium toward the Galactic center. Mitigation of the rapid intraday variability that characterizes Sgr A* has been carried out through the addition of a “variability noise budget” in the observed visibilities, facilitating the reconstruction of static full-track images. Our static reconstructions of Sgr A* can be clustered into four representative morphologies that correspond to ring images with three different azimuthal brightness distributions and a small cluster that contains diverse nonring morphologies. Based on our extensive analysis of the effects of sparse (u, v)-coverage, source variability, and interstellar scattering, as well as studies of simulated visibility data, we conclude that the Event Horizon Telescope Sgr A* data show compelling evidence for an image that is dominated by a bright ring of emission with a ring diameter of ∼50 μas, consistent with the expected “shadow” of a 4 × 106 M ⊙ black hole in the Galactic center located at a distance of 8 kpc.

The Intrinsic Structure of Sagittarius A* at 1.3 cm and 7 mm

Abstract Sagittarius A* (Sgr A*), the Galactic Center supermassive black hole (SMBH), is one of the best targets in which to resolve the innermost region of an SMBH with very long baseline interferometry (VLBI). In this study, we have carried out observations toward Sgr A* at 1.349 cm (22.223 GHz) and 6.950 mm (43.135 GHz) with the East Asian VLBI Network, as a part of the multiwavelength campaign of the Event Horizon Telescope (EHT) in 2017 April. To mitigate scattering effects, the physically motivated scattering kernel model from Psaltis et al. (2018) and the scattering parameters from Johnson et al. (2018) have been applied. As a result, a single, symmetric Gaussian model well describes the intrinsic structure of Sgr A* at both wavelengths. From closure amplitudes, the major-axis sizes are ∼704 ± 102 μas (axial ratio ∼ 1.19 − 0.19 + 0.24 ) and ∼300 ± 25 μas (axial ratio ∼1.28 ± 0.2) at 1.349 cm and 6.95 mm, respectively. Together with a quasi-simultaneous observation at 3.5 mm (86 GHz) by Issaoun et al. (2019), we show that the intrinsic size scales with observing wavelength as a power law, with an index ∼1.2 ± 0.2. Our results also provide estimates of the size and compact flux density at 1.3 mm, which can be incorporated into the analysis of the EHT observations. In terms of the origin of radio emission, we have compared the intrinsic structures with the accretion flow scenario, especially the radiatively inefficient accretion flow based on the Keplerian shell model. With this, we show that a nonthermal electron population is necessary to reproduce the source sizes.

First Space-VLBI Observations of Sagittarius A*

Abstract We report results from the first Earth-space VLBI observations of the Galactic Center supermassive black hole, Sgr A*. These observations used the space telescope Spektr-R of the RadioAstron project together with a global network of 20 ground telescopes, observing at a wavelength of 1.35 cm. Spektr-R provided baselines up to 3.9 times the diameter of the Earth, corresponding to an angular resolution of approximately 55 μas and a spatial resolution of 5.5R Sch at the source, where R Sch ≡ 2GM/c 2 is the Schwarzschild radius of Sgr A*. Our short ground baseline measurements ( ≲ 80 Mλ) are consistent with an anisotropic Gaussian image, while our intermediate ground baseline measurements (100–250 Mλ) confirm the presence of persistent image substructure in Sgr A*. Both features are consistent with theoretical expectations for strong scattering in the ionized interstellar medium, which produces Gaussian scatter-broadening on short baselines and refractive substructure on long baselines. We do not detect interferometric fringes on any of the longer ground baselines or on any ground–space baselines. While space-VLBI offers a promising pathway to sharper angular resolution and the measurement of key gravitational signatures in black holes, such as their photon rings, our results demonstrate that space-VLBI studies of Sgr A* will require sensitive observations at submillimeter wavelengths.

Persistent Non-Gaussian Structure in the Image of Sagittarius A* at 86 GHz

Abstract Observations of the Galactic Center supermassive black hole Sagittarius A* (Sgr A*) with very long-baseline interferometry (VLBI) are affected by interstellar scattering along our line of sight. At long radio observing wavelengths (≲1 cm), the scattering heavily dominates image morphology. At 3.5 mm (86 GHz), the intrinsic source structure is no longer sub-dominant to scattering, and thus the intrinsic emission from Sgr A* is resolvable with the Global Millimeter VLBI Array (GMVA). Long-baseline detections to the phased Atacama Large Millimeter/submillimeter Array (ALMA) in 2017 provided new constraints on the intrinsic and scattering properties of Sgr A*, but the stochastic nature of the scattering Requires multiple observing epochs to reliably estimate its statistical properties. We present new observations with the GMVA+ALMA, taken in 2018, which confirm non-Gaussian structure in the scattered image seen in 2017. In particular, the ALMA–GBT baseline shows more flux density than expected for an anistropic Gaussian model, providing a tight constraint on the source size and an upper limit on the dissipation scale of interstellar turbulence. We find an intrinsic source extent along the minor axis of ∼100 μas both via extrapolation of longer wavelength scattering constraints and direct modeling of the 3.5 mm observations. Simultaneously fitting for the scattering parameters, we find an at-most modestly asymmetrical (major-to-minor axis ratio of 1.5 ± 0.2) intrinsic source morphology for Sgr A*.

Depletion of Bright Red Giants in the Galactic Center during Its Active Phases

Abstract Observations in the near-infrared domain showed the presence of the flat core of bright late-type stars inside ∼0.5 pc from the Galactic center supermassive black hole (Sgr A*), while young massive OB/Wolf–Rayet stars form a cusp. Several dynamical processes were proposed to explain this apparent paradox of the distribution of the Galactic center stellar populations. Given the mounting evidence on the significantly increased activity of Sgr A* during the past million years, we propose a scenario based on the interaction between the late-type giants and a nuclear jet, whose past existence and energetics can be inferred from the presence of γ-ray Fermi bubbles and bipolar radio bubbles. Extended, loose envelopes of red giant stars can be ablated by the jet with kinetic luminosity in the range of L j ≈ 1041– within the inner ∼0.04 pc of Sgr A* (S-cluster region), which would lead to their infrared luminosity decrease after several thousand jet–star interactions. The ablation of the atmospheres of red giants is complemented by the process of tidal stripping that operates at distances of ≲1 mpc, and by the direct mechanical interaction of stars with a clumpy disk at ≳0.04 pc, which can explain the flat density profile of bright late-type stars inside the inner half parsec from Sgr A*.

Effect of Electromagnetic Interaction on Galactic Center Flare Components

Abstract Recently, near-infrared GRAVITY@ESO observations at 2.2 μm announced the detection of three bright “flares” in the vicinity of the Galactic center supermassive black hole (SMBH) that exhibited orbital motion at a distance of about 6–11 gravitational radii from an ∼4 × 106 M ⊙ black hole. There are indications of the presence of a large-scale, organized component of the magnetic field at the Galactic center. Electromagnetic effects on the flare dynamics were previously not taken into account despite the relativistic motion of a plasma in magnetic field leading to the charge separation and nonnegligible net charge density in the plasma. Applying various approaches, we find the net charge number density of the flare components of the order of 10−3–10−4 cm−3, while the particles’ total number density is of the order of 106–108 cm−3. However, even such a tiny excess of charged particles in the quasi-neutral plasma can significantly affect the dynamics of flare components, which can then lead to the degeneracy in the measurements of spin of the SMBH. Analyzing the dynamics of recent flares in the case of the rapidly rotating black hole, we also constrain the inclination angle between the magnetic field and spin axis to α < 50°, as for larger angles, the motion of the hot spot is strongly chaotic.

A Nonthermal Bomb Explains the Near-infrared Superflare of Sgr A*

Abstract The Galactic center supermassive black hole, Sgr A*, has experienced a strong, unprecedented flare in 2019 May when its near-infrared luminosity reached much brighter levels than ever measured. We argue that an explosive event of particle acceleration to nonthermal energies in the innermost parts of the accretion flow—a nonthermal bomb—explains the near-infrared light curve. We discuss potential mechanisms that could explain this event such as magnetic reconnection and relativistic turbulence acceleration. Multiwavelength monitoring of such superflares in radio, infrared, and X-rays should allow a concrete test of the nonthermal bomb model and put better constraints on the mechanism that triggered the bomb.

Unprecedented Near-infrared Brightness and Variability of Sgr A*

Abstract The electromagnetic counterpart to the Galactic center supermassive black hole, Sgr A*, has been observed in the near-infrared for over 20 yr and is known to be highly variable. We report new Keck Telescope observations showing that Sgr A* reached much brighter flux levels in 2019 than ever measured at near-infrared wavelengths. In the K′ band, Sgr A* reached flux levels of ∼6 mJy, twice the level of the previously observed peak flux from >13,000 measurements over 130 nights with the Very Large Telescope and Keck Telescopes. We also observe a factor of 75 change in flux over a 2 hr time span with no obvious color changes between 1.6 and 2.1 μm. The distribution of flux variations observed this year is also significantly different than the historical distribution. Using the most comprehensive statistical model published, the probability of a single night exhibiting peak flux levels observed this year, given historical Keck observations, is less than 0.3%. The probability of observing flux levels that are similar to all four nights of data in 2019 is less than 0.05%. This increase in brightness and variability may indicate a period of heightened activity from Sgr A* or a change in its accretion state. It may also indicate that the current model is not sufficient to model Sgr A* at high flux levels and should be updated. Potential physical origins of Sgr A*'s unprecedented brightness may be from changes in the accretion flow as a result of the star S0-2's closest passage to the black hole in 2018, or from a delayed reaction to the approach of the dusty object G2 in 2014. Additional multi-wavelength observations will be necessary to both monitor Sgr A* for potential state changes and to constrain the physical processes responsible for its current variability.

A Deep Chandra View of a Candidate Parsec-scale Jet from the Galactic Center Supermassive Black Hole

Abstract We have investigated the linear X-ray filament, G359.944−0.052, previously identified as a likely X-ray counterpart of a parsec-scale jet from the Galactic Center supermassive black hole (SMBH) Sagittarius A* (Sgr A*), using a total of ∼5.6 Ms ultra-deep Chandra observations taken from 1999 September to 2017 July. This unprecedented data set enables us to examine flux and spectral variations that might be related to intrinsic properties of the weakly accreting SMBH. We find no flux or spectral variation in G359.944−0.052 after the G2 periapsis passage around early 2014; however, a moderate flux increase of ∼2σ significance might be associated with the periapsis passage of G1 in early 2001. The filament exhibits an unusually hard spectrum (photon index ≲1) in its portion closest to Sgr A* (i.e., near side) and a significant spectral softening in the more distant portion, which can be interpreted as synchrotron cooling of the relativistic electrons moving along the jet path. In particular, the hard spectrum of the near side suggests a piling up of quasi-monoenergetic electrons caused by rapid radiative cooling. The spectral and temporal properties of G359.944−0.052 strengthen the case for it being the X-ray counterpart of a jet launched by Sgr A*.

Test of the Einstein Equivalence Principle near the Galactic Center Supermassive Black Hole.

During its orbit around the four million solar mass black hole Sagittarius A* the star S2 experiences significant changes in gravitational potential. We use this change of potential to test one part of the Einstein equivalence principle: the local position invariance (LPI). We study the dependency of different atomic transitions on the gravitational potential to give an upper limit on violations of the LPI. This is done by separately measuring the redshift from hydrogen and helium absorption lines in the stellar spectrum during its closest approach to the black hole. For this measurement we use radial velocity data from 2015 to 2018 and combine it with the gravitational potential at the position of S2, which is calculated from the precisely known orbit of S2 around the black hole. This results in a limit on a violation of the LPI of |β_{He}-β_{H}|=(2.4±5.1)×10^{-2}. The variation in potential that we probe with this measurement is six magnitudes larger than possible for measurements on Earth, and a factor of 10 larger than in experiments using white dwarfs. We are therefore testing the LPI in a regime where it has not been tested before.

The propagation delay in the timing of a pulsar orbiting a supermassive black hole

The observation of a pulsar closely orbiting the galactic center supermassive black hole would open the window for an accurate determination of the black hole parameters and for new tests of General Relativity. An important relativistic effect which has to be taken into account in the timing model is the propagation delay of the pulses in the gravitational field of the black hole. Due to the extreme mass ratio of the pulsar and the supermassive back hole we use the test particle limit to derive an exact analytical formula for the propagation delay in a Schwarzschild spacetime. We then compare this result to the propagation delays derived in the usually employed post-Newtonian approximation, in particular to the Shapiro delay up to the second post-Newtonian order. For edge-on orbits we also consider modifications of the Shapiro delay which take the lensing effects into account. Our results are then used to assess the accuracy of the different orders of the post-Newtonian approximation of the propagation delay. This comparison indicates that for (nearly) edge-on orbits the new exact delay formula should be used.