Astronomy

How can I obtain raw observation data of stars surrounding Sgr A*?

How can I obtain raw observation data of stars surrounding Sgr A*?


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Are there any publicly available telescope that offers the sensitivity to observe the stars surrounding Sgr A*? If not, is there any raw data available that I could download?


Observations of stars near Sgr A* are done in the near-infrared, usually with adaptive optics. Most of these are done by two groups: Andrea Ghez's group at UCLA, using the Keck Telescopes in Hawaii, and Reinhard Genzel's group at MPE (Max-Planck-Institute for Extraterrestrial Physics), using the European Southern Observatory's Very Large Telescope (VLT) in Chile.

Both telescopes have public data archives, so in principle you can retrieve the raw data for these observations, as long as the observations are at least a year old (which most of them are). You need to know which are the relevant instruments; NACO has been used for most of the images at the VLT, and I think NIRC2 has been used at Keck. (There are also spectroscopic observations using both telescopes.)

So you could, for example, search using the NACO-specific search form in the ESO archive. I would suggest entering "Sgr A*" in the "Target name" field, restricting the "Search Box" field to something like 30 arc seconds (change the default "00 10 00" to "00 00 30"). Note that these observations involve lots of short exposures in different filters, and with no other restrictions on the search, you will get more than 10,000 hits.

(In order to actually retrieve the data, you will need to register as a user of the archive, which is free.)

Something similar might work for the Keck Observatory Archive, though I've never really used that.

You'll need to be familiar with the reduction and analysis of near-IR imaging to get anything from the data, of course. ESO does provide "pipeline" software that can do some of the reduction (search on their site).

You can, in principle, apply to use the VLT yourself, but unless you really know what you're doing, it's very unlikely you'd get time in competition with, say, Genzel's group. Also, NACO has been taken off the VLT; its replacement instrument, ERIS, won't be available until sometime in 2020. (You can't generally apply for Keck time unless you're at one of its member institutions.)


Not much will be visible in optical wavelength as the region will be too bright or nothing will be visible. You can observe in X-ray practically as black holes emit synchrotron radiation and that is visible in x-ray region pretty good. So you can write a proposal to CXO and make them understand your need to observe them Sag A* and they will allot you time. Then you can process that.


Supermassive black hole ejects hyper-velocity star

It’s hard for most of us to comprehend some of the enormous speeds that are related to space exploration, travel or discovery.

The average flight speed of a 747 passenger aircraft, one that many people have experienced, is about 900 km/h. The fastest any human has ever travelled was by the Apollo 10 astronauts, as they soared around the back of the Moon at 39,897 km/h heading back to Earth. Whilst, in November 2018, NASA’s Parker Solar Probe, was clocked in at 343,180 km/h – setting the Guinness World Record.

We picture ourselves trying to imagine how fast this would feel or even look like from a drivers point of view, by mentally comparing our experiences of riding in cars and aeroplanes.

But our brains can’t compute the velocity observed of a new massive object, a star bigger than our Sun, moving across our Milky Way galaxy at over 6,000,000 km/h. At the speed that this newly discovered star is travelling - you could circle Earth’s equator almost 150 times in the same hour or fly from Sydney to London in under 10 seconds.

How could any such object, receive enough energy to blast it across space at extreme speeds? And what could be bigger to give it such a kick?

Australian astronomers, working as part of an international collaboration, have discovered the fastest moving main-sequence star on its journey to depart the Milky Way, after encountering the enormous forces of the Galaxy’s supermassive black hole 4.8 million years ago.

“This discovery is very exciting!” said Geraint Lewis, Professor of Astrophysics at the University of Sydney in addition to being one of the S 5 project leaders.

“A star that spent its life at the centre of the Milky Way has been spat out in a violent interaction with our supermassive black hole and is now speeding out of the Galaxy. What secrets of the inner parts of the Galaxy will it reveal?” he said.

The star, called S5-HVS1, is a hot (

9,600K) A-Class main-sequence star (meaning hydrogen is still fusing in its core), making it is a little larger than the Sun with 2.35 times its mass. It’s traversing across the southern sky, currently in the constellation of Grus (the Crane) at a mind-boggling 6 million km/h.

Tracing its trajectory and velocity backwards, the researchers have indicated that S5-HVS1 is likely to have been part of a binary system which wondered close to Sgr A* (pronounced “Sagittarius A-Star”) the supermassive black hole at the centre of our galaxy. Unfortunately for S5-HVS1’s binary partner, the close proximity to Sgr A* means it was captured whilst the surviving star received an enormous kick of energy – propelling it away from the Galactic Centre.

“I was really surprised when we found a star going so fast. It only sank in when we got follow-up observations that confirmed the speed,” said Dr. Jeffrey Simpson, a post-doctoral research fellow at the UNSW science school of physics, a co-author on the paper.


How can I obtain raw observation data of stars surrounding Sgr A*? - Astronomy

The center of the Milky Way galaxy, with the supermassive black hole Sagittarius A* (Sgr A*) located in the middle, is revealed in these images. As described in our press release, astronomers have used NASA's Chandra X-ray Observatory to take a major step in understanding why gas around Sgr A* is extraordinarily faint in X-rays.

The large image contains X-rays from Chandra in blue and infrared emission from the Hubble Space Telescope in red and yellow. The inset shows a close-up view of Sgr A* only in X-rays, covering a region half a light year wide. The diffuse X-ray emission is from hot gas captured by the black hole and being pulled inwards. This hot gas originates from winds produced by a disk-shaped distribution of young massive stars observed in infrared observations (mouse over the image for the distribution of these massive stars).

These new findings are the result of one of the biggest observing campaigns ever performed by Chandra. During 2012, Chandra collected about five weeks worth of observations to capture unprecedented X-ray images and energy signatures of multi-million degree gas swirling around Sgr A*, a black hole with about 4 million times the mass of the Sun. At just 26,000 light years from Earth, Sgr A* is one of very few black holes in the Universe where we can actually witness the flow of matter nearby.

The authors infer that less than 1% of the material initially within the black hole's gravitational influence reaches the event horizon, or point of no return, because much of it is ejected. Consequently, the X-ray emission from material near Sgr A* is remarkably faint, like that of most of the giant black holes in galaxies in the nearby Universe.

The captured material needs to lose heat and angular momentum before being able to plunge into the black hole. The ejection of matter allows this loss to occur.

This work should impact efforts using radio telescopes to observe and understand the "shadow" cast by the event horizon of Sgr A* against the background of surrounding, glowing matter. It will also be useful for understanding the impact that orbiting stars and gas clouds might make with the matter flowing towards and away from the black hole.


2. OBSERVATIONS AND DATA REDUCTION

In 2012 October, at the advent of the passage of the G2 cloud with respect to Sgr A* (e.g., Gillessen et al. 2012 Narayan et al. 2012), monitoring of the radio flux density of Sgr A* began (see Bower et al. 2015b, who use the same NRAO service observations data as we do here). Each observation lasted for

2 hr, using up to 2 GHz of continuum bandwidth rotating through the standard observing frequencies centered at 1.5, 3.0, 5.5, 9.0, 14.0, 21.2, 32.02, and 41 GHz. Typical on-source times per frequency setup were about 6 minutes. The flux density was calibrated with respect to 3C286 and bandpass shapes were determined using NRAO 530 and 3C286.

The data were calibrated and imaged in AIPS initially and follow-up analysis was made with CASA. To correct for phase instabilities during the scans, phase-only self-calibration was applied (in all observations). Because of the compact nature of both Sgr A* and the magnetar, we used extended array configurations (A & B) and high frequencies. 6 The absolute flux density of these observations may be inaccurate by up to 10% as the elevation of the primary flux calibrator in most observing runs is far different from that of the Galactic center, introducing errors in modeling the atmospheric transmission at the higher frequencies. These measurements are consistent with millimeter monitoring data indicating a stable flux density of Sgr A* during the same period (Bower et al. 2015b). As the measured flux densities of the magnetar that lies 23 SE of Sgr A* are tied to the flux density of Sgr A*, this provides an excellent platform to perform flux density measurements of the magnetar.

We also present the flux density of the magnetar and Sgr A* from three different epochs of observations on 2011 August 4 (JD2455777), 2014 February 21 (JD 2456710), and 2014 March 09 (JD 2456732). Details of these long observations that were taken in the A configuration are described in Yusef-Zadeh et al. (2014b, 2015).


2 METHODS

The Chandra X-ray Visionary Project (XVP) to observe the Milky Way's SMBH, Sgr A* from 2012 February 6 to October 29 resulted in approximately 3 Ms of exquisite data, opening up a completely new regime of insight into BH accretion. Chandra and the XVP program have offered us an excellent opportunity to observe directly the dynamics of hot gas around a BH, and, with proper modelling, hopefully elucidate the inner workings of the enigmatic class of objects known as LL-AGN. Combining this observational data with 2D RRIOS simulations (Ostriker et al., in preparation), we attempt to constrain directly the accretion structure via the power of Bayesian MCMC fitting.

2.1 Data preparation

For a more detailed description of the data reduction and quiescent X-ray image generation, we recommend the reader to Wang et al. ( 2013). However, in short, the data are reduced via standard ciao processing routines (version 4.5 Calibration Database version 4.5.6). Since the differences between individual observation pointings are all within 14 arcsec, the merged data are treated as a single observation. Wang et al. ( 2013) found no apparent calibration issues. Flares are removed from the quiescent data through detection with the ‘ bayesian blocks ’ routine (Neilsen et al. 2013), leading to a total quiescent exposure time of 2.78 Ms. The observed quiescent image over the entire spectral band (1–9 keV) can be seen in Fig. 1. The south-east corner of the image is excluded in the fit due to significant emission from an unmodelled feature in the region (highlighted by white lines in Fig. 1 see also Wang et al. 2013). The region used for fitting extends to a radius of approximately 0.5 rb. Since the source is on-axis, the full width at half-maximum (FWHM) of the instrument is comparable to the pixel size. To utilize additional spatial information from the dithering of observations, we construct the so-called ‘super-resolution’ image with a pixel size of 0.123 arcsec on a side (Wang et al. 2013). The full band image is then split into three bands, to place some spectral constraints on the fit and reduce degeneracy. The bands (1–4, 4–5.5, and 5.5–9 keV) were chosen such that the counting statistics are roughly similar in each image.

Counts image of Sgr A* in the 1–9 keV band taken with a 2775 578-s exposure using Chandra. Colour bar represents total counts in a pixel.


5 DISCUSSION AND SUMMARY

With the emissivity and absorption coefficient from the RIAF model for the Galactic Centre black hole candidate Sgr A*, we solved the radiative transfer using the ray-tracing code to get the simulated shadow images of Sgr A* with an arbitrary set of geometrical parameters, i.e. i and Θ. By taking into account the interstellar scattering, we can obtain the apparent images at different wavelengths.

Comparison of the simulated image sizes with those measurements at both 7 and 3.5 mm seems to prefer a RIAF with a large inclination angle and small position angle for Sgr A*. But, large uncertainties in both the size measurements and the interstellar scattering relationship make these very uncertain at the moment. However, our simulations show that the future submillimetre VLBI images of Sgr A* would reveal a significant deviation from the single Gaussian structure, which can be used to probe the geometry of the RIAF of Sgr A*.

Analysis of the scatter-broadened images also shows that an observing wavelength of 1.3 mm or shorter is needed to identify the shadow shape. However, currently it is difficult to construct a VLBI array operated at 1.3 mm to obtain such an image. We therefore first perform the Fourier transform to obtain the corresponding visibility functions of images at 1.3 and 0.8 mm, then analyse these visibility profiles along some specific directions. By introducing several characteristic baseline lengths (Σn and Σn) and the normalized differences (Sn), we demonstrate that it is possible to determine fundamental parameters (i and Θ) of Sgr A* from the limited detections on some baselines of VLBI observations at a wavelength of 1 mm or shorter (cf. Figs 5 and 6). We can understand the geometry of the radio-emitting region surrounding Sgr A* even without imaging it with a completely (u, v) coverage of a submillimetre/millimetre VLBI array.

It should be mentioned that the four directions chosen in our analysis are somehow arbitrary. Any other combinations would also provide useful constraints on the structure of Sgr A*. For example, it would be interesting to choose such two specific slices, one along the Galactic plane and the other perpendicular to it. In practice, we can perform similar simulations with the projected baselines to be exactly the same as those from the real submillimetre VLBI experiments in the future. Of course, the RIAF model adopted here is still quite simple. We set the static black hole, use pseudo-Newtonian potential ( Yuan et al. 2003) and simply assume a Gaussian distribution of the density as the vertical structure of the accretion flow. Moreover, the possible dynamical role of an ordered magnetic field is not considered. We also neglect the Doppler effect of the radial and angular motions of the accretion flow in the radiative transfer calculation. However, in principle, the visibility analysis outlined in this paper should be applicable even if Sgr A* is a spinning black hole or with other accretion flow geometries and emission models. As a necessary first step trying to solve this complicated problem, this work definitely needs further efforts in both modelling and observations. A more quantitative study will be required in future work.

Furthermore, the fact that the characteristic baseline lengths are about 10 3 km and the expected observing wavelength is about 1 mm encourages us to propose the development of a submillimetre VLBI array. The image of the vicinity of the predicted black hole in Sgr A* is expected to be more easily detected than any other supermassive black hole candidates because of its closest distance to us. If the shadow image could be finally observed, it will be strong evidence for the General Relativity theory.

We would like to thank two anonymous referees for their critical comments on the manuscript. This work was supported in part by the National Natural Science Foundation of China (grants 10543003, 10573029, 10625314 and 10633010) and the Knowledge Innovation Program of the Chinese Academy of Sciences, and sponsored by Program of Shanghai Subject Chief Scientist (06XD14024) and Shanghai Pujiang Program. ZQS and FY acknowledge the support by the One-Hundred-Talent Program of Chinese Academy of Sciences.


4. Analysis

4.1. NIR Flare Statistics

Given the ability of HST to produce continuous observations over many 45 minute orbital visibility periods, along with its long-term photometric stability, the NIR NICMOS data provide an excellent way to investigate the flare strength distribution over many flare episodes. Figure 16 shows a histogram of the NICMOS 1.70 μm net flare emission for the 7 days of data obtained in this campaign. The net flare emission is measured by first subtracting the background emission for each day before the excess flux above the background is selected. Thus, the selected data points do not sample the peak flare emission but rather the flux associated with flaring activity. The peak of values centered at a net flux of zero represents the emission from Sgr A* during "quiescent" periods. The positive half of the histogram, on the other hand, shows a tail of flare emission events extending out to

10 mJy. The "quiescent" distribution is best fitted with a Gaussian, which is expected from the level of random noise in the observations. The tail of flare emission can be fitted with a power-law distribution having an index of −1.19 ± 0.27 and a low-energy cutoff at Sν = 1 mJy. The dotted line in the figure shows the result of simultaneous Gaussian and power-law fits to these two components.

Figure 16. Histogram plot of the detected signals and the noise at 1.70 μm as well as the simultaneous single Gaussian fit and power-law fits to both the noise and the flares. The dotted lines show the Gaussian and power-law fits.

Yusef-Zadeh et al. (2006b) reported that distribution of flare activity seen in our more limited 2004 NICMOS observations could be fitted by two simultaneous Gaussians profiles. A reanalysis of those data, however, now show that a power-law distribution with a low-energy cutoff yields a good fit to the 2004 epoch data as well. Figure 17 shows a histogram of the 2004 1.60 μm data, with Gaussian and power-law fits to the two components shown by the broken lines. The best power-law fit to these data has an index of −1.11 ± 0.13, with a low-energy cutoff of Sν = 0.25 mJy. This is remarkably consistent with the best-fit power-law index of the 2007 data. We note that the fraction of observing time that flare activity has been detected in the 2004 and 2007 campaigns is �% and �%, respectively.

Figure 17. Similar to Figure 16 expect that the 2004 histogram of flare activity (Yusef-Zadeh et al. 2006b) is plotted at 1.60 μm.

The NIR flare histograms for the two epochs show that the probability of measuring flux Sν at any instant is approximately proportional to 1/Sν. Presumably this reflects the statistics of the flaring behavior of Sgr A* at NIR wavelengths. To explore this we construct a simple phenomenological model for the flaring by simulating a light curve and then sample it to construct a simulated histogram. This model shows that the observed 1/Sν behavior arises quite naturally, but does constrain the statistics of the flaring.

Our phenomenological model represents the flaring as a sequence of 100 Gaussian profiles occurring over 100 arbitrary time units, with flare i characterized by peak flux Si, timing of the peak ti, and standard deviation of the flare σi, so that the net light curve may be written as

The parameters Si, ti, and σi are drawn randomly and uniformly from the ranges [0, 1], [0, 100], and [0, σmax], respectively, and the resulting light curve is evenly sampled every 0.2 time units to create a flare histogram. Note that σmax is the only independent parameter of this model, as increasing the number of flares and changing the maximum flare amplitude can be accommodated by rescaling the flux and time units. In addition, changing the sampling rate or the number of flares does not affect the statistics, provided that the light curve has already been adequately sampled (which is the case for our adopted sampling rate of 50 per time unit). We find that σmax 0.5 yields the observed 1/Sν behavior.

A typical simulated light curve and the corresponding histogram for σmax = 0.5 are given in Figure 18(a) and (b), respectively. The slope of S −1 ν is drawn on Figure 18(b). Larger values of σmax lead to significant overlap between flares, tending to give a flatter dependence of the flux probability on Sν. This does not, of course, prove definitively that the flares behave as given by Equation (1). Other choices of functional form or different statistics for Si may also yield the 1/Sν behavior of the histogram. It does, however, seem to require that the flare events do not significantly overlap each other.

Figure 18. (a) Synthetic light curve constructed from the sum of 100 Gaussian profiles with peak positions and, standard deviations drawn uniformly between −1.5 to 101.5 and 0 to 0.5 time units, respectively the probability distribution of the peak fluxes are distributed as 1/(peak flux) between 0.01 and 1 flux units. (b) Distribution of uniformly sampled flux values in the simulated flares. The dashed line indicates a slope of 1/Sν.

4.2. Spectral Index Distribution Between 1.45 μm and 1.70 μm

We have constructed a log–log distribution of spectral index based on the NICMOS 1.45 μm and 1.70 μm data. Figure 19 shows the "color" distribution of all the data selected with S/N = 3. The diagonal line (in red) shows the spectral index of β = 0.6, where Fν ∝ ν −β . For comparison, β of −4, −2, 2, and 4 are also plotted. This figure shows a tendency for the spectral index of low flux values to be steeper than 1, whereas the high flux values are represented by a flatter distribution of spectral index. Because the data points used in making Figure 19 are not taken simultaneously at the two different wavelengths, we attempted to estimate spectral index values of adjacent data points, where the flux of Sgr A* is not varying rapidly, such as during the fast rise or fall of individual flares. The 1.45 and 1.7 μm NICMOS images were acquired back-to-back in long sequences, in which the exposures within each pair are separated in time by about 2.5 minutes. The points shown in Figure 19 represent all adjacent pairs of measurements (adjacent meaning

2.5 minute separation) for which the S/N in the individual measurements is greater than 3 (hence not all available pairs from Figure 3 are included). The fact that the overall Sgr A* flux could be changing within that 2.5 minute timescale is a concern and is why the spectral index values listed in Table 1 were taken from only those measurements where we could see from the light curves that the overall Sgr A* flux was not changing much on that

2.5 minute timescale. The full light curves also indicate that the overall flux of Sgr A* does not often change on such short timescales and therefore the number of suspect measurements in Figure 19 should be a relatively small fraction of all measurements. Hence we only deduce general trends from that diagram.

Figure 19. log–log plot of NIR fluxes in the F170 and F145 filters of NICMOS at 1.70 μm and 1.45 μm, respectively. The thick line in red shows the spectral index β = 0.6. The thin dotted lines to the right and left of the β = 0.6 line correspond to β = −2, − 4, and β = +2, + 4, respectively.

Table 1. Spectral Index Distribution Using NICMOS

Event F(1.45 μm ± σ) F(1.70 μm ± σ) β ± σ
5A 8.55 ± 0.4 9.61 ± 0.4 0.73 ± 0.39
2A 6.77 ± 0.6 7.92 ± 0.5 0.97 ± 0.68
2C 4.54 ± 0.1 6.54 ± 0.7 2.29 ± 0.27
4A 4.77 ± 0.1 6.14 ± 0.3 1.59 ± 0.33
5B 2.31 ± 0.5 3.62 ± 0.4 2.82 ± 1.51
7A 2.85 ± 0.3 3.63 ± 0.2 1.52 ± 0.74

We identified five sets of data points associated with five different flares during which the overall Sgr A* flux is not varying rapidly. Table 1 shows the corresponding flux and spectral index values using data sampled at 144 s intervals. The two brightest flares, 5A and 2A, have spectral indexes 0.73 ± 0.16 and 0.97 ± 0.27, whereas the weaker flares have indexes steeper than β = 1.5. These individual measurements are consistent with the spectral index trend shown in Figure 19. We also find that the spectral index of the brightest flares are consistent with recent Keck measurements, which yield a spectral index of 0.6 (Hornstein et al. 2007). The spectral index of low flux values is also consistent with VLT measurements, which show a steep spectrum for weak flares (Eisenhauer et al. 2005 Gillessen et al. 2006). These measurements suggest that the spectral index of flares varies with the NIR flare strength, support earlier measurements by Gillessen et al. (2006) and disagree with measurements by Hornstein et al. (2007) who claim a constant spectral index in NIR wavelengths. The variation of spectral index with flare emission at NIR wavelengths has important implications on the inverse Compton scattering mechanism of X-ray and soft γ-ray emission from Sgr A* (Yusef-Zadeh et al. 2006b) as well as on the hypothesis that X-ray emission is due to synchrotron mechanism (Dodds-Eden et al. 2009). It is possible that weak flares with a steep energy index of particles are associated with low-level activity of the accretion disk of Sgr A*, whereas the bright flares represent the hot magnetically dominated events that are launched from the disk. Polarization characteristics of the weak and strong flares may constrain models of the flare emission. The correlation of the spectral index and flux has been discussed in the context of electron heating and cooling by a turbulent magnetic field (Bittner et al. 2007). In the synchrotron scenario, the higher value of the spectral index at low NIR fluxes could be an indication of the cooling break.

4.3. NIR Power Spectrum Analysis

Genzel et al. (2003) had reported a possible 17 minute NIR periodicity with implications for the spin of the black hole. Our previous 2004 HST data (Yusef-Zadeh et al. 2006b) showed a marginal detection of power at 33 ± 2 minutes. We investigated the power spectrum of flare data taken with the new NICMOS measurements. We created Lomb–Scargle periodograms (Scargle 1982) to search for periodicities in our unevenly spaced NIR measurements. We performed 1000 simulations of each light curve, with the same sampling and variance as the data, and with simulated noise following a power law (P(f) ∝ f −δ ) chosen to match the periodogram of the data as closely as possible (following Timmer & Konig 1995 Mauerhan et al. 2005), typically with an index δ of 1.5 or 2. Artificial signals are seen at the 90 minute orbital period of HST, and the 144 s filter switching cycle, and discounted. For each point in a light curve, we identify the periodogram simulation at the nth (where n = 99, 99.9) percentile of the distribution, and thus create lines below which n% of the simulations fall. Figure 20 shows the power spectrum as a solid line and the dotted lines show the spectrum of the noise using power-law distributions. Only one HST observation shows any power above the 99.9 percentile line, on 2007 April 4, near 2 hr.

Figure 20. Top and bottom boxes show the light curve of 2007 April 4 based on HST observations and the corresponding power spectrum of the residual flux of Sgr A*, respectively. The dashed lines show the significance of the power spectrum at 99% and 99.9% confidence levels. We explain the significance of the peak in the text.

The 99.9 percentile refers to the local distribution however, the chance of getting a point above the 99.9 percentile line must be computed considering all trials (Benlloch et al. 2001). We sample 158 frequencies above 10.8 minutes, the lower limit of our simulation software, and perform seven observations, so our total is 1106 observations, suggesting

1 peak above the 99.9 percentile line. We have two adjacent points above the 99.9 percentile line, but these points are probably not independent. Altering the index δ within a range consistent with the data does not change the strength of the signal. We conclude that the significance of this possible periodicity is not particularly strong.

The lack of any significant power between 17 and 20 minutes supports the results from an earlier analysis of HST data in 2004 (Yusef-Zadeh et al. 2006b). Recent analysis of data taken with the combined VLT and the Keck observations shows no significant power on short timescales (Do et al. 2008 Meyer et al. 2008).


APPENDIX B: APPARENT SIZES OF COMPACT OBJECTS

Observations of the size of a compact emitting region are necessarily impacted by strong gravitational lensing. In metric theories of gravity, objects associated with deep potential wells will appear larger to observers at infinity. The apparent size of the region is directly related to both the physical size and the redshift of the compact object. Thus, relating the actual size of a compact emitting region to the observed size requires some understanding of the spacetime structure around the object. This is, of course, one of the reasons we chose to cast the constraints upon the existence of a horizon, described in Section 3, in terms of Ra and not a physical object size. Nevertheless, for completeness, we discuss the procedure here.

It is typically very difficult to compute the relationship between the physical and observed size and shape of a compact emitting object. However, in the special case of a spherically symmetric spacetime, this is generally tractable, independent of the particular form of the metric. We assume

where gtt and grr are functions of r alone. Then, in the equatorial plane, the null geodesics are defined by

where the equations for dt/dλ and d/dλ are associated with the existence of a time-like and azimuthal Killing vectors, respectively, the equation for dθ/dλ is fixed by vertical symmetry and the equation for dr/dλ arises from the null ray condition. In these b is the impact parameter at infinity and λ is an arbitrary affine parameter. The minimum radius reached by a given null geodesic occurs at its inner turning point, at which . Alternatively, this corresponds to the maximum b that a null geodesic can have and still impact a surface of radius r. Thus, the apparent radius, Ra, of an object with physical radius R is simply

Some care must be taken, however, when R is smaller than the photon orbit. This is because rays which cross the photon orbit have no radial turning points, and therefore will in all cases be captured. This is clear from the definition of the photon orbit, rγ:

which corresponds to the position of the maximum of the "effective potential" in the radial equation. Thus, if

As a consequence, the apparent radius of objects for which R < rγ is the same as that for objects with R = rγ. Thus, generally,

In the case of the Schwarzschild metric, this gives the well known result

For a rapidly rotating Kerr spacetime, the apparent radius in the equatorial plane may also be computed without undue difficulty (though in this case care must be taken into account for the non-diagonal components of the metric). Generally, this is given by

in which r±γ is the radius of the prograde/retrograde photon orbit. Since these differ for rotating black holes, we generally have three conditions. In the case of a maximally rotating black hole (a = 1), this expression is especially simple:

where R is the object radius in Boyer–Lindquist coordinates. While r = M in these coordinates for a = 1, there remains a finite proper distance between the photon orbit and the horizon, the equality being an artifact of the coordinates themselves. For this reason, we distinguish between these formally, though it makes no difference (since Ra = 9/2 for all R between r and the horizon), as it must not given that Ra is a gauge invariant quantity as a consequence of its definition.

Most important for the present discussion is the fact that Ra for the Schwarzschild and equatorial Kerr spacetimes differs by only about 15%. Thus, despite the vastly different coordinate sizes, an object with R = 1 M embedded in a maximal Kerr spacetime has roughly the same apparent size as an object with R = 3 M embedded in a Schwarzschild spacetime. As a consequence, if the present limit upon the size of the submillimeter emitting region in Sgr A* of 37 μas (Ra = 3.5 M) is interpreted as a photosphere surrounding the stopping region, it constrains the size of a central emitting region to lie well within the photon orbit of both a Kerr and Schwarzschild black hole.

On the other hand, the anomalously small apparent radius might appear unphysical within the context of GR. However, this is easily rectified if the emission region is interpreted instead as the visible arc of an oncoming accretion disk (as a result of Doppler boosting and Doppler shifts, the receding side being considerably dimmer for the same reason Broderick & Loeb 2006a). While the equatorial extent of the arc can be significantly smaller than the minimum apparent radius in this situation, the vertical extent is still roughly 2Ra (see, e.g., Broderick et al. 2009 Broderick & Narayan 2006). Hence, unless the projected baseline was extraordinarily fortuitously aligned, again we would expect large measured sizes for central emission regions larger than the photon orbit radius. It is possible to coincidentally fit the existing spectral, polarization, and millimeter-VLBI observations using orbiting accretion flow models (Broderick et al. 2009). However, this is due at least in part to the fact that the existing millimeter-VLBI size constraint is essentially restricted to the east–west direction. Future millimeter-VLBI observations will be critical to unambiguously determining the morphology of the emitting region (Fish et al. 2009).


3 Applications to individual sources

3.1 Sgr A*

Fig. 1 shows the calculated spectrum for Sgr A* together with the observational data taken from Narayan et al. (1998) except that the new Chandra data denoted by a filled square is taken from Baganoff et al. (in preparation). The thin solid line is for a truncated ADAF with the dashed line is for a jet, and the thick-solid line denotes the total spectrum of the ADAF-jet system. The truncation radius The dotted line is for the ‘not-truncated’ ADAF with the same parameters and outer boundary conditions except Even though we adopt such a weak magnetic field, we find that the synchrotron process still emits too much radio flux and the Comptonization of the synchrotron photons produces an X-ray flux well above the observational measurement. Compared with the ‘not-truncated’ ADAF, the radio flux is significantly suppressed in the truncated ADAF and the X-ray emission is also reduced as a result of the reduction of Comptonized synchrotron photons. From the figure we find that the spectrum below ∼50 GHz is mainly contributed by the jet while those above is principally produced by the disc and the fit to the observation is good.

Although the accretion rate favoured in our model is ∼6 times smaller than the numerical simulation of Coker & Melia (1997), we note that such a discrepancy could be reduced by ∼3 times if we adopted a larger viscous parameter because of the scaling law In this case, the viscous dissipation will produce more energy hence the electron temperature will increase. As a result, more radio flux will be emitted by the synchrotron process. Then the conflict between the ‘not-truncated’ ADAF and the observation will be more serious, while in the truncated ADAF model, a slightly larger truncation radius Rtr is then required to give a satisfactory fit.

Fig. 2 shows the predicted size-frequency relationship of our ADAF-jet model together with the observational data taken from Lo et al. (1998) (for 43 GHz) and Krichbaum et al. (1998) (for 86 and 215 GHz). 1 The solid one is the result of our ADAF-jet model, with the line below and above the break frequency at around ∼50 GHz resultant from the jet and the truncated ADAF respectively. For comparison, we also show by the dashed line the prediction of a best-fitting ‘not-truncated’ ADAF model similar with that in Quataert & Narayan (1999), 2 but with a smaller accretion rate of because of the new Chandra upper limit. Other parameters are and Note in this ADAF model, Ωout is large so it is of disc-like hence &Ṁ is smaller than our Bondi-like model. We see that the two models are both compatible with the data at 86 and 215 GHz, but our ADAF-jet model gives a better fit to the observation at 43 GHz because of the inclusion of the jet. In this context, we note that although the ‘ADAF+wind’ model of Quataert & Narayan (1999) could also interpret the spectrum, even though the high accretion rate favoured by simulation were adopted, the predicted size-frequency relationship would be in conflict with observation at 43 GHz, since that model should produce a similar size-frequency relationship with the ‘not-truncated’ ADAF model.

3.2 Nearby elliptical galaxies

Encouraged by the above success, we further apply our model to the six ellipticals presented in Di Matteo et al. (2000), where jets also exist. As a result of the successful applications of Falcke's jet model to other sources like M81, GRS 1915+105, and NGC 4258 ( Falcke & Biermann 1999), we assume here that for our purpose this model can give enough description to the weak jets (excluding M87) in ellipticals as well. We find that owing to the suppression of the radio flux by the truncation of the disc, the predicted spectra are in good agreement with the observations. We present below three sources as illustrations. The observational data are taken from Reynolds et al. (1996) (for M87) and Di Matteo et al. (1999) (for NGC 4649 and NGC 4636).

3.2.1 NGC 4649

We first model NGC 4649 because it has the best observational constraints in Di Matteo et al.'s (2000) sample. Fig. 3 shows the predicted spectrum of this source together with the observation. The long-dashed line is the result of the truncated ADAF disc, the short-dashed line is for the jet, and the solid line shows the sum. As clearly shown, this source, which can be matched well by the ADAF with winds, also can be matched quite well by a truncated ADAF. However, in the wind model, if we assume the wind were to start at the outer boundary 10 4 Rg, the radius where the accretion starts, a fairly strong suppression of the X-ray emission above ∼5 keV is introduced, which is in conflict with the ASCA data ( Di Matteo et al. 2000). As stated by Di Matteo et al. (2000), this is because the introduction of winds at 10 4 Rg strongly decreases the bremsstrahlung emissivity at where the X-ray emission ≳10 keV mainly originates from. Therefore, in their model, they have to assume the winds to start at a certain radius much smaller than 10 4 Rg, which is not easy to understand. 3 In our model, the X-ray emission above ∼5 keV does not show any suppression, in agreement with ASCA observations. This is because out of the (small) truncation radius Rtr, ADAF is the canonical one in the sense that no winds are introduced. In addition, owing to the introduction of the jet, the radio flux near 1 GHz, which ADAF with winds model underpredict it greatly, can be interpreted as the contribution from the jet, as in the case of Sgr A*.

The predicted spectrum of the ADAF-jet model for NGC 4649 together with the observation. The long-dashed line is the result of the truncated ADAF, the short-dashed line is for the jet, and the solid line shows the sum. The parameters are and

The predicted spectrum of the ADAF-jet model for NGC 4649 together with the observation. The long-dashed line is the result of the truncated ADAF, the short-dashed line is for the jet, and the solid line shows the sum. The parameters are and

3.2.2 NGC 4486 (M87)

This is the only source in our examples for which we have clear observational evidence for the existences of a strong jet and a disc. Its jet is famous, while Hubble Space Telescope (HST) spectroscopy of its nucleus has given strong evidence for a rapidly rotating ionized gas disc at its centre (e.g. Ford et al. 1994). Although its high frequency radio data are consistent with the canonical ‘not-truncated’ ADAF model, the X-ray emission in this case is due to Comptonization of the synchrotron photons and the predicted slope is too soft to be consistent with the ASCA data. Therefore the radio flux must also be significantly smaller than the prediction of a canonical ADAF ( Di Matteo et al. 2000). Fig. 4 shows the predicted radio spectrum of this source by the truncated ADAF together with the observation. Three points need to be emphasized. First, compared with the wind model, the truncated ADAF can fit the 100-GHz VLBI data much better. Although the 5-GHz VLBI data is still strongly underpredicted, the excess may again be as a result of the contribution of the jet, like in the cases of Sgr A* and NGC 4649. Secondly, both winds and the truncated ADAF models can give a good match to the spectrum of this source (and others), but they are intrinsically different. One point reflecting the difference is that, the wind starts at a much larger radius, typically several hundreds of Rg, while in the latter, the theoretically predicted truncation radius at which the jet forms is much smaller. For M87, this radius equals 24Rg. Were it larger, the ADAF would predict a radio flux well below the observed one. On the other hand, as a triumph of precision astronomy, the excellent 43-GHz observation for this source by Junor, Biretta & Livio (1999) indicates that the jet is formed on scales smaller than ∼30Rg from the black hole, in excellent agreement with our prediction.

The predicted spectrum of the truncated ADAF for NGC 4486 (M87) together with the observation. The parameters are and The truncation radius Rtr equals 24Rg.

The predicted spectrum of the truncated ADAF for NGC 4486 (M87) together with the observation. The parameters are and The truncation radius Rtr equals 24Rg.

3.2.3 NGC 4636

We can imagine that there may exist such a case that the jet originates at a moderate large radius so that the radio peak decreases a lot according to equation (1) and it is the jet rather than the disc dominates the radio spectrum. This might be the case for NGC 4636, as Fig. 5 illustrates. For this source, the wind model predicts a synchrotron peak with a much higher frequency than expected by the radio and sub-mm measurements ( Di Matteo et al. 2000). Actually, in that model to fit the peak correctly, a black hole with much larger mass, 10 9 M, than the observational value must be used. Fig. 5 shows this puzzle can be solved in the truncated ADAF model if the truncation radius is as large as 100Rg. To confirm this conclusion, polarization should be observed in radio band, and the future low-frequency radio observation should not exhibit ‘excess’ as in Sgr A*, NGC 4649 and M87.

The predicted spectrum of ADAF-jet model for NGC 4636 together with the observation. The long-dashed line is the spectrum of the truncated ADAF, the short-dashed line is for jet, and the solid line is the sum. The parameters are and

The predicted spectrum of ADAF-jet model for NGC 4636 together with the observation. The long-dashed line is the spectrum of the truncated ADAF, the short-dashed line is for jet, and the solid line is the sum. The parameters are and


Peering Into Our Galaxy's Hidden Dark Heart

Every large galaxy in the visible Universe hides a mysterious dark heart. Even our vast, starlit spiral Milky Way Galaxy holds in its secretive center a gluttonous heart of darkness--a supermassive black hole that weighs millions of times more than our Sun. However, our Galaxy's dark-hearted resident is puny in comparison to some others of its bizarre kind. Indeed, some supermassive beasts that haunt the hidden hearts of their galactic hosts can weigh as much as billions of times solar-mass. Our Milky Way's supermassive black hole is named Sagittarius A* or Sgr A*, for short (pronounced Saj-A-Star), and it is a peaceful old black hole now, sleeping quietly most of the time--except for when a tasty morsel of some spaghettified star or cloud of doomed gas travels too close to its waiting maw. At that point, Sgr A* awakens for one brief shining moment to dine greedily and sloppily on this infalling banquet.

In astrophysics, the term spaghettification refers to the vertical stretching and horizontal compression of objects into long thin shapes in an extremely powerful and homogeneous gravitational field--giving these unfortunate objects a spaghetti-type appearance.

In May 2018, a team of astronomers announced that they have used a global array of telescopes, including the Atacama Pathfinder Experiment (APEX), in order to peer at the beast that lurks darkly in the heart of our Milky Way. This new study reveals the finest details collected so far on event horizon scales in the center of our Galaxy. The event horizon of a black hole is that dreaded point of no return from which nothing, nothing, nothing at all--not even light--can escape from the gravitational grip of the beast, and is doomed to be swallowed.

APEX is a radio telescope 5,100 meters above sea level at the Llano de Chajntor Observatory located in the Atacama desert in northern Chile. This 12 meter radio telescope has been outfitted with special equipment including broad bandwidth recorders and a stable hydrogen maser clock for the purpose of performing joint inteferometric observations with other telescopes at short wavelengths. The goal of these observations is to obtain the best-ever image of the shadow of the hidden black hole. The addition of APEX to the Event Horizon Telescope (EHT), which until recently was composed of antennas only in the northern hemisphere, was able to uncover in new and unprecedented detail the long-enshrouded structure of the secretive Sgr A*. The greatly improved angular resolution provided by the APEX telescope can now show long-hidden details of the asymmetric and not point-like source structure, as small as 36 million kilometers. This corresponds to dimensions that are three times larger than the still-hypothetical size of our Galaxy's resident dark-hearted supermassive beast.

The team of astronomers are seeking the holy grail that will ultimately prove Albert Einstein's Theory of General Relativity (1915)--which is to obtain a direct image of the shadow of a black hole. Their quest to find this elusive shadow is greatly aided by combining radio telescopes that are spread all over the Earth using a technique called Very Long Baseline Interferometry (VLBI). The telescopes participating in this search are located at high altitudes--in order to minimize the disturbance caused by our planet's atmosphere--and are also situated at remote locations with normally clear skies. This allows astronomers to observe the secretive compact radio source that reveals the mysterious presence of Sgr A* lurking in the dark heart of our Milky Way.

Supermassive Beasts

The supermassive black holes, that haunt the hearts of large galaxies, can weigh millions to billions of times more than our Sun. However, a black hole of any size can be described by only three properties: electric charge, spin (angular momentum), and mass. In addition to supermassive gravitational beasts, there are also black holes of "only" stellar mass, that are born when a particularly massive star has managed to burn all of its necessary nuclear-fusing fuel, and has reached the terrible end of that long stellar road when it contains a core of iron. At that point, the massive star collapses in the fiery fury of a supernova tantrum that results in the erstwhile star becoming a black hole of stellar mass. After a stellar mass black hole has formed from the wreckage of its massive progenitor star, it can continue to acquire more and more mass by "eating" ill-fated celestial objects that have wandered too close to its gravitational pull.

Black holes can be large or small, and these bizarre entities can be defined as an area of Spacetime where the tug of gravity has become so extreme that not even light can escape to freedom. The pull of gravity has grown intensely powerful because matter has been squeezed mercilessly into a very small space. Crush enough matter into a sufficiently small space, and a black hole will be born every time.

Most supermassive black holes, like Sgr A*, accrete matter somewhat lazily. This unfortunately makes it difficult for astronomers to distinguish them from the galactic dark hearts in which they lurk. For this reason, Sgr A* provides a valuable exception to this very frustrating rule. This is because astronomers are able to obtain a close view of its rather gentle X-ray emission.

Fortunately, astronomers have been able to learn quite a lot about Sgr A*. Our Galaxy's central supermassive beast weighs-in at about four million times that of our Sun--which, incredibly, makes it a relative runt, at least as far as supermassive black holes go. Sgr A* is encircled by a cluster of glittering baby stars, some of which have been unlucky enough to have wandered in to within only a few billion miles of where the gravitational beast lurks secretively in wait for its dinner. Sgr A* is quiet now, in its old age, but this was apparently not the case about a century ago when it messily feasted on an unfortunate blob of material that had traveled too close to where it lay hidden. This feast is responsible for creating a multicolored shimmering, glimmering explosive fireworks display that lit up our Galaxy's hungry dark heart.

Because Sgr A* is located relatively close to our own planet, it provides important information about the way that extreme gravity behaves, and thus helps shed new light on General Relativity.

The Strange Lair Of Sgr A*

In August 1931, the American physicist, Karl Jansky (1905-1950)--considered to be the father of radio astronomy--detected a mysterious radio signal coming from a location at the heart of our Milky Way. The strange signal originated in the direction of the constellation Sagittarius. Sgr A* itself was discovered on February 13 and 15, 1974, by astronomers Dr. Bruce Balick of the University of Washington and the late Dr. Robert Brown (1943-2014), using the baseline interferometer of the National Radio Astronomy Observatory (NRAO) in Charlottesville, Virgina. The name Sgr A* was first used by Brown in a 1982 research paper. This is because he believed that the mysterious radio source was "exciting"--and excited states of atoms are denoted with asterisks--hence, Sgr A*.

On October 16, 2002, an international team of astronomers, led by Dr. Reinhard Genzel of the Max Planck Institute for Extraterrestrial Physics in Germany, reported that, for more than a decade, they had been observing the movement of a star, dubbed S2, situated near Sgr A*. The team of astronomers proposed that the data they had obtained eliminated the possibility that Sgr A* harbors a cluster of dark stellar objects or a mass of degenerate fermions. Their proposal strengthened the evidence for the existence of a supermassive black hole lurking in the dark heart of our Milky Way.

Sgr A* itself is a very compact, bright radio source, located near the border of the constellations Sagittarius and Scorpius. It is a region located within a larger astronomical feature dubbed Sagittarius A.

Unfortunately, astronomers have not been able to observe Sgr A* in optical wavelengths. This is because it is enshrouded in a thick blanket of dust and gas that is situated between the source and our own planet. Several teams of astronomers have made the effort to image Sgr A* in the radio spectrum using very-long-baseline-interferometry (VLBI). At a distance of 26,000 light-years, the VLBI observations found that the mysterious radio source has a diameter of 44 million kilometers. By comparison, Earth is 150 kilometers from our Sun, and the innermost major planet Mercury is 46 million kilometers from our Sun when it is closest to it (perihelion).

As of April 2017, there have been direct radio images obtained of Sgr A* by astronomers using the Event Horizon Telescope (EHT). However, as of May 2018, this data is still being processed, and images have yet to be released. The EHT succeeded in combining images taken from widely spaced observatories at different locations on our planet. This was done in order for astronomers to obtain a higher picture resolution. It is hoped that the measurements will test Einstein's Theory of General Relativity more rigorously than earlier studies. If discrepancies exist between Einstein's theory and actual observations are found, it will suggests that scientists may have identified physical conditions under which the theory breaks down.

Current observations indicate that Sgr A*'s radio emissions are not being sent out into space by the black hole itself. Instead, the emissions seem to be originating from a bright region surrounding the black hole. This region is near the event horizon, possibly in the accretion disk. Alternatively, it could be a relativistic jet of material being hurled out from the disk. If the position of Sgr A* were precisely centered on the supermassive gravitational beast, it would be possible to observe it magnified larger than its actual size.This is because of the phenomenon of gravitational lensing. Gravitational lensing is a prediction of General Relativity proposing that the gravity of a foreground object can warp, bend, or magnify the light being emitted from a background object that it is aligned with. Thus, gravitational lensing is a natural gift, of sorts, to astronomers trying to observe remote objects that otherwise could not be seen--the foreground lens magnifies, or otherwise warps, the light emanating from the background object that is being lensed--thus making it visible to the prying eyes of curious astronomers. By using gravitational lensing as an observational tool, astronomers were able to determine that our Galaxy's resident supermassive black hole sports a mass of approximately 4 million times that of our Sun.

The Many Mysteries Of Our Galaxy's Heart Of Darkness

The research team of astronomers began their observations of Sgr A* in 2013, using the Very-Long-Baseline Interferometry (VLBI) telescopes located at four different sites. The telescopes that the researchers used include the APEX telescope, the Combined Array for Research in Millimeter Wave Astronomy (CARMA) array in California, the James Clerk Maxwell Telescope (JCMT) in Hawaii, the phased Submillimeter Array (SMA) in Hawaii, and the Submillimeter Telescope (SMT ) in Arizona. Sgr A* was spotted by all stations and the longest baseline length extended up to almost 10,000 kilometers. This suggests an ultra-compact and asymmetric (not point-like) source structure.

"The participation of the APEX telescope almost doubles the length of the longest baselines in comparison to earlier observations and leads to a spectacular resolution of 3 Schwarzschild radii only," commented Dr. Ru-Sen Lu in a May 24, 2018 Max Planck Institute for Radio Astronomy (MPIfR) Press Release. Dr. Lu is of of the MPIfR in Bonn, Germany, and is lead author of the paper describing the new research.

"It reveals details in the central radio source which are smaller than the expected size of the accretion disk," added Dr. Thomas Krichbaum in the same MPIfR Press Release. Dr. Krichbaum is the initiator of the mm-VLBI observations with APEX.

APEX's location in the southern hemisphere considerably improved the quality of the images for a source as far south in the sky as Sgr A*. Indeed, APEX has succeeded in "paving the way" for the inclusion of the large and very sensitive ALMA telescope into the EHT observations, which are currently being undertaken one time annually.

"We have worked hard at an altitude of more than 5000 meters to install the equipment to make the APEX telescope ready for VLBI observations at 1.3 mm wavelengths," explained Dr. Alan Roy in the MPIfR Press Release. Dr. Roy, who is also from the MPRfR, leads the VLBI team at APEX. "We are proud of the good performance of APEX in this experiment," he added.

The team of astronomers used a model-fitting procedure in order to study the event-horizon-scale-structure of Sgr A*. "We started to figure out what the horizon-scale-structure may look like, rather than just draw generic conclusions from the visibilities that we sampled. It is very encouraging to see that the fitting of a ring-like structure agrees very well with the data, though we cannot exclude other models, e.g., a composition of bright spots," Dr. R-Sen Lu explained in the same MPRfR Press Release. Observations in the future with still more telescopes added to the EHT will help sort out residual ambiguities in the imaging.

Our Galaxy's resident supermassive heart of darkness is embedded in a dense interstellar medium. This may affect the propagation of electromagnetic waves along the line of sight. "However, the interstellar scintillation, which in principle may lead to image distortions, is not a strongly dominating effect at 1.3 mm wavelength," noted Dr. Dimitrios Psaltis in the May 24, 2018 MPRfR Press Release. Dr. Psaltis is the EHT project scientist at the University of Arizona in Tucson.

Dr. Sheperd Doeleman, of the Harvard-Smithsonian Center for Astrophysics (CfA) in Cambridge, Massachusetts, and director of the EHT project, noted in the same MPRfR Press Release that "The results are an important step to ongoing development of the Event Horizon Telescope. The analysis of new observations, which since 2017 also include ALMA, will bring us another step closer to imaging the black hole in the center of our Galaxy."

These new findings are published in The Astrophysical Journal.

Judith E. Braffman-Miller is a writer and astronomer whose articles have been published since 1981 in various journals, newspapers, and magazines. Although she has written on a variety of topics, she particularly loves writing about astronomy because it gives her the opportunity to communicate to others some of the many wonders of her field. Her first book, "Wisps, Ashes, and Smoke," will be published soon.


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