Upper Limit on Brackett-γ Emission from the Immediate Accretion Flow onto the Galactic Black Hole

The center of our Galaxy hosts a supermassive black hole (SMBH) whose position coincides with the radio and infrared source, Sgr A* (Ghez et al. 2000; Schödel et al. 2002). Thanks to its proximity, this environment presents a unique opportunity to study in detail the accretion mechanism onto a SMBH. The SMBH is not very active (10⁻⁷ L_Edd; Baganoff et al. 2003) even though it was likely much more active at various times in the past few hundred years (Clavel et al. 2013; Terrier et al. 2018) and a recent unusual peak in its activity has been reported in the infrared (Do et al. 2019b). The accretion rate of hot gas through the Bondi radius (∼1'') of the central SMBH can be estimated from X-ray observations (Baganoff et al. 2003), but the amount of cooler gas very near the black hole is not strongly constrained.

The low activity of Sgr A* (e.g., Witzel et al. 2012) places it in the regime of radiatively inefficient accretion flows. Most models of the accretion flow predict or allow for the formation of a disk (see Yuan & Narayan 2014 for a review). Recent modeling of the accretion flow by Calderón et al. (2020), assuming that the accreted material comes from the winds of nearby young, windy stars, predicts a disk phase in the accretion flow. However, the theoretical formation of a disk is not universally agreed upon. Ressler et al. (2020) also modeled the accretion flow supplied by stellar winds from nearby Wolf–Rayet stars but they find that a disk would not form around Sgr A*. In their modeling, they argue that the magnetic field drives a polar outflow that removes angular momentum, and that the fast inflow and outflow of the gas, together with inefficient cooling, prevent the material from circularizing.

Emission from the accretion flow onto Sgr A* has recently been detected with Atacama Large Millimeter/submillimeter Array (ALMA) observations by Murchikova et al. (2019), who report a very broad (>2000 km s⁻¹) emission feature in the H30α radio recombination line arising within ∼0.2''–0.3'' of Sgr A*. The presence of a velocity gradient across the marginally resolved source led them to conclude that they had observed a disk that is approximately edge-on. Given the reported observation of H30α (n = 31 → 30 transition), one would expect significant emission in the lower-lying Brackett-γ (Brγ) recombination line (7 → 4 transition) at 2.1661 μm.

In this paper, we search for the expected Brγ emission based on data gathered by Galactic Center Orbits Initiative. In Section 2, we briefly describe the data used. Section 3 describes the analysis procedure to extract the Sgr A* NIR spectrum. In Section 4 we report our flux limit. A preliminary version of our limit on Brγ was used by Murchikova et al. (2019) to argue that the H30α emission must be augmented by weak maser action. In Section 5, we discuss our limit in comparison to the reported H30α flux and to accretion flow theories. Our conclusions are reported in Section 6.

The data for this study were taken as part of the Galactic Center Orbits Initiative (GCOI; PI: Ghez, W. M. Keck Observatory 1995–present). We used a subset of the deep observations taken between 2006 and 2018 with OSIRIS, the integral field spectrograph fed by a laser guide star adaptive optics system at W. M. Keck Observatory (Larkin et al. 2006; Wizinowich et al. 2006). All included epochs consist of 900 s exposures in the Kn3 band (2.121–2.229 μm) with a 35 mas plate scale. In this setup, the average spectral resolution is R = 3800, and at the wavelength of Brγ this corresponds to 6 × 10⁻⁴ μm, or 2.5 channels.

The initial stages of data analysis (including sky subtraction and flux calibration) have been described in previous publications (Ghez et al. 2008; Do et al. 2009, 2019a; Ciurlo et al. 2020). We begin with the flux- and astrometrically calibrated, mosaicked data cubes. In this work, we only examined a subset of GCOI raw data that had already been analyzed with a procedure optimized for gas detection reported in Ciurlo et al. (2020), which differs from that used for the measurements of stellar radial velocities. ³ Furthermore, we exclude epochs showing strong OH line subtraction residuals (visible as extremely strong absorption lines), which leaves a total of 19 epochs that are summarized in Table 1. These measurements have an average spatial resolution of 73 mas, based on a Gaussian fit to S0-2 in the mosaicked data cubes. This subset of data is optimized for extracting the spectrum of the region around Sgr A*.

Our goal is to extract a high signal-to-noise spectrum of the immediate surroundings of Sgr A*. In particular, we seek to establish whether there is a counterpart to the disk-like emission of the reported H30α recombination line. We therefore extract a spectrum within a circular aperture centered on the position of Sgr A* and of radius 023 (the same aperture used by Murchikova et al. 2019), corresponding to a diameter of about 30 typical spatial resolution elements. Figure 1 shows the chosen aperture along with contours of the H30α emission lines over a map of the Brγ emission in the region. The gas has complex, multicomponent emission extended in space and velocity. We can identify one component to the west, associated with radio source Epsilon (Yusef-Zadeh et al. 1990), two in the northeast and southeast corners associated with bright Wolf–Rayet stars (IRS16 C and IRS16 SW) and one featuring an almost linear feature immediately adjacent to the position of Sgr A* along the line of sight (Schödel et al. 2011; Peißker et al. 2020). More details on this extended gas emission are reported in Appendix E.

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Our spectral extraction procedure is designed to reduce the effect of bright stars and extended gas emission at the Galactic center. First, to minimize the contribution from bright stars, we create and apply an adaptive mask that tracks the brightest stars and that transmits ∼60% of the aperture area (see Appendix A). The extracted spectra are reported in Appendix B. Second, we apply a continuum subtraction routine to each data cube (see Appendix C) prior to combining the data from all epochs. The individual epochal spectra are rescaled by dividing by their corresponding unmasked area within the aperture. The resulting spectra have a typical noise per spectral resolution element of 0.050 mJy (see Table 1). We then combine the individual spectra using a weighted average where the weight corresponds to the inverse square of the noise. The noise of the combined spectrum (0.015 mJy) is lower by a factor of ∼2.3 than in the best individual epoch.

Figure 2 (top) shows our resulting combined spectrum along with the individual spectra. Subsequent analysis only uses the combined spectrum. Figure 2 (bottom) shows the comparison between the observed Brγ spectrum (not corrected for extinction) and the H30α spectrum reported by Murchikova et al. (2019). The only Brγ emission that rises above the noise is associated with the superimposed lower-velocity gas that is also observed at larger radii (see Figure 1 and Appendix E). There is no qualitative evidence for the presence of a broad Brγ emission line. We want to underline that there is no sign of any broad (>800 km s⁻¹) line in the whole wavelength range covered by the OSIRIS observations (∼12,000 km s⁻¹). Consequently, this means that there is no counterpart to the even broader radio recombination line recently reported by Yusef-Zadeh et al. (2020) (∼4000 km s⁻¹).

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The most straightforward way to extract an upper limit on the flux of the Brγ line, without making any assumptions about the shape or extent of the line profile, is to set the limit at 5 times the rms noise per resolution element. The noise per resolution element is calculated over ranges devoid of spectral features (see Appendix C). In this way, we find an upper limit on the flux density of 0.074 mJy in a 023 radius aperture When corrected for the extinction reported by Schödel et al. (2010), this limit corresponds to 0.71 mJy. This limit can be used with any hypothetical line profile to derive the total line flux expected for the accretion flow.

To quantify the nondetection of any broadband emission (∼2000 km s⁻¹), we create a spectral filter that is sensitive to the wings of the reported H30α line and cuts out the low velocities at which the superimposed gas is emitting. Our notch filter extends from a Brγ velocity of −1100 to +1100 km s⁻¹ excluding the low velocities between −400 and +510 km s⁻¹ (see Figure 2); this filter contains 15 resolution elements.

Using the H30α line profile reported by Murchikova et al. (2019), we proceed next to derive a limit on the Brγ line flux by determining our sensitivity to the detection of a line having that profile in our spectrum. We do this by modeling the published H30α line profile as a double-peaked Gaussian, and then planting the result of that fit on top of our NIR spectrum. We only consider the portion of the resulting spectrum in our notch filter. A limit to the Brγ flux is then determined by identifying the total added flux for which the signal-to-noise ratio of the planted spectrum within the notched filter is greater than 5. The planted-Gaussian spectrum corresponding to our 5σ limit is shown in Figure 3. More details can be found in Appendix D.

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Since we are assuming that the Brγ profile has the same shape as that of the H30α line, we determine that the notch filter would contain 46% of the flux. Hence, we find that the upper limit to the total Brγ flux (calculated over the whole H30α range, −1100 to +1100 km s⁻¹) corresponding to a signal-to-noise ratio of 5 is 2.461 ± 0.003 10⁻¹⁹ W m⁻². The dereddened value corresponds to 23.7 ± 0.03 10⁻¹⁹ W m⁻².

We note that, if we do not mask the brightest stars in our spectral extraction, the resulting 5σ flux limit is ∼15% higher because of higher photon noise.

In order to compare our flux limit to models of the accretion flow and to the reported H30α line, it is necessary to calculate the corresponding emissivities. The total flux integrated over the H30α line (from −1100 km s⁻¹ to +1100 km s⁻¹) is estimated to be 0.3 10⁻¹⁹ W m⁻² (corrected for extinction). Our flux limit over the same velocity range ⁴ for Brγ is 23.7 ± 0.1 10⁻¹⁹ W m⁻² (corrected for extinction). The corresponding emissivity can be calculated as

$$\begin{eqnarray}&&\epsilon =\displaystyle \frac{{F}_{\lambda }\cdot 4\pi {d}^{2}}{V},\end{eqnarray} \tag{ 1 }$$

where F_λ is the total flux of a given emission line, d is the distance to the Galactic Center (7.97 kpc; Do et al. 2019a) and V is the emitting volume. We consider two geometries for the emitting region: (1) a disk of radius 023 (same as the disk reported by Murchikova et al. 2019) and height 003 (13% of the radius), (2) a sphere of radius 023. The disk volume occupies roughly one-tenth of the sphere volume. Using the disk geometries we obtain emissivities for Brγ and H30α of ≤770.9 10⁻¹⁹ and 9.8 10⁻¹⁹ erg s⁻¹ cm⁻², respectively. For a sphere geometry we obtain ≤75.2 10⁻¹⁹ and 0.9 10⁻¹⁹ erg s⁻¹ cm⁻², respectively.

To investigate what ranges of temperature and density can give rise to these emissivities, we use the tabulations of Hummer & Storey (1987). Figure 4 shows the Hummer & Storey (1987) emissivities as a function of density, where the different colored curves correspond to different temperatures. We plot two sets of curves: one for each of Brγ and H30α. The emissivities we derive from the total flux of each line are compatible with a range of densities when considering the temperatures used by Hummer & Storey (1987).

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Given the H30α emissivity derived from observations, we can project the compatible densities onto the Brγ set of temperature curves, hence determining the expected emissivity in Brγ given the observed H30α flux. The same process can be applied to the Brγ upper limit, which implies an upper limit on the expected H30α emission.

We can compare, on the same plot, models of the accretion flow. For instance, Calderón et al. (2020) recently reported simulations of the interactions of stellar winds from stars in the young nuclear cluster that produce a disk on the same scale as the one reported by Murchikova et al. (2019). According to this model, the temperature and density in the disk are, respectively, ∼10⁴ K and ∼10⁵ cm⁻³.

Therefore, we find that: (1) in the case of an emitting disk, our upper limit on the Brγ flux is compatible with the model reported by Calderón et al. (2020), (2) regardless of the modeled emission geometry, the reported H30α emissivity measurement is much higher than that predicted by Calderón et al. (2020) and by our Brγ limit. The width and flux reported by Yusef-Zadeh et al. (2020) would lead to similar conclusions.

Our measured Brγ flux limits, together with the expected values from the reported H30α line and the Calderón et al. (2020) model, are summarized in Table 2. The Brγ flux expected from the H30α observations is several orders of magnitude greater than our reported limit. This discrepancy between the reported H30α and the upper limit on Brγ led Murchikova et al. (2019) to propose a maser effect to amplify the H30α emission. However, such a population inversion is not expected from the calculations of Hummer & Storey (1987), as reported by Scoville & Murchikova (2013) and shown in Figure 4. Although Hummer & Storey (1987) probe only a limited range of temperatures and densities that might not represent the physical conditions appropriate to the Sgr A* accretion flow, we note that, if the gas stays very hot, we should not expect to observe any recombination line, since emissivity declines with temperature (the recombination rate is low at high temperatures because protons are moving too fast).

If the level populations of the H30α line are inverted, maser amplification can occur. Murchikova et al. (2019) have invoked this mechanism in order to reproduce the flux densities that they report, given our upper limit to the Brγ line. However, the nearby presence of the very bright (several Jansky) point source, Sgr A*, at the center of the putative disk is problematical for the maser hypothesis because the preferred gain path for the maser would always be radial, directed away from Sgr A*. In the competition for stimulating new photon emission from the upper state of the H30α transition, the strong emission from Sgr A* would be strongly favored over the relatively weak (few milliJansky), isotropically emitted, spontaneous emission in the H30α line from throughout the accretion disk. Consequently, if that transition were indeed inverted, the resulting maser-enhanced line radiation would always be directed along a radial ray from Sgr A*. Then, rather than observing emission extended along the projected disk and showing a strong velocity difference on opposite sides of the projected disk, as was reported by Murchikova et al. (2019), we should expect to see an unresolved point source of line emission having a velocity width reflecting the line-of-sight velocity gradient in the accretion flow. Furthermore, the reported 2000 km s⁻¹ width of the line is far larger than could be expected for the radial component of gas moving in quasi-circular orbits in an accretion disk. We conclude from these arguments that the maser interpretation of the reported H30α line emission is unlikely.

Analyzing 13 yr of data gathered with the integral field spectrograph OSIRIS at the W.M. Keck Observatory, we extracted the near-infrared spectrum of the immediate vicinity of Sgr A*. Within a radius of 023 we place a 5σ upper limit Brackett-γ emission line (see Table 2 for a summary). Predictions drawn from future modeling of the accretion flow will need to be constrained by this result.

Our limit on Brγ emission is unexpected given the reported millimeter-wavelength detection of the higher-level transition H30α (Murchikova et al. 2019) within the same region. Given our limit on Brγ, the reported excitation of H30α would need to deviate dramatically from current theoretical expectations based on the departure coefficients computed by Hummer & Storey (1987). However, it remains possible that the range of physical conditions applicable to the Sgr A* accretion flow is outside of those they considered. Nevertheless, if strong maser amplification can in principle allow for much stronger H30α emission, we would expect to observe it as an unresolved point source rather than a disk.

Support for this work was provided by NSF AAG grant AST-1412615, Jim and Lori Keir, the W. M. Keck Observatory Keck Visiting Scholar program, the Gordon and Betty Moore Foundation, the Heising-Simons Foundation, and Howard and Astrid Preston. A.M.G. acknowledges support from her Lauren B. Leichtman and Arthur E. Levine Endowed Astronomy Chair. The W. M. Keck Observatory is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.

For each epoch we mask a region around the brightest stars by applying a continuum cut. Specifically, if the total flux in the wavelength range between 2.1343 and 2.1447 μm, a region outside our notch filter and devoid of emission features, is higher than a threshold (1.5 mJy) the pixel is masked. This continuum cut roughly corresponds to masking the brightest stars (K-magnitude < 16). The masking serves two purposes: (1) it reduces the noise added by the extended point spread functions of the bright stars and (2) it reduces the confusion potentially caused by Brγ absorption in the stellar photospheres of luminous young stars.

Figure 5 shows the spectra extracted over the masked aperture for each epoch. The spectral characteristics vary from epoch to epoch, showing different slopes. This is due to the fact that we are considering a very small aperture near Sgr A* through which many stars orbit on short timescales; from year to year different stars enter or exit the aperture. This happens even though we have masked the brightest stars in each epoch; the many fainter stars in the region still contribute weakly to the extracted spectrum. The stars in the region are mostly A and B stars, primarily the so-called S-stars orbiting Sgr A* (Eckart & Genzel 1997; Ghez et al. 1998). The late B and A stars have Brγ absorption that could potentially influence our measurements, although most of the S-stars have radial velocities within ±500 km s⁻¹, and therefore are not in the range we are considering for our limit on the accretion flow. Furthermore, for such stars, which have magnitudes above 16, the flux density in the Brγ line is expected to be well below the noise of our spectra.

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In order to isolate the Brγ line emission, we removed the stellar continuum from each epoch. We do that by selecting several wavelength ranges devoid of emission features: from 2.1343 to 2.1447 μm, from 2.1469 to 2.1503 μm, from 2.1544 to 2.1568 μm, from 2.1752 to 2.1783 μm, and from 2.1808 to 2.1948 μm (displayed in Figure 6). We then estimate the continuum slope with a linear fit in those ranges, using the same procedure as in Ciurlo et al. 2020). In the data reduction each individual exposure is sky-subtracted with a procedure (Davies 2007) that scales OH lines to be consistent with the science exposures. After that we build the mosaics. There could still be small OH lines residuals after this procedure. Because this imperfect sky subtraction could lead to poor continuum estimation, we therefore avoided spectral channels containing bright telluric OH lines within the selected ranges. The ranges used for the continuum estimation and the continuum fit are shown in Figure 6. The continuum estimation is less reliable near the edges of the Kn3 filter, but that does not affect our analysis, as the broad line we are seeking is close to the center of the spectral band.

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To calculate the noise level σ we calculate the rms flux density over ranges devoid of spectral features (the same used for the continuum estimation; see Figure 6). According to the OSIRIS manual, ⁵ the average resolution with the 35 mas plate scale for the Kn3 band corresponds to ∼2.5 channels. Therefore, we smooth the spectrum over the width of a resolution element before calculating the rms noise. Since the single spectra are extracted over a number of pixels that varies from epoch to epoch (because of the star's mask) we rescale each individual spectrum to the same effective area. In this way the measured noise reflects the intrinsic noise of each spectrum.

We model the H30α profile with a double-peaked Gaussian Figure 7. To account for the error in fitting the H30α profile with Gaussians, we draw randomly the width and central wavelength within the uncertainties of the fitted values 1000 times. We vary the flux between 1/100 and 10 times the flux limit estimated from the channel-to-channel noise. We calculate the signal to noise as the total flux in our notch filter, divided by the square root of the number of independent resolution elements times the noise per resolution element. We identify the total fluxes that fall in the interval of (5 ± 0.01)σ and take the median as our final total flux. This way we obtain a limit on the Brγ flux of 1.13 10⁻¹⁹ W m⁻² in our notch filter. We estimate the uncertainty as the rms of the values one obtains by running the procedure 19 times, dropping at each time one of the 19 epochs of data.

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The OSIRIS data show that there are multiple extended foreground and background gas components to the Brγ emission in this region (evident in Figure 5, near the Brγ rest frequency). The gas observed toward SgrA * has complex, multicomponent emission extended in space and velocity. We can identify at least three components (see Figure 8, top and middle): one associated with nearby radio source Epsilon (Yusef-Zadeh et al. 1990), one associated with the bright Wolf–Rayet stars in the field (IRS16 C and IRS16 SW) and one featuring an almost linear feature immediately adjacent to the position of Sgr A* along the line of sight (Schödel et al. 2011; Peißker et al. 2020). Some of these components move enough from year to year to require a specific fit for each epoch if they are to be subtracted from the spectrum. However, given that our goal is to measure or limit very broad Brγ emission (∼2000 km s⁻¹) and given that the foreground and background emission occurs at much lower velocities (<400–500 km s⁻¹), we simply exclude the low-velocity range (between −400 and +510 km s⁻¹) from our analysis of the Brγ emission. We note that by changing the bright star mask from epoch to epoch we sample different portions of the confusing background in different epochs. However, the wavelength extent of the gas does not exceed the boundary of the exclusion zone we set and therefore it does not influence our analysis. Figure 8 (bottom) shows how, at larger radii, this superimposed gas emission becomes more and more challenging to deal with. Therefore, for this work we only focus on a 023 aperture that allows us to compare our limits directly to the Murchikova et al. (2019) observations.

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