Multiwavelength Observations of Sgr A*. I. 2019 July 18

Sagittarius A* (Sgr A*) is the 4.297 × 10⁶ M_⊙ supermassive black hole located at a distance of 8.27 kpc (Gravity Collaboration et al. 2019) in the center of the Milky Way. It is known to be a variable source at radio through X-ray wavelengths (e.g., Yusef-Zadeh et al. 2006; Dodds-Eden et al. 2009; Dexter et al. 2014; Hora et al. 2014) and is a prime target to understand how gas is captured, accreted, and/or ejected from low-luminosity supermassive black holes.

At infrared (IR) and X-ray wavelengths, the emission from Sgr A* is optically thin synchrotron radiation (e.g., Eckart et al. 2004, 2006, 2012; Ponti et al. 2017; Witzel et al. 2021). At submillimeter and radio wavelengths, the variable emission's timescale is much shorter than that of the synchrotron cooling time. Yusef-Zadeh et al. (2006) used an adiabatically expanding synchrotron plasma (van der Laan 1966) to describe the emission observed in this frequency range with much success. Since then, there has been a formidable effort to connect the radio/submillimeter and IR/X-ray regimes with a model that can explain the variable emission across the electromagnetic spectrum. Multiwavelength campaigns (e.g., Yusef-Zadeh et al. 2008; Eckart et al. 2009; Mossoux et al. 2016; Ponti et al. 2017; Subroweit et al. 2020; Witzel et al. 2021) are critical to test this picture. Nonoverlapping observations (due to the rise/set times at different observatories) and time-delayed emission at radio frequencies make this a difficult task. This has been somewhat alleviated by space-based IR instruments, like the Spitzer Space Telescope, in concert with submillimeter observations, like ALMA (e.g., Witzel et al. 2021). Submillimeter observations are key as they lay near the "submillimeter bump" (Zylka et al. 1992, 1995), where Sgr A* is brightest. This bump begins in the millimeter and decays at wavelengths near the far-IR, where the emission becomes increasingly optically thin, and optical depth effects are unimportant (Marrone 2006).

Abuter et al. (2021) recently published an analysis from a multiwavelength campaign on 2019 July 18 using IR and X-ray data. Here, we present simultaneous ALMA observations, which show a time delay relative to the mid-IR data, suggesting an optically thick and dynamically evolving source.

The campaign included data from the Very Large Array (VLA) and Giant Metrewave Radio Telescope (GMRT) on 2019 July 18; however, these light curves are not useful for this date. The VLA data at the Q band could not be calibrated by the VLA pipeline owing to bad weather and long cycle times. Extended structures in the GMRT data dominated Sgr A*, and identifying the intrinsic variability of Sgr A* is difficult. A more detailed account of these data will be given in J. Michail et al. (2021, in preparation).

2.1. Submillimeter: ALMA

The ALMA data used were taken as part of a Cycle 6 Atacama Compact Array (ACA) observatory filler program (project code 2018.A.00050.T), which observed the Galactic Center in Band 7 on 2019 July 18 for about 7 hr. The data set was calibrated and imaged by the ALMA pipeline (Pipeline-CASA54-P1-B, r42254, CASA v5.4.0-70; McMullin et al. 2007). The calibrated measurement set was obtained by restoring the calibration from the ALMA archive using scriptForPI.py. The data consist of four spectral windows of 2 GHz bandwidth and a spectral resolution of 1.953 MHz, with one spectral window centered on the CO transition at 346 GHz and three continuum spectral windows. J1337–1257 and J1924–2914 were used as bandpass and amplitude calibrators. J1700–2610 (J1700) and J1717–3342 were used as phase calibrators throughout the observation. J1733–3722 (J1733) was the phase calibrator during the final execution block. There were calibration issues in the gain amplitudes between the first three execution blocks; this was readily apparent in the light curve of J1700–2610, which showed that the flux varied by approximately 10%. To fix these offsets, we calculate average scale factors for the second and third execution blocks relative to the first using J1700–2610. These amplitude scale factors are applied to Sgr A* and J1700–2610. We chose the first execution block as our standard as its flux was most similar to J1700–2610's on the night of 2019 July 19. We do not complete the same scaling procedure for the last execution block as the phase calibrator is J1733–3722. The observation was imported into AIPS for phase self-calibration. Then, DFTPL was used to extract the light curves from Sgr A* at a 60 s binning time. The light curve for each spectral window is calculated independently using baselines greater than 20 kλ. The ALMA light curves are shown in Figure 1 (left).

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2.2. Mid-infrared: Spitzer

2.3. X-Ray: Chandra

The ALMA, Spitzer, and Chandra light curves for these observations all show the presence of flaring emission. Unfortunately, the submillimeter flare peak appears to occur between ALMA execution blocks. However, a sufficient amount of the flare is present to complete cross correlations with the other simultaneous observations. Throughout this paper, we use the pyCCF (Peterson et al. 1998; Sun et al. 2018) Python module with 5000 Monte Carlo simulations to check for possible delays in the peak emission. A histogram of the 5000 centroid lag times is made, and we characterize the spread in the time delay using the 95% (2σ) confidence interval (CI). We consider a statistically significant time lag if 0 is not contained within this interval. The mean and 95% CI error range is denoted on each histogram plot.

We check for, but do not detect, a time delay between the most widely separated ALMA frequencies; the histogram is shown in Figure 2 (left). We find a time delay of $\delta t={29.95}_{-3.44}^{+3.46}$ minutes between the 334 GHz and mid-IR light curves, where the submillimeter emission is lagging (Figure 2, center). As a secondary check, we use the ZDCF cross-correlation code (Alexander 1997) along with the PLIKE program (Alexander 2013) on the submillimeter and mid-IR light curves. We find a time delay of $\delta t={29.51}_{-6.02}^{+6.28}$ minutes, consistent with the value from pyCCF. A close-up plot of these two light curves is shown in Figure 3 (left). However, as the full submillimeter flare was not observed, the measured time delay between the submillimeter and mid-IR is an upper limit to the true value. In this case, the 2σ CI quoted only measures the statistical error of the observed peaks within the photometric uncertainties and does not characterize the systematic error caused by an incomplete light-curve sampling.

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Eckart et al. (2008) detected delayed flaring emission at 345 GHz relative to near-IR data on the order of 1.5 ± 0.5 hours. Eckart et al. (2009) lists modeled time delays between the IR to submillimeter/radio bands, which range from 0.3 to 1.7 hours. The time-delay upper limit we calculate between the Spitzer and ALMA data here is well within the range of those previously published in the literature.

We find that the 2–8 keV flare is simultaneous with the mid-IR data using pyCCF (Figure 2, right) and agrees with the ZDCF analysis that we perform ($\delta t={1.10}_{-4.29}^{+8.85}$ minutes). Boyce et al. (2019) analyzed more than 100 hr of simultaneous Spitzer and Chandra data. Their analysis found the X-ray data to lead the IR flaring emission by 10–20 minutes at the 68% confidence level. However, they note the time delays of the detected flares contain 0 at a confidence level of 99.7%. Our cross-correlation results match with this more broad study of IR/X-ray time lags and with the previous analysis of this data (Abuter et al. 2021; H. Boyce et al. 2021, in preparation). Additionally, the observed flaring emission in the Gravity K- (2.2 μm) and H-filters (1.63 μm) are simultaneous with the Spitzer observations (Abuter et al. 2021). The lack of time delay at these higher frequencies matches expectations from the adiabatically expanding picture, where the IR data are optically thin.

As noted above, due to noncontinuous ALMA execution blocks, the true submillimeter flare peak may not have been observed. We use a Bayesian analysis technique known as Gaussian Process Regression from the sklearn Python package (Pedregosa et al. 2011) to interpolate the missing data. Our kernel is a compound radial-basis + constant function, which we use to fit the lowest-frequency ALMA data. In the lower left panel of Figure 3 (right), we show the observed ALMA data (red) and the mean Gaussian process fit (black). The shaded purple region is the 95% CI of the fit. We complete a cross correlation between ALMA and Spitzer using pyCCF with the Gaussian-process-fitted data, and their 68% (1σ) CI errors appear to be consistent with the analysis above. The cross-correlation histogram is shown in the right panel, where we find $\delta t={24.04}_{-1.56}^{+1.67}$ minutes.

Both methods find evidence for time-delayed emission between the peaks of the submillimeter and mid-IR data. Neither technique can determine if the delay is conclusive, however. The three test models presented by Abuter et al. (2021) are not able to produce time-delayed emission, which is indicative of an optically thick and dynamically evolving source, nor can it match the observed peak 334 GHz flux. Both point toward submillimeter emission production via an optically thick, adiabatically expanding plasma (van der Laan 1966; Yusef-Zadeh et al. 2006). We consider this possibility in Section 4.

In Section 3, we applied two different methods to check the observed time delay between the submillimeter and mid-IR light curves. However, the gap in our submillimeter data near the peak allows for a range of possible conditions, namely, both simultaneous and time-delayed emission relative to the mid-IR data. If the submillimeter emission is time delayed, the total peak flux is approximately 5.5 Jy (requiring a peak flare flux ≈0.9 Jy). If the emission is simultaneous, the total flux is ≈6 Jy with a peak flare flux of ≈1.4 Jy. This latter value is estimated using a linear extrapolation of the submillimeter data between t = 3:36:00–4:12:00 hr UTC. Note that peak flare fluxes for the simultaneous and time-delayed cases were calculated assuming a quiescent flux of ≈4.6 Jy, approximated from the ALMA light curve.

4.1. Can the Gravity Model Reproduce the Submillimeter Emission?

We focus on the parameters of the synchrotron model PLCool${\gamma }_{\max }$ (PLC) as described by Abuter et al. (2021), which they note is their best-fitting model. With no knowledge of the submillimeter emission, a synchrotron-powered flare (with a cooling break and high-energy cutoff) can describe the IR and X-ray data. However, our analysis above shows a nonzero time-delay upper limit between the mid-IR and submillimeter bands. In this case, a pure synchrotron model is insufficient to describe the submillimeter emission.

The flare detected using Spitzer at 4.5 μm had a redden-corrected flux of approximately 20 mJy. The corresponding Gravity K- and H-filters both observed redden-corrected fluxes of nearly 15 mJy. This is consistent with an electron power-law index of p = 2 (N(E) ∝ E^−p ) and implies an IR spectrum of S_ν ∝ ν^−0.5. The other two parameters in their model are the radius of the flaring region and magnetic field strength, for which they choose 1 R_S (Schwarzschild radius) and 30 Gauss, respectively. For M_BH = 4.297 × 10⁶ M_⊙, 1 R_S = 1.27 × 10¹² cm.

We use these parameters in the context of the adiabatic expansion picture to determine the submillimeter emission. For a spherical region emitting synchrotron radiation, the observed flux (S₀), radius (R₀), and optical depth (τ₀) at frequency ν₀ are related by

$$\begin{eqnarray}&&{S}_{0}=\displaystyle \frac{\pi {R}_{0}^{2}}{{d}^{2}}{J}_{0}\left(1-{e}^{-{\tau }_{0}}\right).\end{eqnarray} \tag{ 1 }$$

d is the distance to the Galactic Center, and J₀ is the source function of a power-law synchrotron source, which is a function of p, ν₀, and B. Solving for the mid-IR optical depth yields τ_IR = 1.36 × 10⁻⁸. In the adiabatic picture, p and the critical optical depth (where the plasma blob becomes optically thin), τ_crit, are related via

$$\begin{eqnarray}&&{e}^{{\tau }_{\mathrm{crit}}}-\left(\displaystyle \frac{2p}{3}+1\right){\tau }_{\mathrm{crit}}-1=0\end{eqnarray} \tag{ 2 }$$

(Yusef-Zadeh et al. 2006). The flux and opacity at any radius R and frequency ν are determined by

$$\begin{eqnarray}&&{S}_{\nu }(R)={S}_{0}{\left(\displaystyle \frac{\nu }{{\nu }_{0}}\right)}^{5/2}{\left(\displaystyle \frac{R}{{R}_{0}}\right)}^{3}\displaystyle \frac{1-{e}^{-{\tau }_{\nu }}}{1-{e}^{-{\tau }_{0}}},\end{eqnarray} \tag{ 3 }$$

and

$$\begin{eqnarray}&&{\tau }_{\nu }(R)={\tau }_{0}{\left(\displaystyle \frac{\nu }{{\nu }_{0}}\right)}^{-(0.5p+2)}{\left(\displaystyle \frac{R}{{R}_{0}}\right)}^{-(2p+3)}.\end{eqnarray} \tag{ 4 }$$

With τ_IR = 1.36 × 10⁻⁸, ν₀ = 66.6 THz (c/ν₀ = 4.5μm), p = 2, R = R_S, and a critical optical depth of τ_crit = 1.51, the submillimeter opacity at 334 GHz is τ_submm = 0.11. Since τ_submm < τ_crit, the submillimeter emission is optically thin and expansion cannot produce a time-delayed submillimeter flare, these parameters produce a submillimeter peak that is simultaneous with the mid-IR. At 334 GHz, the peak flare flux is 0.27 Jy, which underestimates the submillimeter peak flux by a factor of ≈2. Therefore, we consider models with steeper spectra (p > 2), and use the adiabatic expansion model to calculate physical parameters consistent with the submillimeter and IR data in both cases of simultaneous and time-delayed emission.

4.2. Case 1: Optically Thin Submillimeter Emission

The choice of p will affect if the submillimeter emission is delayed relative to the mid-IR. Additionally, it will influence physical parameters such as the equipartition magnetic field strength, cooling time, and initial radius. We show how these parameters depend on p in Figure 4 (left). In these illustrative calculations, we assume the peak flare fluxes at 334 GHz and 4.5 μm are 1 Jy and 20 mJy, respectively. When calculating the equipartition magnetic field strength, B_eq, we assume the electron power-law index is valid between energies of 10 MeV to 1 GeV (20 ≤ γ_e ≤ 2000), and neglect the presence of protons or thermal electrons. To calculate the expansion velocity and velocity-dependent parameters (such as the time delay) in Figures 4 and 5, we use a 15 minute decay timescale. This timescale is estimated from the submillimeter flare's decay rate (Figure 3, left) instead of the less-certain submillimeter/IR time delay.

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In the optically thin case, the flare submillimeter-to-IR spectrum is consistent with S_ν ∝ ν^−0.75 (using the peak flare fluxes at 4.5 μm and 334 GHz noted above). Such an optically thin spectrum is produced when p = 2.5. For this value for p, the equipartition magnetic field strength is B_eq ≈ 27 Gauss with an initial radius of R ≈ 2 R_S. These parameters predict K- and H-filter peak fluxes of ≈12 mJy and ≈9 mJy, respectively (Figure 4, right). The K-filter flux is close to the observed value, but the H-filter flux is underestimated. This is possibly due to a systematic error in the marginal H-filter uncertainty estimate (Abuter et al. 2021). However, the spectrum may flatten between the submillimeter and IR as it does between the IR and X-ray (Abuter et al. 2021).

The synchrotron cooling time for the electrons dominating the submillimeter emission exceeds 2 hr, much longer than the observed flare lifetime, suggesting that the submillimeter decay is either due to the escape of synchrotron-emitting electrons from the source region or by adiabatic cooling as the region expands. We focus on the latter scenario here as it leads to testable predictions; the former possibility is poorly constrained. A factor of 2 decline in the flare flux occurs over approximately 15 minutes. With S_ν (t) ∝ R^−2p = R⁻⁵ in the optically thin case, we estimate an expansion velocity ${v}_{\exp }=({2}^{1/5}-1){R}_{0}/(900\,{\rm{s}})=0.014\,c$ at lower frequencies, within the typical range ${v}_{\exp }=0.003c-0.1\,c$ inferred for previous flares at radio/millimeter frequencies (Yusef-Zadeh et al. 2008). This model cannot explain the ≈30 minute time-delay upper limit between submillimeter and IR wavelengths, but radio/millimeter observations would be delayed (Figure 5, top right).

4.3. Case 2: Time-delayed Submillimeter Emission

We have reported and analyzed the submillimeter light curve of Sgr A* observed as part of a global multiwavelength campaign on 2019 July 18. We confirm that the mid-IR data, observed with the Spitzer Space Telescope, is simultaneous with soft X-ray emission detected with the Chandra X-ray Observatory. Our analysis finds a time delay between the submillimeter light curve, taken with ALMA, and the Spitzer mid-IR light curve. However, the submillimeter data do not sample the entire flare, so the measured time delay is an upper limit to the true value. We analyze the submillimeter and mid-IR emission using adiabatically expanding synchrotron plasma models. We prefer an electron energy spectrum with p = 2.5 if the submillimeter emission is initially optically thin. We do not make conclusions about the electron spectrum at high energies, as a cooling break and high-energy cutoff is preferred (Abuter et al. 2021) but is not modeled here. Since the submillimeter and mid-IR time delay is not certain, we calculate physical parameters of the flaring emission for different values of the electron power-law index, p, which cover both optically thick and thin models. If the submillimeter-to-IR time delay is truly absent, an adiabatically expanding plasma with p = 2.5, R ≈ 2 R_S, equipartition magnetic field strength of B_eq ≈ 27 Gauss, and expansion speed ${v}_{\exp }\approx 0.014c$ can model the data. If the submillimeter emission is delayed by 30 minutes relative to the mid-IR, an adiabatically expanding plasma with initial radius R ≈ 0.8 R_S, p = 3.5, B_eq ≈ 90 Gauss, and ${v}_{\exp }\approx 0.004\,c$ is preferred. In either case, the need for an expanding source region is clear. We showed that multiwavelength observations using at least one lower-frequency band would have been able to break the degeneracy and should be part of future multiwavelength campaigns.

The authors are greatly appreciative to the Spitzer Sgr A* Collaboration for allowing us to use their data in this analysis. The authors are particularly indebted to Joe Hora for answering our questions regarding the Spitzer data. We would also like to thank the anonymous referee for very helpful and constructive comments. This work is partially supported by the grant AST-0807400 from the National Science Foundation. J.M. gratefully acknowledges support for this work, which was provided by the NSF through award SOSP21A-003 from the NRAO. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2018.A.00050.T. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. This work is based on archival data obtained with the Spitzer Space Telescope, which was operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. The scientific results reported in this article are based in part on data obtained from the Chandra Data Archive. This research has made use of software provided by the Chandra X-ray Center (CXC) in the application packages CIAO. This research has made use of data obtained from the Chandra Source Catalog, provided by the Chandra X-ray Center (CXC) as part of the Chandra Data Archive. This research was supported in part through the computational resources and staff contributions provided for the Quest high performance computing facility at Northwestern University which is jointly supported by the Office of the Provost, the Office for Research, and Northwestern University Information Technology.

Facilities: ALMA - Atacama Large Millimeter Array, Spitzer (IRAC) - , Chandra (ACIS) - .

Software: CASA (McMullin et al. 2007), CIAO, bblocks (Scargle 1998; Scargle et al. 2013; Williams et al. 2017), pyCCF (Peterson et al. 1998; Sun et al. 2018), ZDCF (Alexander 1997), PLIKE (Alexander 2013), sklearn (Pedregosa et al. 2011), Scipy (Virtanen et al. 2020), Jupyter Notebook (Kluyver et al. 2016), Pandas (McKinney 2010), Matplotlib (Hunter 2007).