EXTENDED SUBMILLIMETER EMISSION OF THE GALACTIC CENTER AND NEAR-INFRARED/SUBMILLIMETER VARIABILITY OF ITS SUPERMASSIVE BLACK HOLE^*

We obtained sub-mm (870 μm) on-the-fly (OTF) maps of the GC region using the Large APEX Bolometer Camera (LABOCA; Siringo et al. 2009) on the APEX telescope, Chile. The observations were carried out during five nights between 2008 May 27 and June 3 (see observing log details in Table 1), as part of our ground-based, multi-wavelength monitoring program. LABOCA covers a total bandwidth of 60 GHz in the 345 GHz atmospheric window, and is characterized by a beam size (FWHM of the point-spread function (PSF)) of 19'' at 870 μm. From this APEX campaign, the data corresponding to 2008 June 3 have already been published in Eckart et al. (2008b).

During each observing night we took a series of OTF maps of the GC innermost parsecs, interleaved with observations of G10.62 or IRAS16293-2422 as secondary calibrators. For the GC maps we used an integration time of 280 s, a scanning speed of 3' s⁻¹, and a mapping step of 30''. We also systematically changed the observation angle (orthogonal to the galactic plane) by −10°, 0°, and 10°, to avoid spurious artifacts. In this way we end up with 05 × 08 GC maps with an rms noise level of 150 mJy beam⁻¹. For full details of the observation technique, the reader is referred to Eckart et al. (2008b).

Complementary sub-mm 450 and 850 μm archive maps (project m98au64) have also been used. These maps were obtained with the Submillimeter Common-User Bolometer Array (SCUBA; Holland et al. 1999), a continuum array receiver located at the 15 m JCMT in Mauna Kea, Hawaii. They are a subset of the GC survey shown by Pierce-Price et al. (2000). With a field of view of 2.3 arcmin in diameter, SCUBA is formed by two hexagonal arrays of bolometric detectors called Long Wave (LW; 850 μm, 31 pixels) and Short Wave (SW; 450 μm, 91 pixels). Using a dichroic beamsplitter, SCUBA is capable of simultaneously using both arrays. The diffraction-limited resolution corresponds to about 75 at 450 μm, and 14'' at 850 μm.

The observing mode used was scan-mapping, in which the telescope scans the array across the sky while chopping the secondary mirror to produce a differential map of the source. For SCUBA it is recommended to use six different chop configurations: chop throws of 20'', 30'', and 65'' each with chop position angles of 0 deg (Decl. chopping) and 90 deg (R.A. chopping) in a coordinate frame fixed on the sky. For the present case a scan velocity of 24''s⁻¹ was used.

Our NIR adaptive optics (AO) data were obtained between 2008 May 25 and June 3 with NACO (Lenzen et al. 2003; Rousset et al. 2003) at the 8 m ESO VLT unit telescope 4 (YEPUN) in Paranal, Chile (see Table 1). Some of these VLT data have already been published. Specifically, the 2008 May 26 and June 3 light curves have been published in Kunneriath et al. (2010) and Eckart et al. (2008b), respectively. Details of the observations are given in Table 2. From that table it is straightforward to calculate the total integration time as DIT × NDIT × N. The seeing given is that obtained at visible wavelengths in Paranal. The stability of the atmospheric conditions provided good AO corrections all over the run.

Table 2. NACO/NIR Observation Details

λa	DITb	NDITc	Nd	Pixel Scalee	Seeingf
2.2 μm	10 s	4	80	0027	∼10–14
3.8 μm	0.2 s	150	150	0027	∼10–14

Notes. ^aFilter central wavelength. ^bDetector integration time in seconds. ^cNumber of averaged exposures of integration time DIT. ^dN is the number of images.

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We used the dithering technique to produce a mosaic of about 20'' × 20''. Interleaved off-source observations of a dark cloud (60''E and 60''N of Sgr A*) were used to measure the rapid NIR L'-band background variability. The K-band sky background was estimated as the median of several dithered observations of another dark cloud (713''W and 400''N of Sgr A*). See Eckart et al. (2008b) for more details of the observations.

We present additional NIR Ks-band observations obtained by Nishiyama et al. (2009a) at the Subaru telescope (Iye et al. 2004), using the CIAO coronographic imager (Tamura et al. 2003) and the AO36 adaptive optics system (Takami et al. 2004). From this Subaru observing campaign the data from 2009 May 29 were first published by Nishiyama et al. (2009b), and subsequently by Zamaninasab et al. (2010).

Details of the observations are given in Table 1. The image provided by CIAO covers 222 × 222 of the sky. Sky measurements of a dark cloud located a few arcmin northwest from Sgr A* were interleaved with the Sgr A* observations. More details about these observations can be found in Nishiyama et al. (2009a).

The data reduction of the LABOCA data is described in detail in Eckart et al. (2008b). Briefly, we used the BoA¹⁸ software package to perform a standard data reduction, including opacity (τ ∼ 0.3 up to 0.7 toward the GC direction) and flat-field corrections, and correlated sky and instrumental noise removal. This data reduction has been optimized for constraining the Sgr A* flux; hence, the filtering applied may partially affect the extended emission and some flux may be lost in the process. Once the initial data reduction was finished, our main objective was to derive the Sgr A* light curves. To do that, on each individual scan we model Sgr A* as a point-source emitter using a Gaussian fitting and calculating its peak. The modeling process involves the prior removal of the extended sub-mm emission, obtained by co-adding all individual maps (corrected for pointing offsets) and afterward subtracting the resultant averaged central point source. Apart from allowing us to precisely derive the Sgr A* flux, the co-addition of individual maps also provided us with a high signal-to-noise ratio (S/N), 48' × 25', fully sampled map of the sub-mm emission in the GC region (see Figure 1). By subtracting the extended emission we make sure that the background emission is removed, and we are able to better isolate the contribution coming from Sgr A*. The main uncertainty of this process is the subtraction of the point source, which will result in a small intensity offset of the light curve. By testing several models and repeating the data reduction we estimate that, using a model that removes the source without oversubtraction, this effect is less than 10% of the peak flux density of Sgr A*. To calibrate the data we used τ (values based on sky dip and radiometer measurements), secondary calibrators, and compared with the reference map. The flux variation on the secondary calibrators at different epochs is about 10%. However, we estimate the error to be of the order of 4%, which is the relative point-to-point uncertainty in the light-curve calibration. The resulting light curves are shown in Figure 2.

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To further check the significance of the Sgr A* variability, we conducted independent flux measurements of a point-like source observed toward the southwest of the molecular cloud M 0.02-0.02 (labeled A in Figure 1). The uncertainties derived are 8%, 10%, 12%, 5%, and 6% for May 27, 28, 29, 30, and June 3, respectively. The variations in the individual flux values are higher than the 4% uncertainty derived from the different reference sources. This overestimation of the uncertainty is most likely due to the low S/N of this source, rather than to uncompensated opacity variations or pointing issues. However, even considering these uncertainties, the variability of Sgr A* is still significant, therefore validating our method.

The JCMT data have been retrieved fully reduced from the archive. This section gives a summary of the online data reduction procedure. The data were reduced with the SCUBA User Reduction Facility (SURF; Jenness & Lightfoot 1998), which uses the Emmerson 2 deconvolution algorithm to combine the multiple chop throw images of the map field. The data reduction includes flat-fielding the array, correcting for atmospheric extinction, despiking, and generating a rectangularly sampled image. The regridded image can be in any pixel size, and the beam sizes were taken into account: approximately 7 arcsec at 450 μm and 14 arcsec at 850 μm. The online system regrids with 3''pixel⁻¹. The calibrated maps retrieved are shown in Figure 3. The estimated rms is 0.7 and 0.2 Jy beam⁻¹ for the 450 and 850 μm maps, respectively. The total size of the derived maps is about 13' × 13'.

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The NIR data reduction involves flat-fielding, sky subtraction, correction for dead or bad pixels, and sky-background subtraction. There are two main challenges that have to be faced when analyzing the NIR emission coming from Sgr A*. The first is that it is located in a very crowded field, and the second is its intrinsic weakness when it is not in a flaring state. To deal with these, after the basic data reduction was finished, PSFs were subtracted from the images using Starfinder (Diolaiti et al. 2000). Subsequently, we deconvolved the images using the Lucy–Richardson (LR) algorithm (Lucy 1974; Richardson 1972), and restored the beam using a Gaussian beam whose FWHM was the nominal resolution at the correspondent wavelength. We finally obtain a resolution of about 60 and 104 mas at 2.2 and 3.8 μm, respectively.

We used circular aperture photometry (52 mas radius) to estimate the flux density of the individual sources, and A_K = 2.8 and $A_{L^{\prime }}$ = 1.8 to correct for extinction. The K- and L'-band flux densities of IRS16SW, IRS16C, IRS16NE, and IRS21 (R. Schödel 2009, private communication) were used to perform the relative flux calibration.

We used the (known) fluxes and positions of 14 sources within 16 from Sgr A* to carry out its relative photometry, and derived the uncertainties using the reference stars S2 and S10. Finally, the background in the immediate vicinity of Sgr A* was measured, and subsequently corrected, in a close region where no apparent flux was measured. Figures 2 and 4 show the background-subtracted light curves obtained.

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The NIR Subaru data reduction included dark- and flat-field correction, sky-background estimation and subtraction, and bad pixel correction (Nishiyama et al. 2009a). All these steps were performed using the Image Reduction and Analysis Facility (IRAF)¹⁹. Once the images were reduced, the program Starfinder (Diolaiti et al. 2000) was used to extract a PSF via point-source fitting from each image. Each image was afterward deconvolved using the LR algorithm (Lucy 1974; Richardson 1972). The light curves obtained are shown in Figure 2.

One way of checking the reliability of the archive SCUBA maps is to compare the 850 μm map against the LABOCA map. Since the observations and data reduction have been completely independent, this comparison should give us a handle on the expected quality of the results derived with the SCUBA data.

Due to their wavelength proximity, the 870 μm LABOCA and the 850 μm SCUBA maps should in principle exhibit the same structures and flux levels. The differences found could then be attributed to differences in the data reduction (e.g., zero-point definition, filtering), or to observation technique effects (e.g., scanning artifacts).

From a purely morphological point of view, both maps are in good agreement: they show the same structures and approximately the same relative intensities (see Figures 1 and 3, right). The 20 and 50 km s⁻¹ clouds, as well as the secondary clouds, are consistently traced. This accordance is also shown in the low surface brightness regions. In both maps, the central region is dominated by the variable source Sgr A*, along with the northern and southern lobes of the CND.

To quantify the comparison between both maps, we have estimated their percentage flux difference. To do that we first smoothed the higher resolution map (14'' at 850 μm) to the lower one (19'' at 870 μm). Afterward, both maps were aligned by minimizing the difference in the position of the individual clouds, clipped below 0.8 Jy to avoid very low flux contributions (presumably sources of error), and subtracted. Negative fluxes in the most external low surface brightness regions are one characteristic of these SCUBA maps; they are most likely systematic effects from the deconvolution/large-scale filtering. This difference was finally transformed into a percentage value. As shown in Figure 6, most of the regions studied exhibit a high level of agreement (±0%–25%). As for the rest of the map, it shows that there are flux differences from 25% to more than 100%. However, these large values are generally associated with low surface brightness regions (see also Figure 1), and with regions with high flux contrast.

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This comparison shows that for many regions the two long-wavelength maps are in good agreement (25% or better). It also indicates that the use of the 450 μm data will most likely provide information on the true underlying flux ratios in those same regions of the map. Therefore, we decided to consistently derive both the temperature and spectral index maps using only the SCUBA data in the regions where the agreement with the LABOCA map is 25% or better.

Finally, the LABOCA and SCUBA maps both show differences in flux with respect to the 850 μm map from Pierce-Price et al. (2000). In their 850 μm SCUBA map, a flux density of about 5.5–6.6 Jy beam⁻¹ is assigned to the outer regions of the 20 and 50 km s⁻¹ clouds. Being conservative, as the comparison is somewhat qualitative, in the LABOCA map these same regions start approximately in the contour level 3 Jy beam⁻¹, whereas in the SCUBA map they start approximately at the contour level 2 Jy beam⁻¹. We believe that these differences may be due to the data reduction process, in particular to the large-scale applied filtering.

The 450 and 850 μm SCUBA maps consistently trace the structure of the molecular clouds in the GC. It is in the CND and CND-SW regions where their differences are remarkable. While Sgr A*, the CND, and surroundings are shown as bright structures at the longer wavelength, at shorter wavelengths their emission is very weak. At 450 μm, Sgr A* has an upper flux limit level of about 2.5–3.0 Jy, and it is not clearly detected as a point source (see comparison in Figure 5, right). The CND lobes exhibit emission peaks about three times brighter than that corresponding to Sgr A*. The CND-SW source is also detected with a relative flux about 1.5 times larger than that associated with Sgr A*. This low-level emission from the very central regions is somewhat striking (though previously observed with SCUBA maps, e.g., Pierce-Price et al. 2000). One would expect the emissivity and thus the opacity to be larger at the shorter wavelength, so the intensity should be stronger. It is of course possible to argue that there are problems in the map itself, in the zero flux level, or in the instrument which may lead to a non-detection of the point source, Sgr A*. However, this is an unlikely explanation, since all other bright point-like sources present in the region are detected, and no negative fluxes in the CND region have been measured. The low flux level may have a higher impact in secondary structures, but on the other hand their morphology coincides well with the longer wavelength maps. Furthermore, these results agree with those of Dent et al. (1993), who used the UKT14 bolometer at the JCMT, and obtained a detailed map of the region at 450 μm. They do not detect emission at the position of Sgr A*, giving an upper limit to the 450 μm flux of 1.5 Jy. Within the uncertainties, this value is in agreement with our previously mentioned flux limit, especially considering the variable nature of the source. Consistent with the SCUBA map (see Figure 3), Dent et al. (1993) measure the flux peak of the CND lobes to be about 9 Jy beam⁻¹. This low surface brightness emission at the shorter wavelength can be interpreted as an indication of lower temperatures in the CND region than in the rest of the molecular clouds. This is surprising, since this area is close to abundant heating sources. Another possible explanation is that mechanisms other than thermal emission may produce this continuum. The analysis of the physical mechanisms giving rise to these sub-mm structures will be important for interpreting these observations (see Section 6.4).

We have derived a temperature map of the GC central parsecs using only the regions of the SCUBA maps whose fluxes are consistent, within 25%, with the LABOCA ones. This also guarantees a signal higher than a ∼2σ level over the estimated rms of the map. Sgr A* is then excluded from the temperature analysis, although the high error may well be due to the variable nature of the source that gives different flux density values in different observing runs.

Our basic assumption is that the cold dust emission is optically thin at 450 and 850 μm. This can be justified on two grounds. First, the column density required to have opacity 1 at these wavelengths would be too large to be consistent with the known gas column densities. Second, the brightness temperature of the sub-mm emission is far below the dust temperature, even after the surface filling factor is taken into account. Therefore, the dust temperature can be determined from the ratio of the fluxes at two different wavelengths. At temperatures of about 10 K, the blackbody emission peaks at about 500 μm; thus the Rayleigh–Jeans approximation is not applicable for the current data. Therefore, the flux ratio will depend on the value of the emissivity spectral index β (which we assume to be 2.0, the theoretical maximum for crystalline dust grains; see Pierce-Price et al. 2000) and the temperature in the following way (see Kramer et al. 2003; Schnee & Goodman 2005):

$$\begin{equation} \frac{S_{450}}{S_{850}} = \displaystyle \left(\frac{850}{450}\right)^{3+\beta }\frac{{\rm exp}(17\, {\rm K}/T_{{\rm dust}})-1}{{\rm exp}(32\, {\rm K}/T_{{\rm dust}})-1}. \end{equation} \tag{ 3 }$$

Since the temperature is based on a flux ratio (i.e., is a relative measurement), we consider that systematic effects due to the data reduction, filtering, etc., will be smeared out and that they will not have an important impact in our calculations. The flux ratio will of course not account for variations like those caused by the observing weather conditions: high opacities would affect 450 μm more than the 850 μm flux measurements, and may therefore have an impact in the results. In any case, even if the absolute temperature measurements are affected by the data treatment, the relative variations in temperature can be safely investigated. The SCUBA maps have different beam sizes, about 7'' and 14'' for the 450 and 850 μm maps, respectively. To properly compare the maps and derive the temperatures, we smoothed the higher resolution map to the lower one.

The temperature map derived is presented in Figure 7, with values ranging from approximately 5–25 K in the regions under study. The comparison with the 850 μm continuum contours shows an anti-correlation between the flux density and the temperature: the low surface brightness regions are the warmest ones, whereas the bright molecular clouds and the CND regions and surroundings are colder. The regions of the 20 and 50 km s⁻¹ molecular clouds analyzed have dust temperatures ranging between 10 and 20 K, with the 850 μm maxima tracing the low temperatures. This is consistent with dust emission being the dominating mechanism. The median temperature, calculated only in regions where T ⩾ 10 K (see Figure 8), is about 14 ± 4 K. This number compares well, within the uncertainties, with the 21 ± 2 K given by Pierce-Price et al. (2000) for a larger area of the GC, but it is about half the average 30 K estimated by Lis et al. (1991), which we used for the mass derivation. As an example, a temperature decrease of about 10 K would increase the derived mass by a factor of about 1.7. Before re-calculating the masses we have to consider that our temperature map does not cover all the clouds analyzed and that, as we will see below, some temperatures are quite uncertain. Therefore, we decided to keep the previously used 30 K as a temperature average for the mass calculation.

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The apparently coldest regions (<10 K) are mainly located in the CND and its surroundings, with the region encompassing Sgr A* being one of the coldest. There are other small areas with low temperatures, but they are mainly in the outskirts of the area studied. Here the temperature determination may be affected by border effects. This result for the CND is surprising, since one would expect the temperatures there to be the highest ones, and contradicts the conclusions of Latvakoski et al. (1999). Using 31.5 and 37.7 μm maps, these authors found that the color temperature in the internal region of the CND was higher than in the surroundings by about 100 K. It is also in contradiction with the conclusions of the 50 and 90 μm work of Davidson et al. (1992), who found dust temperature between 40 and 70 K in the CND–CND-W region, with the peak located in the close vicinity of Sgr A*.

Our formally derived cold temperatures (below 10 K) are too low and should be considered unphysical. There are two likely explanations for this. The first is that we are dealing with optical depth effects, and it may happen that the emission is not optically thin in all areas, misleading the temperature calculations. The second explanation is that those areas may not be dominated by thermal (dust) emission, and the procedure used to derive the temperature is therefore not applicable.

The first explanation can be cross-checked using the flux–temperature distribution. For the 450 μm continuum map, the distribution has a well-defined projected cone-like shape with its outer envelope showing a tendency for increasing temperature with flux (Figure 8, left). In contrast, the distribution of the 850 μm points does not show such a clear pattern, and the outer envelopes do not reveal any particular trend (Figure 8, right). There are in fact regions with the highest fluxes (>5 Jy beam⁻¹) and very low temperatures (∼6 K). On the other hand, the flux peaks of the map present temperatures above 10 K (see Figure 7). Therefore, we do not have enough evidence to conclude that optical depth effects are responsible for the apparently (very) cold dust measurements. As for the possibility of non-thermal emission in the GC region, this will be analyzed in the next subsection as part of the discussion of the spectral indices.

We have generated a detailed spectral index distribution (see Figure 9) using the 450 and 850 μm SCUBA maps, with the same smoothing and clipping used for the temperature distribution. The spectral indices are derived via the expression

$$\begin{equation} \alpha = \frac{{\rm log}(S_{450 \mu \rm {m}}/S_{850 \mu \rm {m}})}{{\rm log}(\nu _{450 \mu \rm {m}}/\nu _{850 \mu \rm {m}})}. \end{equation} \tag{ 4 }$$

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The morphology of this map is of course equivalent to that of the temperature. However, it is useful to show the map in order to analyze the derived α and discuss the results more easily. In general, the spectral index has values equal to or larger than 2, indicating that the 20 and 50 km s⁻¹ clouds are mostly dominated by thermal emission. This is consistent with the Pierce-Price et al. (2000) results: they have already discussed the emission from dust as the principal mechanism dominating these two clouds. Nonetheless, their spectral indices values are about 1.2 times larger than ours. As mentioned before, this is probably due to the different data reduction processes and their correction for artifacts, which we have not applied.

A direct comparison between the temperature map (Figure 7) and the spectral index distribution (Figure 9) shows that areas associated with excessively low temperatures also have low spectral indices, ranging from −0.6 to 1.0. In the CND and surrounding areas, we have defined three different spectral index regions: from east to west, these represent a radial decrease toward Sgr A*. The first region, with α values between 1 and 2, partially occupies the CND. We can therefore explain the measured spectral indices with equal contributions of synchrotron and dust emission, and a 30% synchrotron and 70% dust contribution. In this calculation 3 is assumed to be the typical spectral index for the dust emission, and a steep −1 for the synchrotron (Sgr A East α values derived from radio data range from −0.5 to about −1.0; Ekers et al. 1983).

Further inward to Sgr A*, the spectral index ranges between 0 and 1. This can be explained with a combination of synchrotron emission (α ∼ −0.75) contributing between 20% and 45% and dust emission (α = 3.0) contributing between 80% and 55%.

Closer to the GC itself, and surrounding Sgr A*, we measure a halo structure with about −0.6 < α ⩽ 0.0, which can be explained with a combination of 90%–70% synchrotron emission and 10%–30% dust and free–free. For the regions surrounding Sgr A*, VLA radio maps at 6 and 20 cm wavelength have been obtained by Yusef-Zadeh & Morris (1987b). They show that we can expect a surface brightness of ∼1 Jy in the 14'' FWHM diameter beam area around Sgr A* that is covered by the SCUBA telescope at 350 GHz. Assuming a spectral index of −0.5, this results already in a contribution of non-thermal radiation of 0.12 Jy at 350 GHz. A significant portion of non-thermal 350 GHz radio emission may also be associated with compact pulsar/neutron stars and their winds. Muno et al. (2008) explained the diffuse X-ray emission in the central 10''–15'' of the Chandra map as being dominated by non-thermal emission from a few tens of pulsar/neutron star winds.

In addition to pulsar winds that are extended on the arcsecond scale, we may also expect a contribution from compact non-thermal radio emission from jet components associated with pulsars and neutron stars (e.g., Pestalozzi et al. 2009; Dubner et al. 2008; Migliari et al. 2007). Here we assume that emission of the order of 1 Jy at 350 GHz can be explained by a few tens of sources with flux densities at the synchrotron self-absorption peak of about ⩽0.2 Jy each. For compact objects with a size of 0.1–0.3 mas (4–12 × 10⁻⁶ pc) diameter and a magnetic field of 1–100 G averaged over the corresponding source volume, one obtains an synchrotron self-absorption turnover at 20–50 GHz. Given this turnover frequency, this assumption is in agreement with an upper limit from these compact sources of 3 mJy at 5 GHz (see the discussion in Muno et al. 2008). It would also be in agreement with high-resolution 100 GHz and 230 GHz CARMA interferometry maps of the mini-spiral region that do not detect compact sources (e.g., IRS13; Kunneriath et al. 2010).

Finally, Sgr A* itself has been left out of the spectral indices analysis, due to the inconsistency between the LABOCA and SCUBA results.

In summary, we find a significant contribution of non-thermal emission in the GC region, especially in the CND and surroundings: the spectral index gets steeper as we approach Sgr A* itself.

For the present analysis we have relied on the SCUBA data, and on the fact that the flux ratio should give a stable result, reasonably independent of the data reduction process. However, to test the validity of our results, we have calculated how variations in flux (derived from the data analysis; see Section 3.1) would affect our results. We find that, if the percentage of missing flux is the same in the two wavelengths, the result will be obviously the same. In the unlikely scenario that only the 450 μm flux has up to 100% flux missing, the thermal emission will dominate more as the 450 μm flux increases, but still the spectral index values will decrease toward the nuclear regions. The spectral index value in the central region will go from steep to flat in the Sgr A* regions as the percentage of missing short-wavelength flux increases. The inverse situation occurs when we consider that only the 850 μm map has missing flux and account for it. This results in an unlikely scenario where the thermal emission becomes less important (even in the molecular clouds) as the long-wavelength flux increases. However, a decrease on the spectral index toward the center is again measured. Finally, if we consider that in both wavelength regimes there is some flux missing, the steeper spectral index in the central region is still detected. For instance, a 30% and 50% increase in the long- and short-wavelength fluxes, respectively, would imply an increase of only 0.2 in α.

This test confirms that, in the sub-mm domain, the CND and surrounding regions are not purely thermally dominated. Therefore, the temperature calculations given in Section 6.3 are not valid for these regions, and the low temperatures obtained are not representative of their physical conditions. To properly disentangle all the proposed mixed mechanisms in adequate ratios, further data would be needed. Quasi-simultaneous multi-frequency measurements using APEX or ALMA will help to further constrain the scenario played here.

In the center of all these complex molecular clouds and streamers lies Sgr A*, the true GC. In the previous part of this paper we have attempted to understand the environment that surrounds Sgr A*, and the main physical mechanisms taking place there. In the following we will not only concentrate on the characterization of the Sgr A* variability, which is key to understanding the processes taking place there, but we will attempt to define a classification scheme for the different types of flares.

The complete set of NIR and sub-mm light curves obtained in the 2008 coordinated VLT–APEX campaign, along with the complementary Subaru data, is presented in Figures 2 and 4. We have NIR data for nine nights and sub-mm data for five. Coordinated observations between APEX, VLT, and Subaru were possible on two nights and between APEX and Subaru for one night of the observing run. However, as we will see in Section 8.3, the APEX and Subaru sites make the synchronism fail, and the light curves are not suitable for modeling. Throughout the text, we define the activity of Sgr A*, or flare, as the presence/occurrence of significant flux density excursions. For instance, a minimal variation of 4σ above the quiescent level in 15 minutes (Bremer et al. 2011) can be used to define a flare. However, this definition is not unambiguous, and no distinct flare description can be found in the literature.

Due to the expansion velocity postulated in the adiabatic expansion model (see Section 8.2), the sub-mm light curves are expected to be broad, since the individual components are mixed and overlap with each other. In the case of the sub-mm light curves, the median activity peak and offset are 4.3 ± 0.4 Jy and 2.9 ± 0.4 Jy, respectively. The total flare length and peak time are in general not well determined; this is due to the insufficient time coverage of the available data. At most, we can state that the lower limit for the sub-mm flare duration is about 3 hr.

The main observational features of the light curves are detailed in Table 4. For each night, these measurements have been derived directly from the observed (discrete) NIR and sub-mm light curves. The values presented are the activity peak and the light-curve minimum, which can be considered as an offset. This offset is meant to distinguish between rapid intra-day variability, and variability that may occur at longer timescales. The activity length and activity start and peak are also shown. We define activity start as the time when the flux increases and no longer shows stable behavior.

The NIR light curves present an average flux density of the flare maxima of 14.1 ± 5.5 mJy, with a typical light-curve minimum of 2.9 ± 2.9 mJy. The average activity length is 5.3 ± 0.7 hr. There is no common or very specific structure for the NIR light curves of Sgr A*. Some of them are dominated by a well-defined main flare, whereas others appear to be formed by short-time events with no clear dominant flare underneath. These flux density variations (i.e., the light-curve structure) can be explained in a disk or jet model (see, e.g., the discussion in Eckart et al. 2006a, 2006b, 2008a). They could also be explained as a consequence of an underlying physical process that can be described as continuous red noise variations (e.g., Do et al. 2009).

Up until now, a classification scheme to categorize the NIR flares has not been defined. However, it would be useful to have a systematic method for separating the light curves according to their structure and activity level. We propose a classification scheme where the observed light curves are defined with a combination of individual short events (i.e., hot spots) and an underlying transient small disk (Meyer et al. 2006a). The proposed classes are as follows.

• 1.  
  Type I. Clustered events with a clear underlying flare. In this case the flare substructure would be due to relativistic events orbiting around the black hole, whereas the main underlying flare is due to instabilities in the underlying transient disk (Meyer et al. 2006a). The (main) flare duration is of the order of one hour or more, with a peak intensity of between 5 and 30 mJy. The main flare, which in general has a Gaussian-like shape, has to clearly go up and down. The sub-flares, with a duration of the order of 20 minutes, are overimposed in the main flare, and generally their structures do not dominate the flare shape. Within the Type I flares there is one outstanding type. It is characterized by an initial steep (⩾10 mJy) rise followed by a smooth decay or a plateau, followed by a milder activity peak (e.g., 2008 May 25 and 26 flares; see Figure 4). These flares are strong and last for several hours. Within the already published flares, there is no case with the inverse structure (smooth rise and final very steep decay). This is because the dissipation time is longer than the disturbance time, and thus the initial steep rise must be followed by a slower decay.
• 2.  
  Type II. Clustered but still discernible individual events, which could be explained as short (about 20 minutes) and frequent localized events whose intensity may vary from a few up to a 40 mJy peak (e.g., 2008 May 30 and June 1; see Figures 2 and 4). The time separation between these events is typically ≲30 minutes.
• 3.  
  Type III. Short (about 20 minutes) localized individual events. This flare type is similar to Type II, but here the frequency of events in not that high, and thus they are separated from each other by more than 30 minutes (e.g., 2008 May 27, 28, and 29; see Figure 2).
• 4.  
  Type IV. No flare activity. Sgr A* is in a quiescent phase.

We have used this method to classify a large number of published NIR Sgr A* light curves (see Table 5). Including the ones presented in this paper, a total of 90 flares obtained in different facilities have been classified. 11% of flares could not be properly classified, mainly due to the time coverage. In addition to this, 18% of flares have been tentative classified. This is mainly because the light-curve time sampling and/or the display chosen by the authors prevented a clear assessment of the flare type. From the remaining 64 light curves, 14% belong to Type I, 27% and 12% to Types II and III, respectively, and 47% to Type IV. Hence, strong variability episodes with an underlying main flare represent about one-sixth of the classified flares, whereas short individual events, either clustered or sparse, are the most common activity types. Sgr A* presents a quiet state in almost 50% of cases. Further unbiased statistics which make use of all observed light curves rather than only the active ones (e.g., H-band light curves in Bremer et al. 2011) are needed to better constrain these results.

The SSC formalism applied has been explained extensively in Sabha et al. (2010). Here only the basics are given.

Following the terminology of Gould (1979) and Marscher (1983), we define a synchrotron source of angular size θ (a few Schwarzchild radii). It is assumed that the emitting electrons follow a power-law distribution,

$$\begin{equation} N(E) = N_{0}E^{-(2\alpha +1)} (\gamma _{1}mc^{2}<E<\gamma _{2}mc^{2}), \end{equation} \tag{ 5 }$$

where γ₁ and γ₂ are the minimum and maximum electron Lorentz factors. A γ₂ value of the order of 10³ is desired to obtain enough SSC in the X-ray domain. α represents the optically thin spectral index. We define the cutoff or turnover frequency ν_m as that where the synchrotron source becomes optically thick. Considering the relativistic bulk motion of the source, we then have a boosting factor δ = Γ⁻¹(1 − β cos ϕ), where ϕ (which we assume to be ∼40) is the angle between the velocity vector and the line of sight, β = v/c (assumed to be ∼0.5) with c the speed of light, and Γ = (1 − β²)^1/2 represents the Lorentz factor.

This formalism allows us to calculate the magnetic field B and the inverse Compton scattered flux density S_SSC as a function of the energy of the X-ray photons E_keV (as given in Marscher 1983). The magnetic field strength is then defined as B∝θ⁴ν⁵_mS_m⁻². Finally, the inverse Compton scattered flux is produced by scattering of the same electron population, and is defined as

$$\begin{equation} S_{\rm SSC}\propto {\rm ln}(\nu _{2}/\nu _{m})\theta ^{-2(2\alpha +3)}\nu _{m}^{-(3\alpha +5)}S_{m}^{2(\alpha +2)}E_{{\rm keV}}^{-\alpha }, \end{equation} \tag{ 6 }$$

where ν₂ is the upper synchrotron cutoff frequency. As explained above, a Lorentz factor of the order of 10³ is required, for which ν₂ lies within the NIR bands. Most of the NIR spectrum can therefore be explained by synchrotron emission, whereas the inverse Compton emission is responsible for the X-ray spectrum (Markoff et al. 2001; Yuan et al. 2003; Eckart et al. 2004).

For the present study, we did not have simultaneous X-ray light curves at our disposal. However, as a further modeling constraint the SSC formalism has been applied, taking care that the derived X-ray values are consistent with literature data.

In the context of non-simultaneous flare emission, most of the observational evidence to date (e.g., Eckart et al. 2006b, 2008b; Yusef-Zadeh et al. 2006, 2009; Marrone et al. 2008) points toward the existence of a time delay of the order of 1–2 hr between the observed sub-mm flares and the prior events observed at shorter wavelengths (either X-ray or IR; see Marrone et al. 2008). There has been some discussion about whether or not these bursts of activity at different wavelengths have any relation. If the NIR/X-ray and radio/sub-mm events are unrelated, one should be able to see a comparable number of radio/sub-mm flares before and after the NIR/X-ray. Since this is not happening, it is therefore safe to assume that these energetic events are part of a common physical process taking place in Sgr A*.

In what follows we will introduce the basics of the adiabatic expansion model that has been applied to the synchrotron components described in Section 8.1. For full details of the adiabatic expansion formalism, the reader is referred to Eckart et al. (2008b) and references therein.

van der Laan (1966) was the first author to present a quantitative description of a model including initially thick synchrotron components that expand over time until they become optically thin at longer wavelengths. In our model the starting point is a compact, uniform spherical blob of radius R. This blob is composed of relativistic electrons and is characterized by an isotropic velocity distribution and a power-law energy distribution n(E)∝E^−p. Initially, the assumption is such that the blob is optically thick at all frequencies. As it expands, the constant magnetic field, the energy of the relativistic particles, and their density change as R⁻², R⁻¹, and R⁻³, respectively (van der Laan 1966).

The cutoff frequency is defined as ν₀, and R₀, S₀, and τ₀ represent the size, flux density, and optical depth of the blob. The optical depth and flux density are defined as

$$\begin{equation} \tau = \tau _{0}\left(\frac{\nu }{\nu _{0}}\right)^{-(p+4)/2}\left(\frac{R}{R_{0}}\right)^{-(2p+3)} \end{equation} \tag{ 7 }$$

and

$$\begin{equation} S_{\nu } = S_{0}\left(\frac{\nu }{\nu _{0}}\right)^{5/2}\left(\frac{R}{R_{0}}\right)^{3}\frac{1-e^{-\tau }}{1-e^{-{\tau _{0}}}} \end{equation} \tag{ 8 }$$

in order to combine the adiabatic expansion model with the SSC formalism. τ₀ is defined as the optical depth corresponding to the frequency at which the flux density is a maximum (van der Laan 1966). Lastly, the dependence of the radius with time, R(t), has been modeled linearly with a constant expansion speed v_exp.

In summary, the present model is an attempt to describe the observed data by explaining the NIR luminosity with the optically thin, and the sub-mm luminosity with the optically thick regimes of the synchrotron emission.

Coordinated observations at NIR (VLT and Subaru) and sub-mm (APEX) wavelengths were possible during several nights of the observing run: 2008 May 27, 28, 29, 30, and 2008 June 3. Due to poor weather conditions, on May 28 the VLT NIR coverage was very short (about 1 hr) and took place in the middle of the sub-mm observations. Also, on the same night, the NIR Subaru data started when the sub-mm light curve finished. These aspects prevent us from providing a convincing simultaneous fit of the light curves. On May 29, we only have the Subaru and APEX data, which do not have a good time overlap. On May 30, the sub-mm light curve also has a poor time coverage, and is not adequate for a proper modeling.

For the other two light curves (May 27 and June 3; see Figure 2), we end up with light curves which are suitable for a simultaneous fitting. The Subaru data have not been used for the modeling because of the lack of time overlap between the facilities. Their main use in the present paper was to improve the statistics in Section 7.

The May 27 light curve presents mild VLT-NIR (Ks-band) variability with well-defined peaks. A strong sub-mm decay of more than 1.5 Jy is also measured, indicating that we missed at least the first half of the flare. This light curve is explained, in the context of our model, with three flare events (see Figure 10), which do not include the Subaru data. In the sub-mm domain the emission is dominated by a broad flare, a combination of the three individual events observed in the NIR.

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In the data set corresponding to June 3, violent variability is detected in the NIR (L' and Ks bands) with, under the assumption of the adiabatic expansion model, a significant counterpart in the sub-mm domain. This flare has been extensively studied and modeled by Eckart et al. (2008b); therefore, here we will only discuss the values to compare them with the present modeling. In that case four different events are necessary to account for the measured NIR variability, while in the sub-mm domain the components blend in a single flare.

To account for the slow variability of Sgr A* (scale of days; see, e.g., Zhao et al. 2001; Meyer et al. 2008), a constant value of 3.2 Jy has been subtracted from the May 27 light curve. This value is in good agreement with the offset of 3.0 ± 0.5 Jy estimated statistically by Eckart et al. (2008b).

8.3.1. Modeling Results

The adiabatic expansion modeling is consistent with a time lag of 3.0 ± 0.5 hr between the VLT and APEX light curves, which is about double the previous results obtained from our team (see Eckart et al. 2008a, 2008b; Kunneriath et al. 2010) and other authors (e.g., Yusef-Zadeh et al. 2009, and references therein). The results from the present campaign, along with other coordinated observing campaigns that include sub-mm monitoring of Sgr A* (Eckart et al. 2006b, 2008b; Yusef-Zadeh et al. 2006, 2009; Marrone et al. 2008), suggest that non-radiative cooling processes, such as adiabatic expansion, are needed. However, the adiabatic cooling model results in very low expansion speeds. Based on the model of millimeter radio flares, Yusef-Zadeh et al. (2008) obtained expansion velocities in the range 0.003c ≲ v_exp ≲ 0.1c. Our value of 0.0018c is at the lower end of this interval. All of these velocities are slow compared to the expected relativistic sound speed and the orbital velocity in the vicinity of an SMBH. These low expansion velocities suggest that the expanding gas cannot escape from Sgr A*, or that it has a large bulk motion superimposed on the expansion (see for instance Marrone et al. 2008; Yusef-Zadeh et al. 2009). This implies that the adiabatically expanding source components have a bulk motion larger than v_exp. Alternatively, the expanding material may be contributing to a corona or disk close to Sgr A*. Differential rotation within the accretion disk may also account for the low expansion velocities.