The variability of Sagittarius A* at 3 millimeter
Juan Li, Zhi-Qiang Shen, Atsushi Miyazaki, Lei Huang, R.J. Sault, Makoto Miyoshi, Masato Tsuboi, Takahiro Tsutsumi
aa r X i v : . [ a s t r o - ph . GA ] M a y The variability of Sagittarius A* at 3 millimeter
Juan Li , , Zhi-Qiang Shen , Atsushi Miyazaki , Lei Huang , R. J. Sault , MakotoMiyoshi , Masato Tsuboi and Takahiro Tsutsumi ABSTRACT
We have performed monitoring observations of the 3-mm flux density to-ward the Galactic Center compact radio source Sgr A* with the Australia Tele-scope Compact Array since 2005 October. Careful calibrations of both elevation-dependent and time-dependent gains have enabled us to establish the variabilitybehavior of Sgr A*. Sgr A* appeared to undergo a high and stable state in 2006June session, and a low and variable state in 2006 August session. We report theresults, with emphasis on two detected intra-day variation events during its lowstates. One is on 2006 August 12 when Sgr A* exhibited a 33% fractional varia-tion in about 2.5 hr. The other is on 2006 August 13 when two peaks separatedby about 4 hr, with a maximum variation of 21% within 2 hr, were seen. Theobserved short timescale variations are discussed in light of two possible scenar-ios, i.e., the expanding plasmon model and the sub-Keplerian orbiting hot spotmodel. The fitting results indicate that for the adiabatically expanding plasmonmodel, the synchrotron cooling can not be ignored, and a minimum mass-lossrate of 9 . × − M ⊙ yr − is obtained based on parameters derived for this mod-ified expanding plasmon model. Simultaneous multi-wavelength observation iscrucial to our understanding the physical origin of rapid radio variability in SgrA*. Subject headings:
Galaxy: center, techniques: interferometric Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical Observatory, ChineseAcademy of Sciences, 80 Nandan RD, Shanghai 200030, China; [email protected], [email protected] Graduate School of the Chinese Academy of Sciences, Beijing 100039, China National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan;[email protected], [email protected], [email protected] Key Laboratory for Research in Galaxies and Cosmology, University of Science and Technology of China,Hefei 230026, China; [email protected] University of Melbourne, School of Physics, Parkville, Victoria 3052, Australia; [email protected] Institute of Space and Astronautical Science, Sagamihara, Kanagawa 229-8510, Japan;[email protected]
1. Introduction
There is compelling evidence that Sagittarius A ∗ (Sgr A*), the extremely compact radiosource at the dynamical center of the Galaxy, is associated with a 4 × M ⊙ black hole(Eckart & Genzel 1996; Ghez et al. 2000; Sch¨odel et al. 2002; Eisenhauer 2003). Since itsdiscovery in 1974 (Balick & Brown 1974), Sgr A* has been observed extensively with radiotelescopes in the northern hemisphere, and temporal flux variations at millimeter wavelengthswere reported. With VLA observations, Yusef-Zadeh et al. (2006b) detected an increase offlux density at a fractional level of 7% and 4.5% at 7- and 13-mm, respectively, with aduration of about 2 hr. The peak flare emission at 7-mm led the 13-mm peak flare by 20-40minutes. Mauerhan et al. (2005) detected intra-day variations (IDVs) of about 20% and insome cases up to 40% at 3-mm using the Owens Valley Radio Observatory (OVRO). Therise and decay occurred on a timescale of 1-2 hr. At 2-mm, Miyazaki et al. (2004) reporteda 30% flux increase in 30 minutes from the monitoring of the Nobeyama Millimeter Array(NMA). On the other hand, flares with violent intensity increases in very short timescaleshave also been detected at infrared and X-ray bands (Genzel et al. 2003; Baganoff et al.2001; Eckart et al. 2006b), inferring that these emissions from Sgr A* originate within veryvicinity of the central massive black hole. This is further strengthened by the simultaneousdetection of X-ray, infrared and sub-mm flares (Eckart et al. 2004, 2006a, 2008a, 2008b;Yusef-Zadeh et al. 2006a, 2008; Marrone et al. 2008).Since Sgr A* is embedded in thick thermal material, it is particularly difficult to observeits intrinsic structure. But observations of IDV can give indirect constraints on the sourceemission geometry and emission mechanisms. However, previous monitoring observations ofSgr A* from the northern hemisphere have been strictly limited to a short observing window( < > ◦ ). As such, the ATCA calibrations and fluxdensity measurements of Sgr A* are expected to be more accurate.In this paper, we report our effort to search for IDV in Sgr A* with the ATCA. We firstintroduce the ATCA observations in §
2. The data reduction and analysis with emphasison the gain calibrations are described in detail in §
3. In §
4, we present the detection ofIDV events in Sgr A*. To interpret the observation, we discuss two possible scenarios in § §
6. Throughout this paper, the fractional variation is defined as 3 – S max − S min ( S max + S min ) , here S max and S min refer to the maximum and minimum value of flux density,respectively.
2. OBSERVATIONS
In 2005 and 2006, we performed 3-mm ATCA flux density monitoring of Sgr A* over 50hr in the following 3 sessions: 2005 October 18, 2006 June 9 and August 9-13. Dual (linear)polarization double sideband (DSB) HEMT receivers were used. The first ever 3-mm ATCAmonitoring of Sgr A* was performed on 2005 October 18 when the data were simultaneouslyrecorded, in both the lower (93.504 GHz) and upper (95.552 GHz) sidebands, in 32 channelsof a total bandwidth of 128 MHz. For the observations in 2006, the data were recorded intwo slightly different 3-mm bands: the lower sideband (86.243 GHz) was set to the transitionfrequency of the SiO J=2-1 v=1 line with 256 channels of a total bandwidth of 16 MHz,the upper sideband (88.896 GHz) was a wideband with 32 channels of a total bandwidthof 128 MHz. Since the continuum data of the lower sideband with narrow bandwidth haverelatively low signal to noise ratio, only the upper sideband data were used for Sgr A* andother continuum sources.On 2005 October 18, we observed Sgr A* in the H168C configuration of the ATCA, witha maximum baseline of 192 m, uv range of 13 - 61k λ and a synthesized beam of 2 . ′′ × . ′′
7. On2006 June 9, the observations were performed in the 1.5D configuration with a maximumbaseline of 1439 m, covering uv range of 20 - 430k λ and yielding a synthesized beam of2 . ′′ × . ′′
3. In 2006 August, the observations were performed in SPLIT5 configuration witha maximum baseline of 1929 m, covering uv range of 3 - 570k λ and yielding a synthesizedbeam of 1 . ′′ × . ′′
2. In this array, the spacing between antennas 2 and 3 and antennas 3 and4 are only 31 m, causing severe shadow effect, especially for antenna 3.Quasar 3C 279 was observed for 10 minutes at the beginning of the observation tocalibrate bandpass. Either a planet or a bright radio source was observed for the fluxdensity calibration. The first 3-mm ATCA observation of Sgr A* lasted for 10 hr on 2005October 18. It alternated between Sgr A* and the only secondary calibrator PKS 1730-130,which was also used as pointing calibrator. The primary calibrator Uranus was observed for10 minutes at the end of the observation. In 2006 June and August, we observed Sgr A*in a total of 6 days with a thoughtful calibration strategy. Up to four secondary calibrators(control sources) including an SiO maser source (OH2.6-0.4) and three continuum sources(PKS 1921-293, PKS 1710-269 and PKS 1730-130) were observed to check the consistencyof the gain calibrations. Limited by the weather, ATCA observed Sgr A* for only 1 hron August 9, 4 hr on August 10 and 2 hr on August 11. Therefore, we will focus on the 4 –measurements on June 9, August 12 and 13. The pointing accuracy was checked every halfan hour by observing VX Sgr, a known strong SiO maser source. The instrumental gain andphase were calibrated by alternating observations of Sgr A* and all secondary calibrators.In 2006 June, the observations were performed using the following sequence: OH2.6-0.4 (2min), Sgr A* (5 min), PKS 1730-130 (2 min), and PKS 1921-293 (1 min). In 2006 August,the observing sequence was PKS 1710-269 (2 min), OH2.6-0.4 (1 min), Sgr A* (10 min),PKS 1710-269 (2 min), OH2.6-0.4 (1 min), PKS 1730-130 (1 min), and PKS 1921-293 (1min). The observing details have been summarized in Table 1.
3. DATA REDUCTION AND ANALYSIS
All the data processing was conducted using the ATNF MIRIAD package (Sault etal. 1995). At millimeter wavelengths, the atmosphere can no longer be approximatelytransparent. The opacity effect is included in an effective system temperature - the so-called“above atmosphere” system temperature (Ulich 1980) for the ATCA measurements at 3-mm. The bandpass corrections were made using the strong ATCA calibrator 3C279. Foramplitude calibration, we first applied a nominal elevation-dependent gains of the antennasand then used calibrators to further determine the additional corrections. On 2005 October18, the flux scale was based on observation of Uranus. On 2006 June 9, the flux density scalewas determined using PKS 1730-130, assuming its flux density of 2.27 Jy at 3-mm. In 2006August, we derived the flux density scale with another brighter radio source PKS 1921-293,which is reported to be 8.44 Jy during our observations from the ATCA calibrator list on web.From the ATCA calibrator flux density monitoring data during 2003 to 2006, we estimatedits mean flux density of 8.66 Jy with a standard deviation of 1.04, implying a dispersion ofabout 12%. PKS 1921-293 is probably better than that of other calibrators simply becausePKS 1921-293 data usually have very high signal-to-noise ratio. So, we expect an accuracy ≤
20% for the absolute amplitude calibration in these observations. After the phase self-calibration, the data were averaged in 5 minutes bin to search for shorter timescale variability.The flux density of Sgr A* was estimated by fitting a point source model to visibilities on theprojected baselines longer than 25k λ (about 85 m at 3-mm) to suppress the contaminationfrom the surrounding extended components (Miyazaki et al. 2004; Mauerhan et al. 2005).Both the fitting error reported by MIRIAD and the rms of the residual visibilities were usedto get the final error estimate.In order to establish strong cases for variability of Sgr A* at millimeter wavelengths, re-liable calibrations of both elevation- and time-dependent gains are crucial. We have carefullyconsidered and corrected the following factors that could affect the measurements during the 5 –calibration process.1. Antenna gain varies with elevation angle mainly because of the gravitational distor-tion of the dish. The antenna efficiency of ATCA has maximum value at an elevation angleof 60 ◦ and minimum value at an elevation angle of 90 ◦ . A nominal gain-elevation correc-tion in MIRIAD is applied at elevations greater than 40 ◦ for 3-mm observations, only thosedata observed at elevation angles above 40 ◦ were used. However, such nominal elevation-dependent gains built in MIRIAD seem hard to fully compensate the gain variation. Wehave plotted flux density as a function of elevation angle and found that a nearby calibra-tor was needed to make further correction, otherwise significant elevation effect (e.g., peaksat about 60 ◦ , or reaches the lowest point at 90 ◦ elevation angle) will be shown up in thelight-curve, which often indicates some calibration errors. PKS 1730-130, which is oftenused to calibrate phase and amplitude during observations from northern hemisphere at mmwavelength (e.g. Miyazaki et al. 2004, Yusef-Zadeh et al. 2008), is proved to be unsuitablefor the ATCA observations. It is 16.2 ◦ away from Sgr A*, and its elevation angle is only72 ◦ when Sgr A* reaches the zenith. Thus, gain corrections derived from this source datacannot fully compensate the elevation effect in Sgr A*, especially for observations at highelevations. Similarly, PKS 1921-293, which reaches the zenith 2 hr later than Sgr A*, is notsuitable, either. So we only use two closer sources PKS 1741-312 and OH2.6-0.4 for the gaincalibration.2. Calibrators are, in general, variable sources which will unavoidably introduce un-certainties into the nominal time-independent gains. For this reason, several secondarycalibrators were actually scheduled to check the consistency. The complex gains derivedfrom one control source were applied to both Sgr A* and other control sources. If such acontrol source is strongly variable, a somehow similar trend in light-curve will appear for allthe other sources (including Sgr A*) after calibration.To check the significance of any detected variability, we introduced the modulation index,which is defined as the rms of the gain correction of five antennas derived from calibratorsand flux density of Sgr A* divided by their mean, corresponding to the degree of variationfor Sgr A*, and the fractional uncertainty in time-dependent gain correction, respectively.Obviously, if the modulation index of Sgr A* flux density is much larger than that of antennagain correction, the detected flux variation is most likely to be real. The modulation indicesof Sgr A* and gain correction of five antennas derived from two nearby calibrators OH2.6-0.4 and PKS 1710-269 on 2006 June 9, August 12 and 13 are plotted in Figure 1. Themodulation indices of Sgr A* were quite large on 2006 August 12 and 13, indicating the realdetection of IDV from Sgr A*. As mentioned in §
2, many data obtained from antenna 3in 2006 August were shadowed and thus not used in obtaining its gain correction, resulting 6 –in a large fluctuation in its gain correction and thus a bigger modulation index. Duringobservations in 2006 August, the 3-mm flux density of PKS 1710-269 is around 0.5 Jy, onlyone fiftieth of that of OH2.6-0.4, therefore the signal-to-noise ratio of PKS 1710-269 datais much lower than that of OH2.6-0.4. This explains why the modulation indices of gaincorrections derived from PKS 1710-269 are relatively high.3. As mentioned in §
2, we only used upper sideband (88.896 GHz) data with a band-width of 128 MHz for Sgr A* and other continuum control sources, and the lower sideband(86.243 GHz) data of 32 MHz bandwidth only for the SiO maser source OH2.6-0.4. Willthere be an additional uncertainty when applying to Sgr A* the gain solutions derived fromOH2.6-0.4 data? We inspect this by comparing the results of the two sidebands on 2006August 12 and 13. Similar to what we did for the upper sideband data, the flux densities ofSgr A* was also estimated from the lower sideband using the same channels as OH2.6-0.4.The results from the lower sideband data show larger error bars mainly because of the rela-tively low signal-to-noise ratio. The average deviations from results of upper sideband dataare 2.4% on August 12 and 3.6% on August 13, much smaller than the fractional variationof Sgr A* (see § ◦ away),proved to be the best control source. As such, it was used as the main secondary calibratorto determine the antenna gain corrections for all the results presented in this paper. 7 –
4. RESULTS
During the first 3-mm ATCA observation of Sgr A* on 2005 October 18, the flux densityof Sgr A* ran up to 3.5 Jy, much brighter than the normally expected 1 . ◦ from Sgr A*) severely limited the amplitude calibration.Because of this, starting from observations in 2006 June and August (see § λ . Following is a detailed description of the results fromeach observation.The flux density of Sgr A* was relatively high (around 3 Jy) but stable on 2006 June9. As shown in Figure 1, the modulation index of Sgr A* is small and comparable to thatof antenna gains. Therefore, no IDV was detected.During the first three days in the 2006 August session (August 9, 10 and 11), verylimited data were available. The flux density of Sgr A* was decreased from 2.52 to 2.25 Jyin 1 hr on August 9, stayed around 1.9 Jy quite stably during the 4 hr run on August 10 andaround 2.0 Jy over the 2 hr observation on August 11. So, we conclude that no ascertainedIDV was detected.Two clear IDV events were seen in the last two days of the 2006 August session. Asshown in the light-curves of Sgr A* and other sources on 2006 August 12 (Figure 3 left), firstthe flux density of Sgr A* decreased from 1.65 to 1.50 Jy, and then increased to 2.11 Jy in2.5 hr before decreasing again to 1.90 Jy. The fractional flux density variation is estimatedto be 33%. On 2006 August 13 (Figure 3 right), the flux density of Sgr A* first increasedfrom 1.95 to 2.14 Jy, reached its first peak before decreasing to 1.80 Jy in 1.7 hr. Then itreached the second peak 2.22 Jy in 1.9 hr, and declined to 1.98 Jy in 1.2 hr. The maximumfractional flux density variation is 21% with a timescale of about 2 hr. As shown in Figure1, the modulation indices of Sgr A* on both August 12 and 13 are much greater than thatof gain corrections, supporting that the observed flux density variations are most likely tobe real.The NMA observations of Sgr A* from 1996 to 2003 indicate that Sgr A* has quiescentand active phases, the peaks of flares were 2-3 Jy at 3-mm while the mean flux densityin a quiescent phase was 1.1 ±
5. DISCUSSIONS
Several models have been invoked to explain the flaring activity of Sgr A*, such as theexpanding plasmon model and orbiting hot spot model. We will discuss them separately.
Expanding plasmon model of van der Laan (1966) was invoked to explain observed timedelay in variation of Sgr A* at 7- and 13-mm (Yusef-Zadeh et al. 2006a, 2006b, 2008).In this model, rather than the synchrotron cooling, the adiabatic cooling associated withexpansion of the emitting plasma is responsible for the decline of flare. Flaring at a givenfrequency is produced through the adiabatic expansion of an initially optically thick blob ofsynchrotron-emitting relativistic electrons. The initial rise of the flux density is producedby the increase in the surface area of blob while it still remains optically thick; the curveturns over once the blob becomes optically thin because of the reduction in the magneticfield, the adiabatic cooling of electrons, and the reduced column density as the blob expands.Such kind of blob ejected from an ADAF is also thought to be a possible explanation fornonthermal flares and recombination X-ray lines in low-luminosity active galactic nuclei andradio-loud quasars (Wang et al. 2000). 9 –Our observed IDVs with different amplitudes and timescales seem consistent with theexpanding plasmon model in the context of jet or outflow. The amplitudes and timescalesvary with the relativistic particle energy distribution, expanding velocity and size of theblob. To apply the model to the light-curves on 2006 August 12 and 13, we first assumed apower-law spectrum of the relativistic particle energy ( n ( E ) ∝ E − p ). Hornstein et al. (2007)reported a constant spectral index of 0.6 using multi-band IR observations of several flares.Here we adopt a spectral index of 0.6, corresponding to the particle spectral index of 2.2, theenergy of the particles was assumed to range from 10 MeV to 3 GeV. The expanding velocitywas supposed to be constant. As is stated by Yusef-Zadeh (2008), the relationship betweenthe quiescent and flaring states of Sgr A* is not fully understood. Their results indicate thatthe quiescent emission at 7- and 13-mm varies on different days. The minimum flux densitywas 1.5 Jy during our 2006 August observing session, the quiescent flux density, if it doesexist, should not be more than this value. We then assume a quiescent flux density of 1.4Jy, while the flare is produced by the blob. Other parameters were derived by means of theweighted least square method. We adopt exponentially increasing step length for numberdensity during the fitting in order to improve efficiency. The uncertainties of the parameterswere assessed by scaling up the 68.3 % confidence region of parameter space, as an increaseof χ from χ min to χ min + χ ν with the reduced chi squares, χ ν = χ min /N dof , where N dof isthe difference between the number of data and the number of fitting parameters (c.f. Shenet al. 2003).We used two blobs to fit for flare observed on 2006 August 12 and three blobs for thoseobserved on 2006 August 13. Initial magnetic field of 20-50 Gauss were derived from the fit.The electron cooling timescale due to synchrotron loss is (e.g., Marrone et al. 2008) t syn = 38 (cid:16) ν (cid:17) − / (cid:18) B (cid:19) − / [hr] . (1)where the frequency ( ν ) is in GHz and magnetic field (B) in Gauss. It is about 3.4 hr witha magnetic field of 50 Gauss at 90 GHz, which is comparable to the observed decreasingtimescale of 2 hr. Thus the synchrotron cooling of the electrons should not be ignored. Wetook this into account and re-did the whole fit. The energy loss rate is given by You (1998):( dγdt ) syn = − × − γ U mag , (2)where U mag = B π . With a constant expanding velocity v , the radius of the blob R can beexpressed as R = R + vt , R is the initial radius of the blob at a specific instant t = 0.Substituting B and t with v , R , R and the initial magnetic field B , Eq.(2) can be writtenas ( dγdR ) syn = 1 v ( dγdt ) syn = − × − B R πv γ R − = − c γ R − (3) 10 –where c = × − B R πv . The energy loss rate due to the adiabatical expanding is( dγdR ) exp = − γR . (4)Thus the total energy loss rate due to both synchrotron cooling and expanding is dγdR = − γR − c γ R − (5)Eq. (5) is a Bernoulli equation with a solution γ = γ (cid:18) RR (cid:19) − ( c γ R − " − (cid:18) RR (cid:19) − + 1 ) − . (6)Then the optical depth scales as τ ( ν, R ) = τ ( ν , R ) (cid:18) νν (cid:19) − ( p +4) / (cid:18) RR (cid:19) − (2 p +3) ( c γ R − " − (cid:18) RR (cid:19) − + 1 ) − p (7)and the flux density scales as S ( ν, R ) = S ( ν , R ) (cid:18) νν (cid:19) / (cid:18) RR (cid:19) − exp( − τ ( ν, R ))1 − exp( − τ ( ν , R )) . (8)where τ ( ν , R ), S ( ν , R ) are optical depth and flux density for frequency ν at the specificinstant t . The critical optical depth τ crit ( R ), at which the flux density for any particularfrequency peaks for radius R , satisfies e τ crit ( R ) −
13 (2 p + 3) τ crit ( R ) − C ( R ) τ crit ( R ) − C ( R ) = c γ R − ( p − (cid:16) RR (cid:17) ( − (cid:26) c γ R − (cid:20) − (cid:16) RR (cid:17) − (cid:21) + 1 (cid:27) − . In the expand-ing plasmon model of van der Laan (1966), optical depth scales as τ ( ν, R ) = τ ( ν , R ) (cid:18) νν (cid:19) − ( p +4) / (cid:18) RR (cid:19) − (2 p +3) , (10)and τ crit ( R ), the critical optical depth at the maximum of the light curve at any frequency,depending only on p through the equation (Yusef-Zadeh et al. 2006b, 2008) e τ crit ( R ) − (2 p/ τ crit ( R ) − . (11) 11 –Comparison between Eq.(7) and (10) indicates that the only difference between these twoequations is factor (cid:26) c γ R − (cid:20) − (cid:16) RR (cid:17) − (cid:21) + 1 (cid:27) − p in the former, which is the result ofsynchrotron cooling. Similarly, the only difference between Eq.(9) and (11) is factor C ( R )of τ crit ( R ) in the former, which decreases as R − . The optical depth at which the flux densitypeaks at t satisfies e τ crit ( R ) −
13 (2 p + 3) τ crit ( R ) − C ( R ) τ crit ( R ) − . (12)For typical values of p = 2 . B = 20 Gauss, γ = 20, R = 4 r g and v = 0 . c , C ( R ) = 13 c γ R − ( p −
1) = 1 × − B γ R ( p − πv = 0 . ≪
13 (2 p + 3) = 2 . τ crit ( R ) mainly depends on p . Since c γ R − ( p − ∝ B , B is themost sensitive parameter for the evolution of flux S ( ν, R ). To illustrate this, we choosetypical values of p = 2 . γ = 20, R = 4 r g and v = 0 . c and show the resulting modellight curves at 90 GHz while B is 10, 20, 30, 40 and 50 Gauss in Figure 4. Results fromexpanding plasmon model of van der Laan (1966) are shown in dotted lines, and results fromexpanding plasmon model with synchrotron cooling are shown in solid lines. The differencesbetween two results are significant above 30 Gauss, implying that the synchrotron coolingof electrons should not be ignored for strong magnetic field.The best-fit model for the light-curve of 2006 August 12 is plotted as a solid line inFigure 5 left. Two blobs were required to fit the data, which were assumed to appear at7.0 and 10.3 UT. We attribute the turnover in light curve to the birth of a new blob, sothe second blob was assumed to appear before the flux increases. The corresponding initialblob radius 1 . +1 . − . r g and 2 . +0 . − . r g , expanding velocity 4 +2 − × − c and 2 +2 − × − c , electronnumber density of 2 . − . × cm − and 5 . +5 . − . × cm − , magnetic field of 19 +30 − and7 +4 − Gauss were derived from the fit. The uncertainty that was failed to be assessed was leftblank, if not such a sensitive parameter. The peak flux densities of two blobs are estimated tobe 0.26 and 0.59 Jy, respectively. The half-power durations are 1.7 and 5.2 hr, respectively.Blob mass of 2 . × g and 1 . × g were estimated.Figure 5 right shows the best-fit model for the light-curve of 2006 August 13. Similarly,three blobs appeared at 6.6, 10.0 and 13.0 UT are required to fit the flare. Initial blobradius 4 . ± . r g , 2 . +0 . − . r g and 2 . +0 . − . r g , expanding velocity 5 +1 − × − c , 5 +3 − × − c and 5 ± × − c , electron number density of 1 . +4 . − . × cm − , 2 . +7 . − . × cm − and5 . − . × cm − and magnetic field of 23 +4 − , 15 +25 − and 13 +8 − Gauss were derived from thefit. The peak flux densities of three blobs are 0.67, 0.66 and 0.48 Jy, respectively. The half-power durations are 3.2, 2.8 and 2.4 hr, respectively. Blob mass of 1 . × g, 8 . × g and 12 –9 . × g were estimated based on derived parameters. The mass-loss rate contributed byblob was then calculated to be 9 . × − M ⊙ yr − . This value is lower than the accretion raterange 2 × − M ⊙ yr − to 2 × − M ⊙ yr − estimated by the rotation measure measurements(Marrone et al. 2007). The derived parameters have been summarized in Table 2.In principle, the expanding plasmon model can also be used to interpret the 2000 March7 NMA short millimeter flare reported by Miyazaki et al. (2004). In their observation, thepeak flux density at the 140 GHz band is apparently larger than that at the 100 GHz band.The spectral variation suggests that the energy injection to photons occurred in the higherfrequency regime first and the emitting frequency was shifted to the millimeter-wavelengthregime with time, which is well consistent with the scenario predicted by expanding plasmonmodel. A time delay of 1.5 hr was observed for NIR and sub-mm flare on 2008 June 3(Eckart et al. 2008b), which has been explained with a similar model with adiabaticallyexpanding source components. There, the spectral index (0.9 to 1.8), expansion velocity(0.005c) and source size ( ∼ r g ) are fairly consistent with the parameters derived here. Inorder to compare with their modeling results, we calculate the optical depth at sub-mmbased on parameters derived here. Take the first blob of 2006 Aug 13 for example, accordingto Pacholczyk (1970), the optical depth at 90 GHz is calculated to be 8 .
23 at t . The criticaloptical depth at which the flux density for any particular frequency peaks at t , is calculatedto be 1 .
82 based on Eq.(12). According to Eq.(7), the optical depth at 345 GHz is 0 . An orbiting hot spot model has been frequently used to mainly explain the observationsof short-term NIR and X-ray variability (Broderick & Loeb 2005, 2006, Meyer et al. 2006a,2006b, Trippe et al. 2007, Eckart et al. 2006b, 2008a). The hot spot is modeled by anoverdensity of non-thermal electrons centred at a certain point of its Keplerian orbit. Thissituation may arise in the case of magnetic reconnection event similar to the solar flare.Due to the Doppler shift and relativistic beaming the approaching portion of the hot spotorbit appears considerably brighter than the receding portion. This model is successful in 13 –explaining the NIR 17 minutes quasi-periodic oscillation (Genzel et al. 2003). The hotspot model is applied to radio band by including the effects of disk opacity for a typicalRIAF model (Broderick & Loeb 2006). In these studies, the hot spot is always close to theinnermost stable circular orbit (ISCO), thus the NIR 17 minutes quasi-periodic oscillationcan be produced. Since the creation of such a hot spot is still under discussion, it is alsopossible that such kind of spot may appear somewhere away from the ISCO and thus producequasi-periodic oscillation with a longer timescale.In the accretion disk, neighboring annuli of differentially rotating matter experiencea viscous shear that transports angular momentum outwards and allows matter to slowlyspiral in towards the center of the potential (Merloni 2002). As a result, the gas rotateswith a sub-Keplerian angular velocity (Narayan et al. 1997). In the following we assumethat the rotation of hot spot is also sub-Keplerian and fit our detected IDV events using asub-Keplerian rotating hot spot model. To simplify the calculation, the angular velocity isassumed to be 0.4 times of Keplerian angular velocity of a Schwarzschild black hole.We assumed the values of most physical parameters of the hot spot model the same asthose in the expanding plasmon model when starting fitting the hot spot model to light-curves. These include: the energy range of relativistic particles, the particle spectral indexand the quiescent flux density. Then we estimated other parameters by means of weightedleast square method. The magnetic field was assumed to range from 1 to 100 Gauss. In RIAFmodel, the electron number density of accretion disk is about 2 × cm − at a distance20 r g from the central black hole (Yuan et al. 2003). Since the hot spot is modeled by anoverdensity of non-thermal electrons, it is safe to assume the electron number density rangesfrom 4 × to 1 × cm − . In addition, the accretion disk is assumed to be edge-on tomaximize the boosting effect (Huang et al. 2007; 2008). The final result is the combinationof the quiescent flux density and flux density of hot spot. The derived parameters aresummarized in Table 3.The hot spot model for the 2006 August 12 flaring is plotted as a solid line in Figure6 left. The quiescent flux density was assumed to be 1.4 Jy. Two hot spots are needed tofit the data. Radius of 6 . ± . r g and 8 . ± . r g , magnetic intensity of 3 +2 and 1 +2 Gaussand electron number density of 4 +26 × cm − and 4 +26 × cm − were derived from theweighted least square fitting. The separation to central black hole is 10 ± r g and 12 +2 − r g .The hot spot model for the light-curve of 2006 August 13 is plotted as a solid line inFigure 6 right. The quiescent flux density was 1.4 Jy too. One hot spot is required to fit thedata. Radius of 4 . ± . r g , magnetic intensity of 6 +2 − Gauss and electron number density of6 +44 × cm − were derived. The hot spot is at 11 . +0 . − . r g from the central black hole. 14 –The electron cooling timescales due to synchrotron losses are calculated to be greaterthan 2 days at 90 GHz, much longer than the observed variation timescale, thus the syn-chrotron energy loss can be ignored in the fitting. Since the synchrotron cooling time islong, the life time of hot spot should mainly depend on the dynamical timescale. Reid et al.(2008) analyzed the limits on the position wander of Sgr A*, ruling out the possibility of hotspots with orbital radius above 15 r g that contribute more than 30% of the total 7-mm flux.All the orbital radius listed in Table 3 are smaller than 15 r g . Hence, the presented hotspotmodel is not in contradiction with their result.The discussion above shows that both the expanding plasmon model and the orbitinghot spot model can be used to interpret the detected two IDV events. Given that theformer model predicts a time delay in flare emission, while the latter does not, the timedelay between different frequencies in flare emission is believed to be critical to distinguishbetween them (Yusef-zadeh et al. 2006b). Recently, Yusef-zadeh et al. (2008) detected timelags of 20.4 ± ±
12 and 20 ± ±
17 minutes between X-rays and850- µ m was observed (Marrone et al. 2008). Though these observations seem to supportthe expanding plasmon model, the hot spot model is still a possible explanation, especiallyfor the observed nearly symmetrical light-curves.
6. SUMMARY
We presented the results of the ATCA flux density monitoring of Sgr A* at 3-mm, withemphasis on the detected two IDV events. Comparison of flux densities in two observingsessions in 2006 indicates that Sgr A* appeared to undergo a high state in June session,and a low state in August session. On 2006 August 12, Sgr A* exhibits a 33% fractionalvariation in about 2.5 hr. Two peaks with a separation of 4 hr are seen on 2006 August 13flare which exhibits a maximum variation of 21% within 2 hr.The short timescales inspire us to consider mechanisms other than synchrotron coolingthat may be responsible for the variation. Both the expanding plasmon model and thesub-Keplerian rotating hot spot model were discussed and applied to interpret the observedlight curves. Because of a relatively large derived magnetic intensity (and thus a shortsynchrotron cooling timescale), we incorporated the synchrotron cooling into the originaladiabatically expanding plasmon model to model the observed IDV data. The radius of blobwas estimated to range from 1 to 5 r g , the expanding velocity range from 0 . c to 0 . c ,the electron number density larger than 1 × cm − and the magnetic field range from7 to 30 Gauss. A minimum mass-loss rate of 9 . × − M ⊙ yr − was deduced based on 15 –these derived parameters. We assume that the rotation of hot spot is sub-Keplerian whileapplying the hotspot model. It seems that both models can reasonably fit the detected IDVevents. Future simultaneous multi-wavelength monitoring is expected to discriminate themand tell us where such kind of IDV events come from.The Australia Telescope Compact Array is part of the Australia Telescope which isfounded by the Commonwealth of Australia for operation as a National Facility managed bythe CSIRO.This work was supported in part by the National Natural Science Foundation of China(grants 10573029, 10625314, 10633010 and 10821302) and the Knowledge Innovation Pro-gram of the Chinese Academy of Sciences (Grant No. KJCX2-YW-T03), and sponsored bythe Program of Shanghai Subject Chief Scientist (06XD14024) and the National Key BasicResearch Development Program of China (No. 2007CB815405). REFERENCES
Baganoff, F.K., et al. 2001, Nature, 413, 45Balick, B. & Brown, R.L. 1974, ApJ, 194, 265Bardeen, J.M., Press, W.H., Teukolsky, S.A. 1972, ApJ, 178, 347Broderick, A. E. & Loeb, A. 2005, MNRAS, 363, 353Broderick, A. E. & Loeb, A. 2006, MNRAS, 367, 905Eckart, A. & Genzel, R. 1996, Nature, 383, 415Eckart, A., Baganoff, F.K., Morris, M. et al., 2004, A&A, 427, 1Eckart A., Baganoff, F.K., Sch¨odel, R. et al., 2006a, A&A, 450, 535Eckart, A., Baganoff, F. K., Sch¨odel, R. et al., 2006b, A&A, 455, 1Eckart, A., Baganoff, F.K., Zamaninasab, M. et al., 2008a, A&A, 479, 625Eckart, A., Sch¨odel, R., Garc˙ia-Mar˙in, M. et al., 2008b, A&A, 492, 337Esin, A.A., McClintock, J.E. & Narayan, R. 1997, ApJ, 489, 865Eisenhauer, F., Sch¨odel, R., Genzel, R. et al. 2003, ApJ, 597, 121 16 –Falcke, H., Goss W. M., Matsuo H., Teuben P., Zhao J.-H. & Zylka R. 1998, ApJ, 499, 731Genzel, R., et al. 2003, Nature, 425, 934Ghez, A.M., Morris, M., Becklin, E.E., Tanner, A., Kremenek, T. 2000, Nature, 4007, 803Glenn, J., Jewell, P.R., Fourre, R. & Miaja, L. 2003, ApJ, 588, 478Herrnstein, R.M., Zhao, J.H., Bower, G.C., & Goss, W.M. 2004, AJ, 127, 339Hornstein, S. D., Matthews, K., Ghez, A. M., Lu, J. R., Morris, M., Becklin, E. E., Rafelski,M., & Baganoff, F. K. 2007, ApJ, 667, 900Huang, L., Cai, M., Shen, Z. & Yuan, F. 2007, MNRAS, 379, 833Huang, L., Liu, S., Shen, Z.Q., Cai, M.J., Li, H. & Fryer, C.L. 2008, ApJ, 676, L119Marrone, D.P., Moran, J.M., Zhao, J.H. & Rao, R. 2007, ApJ, 654, L57Marrone, D.P., Baganoff, M., Morris, M. et al. 2008, ApJ, 682, 373Mauerhan, J.C., Morris, M., Walter, F., & Baganoff, F. 2005, ApJ, 623, L25Miyazaki, A., Tsutsumi, T., & Tsuboi, M.. 2004, ApJ, 611, L97Merloni, A., 2002, in: Cagnoni I. (ed.), Inflows, Outflows and Reprocessing around BlackHoles - Proceedings of the 5th Italian AGN Meeting, p.90 [astro-ph/0210251]Meyer, L., Sch¨odel, R., Eckart, A. et al 2006a, A&A, 458, 25Meyer, L., Eckart, A., Sch¨odel, R. et al 2006b, A&A, 460, 15Narayan, R., Kato, S. & Honma, F. 1997, ApJ, 476, 49Pacholczyk, A. G. 1970, Radio Astrophysics, Freeman, San FranciscoReid, M.J., Broderick, A.E., Loeb, A. Honma, M. & Brunthaler, A. 2008, ApJ, 682, 1041Sault, R.J., Teuben, P.J., & Wright, M.C. H. 1995, in Astronomical Data Analysis Softwareand Systems IV, eds. R. Shaw, H.E. Payne, & J.J.E. Hayers (ASP Conf. Ser., Vol.77), p.433Sch¨odel, R., Ott, T., Genzel, R. et al. 2002, Nature, 419, 694Shen, Z.Q., Liang, M.C., Lo, K.Y. & Miyoshi, M. 2003, Astron. Nachr., 324(S1), 383 17 –Trippe, S., Paumard, T., Ott T., Gillessen, S., Eisenhauer, F., Martins, F., & Genzel, R.2007, MNRAS, 375, 764Tsutsumi, T., Miyazaki, A. & Tsuboi, M. 2002, AAS, 200, 4409Ulich B.L. 1980, Astrophys. Letters, 21, 21van der Laan 1966, Nature, 211, 1131Wang, J.M., Yuan, Y.F., Wu, M. & Kusunose, M. 2000, ApJ, 541, L41Yuan, F., Quataert, E. & Narayan, R. 2003, ApJ, 598, 301You, J.H. 1998, Radiation Mechanisms in Astrophysics, 2nd ed., Beijing: Science Press,p.182Yusef-Zadeh, F., Bushouse, H., Dowell, C.D. et al. 2006a, ApJ, 644, 198Yusef-Zadeh, F., Roberts, D., Wardle, M., Heinke, C.O., & Bower, G.C. 2006b, ApJ, 650,189Yusef-Zadeh, F., Wardle, M., Heinke, C. et al. 2008, ApJ, 682, 361Zhao, J.H., Herrnstein, R.M., Bower, G.C., Goss, W.M. & Liu, S.M. 2004, ApJ, 603, L85
This preprint was prepared with the AAS L A TEX macros v5.0.
18 –
Sgr A* 1 2 3 4 500.10.2 µ ( J un ) OH2.6−0.4Sgr A* 1 2 3 4 500.10.2 µ ( A ug ) Sgr A* 1 2 3 4 500.10.2 PKS1710−269Sgr A* 1 2 3 4 500.10.20.3 µ ( A ug ) Sgr A* 1 2 3 4 500.10.20.3
Fig. 1.— Modulation index of flux density of Sgr A*, and gain corrections of five antennas(labeled 1, 2, 3, 4 and 5). They are derived from calibrators OH2.6-0.4 and PKS 1710-269(from left to right) for three observations on 2006 June 9, August 12 and 13 (from top tobottom). Many data obtained from antenna 3 in August session were shadowed and havebeen flagged, so the uncertainty of this antenna is big compared with other antennas. Duringobservation in 2006 August, the 3-mm flux density of PKS 1710-269 was around 0.5 Jy, onlyone fiftieth of that of OH2.6-0.4, therefore the modulation index of gain corrections derivedfrom this source are particularly high. 19 –Fig. 2.— ATCA 3-mm light-curves of Sgr A* in 2006. Two detected IDV events areindicated (arrows). 20 –Fig. 3.— ATCA 3-mm light-curves on 2006 August 12 (Left) and 13 (Right) of Sgr A*(middle panel), secondary calibrators OH 2.6-0.4 (top panel) and PKS 1710-269 (bottompanel). 21 – S ( Jy ) Fig. 4.— Two kind of theoretical model light curves as a function of expanding blob radius at90 GHz with different B . Results from expanding plasmon model of van der Laan (1966) areshown in dotted lines, and results from expanding plasmon model with synchrotron coolingare shown in solid lines. 22 – f l u x den s i t y ( Jy ) f l u x den s i t y ( Jy ) Fig. 5.— The solid line represents the expanding plasmon model fitting to the observed 3-mm light-curves on 2006 August 12 (left) and 13 (right) with synchrotron radiation coolingtaken into account. An assumed quiescent flux density of 1.4 Jy is indicated by the straightdotted line. The blobs used to fit the data are indicated by dashed curves. 23 – f l u x den s i t y ( Jy ) f l u x den s i t y ( Jy ) Fig. 6.— The light-curves produced by the sub-Keplerian orbiting hot spot model on 2006August 12 (left) and 13 (right). An assumed quiescent flux density of 1.4 Jy is indicated bythe straight dotted line. Two hot spots used to fit the data on August 12 (left) are indicatedby dashed curves. 24 –Table 1: ATCA Observations of Sgr A* in 2006. Length is duration of the observation.IF1&IF2 are intermediate frequencies for the lower and upper sidebands, respectively, withthe corresponding bandwidth of BW1&BW2. Range of baselines are indicated by uv range.Beam is the ATCA synthesized beam.Date Length IF1&IF2 BW1&BW2 uv range Beam(hr) (GHz) (MHz) (k λ )2005 Oct 18 10 93.504&95.552 128&128 13-61 2 . ′′ × . ′′ . ′′ × . ′′ . ′′ × . ′′ t is the time at which the blob was assumed to be generated, R is the initialradius, v is the expanding velocity, N is the initial electron number density, B is the initialmagnetic field strength, S p is the peak flux density of the blob, and χ ν is the reduced chisquares.Date t (hr) R ( r g ) v (10 − c) N (cm − ) B (Gauss) S p (mJy) χ ν . +1 . − . +2 − . − . × +30 − . +0 . − . +2 − . +5 . − . × +4 − . ± . +1 − . +4 . − . × +4 − . +0 . − . +3 − . +7 . − . × +25 − . +0 . − . ± . − . × +8 − R is the radius of hotspot, N e is the electron number density, B is the magnetic field strength, D is the distancebetween hot spot and the central black hole, and χ ν is the reduced chi squares.Date R ( r g ) N e (cm − ) B (Gauss) D ( r g ) χ ν . ± . +26 × +2 ± . ± . +26 × +2 +2 − . ± . +44 × +2 − . +0 . − .2