Sixteen years of X-ray monitoring of Sagittarius A*: Evidence for a decay of the faint flaring rate from 2013 August, 13 months before a rise in the bright flaring rate
AAstronomy & Astrophysics manuscript no. article_29778_v5_printer c (cid:13)
ESO 2018October 18, 2018
Sixteen years of X-ray monitoring of Sagittarius A*:Evidence for a decay of the faint flaring rate from 2013 August,13 months before a rise in the bright flaring rate
Enmanuelle Mossoux , and Nicolas Grosso Observatoire astronomique de Strasbourg, Université de Strasbourg, CNRS, UMR 7550, 11 rue de l’Université, F-67000 Stras-bourg, France Groupe d’Astrophysique des Hautes Energies, Institut d’Astrophysique et de Géophysique, Université de Liège, Allée du 6 Août,19c, Bât B5c, 4000 Liège, BelgiumReceived / Accepted
ABSTRACT
Context.
X-ray flaring activity from the closest supermassive black hole Sgr A* located at the center of our Galaxy has been observedsince 2000 October 26 thanks to the current generation of X-ray facilities. Recently, in a study of X-ray flaring activity from Sgr A*using Chandra and XMM-Newton public observations from 1999 to 2014 and Swift monitoring in 2014, researchers have argued thatthe “bright and very bright” flaring rate has increased from 2014 August 31.
Aims.
As a result of additional observations performed in 2015 with Chandra, XMM-Newton, and Swift (total exposure of 482 ks),we seek to test the significance and persistence of this increase of flaring rate and to determine the threshold of unabsorbed flare fluxor fluence leading to any change of flaring rate.
Methods.
We reprocessed the Chandra, XMM-Newton, and Swift data from 1999 to 2015 November 2. From these data, we detectedthe X-ray flares via the two-step Bayesian blocks algorithm with a prior on the number of change points properly calibrated for eachobservation. We improved the Swift data analysis by correcting the e ff ects of the target variable position on the detector and wedetected the X-ray flares with a 3 σ threshold on the binned light curves. The mean unabsorbed fluxes of the 107 detected flares wereconsistently computed from the extracted spectra and the corresponding calibration files, assuming the same spectral parameters. Weconstructed the observed distribution of flare fluxes and durations from the XMM-Newton and Chandra detections. We corrected thisobserved distribution from the detection biases to estimate the intrinsic distribution of flare fluxes and durations. From this intrinsicdistribution, we determined the average flare detection e ffi ciency for each XMM-Newton, Chandra, and Swift observation. We finallyapplied the Bayesian blocks algorithm on the arrival times of the flares corrected from the corresponding e ffi ciency. Results.
We confirm a constant overall flaring rate from 1999 to 2015 and a rise in the flaring rate by a factor of three for the mostluminous and most energetic flares from 2014 August 31, i.e., about four months after the pericenter passage of the Dusty S-clusterObject (DSO) / G2 close to Sgr A*. In addition, we identify a decay of the flaring rate for the less luminous and less energetic flaresfrom 2013 August and November, respectively, i.e., about 10 and 7 months before the pericenter passage of the DSO / G2 and 13 and10 months before the rise in the bright flaring rate.
Conclusions.
The decay of the faint flaring rate is di ffi cult to explain in terms of the tidal disruption of a dusty cloud since it occurredwell before the pericenter passage of the DSO / G2, whose stellar nature is now well established. Moreover, a mass transfer from theDSO / G2 to Sgr A* is not required to produce the rise in the bright flaring rate since the energy saved by the decay of the number offaint flares during a long period of time may be later released by several bright flares during a shorter period of time.
Key words.
Galaxy: center - X-rays: individuals: Sgr A*
1. Introduction
The center of the Milky Way hosts the closest supermassiveblack hole (SMBH) named Sgr A* at a distance of 8 kpc (Gen-zel et al. 2010; Falcke & Marko ff − times smaller than the Eddingtonluminosity L Edd = × erg s − (Yuan et al. 2003) for aSMBH mass of M = × M (cid:12) (Schödel et al. 2002; Ghezet al. 2008; Gillessen et al. 2009). Above this steady emission,Sgr A* experiences some temporal increases of flux in X-rays(e.g., Bagano ff et al. 2001; Porquet et al. 2003, 2008; Neilsenet al. 2013), near-infrared (e.g., Genzel et al. 2003; Yusef-Zadehet al. 2006a; Dodds-Eden et al. 2009; Witzel et al. 2012) andsub-millimeter / radio (e.g., Zhao 2003; Yusef-Zadeh et al. 2006b,2008; Marrone et al. 2008; Yusef-Zadeh et al. 2009). The near-infrared flare spectra are well reproduced by the synchrotron process (Eisenhauer et al. 2005; Eckart et al. 2006a) and thesub-millimeter / radio may be explained by the adiabatically ex-panding plasmon model (Van der Laan 1966; Yusef-Zadeh et al.2006b), but the radiative processes for the creation of the X-rayactivity are still debated. Moreover, several mechanisms can ex-plain the origin of eruptions in X-rays and infrared: a shock pro-duced by the interaction between orbiting stars and hot accre-tion flow (Nayakshin & Sunyaev 2003; Nayakshin et al. 2004),a hotspot model (Broderick & Loeb 2005; Eckart et al. 2006b;Meyer et al. 2006; Trippe et al. 2007), a Rossby instability pro-ducing magnetized plasma bubbles in the hot accretion flow(Tagger & Melia 2006; Liu et al. 2006), an additional heatingof electrons near the black hole due to processes such as accre-tion instability or magnetic reconnection (Bagano ff et al. 2001;Marko ff et al. 2001; Yuan et al. 2003, 2009), an increase of ac- Article number, page 1 of 22 a r X i v : . [ a s t r o - ph . H E ] A p r & A proofs: manuscript no. article_29778_v5_printer cretion rate when some fresh material reaches the close environ-ment of the black hole (Yuan et al. 2003; Czerny et al. 2013),and tidal disruption of asteroids ( ˇCadež et al. 2006, 2008; Kosti´cet al. 2009; Zubovas et al. 2012).The study of a large number of flares is valuable to constrainthe radiative processes and emission mechanisms at the originof the flaring activity from Sgr A*. Moreover, the survey of theDusty S-cluster Object (DSO) / G2 on its way toward Sgr A* hasincreased the number of observations of the SMBH. Valencia-S.et al. (2015) showed that DSO / G2 is an 1–2 M (cid:12) pre-main se-quence star with an accretion disk producing the Br γ emissionline by magnetospheric accretion onto the stellar photosphereand has survived to its pericenter passage at about 2000 R s fromSgr A* on 2014 April 20 (2014 March 1–2014 June 10).The first statistical study on the X-ray flares of Sgr A* wasmade by Neilsen et al. (2013) thanks to the 2012 Chandra X-rayVisionary Project ( XVP ). During this campaign 39 flares with a2–10 keV observed luminosity larger than 10 erg s − were de-tected using a Gaussian flare fitting on the light curves binned on300 s, resulting in an observed X-ray flaring rate of 1 . + . − . flareper day. The flares detected with the Gaussian fitting method arelimited to a minimum duration of 400 s and a minimum peakcount rate of 0 .
015 ACIS-S3 count s − (corresponding to a meanflux in 2–8 keV of 0 . × − erg s − cm − with their spectralparameters) due to the Poissonian noise of the non-flaring lightcurve and the limitations that the authors put on their Gaus-sian shape to avoid any spurious detection. Neilsen et al. (2013)also tested the Bayesian blocks algorithm used by Nowak et al.(2012) to analyze the individual photon arrival times (Scargle2002, priv. comm.) and detected 45 flares, 34 of which were alsofound with their Gaussian fitting method.Ponti et al. (2015) studied the flaring rate with the Pythonimplementation of the Bayesian blocks algorithm (Scargle et al.2013a) by merging the XMM-Newton and Chandra observationswhere Sgr A* was observed with an o ff -axis angle lower than2 (cid:48) from September 1999 to October 2014 and the 2014 Swiftobservations. These authors reported an increase of the brightand very bright flaring rate (corresponding arbitrarily to flareswith an absorbed fluence larger than 50 × − erg cm − ) from2014 August 31 until the end of the 2014 X-rays observationson November 2 with a level of 2 .
52 flare per day, i.e., 9 . ffi ciency of thismethod was presented in their Fig. 3 as a function of the flareduration and fluence. This method becomes more e ffi cient as theflare fluence increases but is less e ffi cient for the detection offlares longer than 10 ks.However, these di ff erent studies present several issues intheir data analyses, especially for flare detection. Firstly, the au- This Python program can be found athttps: // jakevdp.github.io / blog / / / / dynamic-programming-in-python / thors never correct of the bias of their detection methods , whichwould lead to an intrinsic flaring rate that is higher than those ob-served. Indeed, all of the detection methods presented above areless e ffi cient in the detection of the faintest and shortest flares.This issue is very important for the simultaneous study of datafrom di ff erent instruments (for example, in Ponti et al. 2015 andYuan & Wang 2016) that have di ff erent sensitivities and angu-lar resolutions leading to di ff erent e ffi ciencies for flare detectionand an incoherence in the overall flaring rate.Secondly, the Bayesian blocks method uses a prior on thenumber of changes of the flaring rate (named change point byScargle 1998) to control the rate of false positive detections.As stated by Scargle et al. (2013a), this prior “depends on onlythe number of data points and the adopted value of [false pos-itive rate]”. It thus needs to be calibrated using simulations ofevent lists containing the same number of counts as those stud-ied. The Python implementation of the Bayesian blocks algo-rithm used by Ponti et al. (2015) works with the geometric priorgiven in Eq. 21 of Scargle et al. (2013a). However, as told byScargle et al. (2013a), this geometric prior was obtained for agiven range of number of events (which was unfortunately un-specified). This may explain the inconsistency between the falsepositive rate adopted by Ponti et al. (2015) and their resultingfalse detection probability appearing in their Sect. 5.5. Indeed,they tested how many times a spurious change of flaring rate isdetected by simulating event lists containing the same number offlare arrival times drawn in a uniform distribution and applyingthe Bayesian blocks algorithm to determine how many times achange of flaring rate is detected. Using a false positive rate of0.3% and the geometric prior, they reported a probability of falsedetection of 0.1%, which points out an unreliable calibration be-tween the false positive rate and the prior.Thirdly, Ponti et al. (2015) used WebPIMMS for the com-putation of the flare flux. But WebPIMMS considers the e ff ec-tive area and the redistribution matrix computed for an on-axissource and for the full detector field of view. However, the flarespectra were extracted from circular regions of 1.25 or 10 (cid:48)(cid:48) ra-dius centered on Sgr A*. Since the point spread function (PSF)extraction fraction is not corrected by WebPIMMS, the inferredunabsorbed flux is systematically underestimated by these au-thors. Finally, none of these previous works studied the impacton the flare detection e ffi ciency of the overlap between the flareduration and observing time, i.e., the edge e ff ects when a flarebegins before the observation start or ends after the observationstop.In this work, we use the two-step Bayesian blocks method(Mossoux et al. 2015a,b) with a proper prior calibration sincewe believe this method to be most e ffi cient for flare detection.Indeed, contrary to the Gaussian fitting method used by Neilsenet al. (2013), the Bayesian blocks method is applied directly onthe event lists and is able to detect flares that are shorter than400 s (see Fig. A.2 of Mossoux et al. 2016). Moreover, com-paring the e ffi ciency of the method of Yuan & Wang (2016) withthose of the Bayesian blocks method, we stress that the Bayesianblocks method is more e ffi cient for the detection of long flares.For the shortest and faintest flares, the method of Yuan & Wang(2016) detects more features than the Bayesian blocks methodbut these authors did not control their false positive rate. We alsodetermined the flare detection e ffi ciency by taking the edge ef-fects into account in our simulations. We also use the spectralfitting program ISIS (Houck 2013) and the e ff ective area and re- In Yuan & Wang (2016), the e ffi ciency of their detection method iscomputed but never used.Article number, page 2 of 22nmanuelle Mossoux and Nicolas Grosso: Sixteen years of X-ray monitoring of Sagittarius A* distribution matrix files associated with the spectrum extractionregion to consistently compute the mean unabsorbed flux of theX-ray flares.Owing to the 2015 Swift monitoring and 2015 Chandra andXMM-Newton observations, there are about 459 ks of additionalobservations of Sgr A* allowing us to investigate the persistenceand significance of the bright flaring rate argued by Ponti et al.(2015) based on only 200 ks of observations from 2014 August31. After reducing the 1999–2015 data of XMM-Newton, Chan-dra, and Swift (Sect. 2), we search for flares using the two-stepBayesian blocks algorithm (Mossoux et al. 2015a,b) for XMM-Newton and Chandra and the method proposed by Degenaaret al. (2013) that is optimized for the Swift observations (Sect. 3).We then compute their mean unabsorbed fluxes with the spectralparameters computed by Nowak et al. (2012) for the brightestX-ray flares (Sect. 4). This method of taking the e ff ects of theo ff -axis angle into account allows us to study a large number ofobservations without a drastic limitation on the o ff -axis angle ofSgr A*. To correct the flare detection bias for each observation,we compute the flux and duration distribution of the flares ob-served with XMM-Newton and Chandra and correct it from themerged detection e ffi ciency of the Bayesian block algorithm todetermine the intrinsic flux-duration distribution (Sect. 5). Fromthis intrinsic distribution, we compute the average flare detec-tion e ffi ciency associated with each XMM-Newton, Chandra,and Swift observation and investigate the existence of a flux orfluence threshold leading to a change in the unbiased X-ray flar-ing rate observed from 1999 to 2015 using the Bayesian blocksalgorithm and the relevant prior calibration (Sect. 6). We discussthe physical origin of a change of flaring rate in Sect. 7 and sum-marize our results in Sect. 8.
2. Observations and data reduction
In this work, we extend the flaring analysis to the 1999–2015XMM-Newton and Chandra observations, where Sgr A* wasobserved with an o ff -axis angle lower than 8 (cid:48) , and to the over-all 2006–2015 Swift observations since Sgr A* was mainly ob-served with an o ff -axis angle lower than 8 (cid:48) . Theoretically, ourdata reduction and analysis methods do not have any limitationson the o ff -axis angle but considering larger o ff -axis angles mightlead to more confusion with the di ff use emission of the Galacticcenter. We retrieved the public observations of Sgr A* made withXMM-Newton, Chandra, and Swift from the XMM-Newton Sci-ence Archive (XSA) , the Chandra Search and Retrieval inter-face (ChaSeR) and the Swift Archive Download Portal , respec-tively. Our XMM-Newton, Chandra, and Swift data sample hasa total exposure time that is about 2 . . XMM-Newton (Jansen et al. 2001) has observed the Galacticcenter since 2000 September with the EPIC / pn (Strüder et al.2001) and EPIC / MOS1 and MOS2 (Turner et al. 2001) cam-eras. The 54 observations of Sgr A* from 2000 September to2015 April have a total e ff ective exposure of about 2 . http: // / web / xmm-newton / xsa http: // cda.harvard.edu / chaser http: // / swift_portal The conversion from the Terrestrial Time (TT) registered aboardXMM-Newton to UT is computed using NASA’s HEASARCTool xTime . The duration of the observations reported in Ta-ble A.1 is the sum of the GTI. Most of the observations weremade in frame window mode with the medium filter .The XMM-Newton data reduction is the same as presentedin, for example, Mossoux et al. (2015a). We created the eventlists for the MOS and pn cameras using the emchain and epchain tasks from the Science Analysis Software (SAS) pack-age (version 14.0; Current Calibration files of 2015 June 13). Wesuppressed the time ranges when the soft-proton flare count ratein the full detector light curve in the 2 −
10 keV energy range islarger than 0 .
009 and 0 .
004 count s − arcmin − for pn and MOS,respectively. For the MOS cameras, we selected the single, dou-ble, triple, and quadruple events ( PATTERN ≤
12) and used thebit mask to reject the dead columns and bad pix-els. For the pn camera, we selected the single and double events(
PATTERN ≤
4) and used the more drastic bit mask
FLAG==0 toreject the dead columns and bad pixels.The source + background (src + bkg) extraction re-gion is a 10 (cid:48)(cid:48) -radius disk centered on the Very-Long-Baseline Interferometry (VLBI) radio position of Sgr A*:RA(J2000) = h m s . = − ◦ (cid:48) (cid:48)(cid:48) . . . (cid:48)(cid:48) ; Guainazzi 2013) is very small compared to thesize of this extraction region and the PSF half power diameter(HPD).For observations in frame window (extended) mode, the bkgextraction region is a ≈ (cid:48) × (cid:48) region at ≈ (cid:48) -north of Sgr A*.For observations in small window mode, the background extrac-tion region is a ≈ (cid:48) × (cid:48) area at ≈ (cid:48) -east of Sgr A* (i.e., onthe adjacent CCD). The X-ray sources in the background regionwere detected using the SAS task edetect_chain and filteredout. Chandra has observed the Galactic center since 1999 Septemberwith the ACIS-I and ACIS-S cameras (Garmire et al. 2003). The121 observations of Sgr A* from 1999 September to 2015 Octo-ber have a total e ff ective exposure of about 5 . ff ectiveobservation start and end times reported in Table A.2 in UT cor-respond to the earliest GTI start and the latest GTI stop. TheACIS-S observations of the 2012 XVP campaign, i.e., 2013 May25, and June 6 and 9 and 2015 August 11, were made with theHigh Energy Transmission Grating (HETG), which disperses thesource events on the detector. The ACIS-S observations on 2013May 12, June 4 and after 2013 July 2 were made with an 1 / The website of xTime is: http: // heasarc.gsfc.nasa.gov / cgi-bin / Tools / xTime / xTime.pl Exceptions are the 2000 September 21, 2001 September 4, 2004March 28 and 30 observations, where EPIC / pn was in frame windowextended mode leading to a lower time resolution (199.1 ms instead of73.4 ms); the 2014 April 3 observations, where EPIC / MOS1 and MOS2observed in small window mode leading to a better time resolution(0.3 s instead of 2.6 s) but a smaller part of the central CCD observing(100 ×
100 pixels); the 2002 February 26 and October 3 observations,where EPIC / pn observed with the thick filter and the 2008 March 3 andSeptember 23, where the three cameras observed with the thin filter.Article number, page 3 of 22 & A proofs: manuscript no. article_29778_v5_printer
The data reduction was carried out with the Chandra Inter-active Analysis of Observations (CIAO) package (version 4.7)and the calibration database (CALDB; version 4.6.9). The level1 data were reprocessed via the CIAO script chandra_repro, which creates a bad pixel file, flags afterglow events, and filtersthe event patterns, afterglow events, and bad-pixel events. Forobservations without HETG, the src + bkg events were extractedfrom a 1 (cid:48)(cid:48) . ff raction order wasdetermined with the CIAO task tg_resolve_events . We thenextracted the zero-order events from the 1 (cid:48)(cid:48) . ± (cid:48)(cid:48) . (cid:48)(cid:48) . (cid:48) .
54 south of Sgr A*.
Swift (Gehrels et al. 2004) has regularly observed the Galacticcenter since 2006 with the X-ray telescope (XRT) (PI: N. De-genaar). This camera observes between 0 . (cid:48) . × (cid:48) .
6) with a time resolutionof 2 . ff ective area of 110 cm at 1 . (cid:48)(cid:48) , and a spatial resolutionof 18 (cid:48)(cid:48) HPD on-axis at 1.5 keV (Burrows et al. 2005). The log ofeach yearly campaign is given in Table A.3.
The results of the Swift monitoring of Sgr A* until 2011 Oc-tober 25 were reported in Degenaar et al. (2013). The authorscomputed the mean of the light curve of Sgr A* between 0 . .
011 count s − with a standard deviation of σ = . × − counts s − . Six X-ray flares with an unab-sorbed luminosity larger than 7 × erg s − were observedduring these 821 ks of observation using a GTI-binned detectionmethod with a 3 σ threshold leading to a flaring rate of 0.63 flaresper day. The results of the 2012, 2013, and 2014 Swift monitor-ing were reported in Degenaar et al. (2015). One flare was ob-served on 2014 September 9 with an unabsorbed luminosity of(1 . ± . × erg s − during the 510 ks of these three yearsof observations.On 2016 February 6, a new X-ray transientSWIFT J174540.7-290015 was detected at 16 (cid:48)(cid:48) north of Sgr A*with a 2–10 keV flux of 1 . × − erg s − (Reynolds et al. 2016).This source was identified as a low-mass X-ray binary locatednear or beyond the Galactic center (Ponti et al. 2016). On 2016May 28, a new X-ray transient SWIFT J174540.2-290037 wasdetected in the Swift observations at 10 (cid:48)(cid:48) south of Sgr A* with anunabsorbed 2–10 keV flux of about (7 ± × − erg s − cm − (Degenaar et al. 2016). Since these two new transient sourceshave a large X-ray flux showing long-term variations, theycontaminate the Sgr A* light curves observed by Swift. Thelarge flux variations observed in the short-exposure light curvefrom Sgr A* may thus not be identified as a Sgr A* flare or anaccretion burst from the transient sources. We thus only use theSwift observations from 2006 to 2015 to study the Sgr A* flares. Fig. 1.
Total correction factor (including bad pixels and dead columns,PSF extraction fraction, and vignetting) for the Swift count rate ofSgr A* vs. o ff -axis angle for all Swift observations of the Galactic cen-ter from 2006 to 2015. Fig. 2.
Swift / XRT light curve of Sgr A* from 2006 to 2015. The redpoints are the X-ray flares with the label corresponding to the flare num-ber in Table A.3. The red lines are the non-flaring level of each yearlycampaign with their 3 σ threshold for the flare detection in dashed lines. We reprocessed the level 1 data of the Swift observations madein photon counting mode with the data reduction method of De-genaar et al. (2013). We used the HEASOFT task
XRTPIPELINE (v0 . .
1) and the calibration files released on 2014 June 12 toreject the hot and bad pixels and select the grades between 0 and12. From the resulting level 2 data, we used the HEASOFT task
XSelect (v2 . (cid:48)(cid:48) ra-dius centered on the VLBI radio position of Sgr A*. Since Swiftis on a low-Earth orbit located below the radiation belts, the in-strumental background caused by the soft-proton flares is negli-gible and we thus do not need a background extraction region.The target position on the Swift detector is not fixed. Indeed,the o ff -axis angle of Sgr A* can be as large as 10 (cid:48) . .
77 keV(the median energy emitted in the 10 (cid:48)(cid:48) extraction region) runningthe HEASOFT task
XRTLCCORR (v0.3.8). This task computes thecorrection factors that have to be applied to the light curve countrates for each 10 s interval. Figure 1 shows the mean correctionfactor computed for each Swift observation as a function of theo ff -axis angle of Sgr A*. This correction factor is di ff erent fromone observation to an other, varying from 2 to 24. The correc-tion factor is minimum on-axis with a slightly increasing trendwith the o ff -axis angle because of the increase of the PSF widthand the vignetting. The mean value of the correction factor is Article number, page 4 of 22nmanuelle Mossoux and Nicolas Grosso: Sixteen years of X-ray monitoring of Sagittarius A*
Fig. 3.
Flare detection e ffi ciency of the Bayesian blocks algorithm (toppanel) and the Degenaar et al. (2013) detection method (bottom panel)in the Swift observations. The points are the simulation grid for theGaussian flare light curve above a non-flaring level of 0 .
027 counts s − in the 2–10 keV energy range. The contour levels are the detection prob-abilities in percent. . . . ± .
004 counts s − in the 2–10 keV energyband (see Fig. 2) instead of 0 . ± .
007 counts s − in the 0.3–10 keV energy band. This increase of the corrected non-flaringlevel would lead to a decay of the flare detection e ffi ciency bythe Bayesian blocks algorithm but the count rate standard devia-tion is 1 .
3. Systematic flare detection
To detect X-ray flares observed with XMM-Newton and Chan-dra, we applied the Bayesian blocks method developed by Scar-gle (1998) and refined by Scargle et al. (2013a) on the individualphoton arrival times of the src + bkg and bkg event lists with afalse positive rate for the flare detection of 0 . ff ected by ion-izing particles (i.e., the bad time intervals) by merging the GTIsto obtain a continuous event flux as observed by XMM-Newtonor Chandra. We divided the continuous event list into Voronoicells whose start and end times are half of the interval betweentwo adjacent events. We defined the beginning and end of thefirst and last cell as the observation start and stop, respectively.The count rate in each Voronoi cell is thus the total number ofevents in the cell divided by the cell duration. We then correctedthe CCD livetime (i.e., the ratio between the integration time andCCD readout time) by applying a weight on the duration of theVoronoi cells.To apply the Bayesian blocks algorithm with a consistentfalse positive rate, we calibrated the prior number of changepoints ( ncp _ prior ) for the number of events in the src + bkg andbkg event lists and the desired false positive rate. Following themethod proposed by Scargle et al. (2013a) and used in Mossouxet al. (2015a), we simulated 100 Poisson fluxes with a meancount rate corresponding to the non-flaring level of each obser-vation and containing a number of uniformly distributed eventsthat is the same as in the considered event list. For each set of100 simulations, we increased ncp _ prior from 3 to 8 by a stepof 0.1 and we computed the number of false positives detected.The value of ncp _ prior that corresponds to the considered eventlist is thus the value that retrieves the desired false positive rate(here, p = . , leading to a false positive rate for the flaredetection of 1 − p = . + bkg event list,whereas the bkg contribution at each event arrival time is esti-mated by applying the Bayesian blocks algorithm on the back-ground event list. We then applied the algorithm on the src + bkgevent list where the Voronoi intervals are weighted by the ratio ofthe src + bkg and background-subtracted src + bkg contributions.The non-flaring level of Sgr A* is defined by the count rateof the longest Bayesian block (leading to the lower error onthe count rate) while the flares are associated with the higherBayesian block count rates. The mean count rate of a flare is themean count rate of the flaring blocks subtracted from the non-flaring level. The flares observed by Chandra and XMM-Newtonand detected by the Bayesian blocks algorithm are represented Article number, page 5 of 22 & A proofs: manuscript no. article_29778_v5_printer
Fig. 4.
Evolution of the mean X-ray flaring rate from 1999 to 2015 by Chandra (top panel), XMM-Newton (middle panel), and Swift (bottompanel). The vertical gray stripe with the dot-dashed line is the time range of the DSO / G2 pericenter passage (Valencia-S. et al. 2015). The blueand orange lines are the cumulative number of flares and the cumulative observing time, respectively; the black line is the ratio of these valuescorresponding to the mean flaring rate. in B.1 and Fig. B.2. A comparison with the flare characteristicsobserved by Ponti et al. (2015) is given in Appendix C.In 2004, the XMM-Newton observations revealed an artifi-cial increase of the non-flaring level due to the transient X-rayemission of the low-mass X-ray eclipsing binary located at 2 (cid:48)(cid:48) . (cid:48)(cid:48) . ff ect of the increase of thenon-flaring level is a decay of the sensitivity to the detection ofthe faintest flares (Mossoux et al. 2016). Owing to the low Earth orbit, the duration of Swift observationsare about 1 ks, which is short compared to the flare observed du-rations (from some hundred of seconds to more than 10 ks). Wetested the e ff ect of this short exposure on the detection probabil-ity of the flares with the Bayesian blocks algorithm. We first sim-ulated two non-flaring event lists with a typical exposure of 1 ksand a Poisson flux with a non-flaring level of 0 .
027 counts s − inthe 2–10 keV energy range. We then simulated a third event listwith a Gaussian flare above this non-flaring level using for thesampling 30 mean count rates from 0.035 to 0 . − and30 durations from 300 s to 10 ks in logarithmic scale. We finallyextracted a time range of 1 ks from di ff erent part of the simulatedflare to create a typical Swift event list of a flare; the center ofthe time range is defined to divide the flare duration into 10 timeranges. We applied the Bayesian blocks algorithm on the three (non-flaring, flaring, and non-flaring) concatenated event listsand computed how many times the algorithm found two changepoints. The mean count rates of the flares are converted to themean unabsorbed fluxes using the averaged conversion factor be-tween the mean count rates and mean unabsorbed fluxes in the 2–10 keV energy band of 293 . × − erg s − cm − / XRT count s − , which is computed for N H = . × cm − and Γ = ff ective area, which is computed for the 10 (cid:48)(cid:48) ex-traction region and the redistribution matrix file that correspondsto the 2006 September 15 Swift observation where Sgr A* wason-axis. The resulting detection probability, shown in the toppanel of Fig. 3, has two di ff erent regimes with a small rangeof mean unabsorbed flux where the detection probability jumpsfrom 20% to 100%. For flare durations longer than 800 s, theX-ray flares are either nearly undetected (detection probabil-ity lower than 20%) or always detected with a mean unab-sorbed flux limit of about 0 .
044 counts s − , which correspondsto 13 . × − erg s − cm − . The flare detection e ffi ciency de-creases with the decay of the flare duration with a 100% detec-tion probability at 0 .
044 counts s − for a flare duration of 800 sand 0 .
065 counts s − for a flare duration of 300 s. The Bayesianblocks algorithm thus detects flares with a duration longer thanthe observing time less e ffi ciently and detects only flares with amean unabsorbed flux larger than 13 . × − erg s − cm − whenthe flare duration is larger than the observation exposure.To assess the detection e ffi ciency of the Degenaar et al.(2013) method for the Swift observations, we simulated several1 ks event lists as done previously, but we now work on a loga-rithmic mean unabsorbed flux grid of 30 points between 0 . . × − erg s − cm − and a logarithmic duration grid of 30points between 300 s and 10 . Article number, page 6 of 22nmanuelle Mossoux and Nicolas Grosso: Sixteen years of X-ray monitoring of Sagittarius A* (2013) detection method to compute how many times the flare isdetected. The resulting detection e ffi ciencies p obs for the 2006–2012 observations (i.e., without transient sources) are shown inthe bottom panel of Fig. 3. As for the flare detection with theBayesian blocks method, the detection e ffi ciency jumps from 20to 100% in a small range of mean unabsorbed flux. But the fluxlimits for 100% detection (about 7 × − erg s − cm − ) in theDegenaar et al. (2013) detection method are well below those ofthe Bayesian blocks method, making the former more e ffi cientfor flare detection with Swift.Therefore, we used the GTI-binned method of Degenaaret al. (2013), which is optimized to detect the X-ray flares forthe Swift observing setup. We first selected the src events in the2 −
10 keV energy band to build the Sgr A* light curves binnedon each GTI. We rejected the GTIs whose exposure is lower than100 s since the error bar on the count rate during this short expo-sure is large. For the observations between 2006 and 2012, thenon-flaring level from the src event list in each yearly campaignis computed as the ratio between the number of events recordedduring each campaign and the corresponding yearly exposures.A light curve bin is associated with a flare if the lower limit onthe count rate in this observation is larger than the non-flaringlevel of the corresponding yearly campaign plus three times thestandard deviation of the yearly campaign light curve. Duringthe 2013, 2014, and 2015 Swift campaigns, the non-flaring levelobserved in the Sgr A* light curves displays large variations dueto the presence of the Galactic center magnetar (see Fig. 2 ofLynch et al. 2015). The non-flaring level during these campaignsis fitted using two exponential power laws following Lynch et al.(2015) , i.e., CR = (0 . ± . e − t − t . ± . + (0 . ± . e − t − t . ± . + (0 . ± . − , (1)with t = σ error. The meancount rate of a flare detected with Swift is the mean count rate ofthe observation subtracted from the non-flaring level. The flaresdetected with Swift are represented in Fig. 2. The time of the start and end of the flares observed by XMM-Newton, Chandra, and Swift, as well as the non-flaring levels,are given in Tables A.1, A.2 and A.3 of Appendix A, respec-tively. In total, 107 X-ray flares were detected between 1999 and2015: 19 flares with XMM-Newton, 80 flares with Chandra, and8 flares with Swift. The mean flare duration is 2739 s, the stan-dard deviation is 2210 s, and the median is 2018 s, which im-plies that the flare durations have a nearly homogeneous distri-bution without preferred value. The cumulative number of flaresis given in Fig. 4 (blue line) as a function of time (with ob-serving gaps) for Chandra (top panel), XMM-Newton (middlepanel), and Swift (bottom panel). The flare times are computedas ( t start + t end ) / t start and t end indicating the start and endtimes of the flare. We also represent the cumulative exposure(orange line) for each instrument in this figure. The mean flar-ing rate is then computed as the ratio between these two curves We cannot directly use their fit since they did not correct from thelosses caused by the bad pixels and dead columns, the PSF extractionfraction, and the vignetting. (black line). The mean flaring rates observed by each instru-ment on 2015 November are di ff erent; these are 1 . ± . . ± . , and 0 . ± .
16 flare per day for Chandra, XMM-Newton, and Swift, respectively. This is because of the di ff er-ent sensitivity of the cameras and the di ff erent non-flaring levelsobserved by the instruments, which depend on both the instru-ment sensitivity and angular resolution. It is thus necessary tocorrect the detection bias due to these heterogeneous sensitivi-ties to study consistently the flaring rate obtained by the com-bination of three instruments. To assess the detection e ffi ciencyfor the three instruments, we used two characteristics of flaresthat are independent of the instruments: the flare duration (al-ready computed in this section) and mean unabsorbed flux (seeSect. 4).
4. X-ray flare fluxes
To correctly compute the mean unabsorbed fluxes of the X-rayflares observed with XMM-Newton and Chandra, we extractedtheir spectra, ancillary files (arf), and response matrix files (rmf)with the SAS script especget for XMM-Newton and the CIAOscript specextract for Chandra. For the Swift observations,because of the short exposure time, we extracted the flare spectraduring the entire observation via the HEASOFT task
XSelect ,and we created the corresponding arf via xrtmkarf (version0.6.3). The rmf were taken in the calibration database . The non-flaring spectrum was extracted from the closest in-time observa-tion.We grouped the flare spectra with a minimum of one countwith grppha to fit them with an absorbed power law created with TBnew (Wilms et al. 2000) and pegpwrlw with a dust scatteringmodeled thanks to dustscat (Predehl & Schmitt 1995) using theCash statistic (Cash 1979) in
ISIS . For the XMM-Newton andSwift observations, we fit the spectra with the values of the hy-drogen column density ( N H ) and the power-law index ( Γ ) fixed tothose computed for the two brightest X-ray flares observed withXMM-Newton and the 2012 February 9 bright Chandra flare: N H = . × cm − and Γ =
ISIS with the photon migrationparameter α = (cid:48)(cid:48) .
25 extraction re-gion. We fit the spectra with this pile-up model applied on theabsorbed power-law model with the fixed N H and Γ reportedabove and a free mean unabsorbed flux between 2 and 10 keV.Table A.2 of Appendix A reports the resulting mean unabsorbedfluxes observed by Chandra between 2 and 10 keV.Three flares observed with XMM-Newton and Chandra be-gin before the start of the observation and three other flares endafter the end of the observation. According to the phase of theflare that is not observed, this leads to a lower or upper limit on http: // heasarc.gsfc.nasa.gov / FTP / caldb / data / swift / xrt / cpf / rmf / Article number, page 7 of 22 & A proofs: manuscript no. article_29778_v5_printer
Fig. 5.
Flux–duration distribution of the X-ray flares from Sgr A*.
Top left panel:
The observed flare flux–duration distribution observed withXMM-Newton and Chandra from 1999 to 2015 (black dots) using a false positive rate for the flare detection of 0 . Top right panel:
The observed flare density distribution is shown. Thefilled contours are indicated in logarithmic scale and the corresponding color bar is represented in the right-hand side of the figure in unit of10 s − erg − s cm . Bottom left panel:
The merged detection e ffi ciency with a false positive rate for the flare detection of 0 .
1% for XMM-Newtonand Chandra from 1999 to 2015 in percent. The dots represent the simulation grid.
Bottom right panel:
The intrinsic flare density distributioncorrected from the observing bias is shown. The filled contours use the same logarithmic scale as in the top right panel. the mean unabsorbed flux. Indeed, assuming a Gaussian flare,if we only observe the end of the decay phase or the begin-ning of the rise phase, the resulting mean unabsorbed flux is alower limit on its actual value; if we observe the end of the risephase and decay phase or the rise phase and the beginning ofthe decay phase, the resulting mean unabsorbed flux is an up-per limit on its actual value. For the eight flares observed withSwift, the duration of the flares are associated with the observ-ing time, thereby leading to a lower limit on the mean unab-sorbed flux if the flare duration is lower than the exposure. Ifthe flare duration is larger than the exposure, the orientation ofthe limit depends on which part of the flare is observed. Here-after, we consider these lower or upper limits on the mean un-absorbed flux as the actual value of the flare flux. The averagedmean unabsorbed flux for the X-ray flares observed by XMM-Newton, Chandra, and Swift is 8 . × − erg s − cm − with astandard deviation of 10 . × − erg s − cm − while the me-dian is 4 . × − erg s − cm − . The observed distribution of themean unabsorbed flux is thus skewed toward the faintest flares.However, the di ff erent detection sensitivities of the instruments according to the flare mean unabsorbed flux and duration biasesthe observed distribution toward the highest and longest flares.We thus need to correct of the detection sensitivities to studycorrectly the merged duration and mean unabsorbed flux distri-bution.
5. Intrinsic flare distribution
To determine the intrinsic flare distribution, we computed thedensity distribution of the flares observed only with XMM-Newton and Chandra since the characteristics of the flares ob-served with Swift are not su ffi ciently constrained. We then cor-rected this observed flare density of the merged detection bias ofXMM-Newton and Chandra. The observed flare density is computed from the mean unab-sorbed fluxes and durations of the X-ray flares observed withXMM-Newton and Chandra from 1999 to 2015 using the Delau-
Article number, page 8 of 22nmanuelle Mossoux and Nicolas Grosso: Sixteen years of X-ray monitoring of Sagittarius A* nay tessellation field estimator (DTFE; Schaap & van de Wey-gaert 2000; van de Weygaert & Schaap 2009). We constructedthe minimum triangulation of the Delaunay tessellation (bluelines in the top left panel of Fig. 5). The density associated witha given flare position is then computed via the Delaunay trian-gles connected to this flare and conserving the total flare numberin the reconstructed density field. We computed for each flare, i ,the area W i = (cid:80) A k with, A k , which is the area of the triangle k whose the vertex is the flare i at the location xxx i . The flare den-sity per surface unit in the mean unabsorbed flux duration planethat is associated with the flare i is d i = / W i . The discretizedmap of the flare density is linearly interpolated inside the convexhull of the observed flare set at a point xxx in the Delaunay trian-gle m : d obs = d i + (cid:53) d | m ( xxx − xxx i ) with d | m the estimated constantdensity gradient within m . The resulting filled contour map ofthe observed flare density distribution is shown in the top rightpanel of Fig. 5 with the density levels of the observed flares inlogarithmic scale. The detection e ffi ciency of the X-ray flares depends on the in-strument sensitivity, non-flaring level, and observing time. Weused the flare durations and mean unabsorbed fluxes to com-pute the detection e ffi ciency of the Bayesian blocks algorithm ateach point in this 2D parameter space for each XMM-Newtonand Chandra observation ( p obs ≤ . . × − erg s − cm − and a logarithmic duration sam-pling of 30 points between 300 s and 10 . . × − erg s − cm − / count s − for XMM-Newton / EPIC pn,Chandra / ACIS-S3 subarray, and Chandra / ACIS-I, respectively.For each grid point, we simulated 200 event lists with Pois-son flux reproducing a Gaussian-flare light curve with di ff erentmean count rates and durations (defined from − σ to + σ asin Neilsen et al. 2013 with σ the Gaussian standard deviation)above each of these non-flaring levels. The detection e ffi ciencydepends strongly on the overlap between the flare duration andobserving time, i.e., the edge e ff ects. We thus first define the timerange of the simulated event list as T exp + T flare , where T exp isthe observing time and T flare is the flare duration. We then drew,for each simulation, the time of the flare maximum as uniformlydistributed between T flare / T exp + T flare / T flare and T exp − T flare to create our final event list. Wethen applied the Bayesian blocks algorithm on each of these finalevent lists to compute how many times the algorithm detects theflare for a false positive rate for the flare detection of 0 . p obs of each instrument and each observation computedon the same grid. We firstly weighted the local detection e ffi cien-cies according to the exposure time of the corresponding obser-vation since the impact of the detection e ffi ciency on the numberof observed flare depends on the exposure. We finally summedthe weighted local detection e ffi ciencies to determine the merged(weighted mean) local detection e ffi ciency of XMM-Newton and U n a b s o r b e d f l u x ( − e r g s − c m − ) U n a b s o r b e d f l u e n c e ( − e r g c m − ) Fig. 6.
Temporal distribution of the flare fluxes and fluences. The meanarrival times of the flares without observing gaps and with the correctionof the average flare detection e ffi ciency are represented by vertical lines.The dotted lines are the time of the beginning of the first observation ofthe year. The blue, green, and red lines are the Chandra, XMM-Newton,and Swift flares, respectively. The dashed lines are only lower or upperlimits on the flare flux and fluence due to the truncated flare durationwhen it begins before the start of the observation or ends after the stopof the observation. Top panel:
The mean unabsorbed flux distributionis shown.
Bottom panel:
The mean unabsorbed fluence distribution isshown. U n a b s o r b e d f l u x ( − e r g s − c m − ) U n a b s o r b e d f l u e n c e ( − e r g c m − ) Fig. 7.
Temporal distribution of the flare fluxes and fluences correctedfrom the sensitivity bias. See caption of Fig. 6 for details.
Chandra shown in the bottom left panel of Fig. 5 with the gridpoints. The merged local detection e ffi ciency along the border ofthe convex hull was computed by a linear interpolation betweenthe merged local detection e ffi ciency on either side of the convexhull. The observed flare distribution was finally corrected from themerged local detection e ffi ciency to compute the intrinsic flaresdistribution. The observed flare distribution at each point grid xxx was then corrected by the merged local detection e ffi ciency p merged ( xxx ) ≤ d intr ( xxx ) = d obs ( xxx ) / p merged ( xxx ) (see Eq. 17 of van Article number, page 9 of 22 & A proofs: manuscript no. article_29778_v5_printer de Weygaert & Schaap 2009). The intrinsic flare distribution isshown with filled contour in logarithmic scale in the bottom rightpanel of Fig. 5. The intrinsic flare distribution is now highest forthe faintest and shortest flares.
6. Temporal distribution of the X-ray flares from1999 to 2015
We then combined the overall XMM-Newton, Chandra, andSwift observations and removed the observational gaps to cre-ate a continuous exposure containing the times of the 107 flaresdetected. The observational overlays were also removed to keeponly the most sensitive instrument. Figure 6 shows the flare ar-rival times without observing gaps over the total exposure timeof 107.6 days (corresponding to 9.3 Ms). The height of each ver-tical line representing a flare corresponds to the mean unab-sorbed flux (top panel) and fluence (mean unabsorbed flux timesduration; bottom panel) between 2 and 10 keV. We thus observea flaring rate of 0 . ± .
09 flare per day, which is lower butstatistically consistent with the flaring rate deduced by Neilsenet al. (2013), which was limited to the 2012 Chandra
XVP cam-paign, since XMM-Newton and Swift are less sensitive to fainterand shorter flares. We thus needed to correct the flare count ratefrom the flare detection bias due to the heterogeneous instrumen-tal sensitivities.
To correct the temporal flare distribution of the sensitivity bias,for each observation we determined the average flare detectione ffi ciency η obs by applying the detection e ffi ciencies p obs com-puted in the Sect. 3.2 for Swift and Sect. 5.2 for XMM-Newtonand Chandra. The intrinsic flare distribution d intr ( xxx ) at each gridpoint xxx is a ff ected by p obs ( xxx ) ≤
1, thus leading to the observationof only a percentage of this flare density. By computing the ratiobetween the 2D integral on the convex hull of the intrinsic flaredistribution a ff ected by the local detection e ffi ciency for a givennon-flaring level and the intrinsic flare distribution, we assessedthe average flare detection e ffi ciency η obs < η obs = (cid:82) (cid:82) d intr ( xxx ) p obs ( xxx ) dxxx (cid:82) (cid:82) d intr ( xxx ) dxxx . (2)The values of η obs are reported in Tables A.1, A.2 and A.3.We thus obtained a set of merged observations from XMM-Newton, Chandra, and Swift, each containing N ≥ ffi ciency η obs . To correct the flaring rate from the instrumen-tal sensitivity, for each observing time T we computed the cor-rected observing time as T corr = T η obs , thus leading to a higherand unbiased flaring count rate in the corresponding observation.Figure 7 shows the flares times without observing gaps over thetotal corrected exposure time of 35.6 days. We divided the corrected exposure time in Voronoi cells eachcontaining one flare and whose the separation times are the meantime between two consecutive flares. We applied the Bayesianblocks algorithm on the Voronoi cells with a false positive ratefor the change point detection of p = .
05 and the corre-sponding ncp _ prior = ± Two methods can be used to look for a flux threshold: first, thetop-to-bottom search where, at each step, we remove the flarewith the highest unabsorbed flux, but we keep the correspond-ing exposure time and update the Voronoi cells; and, second, thebottom-to-top search where, at each step, we remove the flarewith the lowest unabsorbed flux or fluence. At each step, we ap-ply the Bayesian blocks algorithm with a false probability rate of p = .
05 on the resulting flare list and we repeat this operationuntil the algorithm found a flaring rate change. The ncp _ prior is calibrated at each step according to the number of remainingflares to ensure a significance of at least 95% of any detectedchange point. Since we cannot argue that one of these two meth-ods is better than the other, we tested both.We first performed a top-to-bottom search. A change of flar-ing rate is detected at 28.5 days, i.e., between the Chandra flareon 2013 May 25 and the second Chandra flare on 2013 July27 (flares . × − erg s − cm − (the less luminous flares) with p = .
05 and the corresponding ncp _ prior = .
18. The result-ing Bayesian blocks are shown in the top panel of Fig. 8 whereonly these 70 flares are shown. The first block contains 65 flareswhile the second block contains 5 flares. The flaring rate de-creases from 2 . ± . . ± . p > . − p = . . × − erg s − cm − (themost luminous flares) with p = .
05 and the corresponding ncp _ prior = .
31. The resulting Bayesian blocks are shown inthe bottom panel of Fig. 8 where only these 66 flares are shown.The change of flaring rate happened on 2014 August 31 (33.36days) between the two XMM-Newton flares . ± . . ± . p = .
048 ( ncp _ prior = . − p = . . − . Article number, page 10 of 22nmanuelle Mossoux and Nicolas Grosso: Sixteen years of X-ray monitoring of Sagittarius A*
Table 1.
Summary of the change of X-ray flaring rates detected between1999 and 2015.
Top-to-bottom Bottom-to-topFlux threshold (10 − erg s − cm − ) ≤ . ≥ . . ± . . ± . . ± . . ± . − erg cm − ) ≤ . ≥ . . ± . . ± . . ± . . ± . method described in Appendix D. We created 500 sets of 107 ar-rival times uniformly distributed in 0–35.6 days. We also consid-ered a constant flux distribution, i.e., we created 500 sets of 107fluxes uniformly distributed in 0 . − . × − erg s − cm − thatwe associated with the flare arrival times. We then performed thetop-to-bottom and bottom-to-top searches and recorded the flar-ing rate changes. We detected a change of flaring rate in both thetop-to-bottom and bottom-to-top search for only 42 trials, corre-sponding to 8.4% of the simulations. In these 42 subsets, noneof the change points were detected after 37 and 41 cuts as isthe case for our observations; but for 71% of these sets (i.e., 32sets), the change points were detected after more than 77 trials,which is a greater number than in our observations. This impliesthat the joint probability to observe a change point in subsamplescontaining 70 and 65 flares is lower than (1 / = × − .Moreover, for 38 of the 42 subsets (90%), the time intervals be-tween the two change points are between − . × − . We can thus statethat the change of flaring rate that we observe is likely due to achange in the flux distribution. We carried out the same study with the unabsorbed fluence. Wefirst performed the top-to-bottom search: a change of flaring ratewas found considering only 65 flares with an unabsorbed fluencelower than or equal to 128 . × − erg cm − (the less energeticflares) with p = .
05 and the corresponding ncp _ prior = . . ± . . ± . p = . ncp _ prior = . − p = . . − . F l a r i n g r a t e ( f l a r e d a y − ) F l a r i n g r a t e ( f l a r e d a y − ) U n a b s o r b e d f l u x ( − e r g s − c m − ) U n a b s o r b e d f l u x ( − e r g s − c m − ) Fig. 8.
X-ray flaring rate from 1999 to 2015 computed by the Bayesianblocks algorithm for the most luminous and less luminous flares. Seecaption of Fig. 6 for the description of the flares and Table 1 forthe values of the thresholds. The Bayesian blocks are indicated withthick black lines.
Top panel:
The results for the top-to-bottom searchare shown.
Bottom panel:
The results for the bottom-to-top search areshown. See text for details. F l a r i n g r a t e ( f l a r e d a y − ) F l a r i n g r a t e ( f l a r e d a y − ) U n a b s o r b e d f l u e n c e ( − e r g c m − ) U n a b s o r b e d f l u e n c e ( − e r g c m − ) Fig. 9.
X-ray flaring rate from 1999 to 2015 computed by the Bayesianblocks algorithm for the most energetic and less energetic flares. Seecaption of Fig. 8 for details. larger than or equal to 91 . × − erg cm − (the most energeticflares) with p = .
05 and the corresponding ncp _ prior = . . ± . . ± . p = . ncp _ prior = . − p = . . − . Article number, page 11 of 22 & A proofs: manuscript no. article_29778_v5_printer
By performing the same simulations as described previously,the probability that the change points found for observations bythe two search methods are due to the detection of a false posi-tive is lower than 6 . × − . We can thus state that the changeof flaring rate that we observe is likely due to a change in thefluence distribution.
7. Discussion
Our high flaring rate Bayesian block for the most energetic flaresidentifies the same five flares that created the increase of flaringrate in Ponti et al. (2015) plus three additional flares observed in2015 with Chandra (flares / G2 pericenter passage near Sgr A* (computed withthe DSO / G2 pericenter passage determined by Valencia-S. et al.2015). As argued in Mossoux et al. (2016), if some material fromDSO / G2 was accreted toward Sgr A*, the increase of flux shouldnot be observed before the end of 2017 considering a pericenterdistance of 2000 R s and an e ffi ciency of the mechanism of angu-lar momentum transport of α = .
1. Two interpretations can thusbe proposed to explain this increase of flaring rate. Firstly, the in-crease of flaring rate could be due to the accretion of matter fromthe DSO / G2 onto Sgr A* considering an e ffi ciency of the mech-anism of angular momentum transport of at least 0 .
6. Secondly,the increase of flaring rate could be explained by the increaseof the e ffi ciency of the mechanisms producing the X-ray flares,such as a Rossby instability producing magnetized plasma bub-bles in the hot accretion flow (Tagger & Melia 2006; Liu et al.2006), additional heating of electrons due to accretion instabil-ity or magnetic reconnection (Bagano ff et al. 2001; Marko ff et al.2001; Yuan et al. 2003, 2009), or the tidal disruption of an aster-oid ( ˇCadež et al. 2006, 2008; Kosti´c et al. 2009; Zubovas et al.2012).Interestingly, the decay of the less luminous and less ener-getic flares occurs about 300 and 220 days before the DSO / G2pericenter passage near Sgr A*, therefore, about 13 and 10months before the increase of the most luminous and most ener-getic flaring rate, respectively. For comparison, we compute theenergy saved during the decay of the flaring rate of less ener-getic flares occurring between 2013 July 27 and October 28 andthe energy lost during the increase of the flaring rate of mostenergetic flares after 2014 August 31 as E saved < F (cid:90) Tt ∆ CR dt = F ∆ CR ( T − t ) (3)and E lost > F (cid:90) Tt ∆ CR dt = F ∆ CR ( T − t ) , (4)where T = . F and F the fluencethresholds, t and t the corrected days of the change points, and ∆ CR and ∆ CR the absolute values of the di ff erence on the flar-ing rate between the first and second block (see Table 1). Forthe less energetic flares, F = . × − erg cm − , ∆ CR = . ± . T − t = . ± . E saved < (9 . ± . × − erg cm − . Forthe most energetic flares, F = . × − erg cm − , ∆ CR = . ± . T − t = . ± .
005 corrected days,which leads to a lost energy of E lost > (5 . ± . × − erg cm − .Therefore, the energy saved by the decrease of the number of lessenergetic flares during several corrected days could be released by a few bright flares during a shorter period. This energy couldbe stored in the distortions of the magnetic field lines and then re-leased during a magnetic reconnection event. This is reminiscentof the behavior of earthquakes, in which stresses produce severalsmall events during a long period of time or may accumulate be-fore releasing in a large event. The input of fresh accreting ma-terial from the DSO / G2 is thus not needed to explain this largeincrease of the most luminous and most energetic flares.
8. Conclusions
The Swift campaigns and Chandra and XMM-Newton observa-tions of Sgr A* from 1999 to 2015 have allowed us to com-pute the intrinsic distribution of the mean unabsorbed flare fluxand duration and to study the significance of a change flaringrate. The 96 X-ray flares observed with Chandra and XMM-Newton were detected via the two-step Bayesian blocks algo-rithm (Mossoux et al. 2015a,b) and 8 X-ray flares observed withSwift were detected via an improvement of the Degenaar et al.(2013) detection method. By correcting the observed flare fluxand duration distribution from the merged local detection e ffi -ciency of XMM-Newton and Chandra, we have been able to es-timate the intrinsic flare flux and duration distributions, whichare maximum for the smallest and shortest flares. The flaringrate observed by Chandra, XMM-Newton and Swift together hasthen been corrected from the average flare detection e ffi ciency ofthe corresponding instruments.No significant change of flaring rate is found with theBayesian blocks algorithm considering the overall flares, whichlead to an intrinsic flaring rate of 3 . ± . . × − erg s − cm − ) and less energetic(lower than 128 . × − erg cm − ) flares by a factor of 3.2 (1.3–10.3, 95% confidence limits) and 2.4 (1.0–7.7, 95% confidencelimits) after 2013 May 25 and 2013 July 27, respectively (seeTable 1). These decays occur about 300 and 220 days beforethe pericenter passage of the DSO / G2, which implies that thischange of flaring rate is di ffi cult to explain by the passage of theDSO / G2 near Sgr A*.We confirm a significant increase of the flaring rate (withprobability larger than 95.1%) for the most luminous (brighterthan 4 . × − erg s − cm − ) and most energetic (larger than91 . × − erg cm − ) flares by a factor of 3.0 (95% confidencelimits of 1.4–5.8 and 1.3–6.2), respectively, from 2014 August31 until 2015 November 2 (i.e., the last observation).The energy released during this increase of bright flaringrate could come from the energy saved during the decay of thefaintest flares. The input of fresh accreting material from theDSO / G2 is thus not needed to explain this large increase of themost luminous and most energetic flares.
Acknowledgements.
We thank the PIs that obtained since 1999 the X-ray obser-vations of Sgr A* used in this work. E.M. acknowledge Université de Strasbourgfor her IdEx PhD grant. This work made use of public data from the Swift dataarchive, and data supplied by the UK Swift Science Data Center at the Univer-sity of Leicester. Swift is supported at Penn State University by NASA ContractNAS5-00136. This research has made use of the XRT Data Analysis Software(XRTDAS) developed under the responsibility of the ASI Science Data Center(ASDC), Italy. This work is also based on public data from the XMM-Newtonproject, which is an ESA Science Mission with instruments and contributions di-rectly funded by ESA member states and the USA (NASA). This work also usespublic data obtained from the Chandra Data Archive.
Article number, page 12 of 22nmanuelle Mossoux and Nicolas Grosso: Sixteen years of X-ray monitoring of Sagittarius A*
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Article number, page 13 of 22 & A proofs: manuscript no. article_29778_v5_printer
Table A.1.
Observation log of public XMM-Newton observations and the X-ray flares detected in this work.
Observations Flares MeanObsID PI Start End Duration Non-flaring level η obs a b Stop b Duration Count rate c Flux d (UT) (UT) (ks) (count s − ) (%) (UT) (UT) (s) (count s − ) (10 − erg s − cm − )112970601 e M. Turner 2000-09-17 18:41:04 2000-09-17 19:13:58 2.0 0 . ± .
005 2.94 ......... ......... ...... ............... ......112970501 f,h
M. Turner 2000-09-21 09:21:08 2000-09-21 15:16:37 24.9 0 . ± .
001 24.2 ......... ......... ...... ............... ......112971601 f M. Turner 2001-03-31 11:31:01 2001-03-31 12:40:31 4.0 0 . ± .
002 13.0 ......... ......... ...... ............... ......112972101 h M. Turner 2001-09-04 02:34:33 2001-09-04 08:41:10 21.7 0 . ± .
003 21.6 1 08:29:45 > >
685 0 . ± .
021 29 . k B. Aschenbach 2002-02-26 06:40:39 2002-02-26 17:55:35 40.0 0 . ± .
001 22.1 ......... ......... ...... ............... ......111350301 k B. Aschenbach 2002-10-03 07:15:59 2002-10-03 11:34:19 15.4 0 . ± .
002 21.6 2 10:08:32 10:52:01 2609 0 . ± .
018 27 . h A. Goldwurm 2004-03-28 16:44:29 2004-03-30 03:25:39 105.6 0 . ± .
001 20.6 ......... ......... ...... ............... ......202670601 h A. Goldwurm 2004-03-30 17:16:48 2004-04-01 03:35:08 107.0 0 . ± .
001 20.1 3 40:38:22 42:10:58 5556 0 . ± .
007 8 .
794 46:51:25 47:31:27 2402 0 . ± .
012 17 . . ± .
002 14.6 5 08:48:44 10:56:42 7678 0 . ± .
008 4 .
996 30:36:54 30:54:29 927 0 . ± .
010 2 . . ± .
001 20.1 ......... ......... ...... ............... ......302882601 R. Wijnands 2006-02-27 04:26:53 2006-02-27 05:49:46 4.9 0 . ± .
004 10.6 ......... ......... ...... ............... ......302884001 R. Wijnands 2006-09-08 17:18:55 2006-09-08 18:42:09 5.0 0 . ± .
003 11.3 ......... ......... ...... ............... ......506291201 e R. Wijnands 2007-02-27 06:07:31 2007-02-27 16:51:07 38.6 0 . ± .
001 23.7 ......... ......... ...... ............... ......402430701 D. Porquet 2007-03-30 21:27:07 2007-03-31 06:28:47 32.3 0 . ± .
002 23.4 ......... ......... ...... ............... ......402430301 D. Porquet 2007-04-01 15:06:44 2007-04-02 17:05:07 101.3 0 . ± .
001 21.8 ......... ......... ...... ............... ......402430401 D. Porquet 2007-04-03 16:43:24 2007-04-04 19:48:15 86.4 0 . ± .
001 21.9 7 29:11:21 30:09:27 3486 0 . ± .
014 14 .
78 35:32:10 35:38:01 351 0 . ± .
009 4 .
529 38:27:12 38:51:31 1458 0 . ± .
009 4 . . ± .
005 2 . . ± .
002 20.5 ......... ......... ...... ............... ......511000301 j R. Wijnands 2008-03-03 23:47:45 2008-03-04 01:19:25 5.1 0 . ± .
004 12.3 ......... ......... ...... ............... ......505670101 A. Goldwurm 2008-03-23 17:21:01 2008-03-24 20:17:25 96.6 0 . ± .
001 21.7 ......... ......... ...... ............... ......511000401 j R. Wijnands 2008-09-23 15:53:29 2008-09-23 17:08:17 5.1 0 . ± .
004 27.2 ......... ......... ...... ............... ......554750401 A. Goldwurm 2009-04-01 01:17:45 2009-04-01 11:58:54 38.0 0 . ± .
001 21.9 ......... ......... ...... ............... ......554750501 A. Goldwurm 2009-04-03 01:55:00 2009-04-03 13:43:39 42.4 0 . ± .
001 27.2 11 08:47:39 09:13:39 1560 0 . ± .
010 10 . . ± .
002 27.2 ......... ......... ...... ............... ......604300601 D. Porquet 2011-03-28 08:11:53 2011-03-28 21:15:04 45.2 0 . ± .
001 22.1 ......... ......... ...... ............... ......604300701 D. Porquet 2011-03-30 09:25:00 2011-03-30 21:12:57 42.3 0 . ± .
001 22.2 12 17:42:01 18:15:46 2025 0 . ± .
010 11 . . ± .
002 22.5 ......... ......... ...... ............... ......604300901 D. Porquet 2011-04-03 08:14:00 2011-04-03 18:55:51 36.5 0 . ± .
002 22.4 13 07:51:24 08:34:59 2615 0 . ± .
008 4 . . ± .
002 22.3 ......... ......... ...... ............... ......658600101 C. Darren Dowell 2011-08-31 23:36:30 2011-09-01 13:04:17 47.6 0 . ± .
001 21.6 ......... ......... ...... ............... ......658600201 C. Darren Dowell 2011-09-01 20:25:57 2011-09-02 10:44:22 51.3 0 . ± .
001 23.5 ......... ......... ...... ............... ......674600601 A. Goldwurm 2012-03-13 04:14:14 2012-03-13 09:47:24 19.6 0 . ± .
002 21.7 ......... ......... ...... ............... ......674600701 A. Goldwurm 2012-03-15 05:09:04 2012-03-15 09:10:51 14.0 0 . ± .
002 23.0 ......... ......... ...... ............... ......674601101 A. Goldwurm 2012-03-17 03:21:30 2012-03-17 10:09:54 25.7 0 . ± .
003 22.8 ......... ......... ...... ............... ......674600801 A. Goldwurm 2012-03-19 04:14:14 2012-03-19 10:12:43 21.0 0 . ± .
002 25.7 ......... ......... ...... ............... ......674601001 A. Goldwurm 2012-03-21 03:52:26 2012-03-21 10:07:06 22.0 0 . ± .
002 23.3 ......... ......... ...... ............... ......694640301 R. Terrier 2012-08-31 11:42:07 2012-08-31 22:57:43 40.0 0 . ± .
001 23.0 ......... ......... ...... ............... ......694640401 f R. Terrier 2012-09-02 19:09:49 2012-09-03 09:34:03 53.0 0 . ± . f R. Terrier 2012-09-23 20:42:07 2012-09-24 09:36:52 46.0 0 . ± . f R. Terrier 2012-09-24 10:38:50 2012-09-24 21:53:44 40.0 0 . ± .
001 15.1 ......... ......... ...... ............... ......724210201 G. Ponti 2013-08-30 20:52:40 2013-08-31 12:26:18 55.6 0 . ± .
003 15.7 ......... ......... ...... ............... ......700980101 D. Haggard 2013-09-10 04:12:07 2013-09-10 14:11:46 35.7 0 . ± .
003 15.9 ......... ......... ...... ............... ......724210501 G. Ponti 2013-09-22 21:54:32 2013-09-23 09:17:52 39.4 0 . ± .
003 16.1 ......... ......... ...... ............... ......723410301 N. Grosso 2014-02-28 18:18:41 2014-03-01 08:53:15 51.9 0 . ± .
002 23.3 ......... ......... ...... ............... ......723410401 N. Grosso 2014-03-10 14:49:09 2014-03-11 05:57:28 54.0 0 . ± .
002 18.6 14 16:44:48 19:03:51 8468 0 . ± .
008 6 . . ± .
002 18.2 15 16:53:00 17:08:44 944 0 . ± .
013 20 . i G.L. Isra¨el 2014-04-03 05:48:45 2014-04-04 05:01:14 83.5 0 . ± .
002 18.2 ......... ......... ...... ............... ......743630201 i G. Ponti 2014-08-30 20:00:24 2014-08-31 04:54:26 28.5 0 . ± .
003 18.2 16 23:46:11 25:19:18 5587 0 . ± .
008 17 .
217 28:36:49 28:53:19 990 0 . ± .
023 18 . . ± .
003 18.5 18 25:21:16 25:55:05 2029 0 . ± .
012 12 . . ± .
002 18.6 ......... ......... ...... ............... ......743630501 G. Ponti 2014-09-28 21:42:09 2014-09-29 08:12:51 33.7 0 . ± .
002 18.1 19 30:06:58 30:12:47 349 0 . ± .
031 14 . . ± .
002 18.9 ......... ......... ...... ............... ......743630701 g G. Ponti 2015-03-31 10:25:12 2015-03-31 10:26:38 0.1 0 . ± .
058 5.71 ......... ......... ...... ............... ......743630801 G. Ponti 2015-04-01 09:14:43 2015-04-01 15:55:24 21.5 0 . ± .
002 19.2 ......... ......... ...... ............... ......743630901 G. Ponti 2015-04-02 09:39:43 2015-04-02 11:35:50 6.2 0 . ± .
004 10.6 ......... ......... ...... ............... ......
Notes. ( a ) The average flare detection e ffi ciency above the corresponding non-flaring level. ( b ) The flare start and end times are given in hh:mm:sssince the day of the observation start. Flares beginning or ending at the start or stop of the observation lead to a lower limit on the flare durationand a lower or upper limit on the flare mean count rate and mean flux. The flux value of these flares were taken equal to this limit in the flaringrate study. ( c ) The flare mean count rates are computed after subtraction of the non-flaring level. ( d ) Mean unabsorbed flux between 2 and 10 keVdetermined for N H = . × cm − and Γ = ( e ) For this observation, the Galactic center was observed only with EPIC / pn. ( f ) For theseobservations, the Galactic center was observed only with EPIC / MOS1 and 2. ( g ) The data transfer from XMM-Newton to the Earth during thisobservation was a ff ected by the GALILEO launch and Early Orbit Phase. ( h ) Frame window extended mode. ( i ) Small window. ( j ) Thin filter. ( k ) Thick filter.Article number, page 14 of 22nmanuelle Mossoux and Nicolas Grosso: Sixteen years of X-ray monitoring of Sagittarius A*
Table A.2.
Observation log of public Chandra observations and the X-ray flares detected in this work.
Observations Flares MeanObsID PI Start End Duration Instrument Non-flaring level η obsa b Stop b Duration Count rate c Flux d (UT) (UT) (ks) (count s − ) (%) (UT) (UT) (s) (count s − ) (10 − erg s − cm − )242 G. Garmire 1999-09-21 02:40:49 1999-09-21 17:03:17 46.5 ACIS-I3 0 . ± . < > . ± .
001 1 . ff . ± . . ± .
014 3 .
523 27:55:35 30:46:46 10335 0 . ± .
004 11 . . ± . . ± .
001 1 . . ± . . ± . . ± . ff . ± . ff . ± . . ± .
002 2 . ff . ± . . ± .
009 0 .
877 37:37:32 39:02:56 5000 0 . ± .
009 1 .
008 53:33:16 53:49:15 959 0 . ± .
008 0 . ff . ± . . ± .
040 0 . . ± .
012 3 . . ± .
016 6 . ff . ± . . ± . . ± . . ± . . ± .
022 4 . ff . ± . ff . ± . ff . ± . ff . ± . ff . ± . . ± .
002 2 . ff . ± . . ± .
004 5 . ff . ± . ff . ± . ff . ± . ff . ± . ff . ± . ff . ± . . ± .
007 6 . ff . ± . ff . ± . ff . ± . . ± .
003 2 . ff . ± . < >
407 0 . ± .
006 3 . ff . ± . ff . ± . ff . ± . ff . ± . ff . ± . ff . ± . . ± . . ± .
002 1 . . ± . . ± . . ± . . ± . . ± . ff . ± . . ± .
007 4 . . ± .
003 2 . . ± .
007 9 . . ± .
015 10 . . ± . . ± .
026 3 . ff . ± . . ± .
003 1 . ff . ± . . ± . . ± . . ± .
011 20 . . ± . ff / HETG 0 . ± . ff / HETG 0 . ± . . ± .
002 1 . . ± .
004 20 . ff / HETG 0 . ± . ff / HETG 0 . ± . ff / HETG 0 . ± . ff / HETG 0 . ± . . ± .
006 4 . ff / HETG 0 . ± . . ± .
006 4 . . ± .
006 4 . . ± .
006 4 . . ± .
008 3 . ff / HETG 0 . ± . ff / HETG 0 . ± . ff / HETG 0 . ± . ff / HETG 0 . ± . . ± .
001 2 . ff / HETG 0 . ± . . ± .
002 2 . . ± .
003 1 . ff / HETG 0 . ± . ff / HETG 0 . ± . . ± .
003 2 . . ± .
002 1 . . ± .
004 9 . . ± .
005 2 . ff / HETG 0 . ± . ff / HETG 0 . ± . ff / HETG 0 . ± . . ± .
003 4 . . ± .
004 2 . ff / HETG 0 . ± . ff / HETG 0 . ± . ff / HETG 0 . ± . ff / HETG 0 . ± . ff / HETG 0 . ± . ff / HETG 0 . ± . < > . ± .
002 2 . . ± .
003 4 . ff / HETG 0 . ± . . ± .
009 5 . . ± .
008 5 . ff / HETG 0 . ± . . ± .
003 2 . . ± .
005 3 . . ± .
001 3 . Article number, page 15 of 22 & A proofs: manuscript no. article_29778_v5_printer
Table A.2.
Continued.
Observations Flares MeanObsID PI Start End Duration Instrument Non-flaring level η obsa b Stop b Duration Count rate c Flux d (UT) (UT) (ks) (count s − ) (%) (UT) (UT) (s) (count s − ) (10 − erg s − cm − )13839 F. Bagano ff / HETG 0 . ± . . ± .
006 3 . . ± .
007 6 . . ± .
005 1 . ff / HETG 0 . ± . . ± .
001 1 . . ± .
002 2 . ff / HETG 0 . ± . < > . ± .
001 8 . > > . ± .
004 9 . ff / HETG 0 . ± . . ± .
006 5 . ff / HETG 0 . ± . . ± .
005 3 . . ± .
004 4 . ff / HETG 0 . ± . . ± .
003 2 . ff / HETG 0 . ± . . ± .
004 3 . . ± .
002 12 . ff / HETG 0 . ± . . ± .
019 11 . ff / HETG 0 . ± . . ± .
007 1 . . ± .
005 34 . ff / HETG 0 . ± . > > . ± .
002 5 . ff / HETG 0 . ± . . ± .
004 6 . ff / HETG 0 . ± . . ± .
005 4 . ff / HETG 0 . ± . . ± .
002 6 . . ± .
001 2 . ff . ± . ff . ± . / subarray 0 . ± . / HETG 0 . ± . . ± .
002 2 . / subarray 0 . ± . / HETG 0 . ± . / HETG 0 . ± . ff / subarray 0 . ± . / subarray 0 . ± . . ± .
021 7 . . ± .
016 4 . / subarray 0 . ± . ff / subarray 0 . ± . / subarray 0 . ± . . ± .
010 38 . ff / subarray 0 . ± . / subarray 0 . ± . ff / subarray 0 . ± . / subarray 0 . ± . / subarray 0 . ± . . ± .
004 3 . . ± .
016 3 . / subarray 0 . ± . / subarray 0 . ± . / subarray 0 . ± . / subarray 0 . ± . / subarray 0 . ± . / subarray 0 . ± . / subarray 0 . ± . / subarray 0 . ± . / subarray 0 . ± . / subarray 0 . ± . / subarray 0 . ± . . ± .
088 25 . / subarray 0 . ± . . ± .
066 6 . / subarray 0 . ± . . ± .
007 6 . / HETG 0 . ± . . ± .
003 6 . / subarray 0 . ± . / subarray 0 . ± . > >
136 0 . ± .
017 5 . Notes. ( a ) The average flare detection e ffi ciency above the corresponding non-flaring level. ( b ) The flare start and end times are given in hh:mm:sssince the day of the observation start. Flares beginning or ending at the start or stop of the observation lead to a lower limit on the flare durationand a lower or upper limit on the flare mean count rate and mean flux. The flux value of these flares were taken equal to this limit in the flaringrate study. ( c ) The flare mean count rates are computed after subtraction of the non-flaring level. ( d ) Mean unabsorbed flux between 2 and 10 keVdetermined for N H = . × cm − and Γ = Table A.3.
Observation log of public Swift observations and the X-ray flares detected in this work.
Observations Flares MeanFirst Last Number Total exposure Non-flaring level η obsa b Count rate c Flux d (UT) (UT) (ks) (count s − ) (%) (UT) (UT) (s) (count s − ) (10 − erg s − cm − )2006-02-24 22:55:12 2006-11-02 14:22:34 198 261 . . ± .
002 24.6 1 2006-07-13 21:57:36 2006-07-13 23:39:50 924 0 . ± .
007 15 . . . ± .
004 24.6 2 2007-03-03 00:38:21 2007-03-03 02:34:56 2018 0 . ± .
004 9 . . . ± .
003 24.6 3 2008-03-25 20:24:00 2008-03-25 23:36:58 707 0 . ± .
011 20 .
84 2008-05-01 14:15:22 2008-05-01 20:39:50 1056 0 . ± .
007 8 .
665 2008-10-17 17:15:22 2008-10-17 22:09:07 1369 0 . ± .
007 11 . .
64 0 . ± .
009 24.6 ..................... ..................... ...... ............... ......2010-04-07 01:10:34 2010-10-31 10:10:34 62 70 .
33 0 . ± .
006 24.6 6 2010-06-12 10:23:31 2010-06-12 12:07:12 1081 0 . ± .
012 49 . .
78 0 . ± .
006 24.6 ..................... ..................... ...... ............... ......2012-02-05 20:12:29 2012-10-31 23:21:07 79 73 .
95 0 . ± .
005 24.6 ..................... ..................... ...... ............... ......2013-02-03 22:26:24 2013-10-31 01:17:46 191 185 . . ± .
009 20.0 e ..................... ..................... ...... ............... ......2014-02-03 18:57:36 2014-11-02 12:56:09 236 231 . . ± .
007 24.3 7 2014-09-09 11:41:17 2014-09-09 11:58:34 975 0 . ± .
013 59 . . . ± .
004 24.6 8 2015-11-02 14:58:34 2015-11-02 15:14:24 993 0 . ± .
009 22 . Notes. ( a ) The average flare detection e ffi ciency above the corresponding non-flaring level. ( b ) The flare duration corresponds to the correspondingobserving time. ( c ) The flare mean count rates are computed after subtraction of the non-flaring level. ( d ) Mean unabsorbed flux between 2 and10 keV determined for N H = . × cm − and Γ = ( e ) Mean flare detection e ffi ciency. Owing to the decay phase of the Galactic centermagnetar, the average flare detection e ffi ciency increases during this campaign: 16.2, 17.9, 18.5, 21.7, 22.5, and 23.3% during 2013 April 4–May11, May 12–17, May 18–29, May 30–June 28, June 29–September 7 and September 8–October 31, respectively. Appendix B: X-ray flares detected from 1999 to2015 with XMM-Newton, Chandra, and Swift
Article number, page 16 of 22nmanuelle Mossoux and Nicolas Grosso: Sixteen years of X-ray monitoring of Sagittarius A*
Fig. B.1.
XMM-Newton flares detected using the Bayesian blocks algorithm with a false positive rate for the flare detection of 0.1% from 2000September to 2015 April. The black crosses are the light curves and their error bars. The bin size of the light curves are reported on the top of eachfigure. The red lines are the Bayesian blocks with their errors in horizontal gray rectangles. The vertical gray stripe is the bad time interval. Eachflare is labeled with the index corresponding to the flare number in Table A.1. The horizontal line is the flare duration. See caption of Fig. B.2 fordetails. Article number, page 17 of 22 & A proofs: manuscript no. article_29778_v5_printer
Fig. B.2.
Chandra flares detected using the Bayesian blocks algorithm with a false positive rate for the flare detection of 0.1% from 1999 to 2015October 21. Each flare is labeled with the index corresponding to the flare number in Tables A.2. See caption of Fig. B.1 for details.Article number, page 18 of 22nmanuelle Mossoux and Nicolas Grosso: Sixteen years of X-ray monitoring of Sagittarius A*
Fig. B.2.
Continued. Article number, page 19 of 22 & A proofs: manuscript no. article_29778_v5_printer
Fig. B.2.
Continued.
Appendix C: Comparison with previous works
As explained in the introduction, Ponti et al. (2015) used thePython implementation of the Bayesian block algorithm to de-tect the X-ray flares observed by Chandra and XMM-Newtonfrom 1999 to 2014. We thus compare the duration and fluenceof the flares detected here using the two-step Bayesian blocksalgorithm (the red circles in Fig. C.2) and those that Ponti et al.(2015) detected (the black circles in Fig. C.2). The flares thatwere detected in both works are connected with a gray line.During the 37 XMM-Newton observations from 2000 to2014 that we have in common with Ponti et al. (2015), we de-tected 19 flares with a false positive rate for the flare detection of0.1% whereas they detected only 11 flares with a false positiverate for the flare detection of 0.25%. Ponti et al. (2015) missedsix of our flares (the red filled circles in Fig. C.1) . Finally, twoadditional flares were observed during the eight XMM-Newtonobservations of 2014 and 2015 recently released (the two aster-isks in Fig. C.1). We missed the flare labeled . We considered the2014 October 20 Chandra flare as a single flare ( (cid:48) o ff -axis angle, they did not study the 2011 July 21 Chandra obser-vation where we detect one flare ( Their missed XMM-Newton flares are on 2004 March 31 (flare Their missed Chandra flares are on 1999 September 21 (flare
Fig. C.1.
X-ray flare fluences (top panel) and durations (bottom panel)observed with XMM-Newton from 1999 to 2014. The red circles indi-cate the values computed in this work. The black circles indicate thevalues computed by Ponti et al. (2015). The red filled circles indicatethe flares detected in our work that Ponti et al. (2015) missed. The graylines connect the same flares. The x-axis reports the flare index cor-responding to its numbering in Table A.1 and Fig. B.1. The asterisksdenote the flares detected in the observations recently released.
Fig. C.2.
X-ray flare fluences (top panel) and durations (bottom panel)observed with Chandra from 1999 to 2014. The red circles indicate thevalues computed in this work. The black circles indicate the values com-puted by Ponti et al. (2015). The black filled circles indicate their puta-tive flares. The red filled circles indicate the flares detected in our workthat Ponti et al. (2015) missed. The gray lines connect the same flares.The x-axis reports the flare index corresponding to its numbering inTable A.2 and Fig. B.2. The asterisks denote the flares detected in theobservations recently released or where Sgr A* has an o ff -axis anglelarger than 2 (cid:48) . detected by Bélanger et al. (2005) and Porquet et al. (2005). TheXMM-Newton flare on 2007 April 4 ( that we do not confirm with our more robust method (the blackfilled circles in Fig. C.2). Their inconsistency in flare detectionwith respect to previous studies and our work may be explainedby their blind use of the geometric prior. This e ff ect is clearlyvisible with their putative Chandra flares: the black filled circles Their putative Chandra flares are on 2012 August 4 19:32:37, 2013August 11 10:04:15, 2013 August 31 16:07:43, 2013 September 2011:21:00, 2013 October 17 16:12:36, 2014 February 21 00:51:18, 2014August 30 12:26:19Article number, page 20 of 22nmanuelle Mossoux and Nicolas Grosso: Sixteen years of X-ray monitoring of Sagittarius A* in Fig. C.2 are clustered when the contribution of the Galacticcenter magnetar SGR J1745-29 in the Sgr A* event lists is high(i.e., between 2013 and 20114). Owing to the higher noise levelof these observations, the absence of calibration of the prior maylead to spurious detection of blocks with a very small increaseof the count rate compared to the non-flaring level and thus verylow fluence. Conversely, due to the low signal-to-noise ratio ofthe Chandra data from Sgr A* before 2013, the calibration of theprior is highly sensitive to the number of events in each observa-tion. Therefore, Ponti et al. (2015) missed several Chandra flaresowing to the inconsistency between their false positive rate, thenumber of events in the Chandra observations, and the prior. Thise ff ect has a smaller impact on the XMM-Newton observationsdue to their higher signal-to-noise ratio.For the flares in common, the flare durations are roughly con-sistent but the improved fluences computed in this work are typ-ically larger than those computed in Ponti et al. (2015) becauseof their utilization of WebPIMMS for the computation of theflare flux. Indeed, WebPIMMS considers the e ff ective area andthe redistribution matrix computed for an on-axis source and forthe entire field of view. However, the flare events were extractedfrom a circular region of 1.25 and 10 (cid:48)(cid:48) radius centered on thesource (with a maximum o ff -axis angle of 2 (cid:48) ). Since the PSFextraction fraction is not corrected by WebPIMMS, the inferredunabsorbed flux is systematically underestimated by Ponti et al.(2015). Appendix D: Simulation of Poisson flux todetermine the flare detection efficiency
We recall that for homogeneous Poisson flux, i.e., a constantmean count rate CR , the average number of recorded events dur-ing an exposure T is N = CR × T with a standard deviationof √ N . Therefore, we simulate a constant Poisson flux by firstdrawing the total number M of events in the simulated event listfollowing a Poisson probability distribution, i.e., P ( M ) = N M M ! e − N , (D.1)and then by drawing M values uniformly distributed between 0and 1 and sorted by ascending order and multiplying them by T .This two-step method is equivalent to the iterative methodof Klein & Roberts (1984), which determines the waiting timebefore the next event considering their decreasing exponentialdistribution until the simulated arrival time of the event exceedsthe exposure time. Their resulting total number of events thusfollows a Poisson distribution.To determine the flare detection e ffi ciency, we consider aGaussian-shaped flare superimposed on a constant level leadingto a non-homogeneous Poisson process. The constant level ischaracterized by a constant Poisson flux of mean count rate CR during a total observing time T leading to an average number ofevents N c = CR × T , whereas the flare light curve peaks at t peak with a count rate amplitude A peak leading to an average numberof events, N g = A peak (cid:90) T e − ( t − t peak)22 σ dt . (D.2)The total number of events M in each simulation thus follows aPoisson distribution of mean N = N g + N c .We use the inverse method (see Klein & Roberts 1984, Chap-ter 7 of Press et al. 1992 and Fig. 2 of Harrod & Kelton 2013) Fig. D.1.
Simulation of an X-ray light curve with a flare.
Top panel:
Thecumulative distribution function (CDF) of a constant function (greenline) representing the non-flaring emission and a Gaussian function(blue line) representing the flaring emission. The non-flaring emissionhas a count rate CR = . − . The flare is defined with a peakamplitude A peak = . − at t peak = σ = N g = Bottom panel:
The constant andGaussian light curve models are represented in green and blue, respec-tively. The red line indicates the model of the light curve with flare.The ticks at the top of this panel represent 5% of the simulated arrivaltimes. The resulting light curve and its error bars are computed for a bintime of 100 s. The results of the Bayesian block algorithm with a falsepositive rate for the flare detection of 0 .
1% are shown with dashed lines. based on the reciprocal of the cumulative distribution function(CDF) to simulated the arrival times of these M events. TheCDFs for the non-flaring level and for the flare are, respectively, CDF c ( t ) = t / T , (D.3)and CDF g ( t ) = A peak σ N g (cid:114) π (cid:32) erf (cid:32) t peak √ σ (cid:33) + erf (cid:32) t − t peak √ σ (cid:33)(cid:33) . (D.4)We combine the constant and Gaussian CDFs as CDF c + g ( t ) = CDF c ( t ) N c N g + N c + CDF g ( t ) N g N g + N c . (D.5)We then draw M values of y uniformly distributed between 0 and1 and sort these values in ascending order. The correspondingarrival times of the events are finally obtained from CDF − + g ( y ).The top panel of Fig. D.1 shows these CDFs for typ-ical exposure of 35 ks with a non-flaring level of CR = . − , which corresponds to those observed by XMM-Newton EPIC / pn, and a flare peaking at the exposure center withan amplitude of A peak = . − , which corresponds to themean amplitude measured in the X-ray flares, thus leading to N g =
752 counts. The corresponding constant and Gaussian light
Article number, page 21 of 22 & A proofs: manuscript no. article_29778_v5_printer curve models are shown with the corresponding color in the bot-tom panel. The simulated arrival times are the black ticks at thetop of the bottom panel of Fig. D.1 (only 1 arrival time in 20 areshown here for clarity purpose). The resulting simulated lightcurve binned on 100 s is shown in the bottom panel of this fig-ure. For illustration purpose, the Bayesian blocks computed fora false positive rate for the flare detection of 0 .
1% are also rep-resented in this figure.1% are also rep-resented in this figure.