Estimation of the TeV gamma-ray duty cycle of Mrk 421 with Milagro
aa r X i v : . [ a s t r o - ph . H E ] J a n RD I NTERNATIONAL C OSMIC R AY C ONFERENCE , R
IO DE J ANEIRO T HE A STROPARTICLE P HYSICS C ONFERENCE
Estimation of the TeV gamma-ray duty cycle of Mrk 421 with Milagro
B. P
ATRICELLI , M.M. G ONZ ´ ALEZ , N. F RAIJA , A. M ARINELLI FOR THE M ILAGRO C OLLABORATION . Instituto de Astronom´ıa, UNAM, M´exico D.F., 04510, M´exico Instituto de Fisica, UNAM, M´exico D.F., 04510, M´exico [email protected]
Abstract:
The blazar Markarian 421 (Mrk 421) is one of the brightest sources in the extragalactic X-ray/TeVsky. It is also one of the fastest varying TeV g -ray sources, showing flaring activity on time scales as shortas tens of minutes. To know the level of activity of this source, Tluczykont et al. (2007) [1] calculated thefraction of time spent by Mrk 421 in flaring states with fluxes above 1 Crab at TeV energies (i.e., TeV - dutycycle). Here we present an alternative approach to calculate the TeV duty cycle of Mrk 421 taking advantage ofthe continuous monitoring of the source by the Milagro observatory. Milagro was a water Cherenkov detectorsensitive at energies between 100 GeV and 100 TeV. We present our estimation of the TeV - duty cycle and studyits robustness. Keywords:
VHE gamma-rays, blazars, duty cycle.
Blazars are a subclass of active galactic nuclei (AGN) char-acterized by broadband non-thermal emission from radioto very high energies (VHE, E >
100 GeV, Horns 2008[2]). They show strong flux variability at almost all fre-quencies of the spectral energy distribution on differenttime scales, from minutes (see, e.g., Aharonian et al. 2007[3]) to months (see, e.g., von Montigny et al. 1995 [4]).This large spread in time variability makes it difficult toquantify important parameters such as the duty cycle (DC).The DC is defined as the fraction of time spent in a high(“flaring”) state, thus, DC = (cid:229) i t i (cid:229) i t i + T baseline = T flare T flare + T baseline , (1)where t i is the time that the source spends in a i flaring stateand T baseline is the total time in which the source is in thebaseline flux state. The definition of a flaring state variesfrom author to author (see e.g. Krawczynski et al. 2004[5], Wagner 2008 [6]). The baseline flux may be stableand constant with time, although it may present intrinsicvariations. In the former case, a flaring state can be definedas any state with flux higher than the baseline flux. Inthe latter case, a flaring state must be defined taking intoaccount the assumed or measured intrinsic variations ofthe baseline flux. The identification of a baseline level isalso needed to identify the blazar quiescent level: withouta proper baseline level, only an upper limit of the flaringflux can be determined (Wagner 2011 [7]).Mrk 421 is one of the closest (redshift z=0.03; de Vau-couleurs et al. 1991 [8]) and brightest blazars known; itwas also the first BL Lac source detected at energies above100 MeV by EGRET in 1991 (Lin et al. 1992 [9]) and thefirst extragalactic object detected in the TeV energy band,by the Whipple Collaboration (Punch et al. 1992 [10]).The duty cycle at TeV energies has been estimated forMrk 421 by Tluczykont et al. (2007) [1]. They collecteddata from different imaging atmospheric Cherenkov tele-scopes (IACTs: HEGRA, HESS, MAGIC, CAT, Whippleand VERITAS) from 1992 to 2009. They combined the light curves from the different experiments converting themeasured integral flux to flux values in units of the CrabNebula flux and normalizing to a common energy thresh-old of 1 TeV and obtained a distribution of flux states forMrk 421. Finally, they estimated the TeV duty cycle as thetime that the source spent in a flaring state to the total ob-servation time of the telescopes. They considered differentflare flux thresholds. For a flare flux threshold of 1 Crab,they found a TeV DC of ∼
40 %. This value may overes-timate the true DC since IACT observations are biased to-wards high flux states due to their external and self trig-gering on high states (Tluczykont et al. 2007 [1]). In thepresent paper, we use the definition of flaring state as de-fined by Tluczykont, et al. (2007) [1] for a flux thresholdof 1 Crab. This is a conservative definition and allows usto compare our results with existing results [1]. We presenta different approach with respect to Tluczykont et al. 2007[1] to calculate the TeV DC of Mrk 421, that take advan-tage of the continuous and unbiased long term monitoringof the source by the Milagro detector. Milagro (see Atkins et al. 2004 [11]) was a large water-Cherenkov detector located in the Jemez Mountains nearLos Alamos, New Mexico, USA at an altitude of 2630 mabove sea level. It was designed to detect very high energy(VHE) gamma rays at energies between 100 GeV and 100TeV (Abdo et al. 2008a,b [12, 13]). It had a ∼ ≥
90% duty cycle that allowed it to contin-uously monitor the entire overhead sky. It operated from2000 to 2008. It was composed of a central 80 m ×
60 m × stimation of the TeV g -ray duty cycle of Mrk 421 with Milagro33 RD I NTERNATIONAL C OSMIC R AY C ONFERENCE , R
IO DE J ANEIRO sparse 200 m x 200 m array of 175 “outrigger” was addedaround the central reservoir. This array increased the areaof the detector and improved the gamma/hadron separation.The detector reached its final configuration in September2005.
Milagro detected Mrk 421 in the period from September21, 2005 to March 15, 2008 with a statistical significanceof 7.1 standard deviations at a median energy of 1.7 TeV.From the analysis of the light curve we found (Abdo etal. 2013 [14]) that the Mrk 421 flux is consistent with be-ing constant along the whole 3-year observation period,with an average value above 1 TeV of ¯ f = (2 . ± . × − cm − s − ( c =134 for 122 degrees of freedom)equivalent to 0.85 ± F baseline , and the contri-butions of the fluxes of any other higher (“flaring”) state i , f flare , i . Thus,¯ f × T Milagro = F baseline × T baseline + F flare , (2)where T Milagro is the total observation period of Milagrogiven by T baseline + T flare and F flare is the total fluence of allhigh states given by (cid:229) i f flare , i t i The knowledge of ¯ f is not enough to estimate the TeV DC , as the same value of F flare could be obtained byconsidering many long-duration low-flux flares or a fewshort-duration high-flux flares, leading to different DC val-ues. Therefore, a distribution of flux states of Mrk 421 isneeded. We used the same distribution of flux states above1 TeV used by Tluczykont et al. 2007 [1]. This distribu-tion is well fit by a function f ( x ) which is the sum ofa Gaussian component, describing the baseline flux stateplus a log-normal function, describing the flaring states(Tluczykont et al. 2010 [15]). The mean of the Gaussiancomponent ( ∼ F baseline (Tluczykont et al. 2010 [15]) becausesome lower fluxes may be missing. The detectors may notbe sensitive enough to detect them for short observation pe-riods.We used the distribution of Tluczykont et al. 2010 [15]to calculate the average flare flux, < f flare > , given by, < f flare > = R F lim x f ( x ) dx R F lim f ( x ) dx (3)with F lim the maximum flux considered in the distribu-tion, i.e. F lim =10 Crab [15]. Then, we have < f flare > = 2.64Crab. F flare can be written in terms of < f flare > as following, F flare = < f flare > × T flare . (4)By inserting Eq. 4 in Eq. 2 we obtain T flare = (cid:0) ¯ f − F baseline (cid:1) T Milagro < f flare > − F baseline (5)Then, Eq. 1 becomes, DC = (cid:0) ¯ f − F baseline (cid:1) < f flare > − F baseline . (6)Equation 6 gives the DC as a function of three quantities:1) the average flux of Mrk 421 ( ¯ f ) which has a unique value
10 20 30 40 0 0.05 0.1 0.15 0.2 0.25 0.3 D u t y C yc l e ( % ) F baseline (Crab) Figure 1 : Duty cycle calculated by considering as flaringstates all those having a flux above 1 TeV greater than 1Crab. The shadowed blue area represents the error associ-ated to DC , obtained by taking into account the uncertaintyon ¯ f .of 0.85 ± F baseline )between 0 and the maximum value of ∼ f ( x ) and the maximum flux ( F lim ) chosen to be10 Crab. Therefore, we calculated the DC , given in Figure1, for values of F baseline from 0 to the upper limit of ∼ f . The un-certainty given by the choice of F lim and f ( x ) are discussedin Sec. 3.1 and 3.2.It can be seen from Figure 1 that the DC ranges from23 + − % ( F baseline =0.33 Crab) to 32 + − % ( F baseline =0 Crab).These values are generally lower but marginally consis-tent within the error with the ∼
40% value obtained byTluczykont et al. 2007 [1]. It is not surprising since, as al-ready explained in Section 1, Tluczykont et al. 2007 [1] es-timated the DC with an observational bias to continue ob-servations of the source in high states, leading to an over-estimation of DC . F lim The distribution of flux states obtained by Tluczykont etal. 2010 [15] is based on observations and is not modeldependent. The extrapolation of f ( x ) above 10 Crab is nottrivial. For instance, we do not know if the source canmaintain a flaring state with a flux higher than 10 Crabfor a time equal to the duration of the flares in the fluxdistribution reported in Tluczykont et al. 2010 [15]. A cut-off in the distribution is expected at some flux value, justas a result of the limited available energy of the source.Therefore, the extension of f ( x ) above 10 Crab can not bedone much further than 10 Crab.We calculated the DC by considering F lim equal to 15Crab just by extrapolating the function f ( x ) up to 15 Crab.The results are shown in Figure 2. It can be seen that, byconsidering F lim =15 Crab the TeV DC goes from 30 % to21 %. These values are between 6% and 8% lower than the
1. The variable x represents the flux of Mrk 421 above 1 TeV inCrab unit.stimation of the TeV g -ray duty cycle of Mrk 421 with Milagro33 RD I NTERNATIONAL C OSMIC R AY C ONFERENCE , R
IO DE J ANEIRO D u t y C yc l e ( % ) F baseline (Crab) F lim =10 CrabF lim =15 Crab Figure 2 : Duty cycle calculated by considering as flaringstates all those having a flux above 1 TeV greater than 1Crab. The black and the red lines correspond to the calcula-tion done by assuming F lim =10 Crab and 15 Crab, respec-tively.ones obtained with F lim =10 Crab, but are well within therange found including the error on ¯ f . The flaring state distribution can be fit by different func-tions, f ( x ) . We chose the sum of a Gaussian componentplus a log-normal function. Tluczykont et al. 2010 [15]also consider an exponential function above 0.25 Crab. Wechose an extreme case to calculate the DC . Instead of f ( x ) ,we took the actual set of data used to get the distributionof flux states by Tluczykont et al. 2010 [15]. Then, we ob-tained a value for < f flare > of 2.83 Crab. The results forthe DC are shown in figure 3. It can be seen that, like in thecase F lim =15 Crab, the TeV DC goes from 30 % to 21 %. We have presented a new approach to estimate the TeV DC of Mrk 421, based on the continuous monitoring ofthe source with the Milagro observatory. We have consid-ered the activity of the source above 1 Crab, finding that,depending on the assumed value for the baseline flux ofMrk 421, DC ranges from 23 + − % to 32 + − %. These valuesare lower but consistent, within the errors, with the valuefound by Tluczykont et al. 2007 [1]. We also tested the ro-bustness of our calculation, finding that the range of valueslowers by 6% - 8% when a discrete distribution functionfor the Mrk 421 flux states instead of a continuous func-tion is considered; the same result has been obtained if thedistribution is extrapolated up to values of flux greater thanthe observed 10 Crab. These uncertainties are lower thanthe one associated to the error on ¯ f .The value of 1 Crab chosen as flare flux thresholdrepresents an overestimate of the minimum flux requiredto define a flaring state: in fact, from the distribution ofTluczykont et al. 2010 [15] it is clear that above a fewtenths of Crab the distribution of flux states presents thetypical behaviour of “high” states. The estimation of theTeV DC for more realistic assumptions on the threshold D u t y C yc l e ( % ) F baseline (Crab) with f(x)with real data Figure 3 : Duty cycle calculated by considering as flaringstates all those having a flux above 1 TeV greater than1 Crab. The black and the green lines correspond to thecalculation done by using, for the distribution of flux states,the function f ( x ) and the discrete set of data (Tluczykontet al. 2010 [15]), respectively.flare flux will be presented elsewhere, together with a com-parison of the TeV DC with the X-ray DC . Acknowledgment:
We gratefully acknowledge Scott Delayand Michael Schneider for their dedicated efforts in the construc-tion and maintenance of the Milagro experiment. This work hasbeen supported by the Consejo Nacional de Ciencia y Tecnolog´ıa(under grant Conacyt 105033), Universidad Nacional Aut´onomade M´exico (under grants PAPIIT IN105211 and IN108713) andDGAPA-UNAM.