Title: Quién le pone el cascabel al gato ? J. F. Albacete Colombo Univ. de Rio Negro, Viedma, ARG & Ettore Flaccomio Osservatorio Astronomico di Palermo, Sicilia, ITA

J. F. Albacete Colombo Univ. de Rio Negro, Viedma, ARG & Ettore Flaccomio Osservatorio Astronomico di Palermo, Sicilia, ITA Determination of uncertainties in Chandra ACIS-I faint spectra UNCERTAINTY DETERMINATION OF X-RAY SPECTRAL PARAMETERS IN THE LOW PHOTON STATISTIC REGIME FOR CHANDRA ACIS-I X-RAY SPECTRA <---- ApJ Sup. Series 2014, special edition, in prep. Paper title:

The ACIS-I Chandra camera: Launch: 1999 ACIS (Advanced CCD Imaging Spectrometer) Amazing facts Spatial (X,Y) - Time - Energy ACIS-I camera is one of the most sensitive camera (f x limit ~ 4x erg/cm 2 /s). It’s usable to perform X-ray surveys, SFRs, Galaxies, Clusters, etc. It’s so sensitive that X-rays photons from the faintest sources can arrive at a rate of 1 every 4 days ! The electrical power required to operate Chandra is the same power as a hair dryer (1-2 kilowatts) ! Albacete-Colombo et. al 2007, A&A, 464, p211

A typical phrase in X-ray articles... Photometric X-ray flux methods are usually used to get X-ray fluxes in source with a “few” counts (Getman et al. ApJ. 2010, 708, p1060) NO ERROR ESTIMATION BAD FLUX DETERMINATION Absorption, Temperature, Flux, by comparison with photometric X- ray fluxes from known sources with high S/N spectra. COLOR-COLOR X-RAY DIAGRAMS BIAS IN THE SPECTRAL PROPERTIES

For a given X-ray source, we have photons and “eventually” a representative distribution of the energy photons knowns as the X-ray source spectrum. Data modeling requires some astrophysics approximation --> the goodness of such a fit essentially will depends of the source photon statistics (source net counts). A new perspective of the problem... Ok, our X-ray source is faint in the ACIS-I Chandra data, so... - What really means faint ? (Nobody knows) - Can we get some spectral information from spectral fits ?... when ? (Nobody knows) - If any, how reliable is our spectral fit solution ?... I mean, the errors ? (Nobody knows)

Our strategy - I To our computers,... we (Ettore and me) are something like a god ! We create fake stars that emits in X-rays in an exactly physical condition that we impose (SPECTRAL PARAMETERS --> NH, kT, or gamma-index). We create a family of stars (more than ~ MC simulations) that emits in a family of different astrophysical ways... We impose how much radiates each of these fake stars (X-RAY FLUX). We distributes its along the Universe by adopting an arbitrary distance... (Normalization). We known how the ACIS-I instrument responds to the observations.

- X-ray “faint” stars are usually modeled by one temperature thermal plasma, with a non- solar (~ ) elemental abundances (Maggio et al. 2007, ApJ, 660, p1462). - Different absorption (N H ) plays a “huge” role on spectral fit (energies < 2 keV). - For faint ( we fit 1-Temp plasma model Fit(counts, N H, kT) with Z=0.3 fixed counts = [ 10,15, 20, 25, 30, 35, 40, 50, 60, 90, 120, 160, 220, 350 ] XSPEC model --> tbabs x apec N H = [1.0x10 21, 3.3x10 21, 10 22, 3.3x10 22,10 23, 3.3x10 23 ] cm -2 kT= [ 0.5, 0.8,1.2, 2.0, 3.0, 4.0, 6.0, 10.0 ] keV - We use XSPEC fakeit command to simulate X-ray spectra (S/N>3 ; bin > 1 ph./channel). - X 2 statistic assumes that energy-channels are Gaussian distributed. it’s not true for small numbers of counts ---> C-statistic minimization. - We assume low background contamination, but... Our strategy - II

X-ray spectral sims: input [F mod, N H, kT, counts ] --> [ F fit, N H fit, kT fit, CNT fit ] counts ~15 counts ~30 counts ~60counts ~200

Flux, NH and kT uncertainties in terms of 1 sig quantiles U Flux =log(F fit /F inp ) --> U kT =log(kT fit /kT inp ) --> U NH =log(NH fit /NH inp ) --> QkT - U kT QNH - U NH Qf - U Flux Qf(CNT,kT,NH) Qkt(CNT,kT,NH) Qnh(CNT,kT,NH)

Flux (NH or kT) uncertainties curves and 2D maps

3D Quantile flux determination QFLUX_Possitive = interpolate( QF_possitive, NH, KT, CNT ) QFLUX_Negative = interpolate( QF_negative, NH, KT, CNT ) Counts QF log(kT) log(NH)

3D (N H,kT,counts) quantile flux determination Possitive Q flux Negative Q flux log(kT) counts [10:15] log(NH) Factor 2 | Factor3 |

3D (N H,kT,counts) quantile flux determination

How background affects our uncertainty determination ?

How background affects our uncertainty determination Texto bkg_frac = bkg_cnt bkg_cnt + net_cnt ________________ ACIS Extract (Broos et al 2004) -->

How background affects our uncertainty determination ? - We simulate X-ray spectra for bkg affected sources by adopting proper ARFs, RMFs, at different -Source counts: 30, 100, 300 photons - 7 source emission models Flux, kT, or NH 2D maps

How to compute the Uncertainty on true source X-ray spectra ? Flux, kT, or NH 2D maps Model 1 kT=3.0 NH=10 22 Choose your model The same analysis for a non-thermal emission models kT --> Gamma index (power-law)

Thermal models Non Thermal models 20 X-ray photons in the spectra

Further Perspectives... - A denser kT-NH grid of simulations that includes background effects is needed. - An equivalent 2D grid for Gamma-NH that includes bkg_fraction effects in spectral fits. New models (still running): 8- NH=2E23 & kT=1.2 keV 9- NH=1E23 & kT=3.0 keV 10- NH=7E23 & kT=1.2 keV - To distinguish between a Thermal or Non thermal X-ray emission in spectra at low photon statistics regime > very useful for studies of AGNs population ! Energy (keV) Thermal emission ?Non-thermal emission ?

A NEW, but powerful tool to compute exposure times for X-ray proposals ! but most important... 1) You want to observe an point X-ray source with the ACIS-I Chandra camera. 2) You need to account for how many photons are needed to understand the X-ray properties of such a source. 3) You need to suppose an intrinsic X-ray emission source model. 4) Go to our procedure and estimates the uncertainty in the X-ray spectral parameters. 5) When you feels happy, thats the number of X-ray photons you need (net_count). 6) As you also known the X-ray flux, then you exactly knows the source count-rate. 7) Required observing time = count-rate / net_count This tool will be available soon for you !,... thanks