1. 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

2. J. F. Albacete Colombo Univ. de Rio Negro, Viedma, ARG & Ettore Flaccomio Osservatorio Astronomico di Palermo, Sicilia, ITA 47.9430 41.4802 24.1129 82.9727 31.5034 49.3290 70.7784 12.6222 9.11620 86.9843 36.5893 91.4728 36.4354 79.5255 10.5213 41.2974 19.8671 4.09888 9.82141 59.3807 16.9918 89.1797 6.75062 27.7335 49.4259 15.4687 31.6581 76.5401 26.8408 92.9103 40.1226 76.1259 95.7361 14.3060 92.1224 63.5069 65.3174 2.84524 26.9423 18.0783 34.5763 17.5361 31.0962 37.4532 58.2413 73.0615 72.2282 25.1846 77.0928 11.4857 13.9414 3.85849 28.6926 32.0193 9.25438 33.3937 41.6187 75.3055 68.0091 98.3105 17.9966 47.4547 50.9228 29.2340 23.6184 88.2934 60.4996 11.8393 16.4896 64.3899 55.6134 60.2502 77.8285 1.04427 52.0180 22.1233 6.49256 46.3797 1.18443 31.7242 96.9386 28.2538 80.9995 33.7562 93.8547 72.9343 13.0114 15.4254 96.3117 84.9769 56.9603 25.2446 94.6503 79.5382 25.4392 99.1314 53.7785 9.66788 53.0686 57.8366 3.18484 91.5750 71.3307 87.9062 86.1444 76.7540 59.0922 18.7214 52.3145 54.6100 25.3463 22.8215 58.1981 38.7461 7.55468 77.5012 43.6817 96.7716 92.4320 20.8583 29.8223 10.6893 92.7992 54.8132 74.4990 75.1708 80.4114 49.7729 7.97937 87.2544 21.7085 63.4109 35.9736 38.6242 37.5449 15.4403 49.3539 93.4674 98.1390 7.29326 39.8295 98.8290 21.1107 14.8071 99.3495 57.5067 2.52272 51.4111 18.1047 82.0786 53.3218 55.0572 17.0754 8.68807 19.3257 11.3794 9.62184 71.3506 26.1703 11.2345 48.4865 67.8055 42.9725 58.0971 25.5099 98.8997 20.8046 18.6980 55.1066 56.5339 85.8001 33.0383 7.45590 1.27356 44.6561 40.2476 97.7652 60.8279 83.9375 11.4291 52.3415 14.0751 73.8202 52.6931 81.4511 1.43340 58.1180 79.4456 53.5499 28.1491 5.12531 35.0699 96.4529 82.3417 20.6708 47.0947 39.6906 42.6226 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:

3. 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 ~ 4x10 -15 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

4. 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

5. 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)

6. 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 ~170.000 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.

7. - X-ray “faint” stars are usually modeled by one temperature thermal plasma, with a non- solar (~0.3 - 0.4) 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

8. 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

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

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

11. 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)

12. 3D (N H,kT,counts) quantile flux determination Possitive Q flux Negative Q flux log(kT) counts [10:15] log(NH) Factor 2 | Factor3 |

13. 3D (N H,kT,counts) quantile flux determination

14. How background affects our uncertainty determination ?

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

16. 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

17. 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)

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

19. 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 ! 0.5 0.6 0.7 0.8 0.9 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Energy (keV) Thermal emission ?Non-thermal emission ?

20. 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