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The Crab: the absorption model and consequences for absolute effective area calibration
Jelle S. Kaastra SRON


Using the Crab nebula as calibration source
· Good calibration sources should obey: 1) Simple continuum 2) Known continuum 3) Constant in time 4) Point source 5) No dust scattering halo Crab only obeys rule 1 and 3 partially, but except for White dwarf spectra there is nothing better


Extended emission
· Crab is extended: synchrotron nebula + dust scattering · RGS detectors (5' width) contain ~90 % of flux · Fraction energydependent · Determine using power law fits to tail spatial distribution


Enclosed fraction
· RGS1 and RGS2 slightly different (~2 % difference) · Correction factor contains structures near dust scattering edges: Ne, Fe, O · For >25 å poorly determined (lower CR, higher BG, more scattering)


Pile-up
· In full CCD mode, Crab shows pile-up up to 8 % · Use observations at 1, 2, 4 and 8 CCD mode to set-up model of pileup · Single CCD mode (0.574 s) < 1% pile-up but taken into account as arf correction for 1st order · Plot shows arf-correction for 8 CCD mode


Pile-up model
· Pile-up depends on intensity at a given pixel · Possible to determine empirically correction factor


Production of Crab arf
· Use polynomial correction based on blazar PL fits 10-25 å · Correct for timedependent Ccontamination · Correct for cross-disp loss · Include pile-up correction · Correct for 98 % PI selection


Spectral fitting
· Spatial profile in dispersion direction ~0.2 å FWHM · Determined from MOS image


Unabsorbed continuum model
· Based on fits to Crab with BeppoSAX; separate pulsar (curved spectrum) + nebula (Powerlaw, =2.147±0.002, Norm=9.31 (Kuiper et al.) · Toor & Seward · Kirsch et al. pn


Absorption model
· Model ("hot") from SPEX (Verner et al. cross sections, plus lines) · Abundances protosolar (Lodders) · Free abundance of H, N, O, Fe I & Fe II, Ne


Spectral fit
· Fit first order, RGS1 & RGS2, 1CCD & 2CCD mode spectra simultaneously · No free renorm for instruments, except: · Multiply model by PL: Na, N & a free, in order to allow for unknown absolute slope & norm of blazar spectra · RGS absolute area · Practice: determine PL by its (extrapolated) value @ 5 and 40 å


Results of fit
· Fit restricted to 7-30 å · Below 7 å grating scattering · Above 30 å arf-correction uncertain @ loss off events at low PI (extended source, wider selections) · Omit small region near O I and Fe I edge (arf poorly determined, narrow features)


Rebinning: how good is the fit
· Fit good within 2 % systematic uncertainty · RGS1 & RGS2 · 1CCD (upper) & 2CCD (lower) panel


Residuals near O-edge
· Caused by -dependent dust scattering in crossdisp correction (can be determined within ~0.5 å bins only, due to statistics) · Is also smeared out by ~0.2 å in disp · Plus uncertainty in atomic physics O-edge (atomic & dust)


Residuals near Fe I 2p edges


Fun: old fits to RGS Crab spectrum (Escorial meeting)
· Improvement due to dedicated off-axis measurements in cross-disp direction last February


Derived abundances
· · · · · · · · · · Best fit (brackets: predicted proto-solar value): NH = 3.14±0.02 x 1021 NN = 2.14±0.26 x 1017 2.49 18.07 NO = 19.36±0.18 x 1017 NNe = 5.25±0.16 x 1017 2.80 NMg = 0.95±0.30 x 1017 1.31 1.09 Nfe I = 0.63±0.06 x 1017 Nfe II = 0.37±0.06 x 1017 incl. Fe I O I / O II < 0.005 Conclusion: proto-solar, except Ne 1.9 x solar


Fudge factor:
· · · · (0.946±0.012)/N (/10)-0.089±0.012 Fudge @ 5 å: 1.006±0.009 Fudge @ 40 å: 0.836±0.020 However, true error at 40 å may be 0.05, due to correlation with NH (1CCD & 2 CCD mode give slightly different results, differ by 0.05 from the mean fit) · Ultimate accuracy: using also WD spectra LETGS?


Caveat: curved continuum spectrum nebula?

Mori et al., Chandra imaging


Conclusions
· RGS observations allow for accurate model for depth ISM absorption edges towards Crab · Needed for any observatory that uses Crab below 1 keV · Some further fine-tuning may be needed (lowest E, bending continuum)