SPEX User's Manual - SRON

More documents

Recommendations

Info

24 Syntax overview Examples elim 0.5 4.5 - give fluxes between 0.5 and 4.5 keV elim 500 4500 ev - give fluxes between 500 and 4500 eV (same result as above) elim 5 38 a - give fluxes in the 5 to 38 Å wavelength band 2.11 Error: Calculate the errors of the fitted parameters Overview This command calculates the error on a certain parameter or parameter range, if that parameter is thawn. Standard the 1σ rms error is calculated. (this is not equivalent to 68 %, as the relevant distributions are χ 2 and not normal!). So ∆χ 2 is 2, for a single parameter error. The ∆χ 2 value can be set, such that for instance 90 % errors are determined. SPEX determines the error bounds by iteratively modifying the parameter of interest and calculating χ 2 as a function of the parameter. During this process the other free parameters of the model may vary. The iteration stops when χ 2 = χ 2 min + ∆χ2 , where ∆χ 2 is a parameter that can be set separately. The standard errors of SPEX (rms errors are for ∆χ 2 = 2. The iteration steps are displayed. It is advised to check them, because sometimes the fit at a trial parameter converges to a different solution branch, therefore creating a discontinuous jump in χ 2 . In those situations it is better to find the error bounds by varying the search parameter by hand. Finally note that SPEX remembers the parameter range for which you did your lat error search. This saves you often typing in sector numbers or component numbers if you keep the same spectral component for your next error search. Warning: A parameter must have the status ”thawn” in order to be able to determine its errors. Syntax The following syntax rules apply: error [[[#i1:] #i2:] #a:] - Determine the error bars for the parameters specified by the sector range #i1: (optional), component range #i2 (optional) and parameter range #a: (optional). If not specified, the range for the last call will be used. On startup, this is the first parameter of the first component of the first sector. error dchi #r - This command changes the ∆χ 2 , to the value #r. Default at startup and recommende value to use is 2, for other confidence levels see Table 2.4. error start #r - This command gives an initial guess of the error bar, from where to start searching the relevant error. This can be helpful for determining the errors on normalization parameters, as otherwise SPEX may from a rather small value. To return to the initial situation, put #r=0 (automatic error search). Examples error norm - Find the error for the normalization of the current component error 2:3 norm:gamm - determines the error on all free parameters between ”norm” and ”gamm” for components 2:3 error start 0.01 - Start calculating the error beginning with an initial guess of 0.01 error dchi 2.71 - Calculate from now onwards the 90% error, for 1 degree of freedom. (Not recommended, use r.m.s. errors instead!)
2.12 Fit: spectral fitting 25 Table 2.4: ∆χ 2 as a function of confidence level, P, and degrees of freedom, ν. ν P 1 2 3 4 5 6 68.3% 1.00 2.30 3.53 4.72 5.89 7.04 90% 2.71 4.61 6.25 7.78 9.24 10.6 95.4% 4.00 6.17 8.02 9.70 11.3 12.8 99% 6.63 9.21 11.3 13.3 15.1 16.8 99.99% 15.1 18.4 21.1 13.5 25.7 27.8 2.12 Fit: spectral fitting Overview With this command one fits the spectral model to the data. Only parameters that are thawn are changed during the fitting process. Options allow you to do a weighted fit (according to the model or the data), have the fit parameters and plot printed and updated during the fit, and limit the number of iterations done. Here we make a few remarks about proper data weighting. χ 2 is usually calculated as the sum over all data bins i of (N i − s i ) 2 /σi 2, i.e. n∑ χ 2 (N i − s i ) 2 = , (2.1) i=1 where N i is the observed number of source plus background counts, s i the expected number of source plus background counts of the fitted model, and for Poissonian statistics usually one takes σ 2 i = N i . Take care that the spectral bins contain sufficient counts (either source or background), recommended is e.g. to use at least ∼10 counts per bin. If this is not the case, first rebin the data set whenever you have a ”continuum” spectrum. For line spectra you cannot do this of course without loosing important information! Note however that this method has inaccuracies if N i is less than ∼100. Wheaton et al. ([1995]) have shown that the classical χ 2 method becomes inaccurate for spectra with less than ∼ 100 counts per bin. This is not due to the approximation of the Poisson statistic by a normal distribution, but due to using the observed number of counts N i as weights in the calculation of χ 2 . Wheaton et al. showed that the problem can be resolved by using instead σ 2 i = s i , i.e. the expected number of counts from the best fit model. The option ”fit weight model” allows to use these modified weights. By selecting it, the expected number of counts (both source plus background) of the current spectral model is used onwards in calculating the fit statistic. Wheaton et al. suggest to do the following 3-step process, which we also recommend to the user of SPEX: 1. first fit the spectrum using the data errors as weights (the default of SPEX). 2. After completing this fit, select the ”fit weight model” option and do again a fit 3. then repeat this step once more by again selecting ”fit weight model” in order to replace s i of the first step by s i of the second step in the weights. The result should now have been converged (under the assumption that the fitted model gives a reasonable description of the data, if your spectral model is way off you are in trouble anyway!). There is yet another option to try for spectral fitting with low count rate statistics and that is maximum likelyhood fitting. It can be shown that a good alternative to χ 2 in that limit is C = 2 σ 2 i n∑ s i − N i + N i ln(N i /s i ). (2.2) i=1
Page 1: SPEX User’s Manual Jelle Kaastra
Page 4 and 5: 4 CONTENTS 2.29 System . . . . . .
Page 6 and 7: 6 CONTENTS 5.8.3 ASCA SIS0 . . . .
Page 8 and 9: 8 Introduction 1.2.2 Sky sectors Fi
Page 10 and 11: 10 Introduction
Page 12 and 13: 12 Syntax overview Table 2.2: Abund
Page 14 and 15: 14 Syntax overview tcl: the continu
Page 16 and 17: 16 Syntax overview Examples calc -
Page 18 and 19: 18 Syntax overview by averaging the
Page 20 and 21: 20 Syntax overview dem gene #i1 #i2
Page 22 and 23: 22 Syntax overview distance om #r -
Page 26 and 27: 26 Syntax overview This is strictly
Page 28 and 29: 28 Syntax overview Currently these
Page 30 and 31: 30 Syntax overview Syntax The follo
Page 32 and 33: 32 Syntax overview status, range an
Page 34 and 35: 34 Syntax overview par write mypar
Page 36 and 37: 36 Syntax overview plot box col #i
Page 38 and 39: 38 Syntax overview plot type data -
Page 40 and 41: 40 Syntax overview 2.26 Simulate: S
Page 42 and 43: 42 Syntax overview step axis 2 par
Page 44 and 45: 44 Syntax overview Examples use 100
Page 46 and 47: 46 Syntax overview width. On top of
Page 48 and 49: 48 Syntax overview
Page 50 and 51: 50 Spectral Models acronym pow delt
Page 52 and 53: 52 Spectral Models Finally, we have
Page 54 and 55: 54 Spectral Models where Q is the l
Page 56 and 57: 56 Spectral Models 3. set=3: for R
Page 58 and 59: 58 Spectral Models 3.14 Hot: collis
Page 60 and 61: 60 Spectral Models can be transform
Page 62 and 63: 62 Spectral Models The emission mea
Page 64 and 65: 64 Spectral Models 3.23 Refl: Refle
Page 66 and 67: 66 Spectral Models • type=3: b 1
Page 68 and 69: 68 Spectral Models 4.8, 4.9, 5.0 wi
Page 70 and 71: 70 More about plotting Table 4.1: A
Page 72 and 73: 72 More about plotting 4.4 Plot lin
Page 74 and 75:
74 More about plotting Table 4.2: A
Page 76 and 77:
76 More about plotting 4.6 Plot cap
Page 78 and 79:
78 More about plotting 4.8 Plot axi
Page 80 and 81:
80 More about plotting bin cou cs k
Page 82 and 83:
82 More about plotting
Page 84 and 85:
84 Response matrices models. Since
Page 86 and 87:
86 Response matrices Table 5.1: Wei
Page 88 and 89:
88 Response matrices Table 5.2: Sca
Page 90 and 91:
90 Response matrices since the larg
Page 92 and 93:
92 Response matrices Figure 5.1: Di
Page 94 and 95:
94 Response matrices for the Cauchy
Page 96 and 97:
96 Response matrices bin j of this
Page 98 and 99:
98 Response matrices The approximat
Page 100 and 101:
100 Response matrices particular bi
Page 102 and 103:
102 Response matrices reduced by ab
Page 104 and 105:
104 Response matrices where as befo
Page 106 and 107:
106 Response matrices 5. Determine
Page 108 and 109:
108 Response matrices practical pro
Page 110 and 111:
110 Response matrices Table 5.10: T
Page 112 and 113:
112 Response matrices Table 5.11: F
Page 114 and 115:
114 Response matrices Figure 5.7: B
Page 116 and 117:
116 Response matrices Table 5.15: R
Page 118 and 119:
118 Response matrices
Page 120 and 121:
120 Installation and testing
Page 122 and 123:
122 Acknowledgements
Page 124 and 125:
124 BIBLIOGRAPHY [2003] Peterson, J
show all

SPEX User's Manual - SRON

Create successful ePaper yourself

Delete template?

Save as template?