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Alignment of the RGS1 and RGS2 wavelength scales D. Coia & A.M.T. Pollo ck 30 April 2008

1

Abstract

Previous work has allowed accurate estimates of the mean displacements of lab oratory lines in the XMMNewton RGS. These are used to adjust the angles of incidence in RGS1 and RGS2 in the CCF in order to align their wavelength axes with adjustments of -2.44 and -6.93 m °, resp ectively. A consistency check was A made with the OVI I interstellar absorption line in accumulated sp ectra of two blazars. No evidence was found of the need to make adjustments to the geometry of individual CCDs.

2

Intro duction

Disagreement b etween the wavelengths of lines measured in RGS sp ectra and the corresp onding lab oratory values has b een known since the early stages of the XMM-Newton mission. A previous document quantified A A the mean first order displacement in the range -10 < (m °) < +20 with 8 ° (Coia & Pollock 2007). The analysis was carried out on 66 observations of four stars. One of the aims of the present document is to investigate how the agreement can b e improved b etween lab oratory and observational values. The means of the distributions of displacements for RGS1 and RGS2 for b oth sp ectral orders were found to b e (Fig.1): · · · ·
RGS 1,m=-1 RGS 1,m=-2 RGS 2,m=-1 RGS 2,m=-2

= (+2.35 ± 0.09) m° A A = (+1.31 ± 0.07) m° = (+7.39 ± 0.10) m° A = (+2.93 ± 0.07) m° A

3

Wavelength shifts and calibration of the RGS wavelength scale

To reach a b etter mean agreement b etween lab oratory and observational values and also b etween RGS1 and RGS2, the incidence angle may b e modified in the CCFs according to the mean wavelength shifts already determined. To this aim the values from b oth orders for each RGS can b e combined by taking the weighted means of m, obtaining the mean wavelength shifts for RGS1 and RGS2: · m · m
RGS 1 RGS 2

A = (+2.44 ± 0.77) m° = (+6.93 ± 0.84) m° A

These weighted wavelength shifts are then converted into corrections to b e applied to via the disp ersion equation: m = d â (cos - cos) (1)

1


Figure 1: Distribution of first and second order wavelength shifts for RGS1 and RGS2 (Coia & Pollock 2007).

2


° where m is the sp ectral order, is the wavelength of the X-ray on the detector, d = 15489.455 A is the grating line spacing, is the diffraction angle and = 1.576191 is the incidence angle as rep orted in /ccf/pub/XMM MISCDATA 0022.CCF. Equ. 1 b ecomes: = m â (d â sin())
-1

(2)

With Equ. 2 the wavelength shifts rep orted ab ove b ecome displacements in the angle of incidence of:

· RGS 1 = (+1.18 ± 0.37) arcsec · RGS 2 = (+3.35 ± 0.41) arcsec It is worth noting that these values are within the estimated inaccuracy of 5 arcsec in the angle of incidence onto the grating plates (Erd 2001).

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3.1

The OVI I absorption line in Mkn 421 and PKS 2155-304

We have p erformed a check with the measured p osition of the interstellar OVI I 1s-2p absorption line whose lab oratory wavelength according to ATOMDB 1 is lab = 21.6015 ± 0.0070°, in the accumulated continuum A sp ectra of the blazars Mkn 421 and PKS 2155-304 (Table 1). This line is exp ected to b e at close to zero velocity. The data analysed were downloaded from the XMM-Newton public archive as ODFs: 43 observations for MKN 421 and 17 for PKS 2155-304 (Tables 3, 4 in App endix). The sp ectra were generated using the rgsproc command in SAS v7.1 with SIMBAD coordinates. Resp onse matrices with a resolution of 20000 were created with rgsrmfgen for each sp ectrum. An attempt to produce one single combined sp ectrum for b oth targets was made within XSPEC. However XSPEC v12.4.0 was unable to even just load all sp ectra and relative resp onse matrices at the same time. Therefore, for this part of the analysis IDL v6.4 was used. The sp ectra were combined and the p ositions of the OVI I absorption line measured by fitting the observed line with a gaussian function (Figs. 2, 3). As a result of this analysis, the p osition of the OVI I line is found to b e = (21.6007 ± 0.0019) ° for Mkn 421 A A and = (21.6006 ± 0.0042)° for PKS 2155-304. The observed wavelength error currently quoted for this line in ATOMDB is 7 m°. A Table 1: The sample. Columns are: name of target, coordinates from SIMBAD, redshifts and numb er of RGS observations p er target. TARGET Mkn 421 PKS 2155-304 RA(2000) 11h 04m 27.314s 21h 58m 52.065s DEC(2000) +38o 12'31.80" -30o 13'32.12" Redshift 0.030 0.116 Numb er of observations 43 17

1

http://cxc.harvard.edu/atomdb/

4


Figure 2: The OVI I line (1s-2p, lab = 21.6020°, blue line) in the accumulated sp ectrum of Mkn 421. A Line and continuum were fitted with a gaussian function (red line). The measured p osition of the line was (21.6007 ± 0.0019)°. The deep feature at 21.8° close to the p osition of the OVI I intercombination line A A is due to a detector defect.

Figure 3: The OVI I line (1s-2p, lab = 21.6020°, blue line) in the accumulated sp ectrum of PKS2155-304. A Line and continuum were fitted with a gaussian function (red line). The measured p osition of the line was (21.6006 ± 0.0042)°. The deep feature at 21.8° is due to the same detector defect as in Fig. 2. A A

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3.2

The new XMM MISCDATA CCF

The modified values for the angle of incidence ( + ) for b oth RGS1 and RGS2 were included in a test /ccf/pub/XMM MISCDATA 9999.CCF. New sp ectra and resp onse matrices of resolution 20000 were produced and the displacement in wavelength scale analysed with satisfactory results (Table 2). It is therefore recommended that the values of the angle of incidence b e changed in the following way: · RGS1: from 1.576191 to 1.576519 · RGS2: from 1.576191 to 1.577122


With the new values, the difference in m lambda from the EVENT files b efore and after correction of the incidence angle in the CCFs is 2.44 m ° for RGS1 and 6.96 m° as exp ected. A A Systematic errors are still present, but the mean of the distribution of the displacements will b e 0 and RGS1 and RGS2 will b e aligned. Table 2: Displacements measured for RGS1 for a numb er of observations for AB Doradus after modification of angle of incidence in CCFs. The measurements are taken b oth when subtracting and adding 1.18 arcsec to and the differences computed. OBS ID 0 [m°] A +6.77 +2.43 +3.57 -3.50 -3.72 +2.61 RGS1 0 + [m°] A +3.57 +1.37 +2.62 -9.38 -3.77 -3.23


0123720201 0134522201 0160363201 0412580101 0160362801 0133120201

[m°] A +3.20 +1.06 +0.95 +5.88 +0.05 +5.84

0 [m°] A +9.07 +7.82 +7.77 -0.58 -0.08 +1.18

RGS2 0 + [m°] A +0.39 +0.95 +1.00 -6.73 -3.57 -0.31



[m°] A +8.68 +6.87 +6.77 +6.15 +3.49 +2.12

4

Investigation of the geometry of individual CCDs

In Coia & Pollock (2007), wavelength shifts relative to the overall geometry of the RGS arrays were measured. However, the RGS consist of nine CCDs whose individual geometrical p ositions are required to derive wavelengths. These p ositions are sub ject to small uncertainties that can b e checked by constraining an equal extra shift for all the lines located on an individual CCD. This task is p erformed in a similar fashion as that describ ed in Coia & Pollock (2007) for the measurement of the displacements of the sp ectral lines along the entire instrument. The difference is that this time the lines are allowed to move indep endently in each individual CCD instead of having them consistenly moved along the whole array. The distributions of the displacements measures with this method are shown in Figs. 4, 5 for RGS1 and RGS2 resp ectively and for each CCD. As the figures show, the b est cases for b oth instruments are for CCDs #4, 5, and 6, i.e. where most of the lines are found and measurements are therefore more reliable. Measurements on CCDs #1, 9 show a much larger scatter. Figure 7 shows the displacements measured on CCD #5 against the measurements on all other CCDs. No correlation are found b etween the various arrays. Figure 8 show the C-statistic obtained for CCDs #4, 5, and 6 for observation 0123720202 (AB Dor). The figure shows that although the C-statistic app ears irregular (partly due to the resolution of the matrix and on the numb er of steps used), the values measured corresp ond to the exp ected displacements. In conclusion, although displacements are indeed present for each CCD, it is not practical at this stage apply a correction to the CCFs to take into account the geometry of RGS. 6


Figure 4: Distributions of displacements on wavelength scale due to CCD geometry for RGS1 measured for each individual CCD.

7


Figure 5: Distributions of displacements on wavelength scale due to CCD geometry for RGS2 measured for each individual CCD.

8


Figure 6: Displacements for all observations measured on each individual CCD for RGS2.

9


Figure 7: Displacement on CCD #5 against displacements measured on all other CCDs.

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ABDor 0123720201 shift2 CCD 4 (param 151 from -5 to 5 in 100) 31/3/2008 1.0342â104 1.0344â104 1.0346â104 1.0348â104 1.034â10 -4 -2 0 2 Parameter: shift2 (mAngstrom) 4
dcoia 31-Mar-2008 12:09 4

ABDor 0123720201 shift2 CCD 5 (param 181 from 0 to 10 in 100) 28/3/2008

Statistic: C-Statistic

1.0344â10

4

1.0346â10

4

1.034â10

4

1.0342â104

Statistic: C-Statistic

0

2

4 6 Parameter: shift2 (mAngstrom)

8

10
dcoia 31-Mar-2008 12:43

ABDor 0123720201 shift2 CCD 6 (param 231 from 0 to 10) 31/3/2008

Statistic: C-Statistic

1.034â104 0

1.0345â10

4

1.035â104

2

4 6 Parameter: shift2 (mAngstrom)

8

10
dcoia 31-Mar-2008 12:03

Figure 8: Examples of C-statistic on CCD #4, 5, 6 for observation of AB Doradus 0123720202.

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5

Conclusions
· The mean discrepancies b etween the lab oratory and observed wavelengths of bright coronal lines are 2.44 m° and 6.93 m° for RGS1 and RGS2 resp ectively; A A · The angles of incidence for RGS1 and RGS2 can b e adjusted so that these means b ecome 0 as follows: ­ RGS1: from 1.576191 to 1.576519 ­ RGS2: from 1.576191 to 1.577122


· No corrections to individual CCD geometries are required at this stage; · The measured p osition of the OVI I line in RGS1 is consistent with the lab oratory value b oth b efore and after this adjustement althought the uncertainty quoted in ATOMDB is surprisingly large at 7 m°; A · The test CCF XMM MISCDATA 9999.CCF is delivered with this rep ort.

6

References

Coia D. & Pollock A.M.T. 2007, The RGS wavelength scale Erd C. 2001, First results from the monitoring of the RGS wavelength scale, XMM-SOC-CAL-TN-0020

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7

App endix

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Table 3: Observations of MKN421. Columns are: revolution; ID and date of observation, displacements in the disp ersion and cross-disp ersion directions and count rates for b oth RGS1 and RGS2. O ID 0099280101 0099280201 0136540101 0136540201 0153950601 0153950701 0153950801 0136540301 0136540401 0136540501 0136540601 0136540701 0136540801 0136540901 0136541001 0136541101 0136541201 0158970101 0158970201 0158970701 0150498701 0162960101 0158971201 0153951201 0153951301 0158971301 0411080301 0411080701 0411080801 0510610201 0411081301 0411081401 0411081501 0411081601 0510610101 0411081701 0411081901 0411082001 0411082101 0411082201 0411082301 0411082401 0411082501 BS Date 2000-05-25 2000-11-01 2001-05-08 2001-05-08 2002-05-04 2002-05-05 2002-05-05 2002-11-04 2002-11-04 2002-11-04 2002-11-04 2002-11-14 2002-11-14 2002-11-15 2002-12-01 2002-12-02 2002-12-02 2003-06-01 2003-06-02 2003-06-07 2003-11-14 2003-12-10 2004-05-06 2005-11-07 2005-11-07 2005-11-09 2006-05-28 2006-12-05 2006-12-05 2007-05-08 2007-05-10 2007-05-10 2007-05-10 2007-05-10 2007-05-08 2007-05-10 2007-11-19 2007-11-19 2007-11-19 2007-11-20 2007-11-20 2007-11-21 2007-11-21 (") +3.7 -6.3 +3.1 +3.2 -147.9 -145.3 -152.5 -3.7 -4.6 -1.5 -3.1 -0.2 -10.9 -4.8 -2.2 -11.7 -4.0 -5.7 -6.5 -4.5 +4.6 +1.8 +3.0 +4.9 -1.3 -1.1 -2.5 -0.3 -22.5 +1.4 +2.6 -29.7 -17.6 +14.8 +1.5 +23.0 -0.9 -30.9 -18.2 +13.8 +24.8 -4.1 +4.2 MKN421 RGS1 (") count rate (s -1 ) -14.2 14.739 ± 0.024 -3.1 5.912 ± 0.012 -3.7 13.077 ± 0.019 -4.2 11.910 ± 0.069 -0.2 6.140 ± 0.012 +120.9 3.749 ± 0.014 -118.6 4.314 ± 0.014 -7.4 13.049 ± 0.024 -5.9 15.269 ± 0.026 +113.4 18.835 ± 0.029 -129.2 18.421 ± 0.029 -5.8 15.443 ± 0.042 +115.7 17.645 ± 0.040 -128.2 16.069 ± 0.037 -2.6 9.163 ± 0.011 +119.5 10.052 ± 0.029 -124.6 11.104 ± 0.032 -3.4 10.073 ± 0.015 -2.4 10.770 ± 0.035 -3.5 5.719 ± 0.011 -10.6 22.461 ± 0.021 -6.1 11.032 ± 0.019 -5.0 21.963 ± 0.018 +113.6 19.767 ± 0.045 -127.0 19.404 ± 0.046 -1.9 21.853 ± 0.019 -3.2 24.879 ± 0.023 -2.4 9.120 ± 0.022 -6.1 8.558 ± 0.028 -6.8 8.497 ± 0.029 -4.5 7.629 ± 0.021 -4.7 8.189 ± 0.031 -5.2 8.554 ± 0.031 -4.5 8.273 ± 0.031 -6.7 8.053 ± 0.018 -6.5 8.201 ± 0.036 -4.0 11.985 ± 0.025 -2.9 13.383 ± 0.038 -4.5 13.147 ± 0.034 -3.3 12.696 ± 0.038 -5.5 12.789 ± 0.032 -123.2 10.965 ± 0.035 +115.6 12.640 ± 0.038 RGS2 (") count rate (s-1 ) -3.3 13.867 ± 0.024 +7.8 6.290 ± 0.013 +7.1 14.093 ± 0.020 +6.7 12.822 ± 0.078 +10.2 6.178 ± 0.013 +131.5 3.622 ± 0.013 -108.1 4.453 ± 0.014 +3.4 13.984 ± 0.025 +4.9 17.007 ± 0.027 +124.3 21.158 ± 0.031 -118.3 22.078 ± 0.032 +5.0 18.392 ± 0.028 +126.6 19.146 ± 0.042 -117.2 18.567 ± 0.040 +8.2 9.916 ± 0.012 +130.4 10.412 ± 0.030 -113.7 12.445 ± 0.033 +7.5 10.736 ± 0.016 +8.4 11.488 ± 0.036 +7.3 6.040 ± 0.011 +0.2 24.541 ± 0.022 +4.7 11.950 ± 0.020 +5.8 24.544 ± 0.019 +124.6 21.346 ± 0.047 -116.0 21.613 ± 0.049 +8.9 23.730 ± 0.020 +7.6 27.586 ± 0.024 +8.5 9.661 ± 0.023 +4.7 9.081 ± 0.029 +4.2 8.782 ± 0.020 +6.3 8.057 ± 0.021 +6.1 8.618 ± 0.032 +5.6 9.000 ± 0.032 +6.4 8.720 ± 0.032 +4.1 8.411 ± 0.026 +4.4 8.724 ± 0.038 +6.8 12.369 ± 0.026 +7.8 13.756 ± 0.038 +6.3 13.532 ± 0.034 +7.5 13.064 ± 0.039 +5.4 12.921 ± 0.032 -112.2 11.400 ± 0.036 +126.6 12.926 ± 0.038

REV 0084 0165 0259 0259 0440 0440 0440 0532 0532 0532 0532 0537 0537 0537 0546 0546 0546 0637 0637 0640 0720 0733 0807 1083 1083 1084 1183 1279 1279 1356 1357 1357 1357 1357 1357 1358 1454 1454 1454 1454 1455 1455 1455

(") +15.1 +4.8 +14.4 +14.5 -136.4 -134.2 -140.7 +7.5 +6.7 +9.4 +8.5 +11.1 +0.0 +6.8 +9.1 -0.7 +7.6 +5.5 +4.8 +6.7 +15.9 +13.1 +14.3 +15.9 +10.3 +10.1 +8.7 +10.9 -11.1 +12.8 +13.9 -18.3 -6.3 +26.1 +12.9 +34.3 +10.4 -19.5 -6.8 +25.2 +36.1 +7.6 +15.2

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Table 4: Observations of PKS2155-304. Columns are: revolution; ID and date of observation, displacements in the disp ersion and cross-disp ersion directions and count rates for b oth RGS1 and RGS2. O ID 0124930101 0124930201 0080940101 0080940301 0080940401 0080940501 0124930301 0124930501 0124930601 0158960101 0158960901 0158961001 0158961101 0158961301 0158961401 0411780101 0411780201 BS Date 2000-05-30 2000-05-31 2000-11-19 2000-11-20 2000-11-19 2000-11-21 2001-11-30 2002-05-24 2002-11-29 2003-11-23 2004-11-22 2004-11-23 2005-05-12 2005-11-30 2006-05-01 2006-11-07 2007-04-22 (") +17.1 +11.5 +6.5 +6.7 +6.5 +6.6 -12.4 +2.0 -1.8 +0.5 +0.9 +3.0 +0.5 -2.1 -0.3 +3.2 +5.8 PKS2155-304 RGS1 (") count rate (s -1 ) -6.3 4.247 ± 0.008 -8.1 4.223 ± 0.008 -7.4 3.188 ± 0.007 -15.4 2.690 ± 0.006 -7.4 4.304 ± 0.021 -20.4 2.987 ± 0.027 -9.7 6.253 ± 0.008 -5.9 2.562 ± 0.005 -2.0 1.990 ± 0.004 -5.1 1.699 ± 0.008 -5.8 1.897 ± 0.008 -5.2 2.414 ± 0.008 -3.3 3.108 ± 0.011 -0.4 3.384 ± 0.007 -6.1 1.261 ± 0.004 -8.7 1.782 ± 0.004 -13.9 3.268 ± 0.007 RGS2 (") count rate (s-1 ) +4.5 3.998 ± 0.008 +2.7 3.919 ± 0.007 +3.4 3.354 ± 0.007 -4.4 2.777 ± 0.007 +3.4 4.550 ± 0.022 -9.5 3.112 ± 0.027 +1.1 6.367 ± 0.008 +4.9 2.664 ± 0.005 +8.9 2.209 ± 0.004 +5.8 1.751 ± 0.008 +5.0 1.963 ± 0.008 +5.6 2.513 ± 0.008 +7.5 3.275 ± 0.011 +10.5 3.524 ± 0.007 +4.7 1.347 ± 0.004 +2.1 1.898 ± 0.004 -2.9 3.404 ± 0.007

REV 0087 0087 0174 0174 0174 0174 0362 0450 0545 0724 0908 0908 0993 1095 1170 1265 1348

(") +28.4 +22.8 +17.9 +18.1 +17.9 +18.0 -1.1 +13.4 +9.4 +11.8 +12.2 +14.3 +11.9 +9.2 +11.0 +14.6 +17.2

15