Improved data of solar spectral irradiance from 0.33 to 1.25μ

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<ul><li><p>IMPROVED DATA OF SOLAR SPECTRAL IRRADIANCE </p><p>FROM 0.33 TO 1.25tt* </p><p>HEINZ NECKEL </p><p>Hamburger Sternwarte, Hamburg-Bergedorf, F,R.G. </p><p>and </p><p>DIETRICH LABS </p><p>Landessternwarte K6nigstuhl, Heidelberg, F.R.G. </p><p>Abstract. The conversion of our centre of disk intensities published in 1968/70 into mean disk intensities has been repeated, using more accurate data for the centre-to-limb variation of both continuous radiation and strong absorption lines. </p><p>The random observational mean error of the new irradiance data very likely is not larger than 1.5% in the UV and not larger than 1% in the visible and infrared. Comparison with the fluxes of Sun-like stars observed by Hardorp (1980) confirms these errors and seems to exclude the possibility of a systematic, wavelength-dependent scale error which would correspond to a temperature difference larger than 50 K. </p><p>The resulting integral value of the irradiance between 0.33 and 1.25 Ix is 1.060, the corresponding value of the solar constant lies between 1.368 and 1.377 kW m -2. </p><p>1. Introduction </p><p>With respect to the divers plans to search for variations in the solar irradiance, it may be profitable to have a base from which to start and which is as solid as </p><p>possible. Therefore we do not hesitate to represent here improved data of the </p><p>irradiance, even if hereby observations are involved, which were made nearly 20 years ago. </p><p>In the early 60's we measured absolute intensities at the centre of the solar disk </p><p>in spectral bands 20 .0 /20 .5 /~ wide, using an almost rectangular apparatus profile. </p><p>The corresponding intensity integrals we called X (Labs and Neckel, 1962, 1963, 1967): </p><p>Ai+AA/2 </p><p>f AA=20.5 /~ for A i - -4001.05 /~, Zi J I , dA ' AA=20.0 /~ for A i - -&gt;4020.0~. (1) Ai-AA/2 </p><p>Later on (Labs and Neckel, 1968, 1970) we used these X-integrals to derive the </p><p>corresponding integrals of the mean intensity (4,) and of the irradiance (0), using the relations </p><p>. . . . . . ) </p><p>ffOi = 2'i~i i = ~i \ I (0)/co,t [ 1 -- T'lcentreJ I (2) </p><p>Oi = 6.800 X 10 -s &amp;i, (3) </p><p>(F/I(O))cont is the ratio of mean to central intensity as derived from centre-to- l imb </p><p>* Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16-19 September 1980, Scheveningen, The Netherlands. </p><p>Solar Physics "/4 (1981) 231-249. 0038-0938/81/0741-0231 $02.85. Copyright (~ 1981 by D. ReideI Publishing Co., Dordrecht, Holland, and Boston, U.S.A. </p></li><li><p>232 HEINZ NECKEL AND DIETR ICH LABS </p><p>observations of the continuous radiation (in UV of 'window'-intensities!), and the r/'s are the line blocking coefficients for the 20 ~k bands for disk-averaged radiation (irradiance) and central intensity, respectively. </p><p>Since Equation (2) has often been incorrectly interpreted, it should be empha- sized, that it does not mean a simple derivation of the irradiance from a continuum- curve and line blocking data. The basic observed quantity ~ includes a priori all lines, and the third factor takes into account just the centre to limb variation of their strengths. </p><p>Most recently our irradiance data were used by Hardorp (1980) to compare them with the flux distribution of Sun-like stars. Thereby Hardorp found some differences between stellar and solar radiation, which demanded a clarification whether being real or not. </p><p>Therefore we checked the observed central intensities ~ as well as the data used to derive the corresponding irradiance values. With respect to the three factors forming the right-hand side of Equation (2), the result may be summarized as follows: </p><p>(1) Our observed ~ 's are even more accurate than we have quoted so far. (2) For the ratio F/I(O) of mean to central intensity more reliable values are now </p><p>derivable from the recent centre-to-l imb observations of Pierce and Slaughter (1977a, b). </p><p>(3) The former correcting factors taking into account the centre-to-l imb variation of the r/'s were erroneous for spectral bands with strong lines. </p><p>2. Random Errors of Central Intensity Integrals </p><p>While tests for possible systematic errors of our observations will be given in Sections 6 and 7, here we deal only with the random observational error, which can be infered from the agreement of repeated observations, but also - and more conclusively - from the scatter around an appropriate smoothing curve. </p><p>Since the Z 's themselves don't follow any smoothed curve if plotted against wavelength, the most objective way to exhibit their accuracy is to plot instead the resulting continuum intensities or the related radiation temperatures. This was done in Figure 1. </p><p>For A &lt; 0.66tx, T was derived from the window-intensities in Z-cal ibrated atlases (Labs and Neckel, 1968, 1970, Table 5A), for A &gt;0.66p~ from the quotients .~ / (1 - - r lcentre), where "]']centre was either obtained from summation of the equivalent widths given by Moore et al. (1966) or - for A &gt; 0.877jx - deduced from the atlas of Delbouille and Roland (1963). The occasional inclusion of terrestrial lines, which so far had been neglected, has now been taken into account. The resulting tem- peratures can be smoothed rather precisely by two r.m.s, parabolas: </p><p>A--3999.9A: T=6046+ 2021(A-0 .8699) 2 . (5) </p></li><li><p>60</p><p>0 </p><p>;50</p><p>0 </p><p>40</p><p>0 </p><p>~300 </p><p>~20</p><p>0 </p><p>~00</p><p>~00</p><p>0 </p><p>: T</p><p>(X,l</p><p>win</p><p>do</p><p>w) </p><p>: T</p><p>(X</p><p>.~</p><p>) </p><p>/" .':.</p><p>7". </p><p>./ </p><p>z 2.</p><p>0~ </p><p>I *-</p><p> 1.6 </p><p>% </p><p>24 p</p><p>ts. </p><p>28</p><p> pts</p><p>. </p><p>i I </p><p>L3 </p><p>0.4</p><p>or </p><p>k </p><p> 0.6</p><p>6t/ </p><p>, 0</p><p>.39</p><p> IX :</p><p> T </p><p>,b."</p><p> ":,</p><p>"~52</p><p>:~ </p><p>.. </p><p>9 '- .</p><p>.~.~</p><p> ",.</p><p>..'~.. </p><p>~ </p><p>(0) </p><p>r =</p><p> 62</p><p>06</p><p> 9 2</p><p>38</p><p>39</p><p>1(x</p><p>-0.3</p><p>49</p><p>8) z</p><p>= 6</p><p>04</p><p>6 </p><p> 20</p><p>21 (</p><p>),-0</p><p>.86</p><p>99</p><p>)2 </p><p>9 0 </p><p>o </p><p>jJ </p><p>/ J </p><p>e </p><p>o / </p><p>*-1</p><p>.0~</p><p> [ </p><p>*-1.</p><p>2~ </p><p>1*-</p><p>1.3</p><p>% [</p><p> *-</p><p> 1.0</p><p> % </p><p>3O</p><p>pts</p><p>. 3</p><p>8 p</p><p>ts. </p><p>36</p><p>pts</p><p>. 2</p><p>6 p</p><p>ts. </p><p>I . </p><p>L I </p><p>i I </p><p>i I </p><p>, l </p><p>~ I </p><p>. 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'</p><p>Ob</p><p>se</p><p>rve</p><p>d' </p><p>co</p><p>nti</p><p>nu</p><p>um</p><p> in</p><p> up</p><p>pe</p><p>r pa</p><p>rt: W</p><p>ind</p><p>ow</p><p>-in</p><p>ten</p><p>siti</p><p>es </p><p>(La</p><p>bs </p><p>an</p><p>d Ne</p><p>cke</p><p>l, 19</p><p>70</p><p>, Tabl~</p><p> 5A</p><p>) ob</p><p>tain</p><p>ed</p><p> fr</p><p>om</p><p> X-c</p><p>ali</p><p>bra</p><p>ted</p><p> a</p><p>tla</p><p>ses;</p><p> in</p><p> low</p><p>er p</p><p>art</p><p>: Inte</p><p>nsi</p><p>tie</p><p>s resu</p><p>ltin</p><p>g </p><p>fro</p><p>m th</p><p>e X's</p><p>, aft</p><p>er c</p><p>orr</p><p>ecti</p><p>on</p><p> fo</p><p>r lin</p><p>e ab</p><p>sorp</p><p>tio</p><p>n, </p><p>wh</p><p>ich</p><p> is ta</p><p>ke</p><p>n </p><p>he</p><p>re as t</p><p>he</p><p> sum</p><p> of e</p><p>qu</p><p>iva</p><p>len</p><p>t wid</p><p>ths o</p><p>f all </p><p>lin</p><p>es i</p><p>nclu</p><p>de</p><p>d in t</p><p>he</p><p> 20</p><p> A-b</p><p>an</p><p>ds (=</p><p>[Wz]</p><p>). Fo</p><p>r po</p><p>ints</p><p> wit</p><p>hin</p><p> the</p><p> ma</p><p>rke</p><p>d sp</p><p>ectr</p><p>al re</p><p>gio</p><p>ns m</p><p>ea</p><p>n dif</p><p>fere</p><p>nce</p><p>s ([v]</p><p>/n) a</p><p>nd</p><p> st</p><p>an</p><p>da</p><p>rd </p><p>de</p><p>via</p><p>tio</p><p>ns (~</p><p>/[(v</p><p>- ~)2</p><p>]/(n</p><p> -1))</p><p> are</p><p> giv</p><p>en</p><p>. </p><p>4~</p><p>N </p><p>Z </p><p>m </p><p>&gt; </p><p>z ~7 </p><p>N </p><p>t~ </p></li><li><p>IMPROVED DATA OF SOLAR SPECTRAL IRRADIANCE 235 </p><p>The corresponding standard deviations of the intensities are given at the bottom of the figure separately for 6 spectral subdivisions (e =~/~-] /n , n =number of points). They are - of course - only upper limits for the errors of the X's: (1) They include for h &lt; 0.661x the errors of the atlas calibration and of the read-off of the window intensities as well as the intrinsic scatter of the window intensities, and for h &gt; 0.661x the errors of the equivalent widths; (2) very likely the r.m.s.-parabolas do not represent the real solar continuum. </p><p>The contribution of the window errors becomes evident in Figure 2. Here we plotted the deviations of the observed continuum intensities from the smoothed intensity curve, in the upper part for the window intensities (same value as in Figure 1), in the lower part for the values resulting from the X's and the sum of equivalent widths (for h &gt; 0.66~ same values as in Figure 1). </p><p>For wavelengths below H/3 the sum of the equivalent widths obviously does not yield reliable line blocking coefficients, but above H/3 the scatter is significantly smaller in the lower than in the upper part. </p><p>Disregarding the noticeable step at 0.61 ~x, below 0.661x the scatter is characterized by a mean error of only +0.6%, but which still includes the errors of the equivalent widths. So it can be taken as a confirmation of the error derived for the average ratio 2e/(~Xar, p reflectivity of collimating mirror) obtained from repeated observations at the same wavelength: 0.3 to 0.7% in the visible and infrared (Labs and Neckel, 1967). </p><p>The reason for the step, which is detectable also in the upper part, could not be found. It may be due to a fault in our observations, or in the recordings of the Utrecht atlas, or may be a real feature. </p><p>After all it seems to be pretty sure, that at least in the visible and infrared the random observational error of the s is not larger and may be even smaller than +1.0%. </p><p>3. Ratio of Mean to Central Intensity for the Continuum </p><p>Next let us consider the situation for the second factor in Equation (2), (F/I(O))cont. In Figure 3 we plotted the values which result from the centre-to-l imb variations as observed by Pierce and Slaughter (1977a, b), as well as our former values, which were based mainly on the data published by David and Elste (1962). Since Pierce and Slaughter tabulated the coefficients for the fifth order fit of the CLV-curves, </p><p>I (0 ) / I (0 ) = A +B cos 0 + C cos 2 0 +D cos 3 0 +E COS 4 Z~ q +F cos 5 0 , </p><p>(6) the corresponding F/1-ratios are easily obtained from </p><p>F / I = 2(A/2 + B/3 + C/4 + D~ 5 + 17./6 + F/7) . (7) </p><p>Three types of differences are very obvious: </p><p>(1) For shorter wavelengths the new data are systematically higher. </p></li><li><p>F/I</p><p>0.9</p><p>0.8</p><p>0.7</p><p>I ~</p><p> ~</p><p>.~io</p><p>. 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(1</p><p>) De</p><p>riv</p><p>ed</p><p> ac</p><p>co</p><p>rdin</p><p>g </p><p>to E</p><p>qu</p><p>ati</p><p>on</p><p> (7) f</p><p>rom</p><p> the</p><p> lim</p><p>b da</p><p>rke</p><p>nin</p><p>g </p><p>da</p><p>ta of P</p><p>ierc</p><p>e an</p><p>d Sla</p><p>ug</p><p>hte</p><p>r (1</p><p>97</p><p>7a</p><p>, b);</p><p> (2) v</p><p>alu</p><p>es w</p><p>hic</p><p>h en</p><p>tere</p><p>d </p><p>into</p><p> ou</p><p>r fo</p><p>rme</p><p>r de</p><p>riv</p><p>ati</p><p>on</p><p> o</p><p>f so</p><p>lar ir</p><p>rad</p><p>ian</p><p>ce</p><p> (w</p><p>ith</p><p> two</p><p> pu</p><p>nc</p><p>hin</p><p>g </p><p>err</p><p>ors</p><p> ne</p><p>ar A</p><p> = 0</p><p>.59</p><p>p,)</p><p>. Th</p><p>e cu</p><p>rve</p><p>s sm</p><p>oo</p><p>thin</p><p>g </p><p>the</p><p> da</p><p>ta of P</p><p>ierc</p><p>e </p><p>an</p><p>d S</p><p>lau</p><p>gh</p><p>ter are</p><p> sec</p><p>on</p><p>d ord</p><p>er r</p><p>,m.s</p><p>, fits</p><p> for </p><p>the</p><p> inte</p><p>rva</p><p>ls ma</p><p>rke</p><p>d by</p><p> sh</p><p>ort</p><p> ve</p><p>rtic</p><p>al li</p><p>ne</p><p>s. Th</p><p>e r</p><p>esu</p><p>ltin</p><p>g sta</p><p>nd</p><p>ard</p><p> d</p><p>ev</p><p>iati</p><p>on</p><p>s are</p><p> giv</p><p>en</p><p> for </p><p>ea</p><p>ch</p><p> inte</p><p>rva</p><p>l. </p><p>I'O</p><p> e,</p><p> a9</p></li><li><p>IMPROVED DATA OF SOLAR SPECTRAL IRRADIANCE 237 </p><p>(2) Since in the vicinity of the Balmer limit no data had been available, we had </p><p>adopted a much too ideal Balmer ' jump'. (3) Between 0.57 and 0.601x the computer had been fed with faulty data due to </p><p>incorrect punching. (Fortunately, this error has stolen just into Table 4 of our 1968 paper, but did not enter into any other data!) </p><p>For our new reduction, the proper F/I-values were taken from second order curves fitted to the new F/I data. The random errors of these r.m.s, curves are neglectable. </p><p>4. Correction for Centre-to-Limb Variation of Fraunhofer Lines </p><p>The third and last factor in Equation (2), {(1--T/disk)/(1--T/centre)}i , is the most problematic one. The plague is not the T/centre -- it can be derived with high reliability for each of our spectral bands - but the corresponding T/disk. For its derivation we profited from the facts, that for many lines equivalent widths are known not only for the centre of the disk, but also for the limb region at # = cos O = 0.3, and that the CLV of the line blocked radiation can be approximated with sufficient accuracy </p><p>by </p><p>T/cos ~ = T/centre + rn(1 --cos O). (8) </p><p>Equation (8) implies that </p><p>T/disk - - T/Tcentre = k (T/, =o.3 - T /cent re ) , (9 ) </p><p>where k does not depend on T/centre or m at all, but instead is a unique function of the limb darkening coefficients: </p><p>1 (1 A/3+B/4+C/5+D/6+E/7+F/8~ k = 1 -0 .3 -A/2+B/3+C/4+D/5+E/6+F/7] ' (10) </p><p>k increases from 0.38 at 0.331x to 0.44 at 1.25tx. In deriving our former irradiance tables, we had not only taken k as a constant </p><p>(=0.6), but also had neglected that the fraction of radiation blocked by 'strong' lines T/s exhibits another CLV than the fraction T/n blocked by 'normal' lines, for which the average ratio T/~=0.3/T/cnentre is 1.05 (Labs and Neckel, 1968). </p><p>As a consequence, for bands affected by strong lines such as H and K of Ca H and the hydrogen lines - or their wings - the obtained irradiance data were wrong. </p><p>In our new reduction all significant strong lines, for which relevant data (CLV of profiles, wing intensities etc.) are available (David, 1961; de Jager, 1952; Allen, 1973), were separated from the bulk of the 'normal' lines and treated individually. For this procedure the third factor of Equation (2) has to be written - applying Equation (9) - as </p><p>1 - - T/dis k = 1 - k T/t'L =0"3 - - T /centre - - 1 - - k 0"05 T/cnentre q- sT /Sent re (11) 1 - T /centre 1 - - T /centre 1 - - (T/cnentre -~- T /Sent re ) ' </p></li><li><p>238 HEINZ NECKEL AND DIETRICH LABS </p><p>where s = (TlT~=0.3/T~Sentre) - - 1. It usually was found to lie between the limits -0.68 and +0.14. Only for bands, which are affected by the wings of the strong H-lines

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