Is the solar spectrum latitude dependent? An investigation with SST/TRIPPEL
Dan Kiselman, Tiago Pereira, Bengt Gustafsson, Martin Asplund, Jorge Meléndez, Kai Langhans
AAstronomy & Astrophysics manuscript no. sun˙latitudes c (cid:13)
ESO 2018November 3, 2018
Is the solar spectrum latitude dependent?
An investigation with SST/TRIPPEL
Dan Kiselman , , Tiago M. D. Pereira (cid:63) , Bengt Gustafsson , , Martin Asplund , , Jorge Mel´endez , and KaiLanghans , (cid:63)(cid:63) The Institute for Solar Physics of the Royal Swedish Academy of Sciences, AlbaNova University Centre, SE-106 91 Stockholm,Sweden Stockholm Observatory, Department of Astronomy, Stockholm University, AlbaNova University Centre, SE-106 91 Stockholm,Sweden Research School of Astronomy and Astrophysics, Australian National University, Cotter Rd., Weston, ACT 2611, Australia Department of Physics and Astronomy, Uppsala University, Box 515, SE-751 20 Uppsala, Sweden Nordita, AlbaNova University Centre, SE-106 91 Stockholm, Sweden Max-Planck-Institut f¨ur Astrophysik, Postfach 1317, 85741, Garching b. M¨unchen, Germany Departamento de Astronomia do IAG / USP, Universidade de S˜ao Paulo, Rua Mat˜ao 1226, S˜ao Paulo, 05508-900, SP, BrazilReceived / Accepted
ABSTRACT
Context.
In studies of the solar spectrum relative to spectra of solar twin stars, it has been found that the chemical composition ofthe Sun seems to depart systematically from those of the twins. One possible explanation could be that the e ff ect is due to the specialaspect angle of the Sun when observed from Earth, as compared with the aspect angles of the twins. Thus, a latitude dependence ofthe solar spectrum, even with the heliocentric angle constant, could lead to e ff ects of the type observed. Aims.
We explore a possible variation in the strength of certain spectral lines, used in the comparisons between the composition ofthe Sun and the twins, at loci on the solar disk with di ff erent latitudes but at constant heliocentric angle. Methods.
We use the TRIPPEL spectrograph at the Swedish 1-m Solar Telescope on La Palma to record spectra in five spectralregions in order to compare di ff erent locations on the solar disk at a heliocentric angle of 45 ◦ . Equivalent widths and other parametersare measured for fifteen di ff erent lines representing nine atomic species. Spectra acquired at di ff erent times are used in averaging theline parameters for each line and observing position. Results.
The relative variations in equivalent widths at the equator and at solar latitude ∼ ◦ are found to be less than 1 .
5% for allspectral lines studied. Translated to elemental abundances as they would be measured from a terrestrial and a hypothetical pole-onobserver, the di ff erence is estimated to be within 0.005 dex in all cases. Conclusions.
It is very unlikely that latitude e ff ects could cause the reported abundance di ff erence between the Sun and the solartwins. The accuracy obtainable in measurements of small di ff erences in spectral line strengths between di ff erent solar disk positionsis very high, and can be exploited in studies, e.g. of weak magnetic fields or e ff ects of solar activity on atmospheric structure. Key words.
Sun: abundances – Sun: atmosphere – Sun: spectrum – techniques: spectroscopic
1. Introduction
In recent studies it has been found that the chemical composi-tion of the Sun, as compared with those of very similar stars,so-called solar twins, is systematically di ff erent: the Sun is com-paratively less rich in refractories, i.e. elements that easily con-densed to solids for instance in the solar protoplanetary nebula,than in volatiles (Mel´endez et al. 2009; Ram´ırez et al. 2009).The range of the e ff ect is about 20% for volatiles as comparedwith refractories. Several possible explanations for this interest-ing phenomenon have been discussed (see Mel´endez et al. 2009;Gustafsson et al. 2010), including cleansing of the protoplane-tary disk by planetesimal formation. A more mundane explana-tion could be an obvious selection e ff ect: in Earth-based studiesthe Sun is by necessity observed from a position close to the Send o ff print requests to : Dan Kiselman, e-mail: [email protected] (cid:63) Current Address: NASA ARC, Mail Stop 245-3, P.O. Box 1,Mo ff ett Field, CA 94035, USA (cid:63)(cid:63) Current address: Gothmunder Weg 8, 23568 L¨ubeck, Germany solar equatorial plane. The solar twins, on the other hand, arepresumably observed with aspect angles randomly distributedwith respect to their rotation axes. Thus, if the solar spectrum,integrated across the disk, for some reason were somewhat dif-ferent as seen from a position far from the equatorial plane, thedi ff erences interpreted as abundance di ff erences might have thisexplanation instead. An empirical way of exploring this is toobserve solar photospheric spectra at di ff erent disk positions,though with a common angular distance from the disk centreso that the first-order centre-to-limb variations can be directlycompensated for. Here, such a study is presented.Studies of centre-to-limb variation of the solar spectrum havebeen pursued for more than a century (cf. Hastings 1873; Hale &Adams 1907) Some observational studies have been devoted tothe question whether there are any di ff erences between spectrafrom regions along the solar equator as compared with along ameridian. These studies have mostly been concentrated towardsvariations in line shifts and line shapes (bisectors) (e.g. Caccinet al. 1976, 1978; Beckers & Taylor 1980; Brandt & Schroeter1982; Andersen 1984), variations that have generally been inter- a r X i v : . [ a s t r o - ph . S R ] A ug iselman et al.: Is the solar spectrum latitude dependent? preted as variations in the photospheric velocity fields with lati-tude. There are few studies of the variations, or constancy, in theline strengths (equivalent widths). One notable example is thestudy by Rodr´ıguez Hidalgo et al. (1994) of the variation alongthe equator and a meridian of four lines of C i , Si i , Mn i and Fe i .In addition to studies of line widths and bisectors, these authorsalso included measurements of the variations of the equivalentwidths. For Si i , Mn i and Fe i lines they found the lines to be afew percent weaker along the equator than along the meridian atgiven µ ≈ .
6, while the C i line showed less variation. Althoughnot very pronounced this tendency has the direction needed toexplain the apparently low ratio of refractories / volatiles in theSun compared to the twins. However, three of the four spectrallines studied by Rodr´ıguez Hidalgo et al. are on the flat partof the curve of growth, while the lines used in the analyses ofMel´endez et al. (2009) and Ram´ırez et al. (2009) are almost allon the linear part with line strengths insensitive to the velocityfields (among the lines of Mel´endez et al. is C i ff ects on abun-dances derived from solar flux spectra at di ff erent aspect angles.Instead, a direct comparison of line strengths of the mostly weaklines used in the Sun–twin abundance comparison is needed.It is clear from the previous work on the latitude dependenceof the solar spectrum that considerable care must be exercisedin positioning the spectrometer slit and averaging properly overgranulation and other inhomogeneities. A strictly di ff erential ap-proach must be adopted, in order to minimise the e ff ects of straylight and other instrumental issues.
2. Observations
The observations were made with the Swedish 1-m SolarTelescope (SST) on La Palma (Scharmer et al. 2003) employ-ing the TRIPPEL spectrograph during the period of 3–15 May2010. Since this instrument has not yet been subject to a detaileddescription in the literature, we use this opportunity to give asummary of its properties.
The TRI-Port Polarimetric Echelle-Littrow (TRIPPEL) spectro-graph had the following design goals: – allow simultaneous observations at three separate wave-lengths – in principle exploit the full spatial resolution of the SST – wavelength range about 380 nm – 1100 nm – good polarimetric properties – moderate (for a solar spectrometer) spectral resolution ( R ≈ , / Table 1.
Some properties of the TRIPPEL spectrograph
Slit width 25 µ m ( ≈ . (cid:48)(cid:48) − Blaze angle 63.43 ◦ Grating size 154 ×
306 mmFocal length 1500 mmLittrow lens aperture 135 mm slit plate can be rotated around a vertical axis to allow the re-flected light to be directed towards slit-jaw imagers. It can alsobe rotated around an horizontal axis orthogonal to the opticalaxis to adjust the tilt of the slit relative to the dispersion direc-tion. There are two movable jaws behind the slit plate that can beused to cover parts of the slit to minimise the amount of light en-tering the spectrograph, and to allow dark areas on the spectrumcamera for reference.The Littrow doublet lens is mounted on a translational stage.To get the required large di ff raction-limited field-of-view, ameniscus field lens is placed close to the focal plane so that thelight passes twice through it. The optical design fixes the Littrowlens position relative to this field lens. The translational stage isthus only used when checking the spectrograph focus and neverfor focusing the spectrograph cameras.The grating from Richardson Grating Laboratory has excel-lent polarization properties, with the maximum di ff erence be-tween S and P e ffi ciency being about 10 % in the visual region.The grating is mounted on a rotational stage with 0.01 ◦ settingprecision.Three silver-coated mirrors pick o ff light to the exit ports.For the two ports with horizontal light beams (designated A andB), the cameras are mounted on holders sliding on a rail of thesame type as is used for the SST imaging setups, thus allowingfreedom in camera choice. The third port (C), which has a ver-tical light beam, currently uses a special holder for a RedlakeMegaplus ii camera (ES1603).Apart from some image distortion caused by the correctorlens, TRIPPEL has an o ff -plane design which leads to curvatureof the spectral lines (smile) and also of the dispersion direction(keystone). The curvature over the typical CCD size is small,so the greatest e ff ect of the smile is to cause the spectral linesto tilt relative to the axis defined by the direction of the gratinggrooves. The slit is rotated about 3.5 ◦ from the vertical directionto partly compensate for this.Since all spectral orders fall on top of each other in the fo-cal plane, interference filters placed just in front of the CCDsare used to select the desired order. This also has the advantageof blocking straylight outside the filter passband. The transmis-sion profile of two-cavity filters typically has a base that is toowide to be practical, so three-cavity filters are used. Assuminga profile for a three-cavity interference filter, requiring that thetransmission at a distance of a full spectral range from the centralwavelength is 10 − of its peak value, and applying a significantmargin of safety, result in the filter widths in Table 2.The dispersion decreases with decreasing order and thus withincreasing wavelength. The theoretical spectral resolution is lim-ited by the slit width and so stays rather constant between di ff er-ent orders: it is between 1.1 and 1.4 km / s or R = λδλ ∼ Table 2.
Nominal TRIPPEL parameters at the wavelengths ofsome interesting lines.
Line λ fwhm n Bandpass dx / d λ W [nm] [nm] [km / s] [mm / nm] [nm]Ca ii i i i i ii Notes. fwhm : recommended width of a 3-cavity interference filter. n :spectral order. Bandpass: slit-limited. dx / d λ : dispersion. W : wavelengthcoverage for a 13.8 mm CCD (Megaplus 1.6). C AB
Fig. 1.
Schematic view of the TRIPPEL spectrograph as seenfrom above. Components from left to right: entrance slit, pick-o ff mirrors for ports A-C, field lens, Littrow doublet, grating.Spectral port A has a CCD camera with an interference filter.many combinations are possible, especially because some free-dom of camera movement in the dispersion direction is available.Table 2 lists some nominal instrumental parameters at thewavelengths of some interesting lines.The spectrograph is focused by pressing a perpendicular slitagainst the spectrograph slit. This creates a small rectangle thatis seen on the spectrum cameras as a very narrow spectrum. TheLittrow lens is then moved between two out-of-focus positionfor a range of camera positions. The camera position where thetwo lens positions create spectra of similar sharpness is taken asits focus position. With some training it is not di ffi cult to assessthe sharpness from the spectrum image displayed on the screen.The other crucial focusing, that of the solar image on thespectrograph slit, is done with a similar technique. But instead ofplacing a physical slit crossing the spectrograph slit, an image ofa slit is placed there by mounting a physical slit in the telescopefocus at the exit port of the vacuum system. The adaptive opticsis locked on a pinhole next to that slit. The wavefront sensor isthen adjusted (which leads to the image moving back and forth)until symmetry in the out-of-focus spectra is achieved.Finally, TRIPPEL allows some auxiliary instruments. Thewavefront sensor that controls the adaptive mirror and the cor-relation tracker camera are fed via a beamsplitter cube in frontof the slit. The reflective slit plate makes slit-jaw imaging possi-ble. For the current observations, we employed up to two slit-jaw cameras fed with reimaging optics. These cameras wereequipped with interference filters with central wavelengths closeto the spectral regions observed. The slit-jaw imaging was usedfor pointing control, and for keeping track of the seeing qualityand the light-intensity level. In the present study we have selected some spectral lines usedby Mel´endez et al. (2009) in their analysis of the Sun and solar
Table 3.
Spectral lines observed
Spectral Species
CWL E l Class region [nm] [eV]538 C i i i i i i i i i i i i i i i twins, ensuring that both refractories, volatiles, and intermedi-ate elements were represented and that as many lines as possi-ble were observable simultaneously. The spectral regions wereranked in priority and the setup was changed to the next set ofregions when enough data had been secured. Table 3 lists thelines observed and Table 4 the setup combinations used. Fig. 4shows plots of all the lines in their spectral context of our solarobservations. We assume that a latitude dependence of line equivalent widthsthat is strong enough to give a significant e ff ect in the flux spec-trum, must be present also at a moderate distance from solardisk centre. We choose a heliocentric distance of 45 degrees or µ = √ / ∼ .
71. For the solar meridian, this corresponds tothe point that is seen at the same µ for an observer in the eclipticplane and one that would observe the Sun pole-on. It is also closeto µ = /
3, which is where, according to the Eddington-Barbierrelations, the outgoing intensity spectrum should be characteris-tic of the flux spectrum and thus relevant for stellar observations.In order to decrease bias from north-south and east-west sys-tematic di ff erences, perhaps due to random activity patterns, weselected eight di ff erent position angles and named these pointsN, W, S, E, NW, SW, SE, and NE. To test the stability of theresults, the solar disk centre was observed frequently and inter-spersed with the µ = .
71 pointings. The solar latitudes of theobserved points are given in Table 4. The heliographic latitudeat the time of observations was approximately − ◦ .An observational sequence consisted of a series of pointingswith about 5 min spent at each. Before and after each sequenceflat fields were acquired. The sequence typically started at diskcentre and then going to all the eight µ = .
71 points, after whichdisk centre was observed again. All the time during observations,the Ca ii H imaging camera was used to make sure that the re-gions observed were quiet.After the first days of observations when inspection of thedata confirmed that the stability of the results was quite high, theintermediate points (NW, SW, SE, NE) were abolished from theobserving sequence, and only observations in the N, W, S, and Epositions, as well as the disk centre, were made.The first data sets were taken with fixed pointing. In or-der to increase the spatial sampling, a procedure where the slit
Table 4.
Observational setups and the number of data sets from each day used in the final analysis.
Port A Port C Port B DC N NW W SW S SE E NEDate − ◦ ◦ ◦ -3 ◦ − ◦ − ◦ − ◦ − ◦ ◦ ...
777 6 5 0 4 0 5 0 5 02010-05-14 768 ...
777 1 1 0 0 0 0 0 0 02010-05-15 869 ...
616 7 4 0 4 0 4 0 4 0
Notes.
DC is solar disk centre. Solar latitudes are given for each disk position.
Fig. 3.
Equivalent widths for all lines and data sets for µ = √ /
2. The deviation from the mean value from each data set is plottedin units of percent of the overall mean value and as a function of the time of day in hours when it was acquired. Symbols accordingto solar disk position. Asterisk: N, Plus: S, Triangle: W, Square: E.
Fig. 2. Temporal sequence of the Al i
783 nm line at disk center.The six quantities are plotted as function of time in minutes after10:00 UT. Equivalent width and continuum intensity are plottedas the deviation in percent from their respective mean values.Each point corresponds to the mean spectrum along the slit forone exposure.was scanning back and forth over 3 (cid:48)(cid:48) was implemented. This wasdone via the correlation tracker.
The data reduction procedures follow those described by Pereiraet al. (2009) with few deviations. Each data set requires a set offlat-field and dark exposures. The flat-fields are acquired by tak-ing many exposures while the telescope is scanning over a des-ignated area around disk centre that should be devoid of spots.For the current observations, a new procedure was used wherethe adaptive mirror of the SST is fed with random voltages inorder to smear out spatial structures even more. The darks areacquired with the light beam blocked close to the telescope exitwindow.The flat-field exposures are used to compute gain tables andmapping the geometric distortions of the spectrograms. They arealso used for wavelength calibration and scattered-light correc- tions in a procedure similar to that of Allende Prieto et al. (2004),thus comparing the observed spectra with the Fourier TransformSpectrometer at the McMath-Pierce Telescope (hereafter calledthe FTS atlas) of Brault & Neckel (1987).
Wavelength calibration is done by fitting line cores. The re-sulting wavelength scale is thus that of the FTS atlas.
Straylight inside the spectrograph is treated as a constantwhich is determined simultaneously with the spectral resolutionby a least-squares fit to the reference spectrum. Typical valuesare 5-6 % of the spectral continuum.
Telluric lines are identified and excluded from the fitting pro-cedures.Remaining artefacts in the continuum level – caused for ex-ample by residual components of fringes perpendicular to thedispersion direction– are also removed with the help of the ref-erence spectrum. The result is a set of parameters that maps theobserved disk-centre average spectrum to that of the atlas.The process described above produces spectrograms readyfor analysis. In the current work, we proceed by coadding eachspectrogram over the spatial direction to get a one-dimensionalspectrum that is the average spectrum under the spectrographslit. A number of these spectra are then coadded, thus forming anaverage also over time. Various quantities for the spectral lines ofinterest are then calculated from such average spectra:
Line cen-tre is the velocity di ff erence between the local line core and thecalibration spectra –it is thus relative to the FTS atlas; FWHM isthe usual full width at half maximum line depth;
Line asymmetry is the distance between the local line core and the line bisectorat half maximum line depth;
Equivalent widths are measured bydirect integration over a predefined interval which is centred onthe line core and thus follows any local Doppler shift – this isillustrated in Fig. 4.
Sources of errors and other e ff ects that would undermine the ob-servational strategy could be imprecise and non-reproduceablepointing, seeing, variations on the Sun from granulation, oscilla-tions, or activity, and instrumental drifts. Figures 5–7 illustratesthis by showing several disk-centre spectral profiles of threelines. The exact pointing of the telescope is of utmost importance sincethe equivalent width of the most sensitive lines in our sample –the C i lines at 711 nm – is predicted to change by 5% for a 1 (cid:48) shift( ∆ µ ≈ .
05) along the radius vector. We used the solar limbin four positions to calibrate the telescope pointing before eachsequence. After such a sequence we returned to the solar limbto estimate the drift in pointing during the sequence. Sometimesthis error was found to be small but it could typically amount to25 (cid:48)(cid:48) .The spectrograph slit is fixed in the laboratory frame andits orientation in the sky plane will change during the day. Noe ff ort was made to measure the orientation. The finite slit length( ∼ (cid:48)(cid:48) ) thus adds to the positional coverage of each spectrum,but does not a ff ect the mean position of the slit. If a line is significantly blended with a telluric line, its measuredproperties will be a function of the airmass and thus the time of the observations. This is obvious for the C i ∆ W / W = . The ever-changing seeing causes the spatial resolution to varywith time. Because the current project does not require very highspatial resolution – indeed some spatial averaging is necessaryand beneficial – one might surmise that seeing is irrelevant. Wedid not take that approach. Bad seeing implies that light from faraway on the solar disk will be scattered into the spectrograph slitwithout any control. We therefore compared results from periodswith di ff erent seeing but could not discern any significant di ff er-ences in the measured line properties. Still we excluded the datasets with the worst seeing, and for those that were included, wekept the 50 best frames (100 for disk-centre spectra) as selectedfrom continuum contrast values. We note that really bad seeingcan cause tracking loss which itself is a source of error.We caution, however, against assuming that seeing is unim-portant in studies like this. We note that in our case the observedpoints were far from the limb, that the centre-to-limb variation ofthe equivalent widths are rather linear (thus symmetric blurringwill still give the same results), and that the intensity spectrumat this µ should anyway be similar to the flux spectrum.A similar comparison of data from periods where thin highclouds were intermittently in view gave a di ff erent result. Herethe spectra did change significantly and any cloud-a ff ected ob-servations were subsequently excluded from analysis. Intrinsic variations of the solar target and instrumental drifts canin principle be di ffi cult to disentangle. Figure 2 shows the resultof a run where the telescope was pointed at disk centre for morethan 20 min. Each point in the plot corresponds to one expo-sure. Pointing errors should be negligible here. As seen from thecontinuum contrast, the seeing was varying but improved dur-ing the period. The line-centre variations show clear evidence of5-minute oscillations. The continuum intensity is clearly corre-lated with these. The variations of the other line parameters donot seem to correlate with oscillations but seem consistent withbeing caused by granulation – mainly from its time evolution butprobably with contribution from slit drifts and rotation relative tothe solar image. There is a noise envelope, probably caused by acombination of photon noise and seeing jitter, totally amountingto about 1% in equivalent width. All in all, the di ff erential approach taken here should minimisemany systematic errors. The results from the tests are consistentwith the dominant errors being from solar variations and frompointing. These are random in nature, and given the number ofdata sets, it seems reasonable to use the spread of the individ-ual data points – graphically shown in Fig. 3 – to estimate theuncertainties in the mean values using the standard error of themean computed separately for the S + N data points and the W + Edatapoints. .
01 538 .
02 538 .
03 538 .
04 538 . Wavelength [nm] . . . . . . . . . Fig. 5.
Disk-centre spectra for C i
538 nm. Black 2010-05-05,Blue 2010-05-06. Red 2010-05-07. .
12 711 .
14 711 .
16 711 . Wavelength [nm] . . . . . Fig. 6.
Like Fig. 5 but for C i .
52 783 .
54 783 .
56 783 .
58 783 .
60 783 . Wavelength [nm] . . . . . . Fig. 7.
Like
Fig. 5 but for the two lines of Al i at 783 nm.
3. Quiet Sun results
Figure 3 displays the equivalent widths from all data sets.Di ff erent symbols are used for the four di ff erent disk positions.From the plots alone, no clear di ff erence between the di ff erentdisk position is obvious for any line, with one possible excep-tion. We note that for the three O i lines, four of the S points liebelow all of the N points. The fact that the fifth point does notindicates that this N-S divergence may be due to activity or erro-neous pointing since the four deviating data sets were recordedon a di ff erent day.Figure 8 illustrates the data points by showing examplesof line profiles for the di ff erent disk position for four lines asrecorded during the same day. .
95 538 .
00 538 .
05 538 . . . . . . C I .
00 616 .
05 616 .
10 616 . Na I .
45 616 .
50 616 .
55 616 . Fe I .
55 616 .
60 616 .
65 616 . Ca I .
85 616 .
90 616 . Ca I .
05 711 .
10 711 .
15 711 . . . . . . C I .
25 711 .
30 711 .
35 711 . C I .
55 768 .
60 768 .
65 768 . S I .
85 769 .
90 769 . K I .
10 777 .
15 777 .
20 777 . O I .
35 777 .
40 777 .
45 777 . Wavelength [nm] . . . . . O I .
45 777 .
50 777 .
55 777 . Wavelength [nm] O I .
50 783 .
55 783 .
60 783 . Wavelength [nm] Al I .
50 783 .
55 783 .
60 783 . Wavelength [nm] Al I .
40 869 .
45 869 .
50 869 . Wavelength [nm] Si I Fig. 4.
All spectral lines of the present study. Shaded region shows the integration range for the equivalent widths. This range isshifted according to the line core for every individual spectrum. .
88 616 .
89 616 .
90 616 .
91 616 .
92 616 . Wavelength [nm] . . . . . . . Ca I .
28 711 .
30 711 .
32 711 .
34 711 . Wavelength [nm] . . . . . . C I .
39 777 .
40 777 .
41 777 .
42 777 .
43 777 .
44 777 . Wavelength [nm] . . . . . . O I .
51 783 .
52 783 .
53 783 .
54 783 . Wavelength [nm] . . . . . Al I NSWE
Fig. 8.
Two sample spectra for each of the four main disk positions acquired during the same day. The E and W spectra have beenadjusted for solar rotation by applying a nominal Doppler shift of ± . / s · sin 45 ◦ .Computing the mean values separately for the S + N andE + W disk positions, and using the standard error in each meanvalue as error estimate, gives the result in Figure 9. Here, the rel-ative di ff erence in low-latitude (average of E and W) and high- latitude (average of N and S) equivalent width, ∆ W (cid:104) W (cid:105) = ( W low − W high ) (cid:104) W (cid:105) , Fig. 9. Di ff erence between low-latitude and high-latitude equivalent widths for all lines. Error bars are based on the standard errorsin the respective mean values. Fig. 10. Di ff erence between “polar” and “equatorial” abun-dances for all elements as function of their condensation tem-peratures according to Lodders (2003).is plotted for each line. The error bars are the standard errors inthe mean values (1 σ ). The departure from zero of the relativedi ff erences ∆ W / (cid:104) W (cid:105) must be considered insignificant.Our initial goal was to estimate the di ff erence between thespectral analysis an observer close to the equatorial plane of theSun and one who sees the Sun pole on. The polar observer willsee a flux spectrum which is characterised by our high-latitudespectra. The equatorial – or terrestrial – observer will see a fluxspectrum that is a mix of low-latitude and high-latitude contri-butions. We approximate this mix to be 1:1. Thus the e ff ective relative di ff erence in flux equivalent width is ∆ W e ff (cid:104) W (cid:105) = ∆ W (cid:104) W (cid:105) . The final result is shown in Fig. 10 where the di ff erencein derived abundances per element is plotted as a function ofcondensation temperature. The average values used for this plotwere computed without any weights.The di ff erence in derived abundance is computed with thehelp of theoretical LTE curves of growth using ∆ W e ff / (cid:104) W (cid:105) asinput. The di ff erence between “polar” and “equatorial” abun-dances is within 0.005 dex for all elements and to within 0.002dex for the refractory elements. The error bars are computed di-rectly from those in Fig. 9. It is clear that there is no signifi-cant di ff erence and that, in particular, no trend with condensationtemperature is present.
4. Solar activity
The principal goal of this work was to look for possible latitude-e ff ects in the quiet Sun and e ff orts were made to avoid any ac-tivity. The result was negative, but that leaves the possibility thatthe Sun, or a star, could have significant inclination-dependentspectra due to activity. The point is that even if two stars have thesame level and kind of magnetic activity as the Sun, the activeregions tend to keep to lower latitudes. Alternatively, one couldargue that the studies by Mel´endez et al. (2009) and Ram´ırezet al. (2009) were made when the Sun was in an unusual deepactivity minimum. It the solar twins happened to have system-atically higher levels of activity, perhaps their spectra would bedi ff erent, regardless of inclination angle.An investigation of this possibility is beyond the scope ofthis paper. (During our observing run, some data were in factacquired from regions of moderate activity but the amount of data is not enough to allow any conclusions.) However, sometentative remarks can be made based on the existing literature.It seems likely that lines that are strongly a ff ected by activ-ity also would display a variation with the solar cycle. Indeed,the long-term monitoring of solar spectral features of Livingstonet al. (2007) shows that some strong lines with chromosphericcontributions display variations in phase with the solar cycle. Butamong weaker, clearly photospheric, lines only Mn i ff ect and very high contrast of mag-netic structures in the line. Otherwise, C i
538 nm was foundto be constant by Livingston et al. (2007) within 1.5% ( ∆ log (cid:15) < .
006 dex) with no signs of cycles or trends as were other photo-spheric lines, e.g. the 777-nm O i triplet whose equivalent widthsall lie within their noise envelope of 1%.So, while the influence of magnetic activity on lines usedfor abundance analysis is well worth more investigations, itis unlikely to explain abundance patterns like those found byMel´endez et al. (2009) and Ram´ırez et al. (2009).
5. Discussion and conclusions
We draw the following conclusions:The TRIPPEL Spectrograph performs well and has a highstability suitable for comparative studies of the kind presentedhere.The method of di ff erential comparison is precise and insen-sitive to, e.g., seeing variations.The di ff erence in equivalent widths for the lines observedat the equator and at latitudes around 45 ◦ is less than 1% at µ = √ /
2, except for the telluric-a ffl icted C i ff ect found by Mel´endezet al. (2009) in the comparison of the composition of the Sunwith those of the solar twins, for refractories relative to volatilesand amounting to about 20% in elemental abundance, could bedue to the systematically di ff erent aspect angles when observingthe Sun relative to the twins.Finally, we note that while we have argued that it is unlikelythat solar activity could modify our qualitative conclusions, thee ff ects of magnetic activity on abundances derived from high-resolution spectra need further investigation. A natural follow-upstudy to the current work would be to apply the same methodsto explore in detail the di ff erences between photospheric spec-tra in solar active regions, as compared with inactive regions. Inthe present age of high-precision spectroscopy, in particular indetailed di ff erential work, it may be important to take the activ-ity state into consideration when detailed abundance analysis ismade. Acknowledgements.
The Swedish 1-m Solar Telescope is operated on the islandof La Palma by the Institute for Solar Physics of the Royal Swedish Academyof Sciences in the Spanish Observatorio del Roque de los Muchachos of theInstituto de Astrof´ısica de Canarias. BG acknowledges support from the SwedishResearch Council, VR. J.M. thanks support from FAPESP (2010 / References