For all women in physics fighting for their right to be judged notby gender but as fellow scientists. Your strength is my

inspiration, always.

List of Papers

This thesis is based on the following papers, which are referred to in the textby their Roman numerals.

I Önehag, A., Gustafsson, B., Eriksson, K., Edvardsson, B. (2009)“Calibration of Strömgren uvbyH photometry for late-type stars– a model atmosphere approach”, Astronomy & Astrophysics 498,527–542

II Önehag, A., Korn, A., Gustafsson, B., Stempels, E., VandenBerg,D.A. (2011) “M67-1194 an unusually Sun-like solar twin in M67”,Astronomy & Astrophysics, 528

III Önehag, A., Heiter, U., Gustafsson, B., Piskunov, N., Plez, B., Rein-ers, A. (2011) ‘M dwarf metallicities - A high-resolution spectroscopicstudy in the near-infrared”, Astronomy & Astrophysics (submitted)

Reprints were made with permission from the publishers.

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.1 The difficult target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Stellar atmospheres and photometric applications . . . . . . . . . . . . . . 152.1 Adding colours to the stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 Synthetic colours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.1 Paper I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 The solar twin problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1 Chasing the Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1.1 Solar applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 The Li problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3 Messier 67 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.4 M 67 – 1194 (Paper II) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.4.1 Equivalent width and curve of growth . . . . . . . . . . . . . . . 263.4.2 Deriving the atmospheric parameters . . . . . . . . . . . . . . . . 273.4.3 Equivalenth width, 2, and the spectroscopists eye . . . . . . 283.4.4 The peculiar composition of the Sun . . . . . . . . . . . . . . . . 30

4 M dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.1 The M dwarf spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2 The metal content of M dwarfs (Paper III) . . . . . . . . . . . . . . . . 34

4.2.1 Less molecular features – more telluric lines . . . . . . . . . . 354.2.2 The unknown infrared . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5 Perspectives for the future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 My contributions to the included papers . . . . . . . . . . . . . . . . . . . . . 417 Swedish summary – Svensk sammanfattning . . . . . . . . . . . . . . . . . 43

7.1 Stjärnatmosfärsmodeller och fotometri (Artikel I) . . . . . . . . . . 437.2 Solen och dess tvillingar (Artikel II) . . . . . . . . . . . . . . . . . . . . 447.3 Grundämnessammansättningen hos M-dvärgar (Artikel III) . . . 45

8 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

1. Introduction

Calibrations are essential for most astrophysical applications. The success oflarge surveys such as the Hipparcos mission (ESA) and the Hipparcos-Tychocatalogue presenting detailed positions of over two and a half million stars, arebased on detailed calibrations of the observations. Depending on the scientificgoal and the desired accuracy of the outcome, different calibration objects orroutines can be applied. High-accuracy measures of radial velocities, e.g. usedto discover planets, require high-resolution and a large spectral coverage. Ac-curate stellar abundance determinations require high signal-to-noise and highspectral resolution in order to separate lines that are partially blended withadjacent features. The accuracy of derived stellar properties from photomet-ric measures depends on the uncertainties of the photometry. These variousmethods need different types of calibrations, like radial velocity standard linesand standard stars, comparison stars for abundance scales or g f values, andcomparison stars with well-known fundamental parameters for photometriccalibration. It is clear that the calibration object should be chosen with greatcare depending on the desired outcome.

1.1 The difficult targetThe brightest object in the sky, our Sun, ought to be a natural reference sourcefor calibrating stellar observations. The amount of information available forthe Sun greatly exceeds that available for all other stellar objects. Despitethis, direct observations of the Sun are rarely used to anchor photometric andspectroscopic surveys. The Sun’s proximity, brightness and large apparent di-ameter make it a difficult target for an accurate direct spectro-photometriccomparison with the much fainter point-like stellar objects. Instruments de-signed for distant stars and filter systems utilized for astronomical purposescan hardly be used on the exceedingly bright Sun.

Different approaches have been used to circumvent the difficulties in usingthe Sun as a reference point. For instance, theoretical stellar atmospheremodels have been used to calculate high-resolution synthetic spectra of theSun. Such synthetic spectra are used in direct spectroscopic comparisons orif convolved with the different response functions of various filters, the solarmagnitudes in different photometric systems can be derived. Theoreticalmodels, however, suffer from both inadequacies in the assumptions and

11

simplifications made of the basic physics not to mention the inaccurate ormissing information available on the atomic and molecular lines involved.Furthermore, when comparing synthetic and observed spectra, one needsto estimate the usually not sufficiently known instrumental profile of theobservations in order to match the actual resolution. For a photometricapproach, i.e. when calibrating observed photometry with synthetic colours,one needs to consider the fact that filters age and tend to differ from the filterresponses measured at manufacture. The actual transmission functions atthe time of observation are therefore usually not fully known. The use offilters with passbands different from the original definitions complicates thesituation further (Bessell 2005).

Direct spectroscopic observations of the Sun integrated over the full disk(e.g. Kitt Peak Atlas, Kurucz et al. 1984) are used as reference material forcalibrating spectroscopic observations of stars. However, this too has in manyrespects proven to have its deficits. Daytime observations of the solar diskwith instruments whose properties and designs considerably differ fromnighttime faint-target instruments can introduce deviations stemming fromthe instruments themselves.

Indirect measures of the solar spectrum can be performed at daytime by ob-serving the Rayleigh scattered sun light in the atmosphere, a so-called daytimesky-spectrum. Such observations can be obtained with a nighttime telescopeand diminish the issues of using different instrumentation. The different illu-mination of the slit by the sky as compared to the stellar point-like shapes canhowever introduce unwanted effects. Scattered light from the bright sky notfollowing the desired path way within the instrumentation and a resolutionvarying as a function of position on the slit, are part of the problematics.

Nighttime indirect observations of the Sun have the great advantage of thepossibility to carry out the calibration observations in connection with the tar-get observations themselves. The reflected light from the Moon or a bright as-teroid are favourable targets. This, however, assumes that the solar light is notmodified to any great extent by the properties of the reflectant surface. Manyasteroids are also crossing the sky at a rate that may be difficult to achievewith the available tracking systems of the larger telescopes.

Summarizing all listed challenges, one would optimally wish to have abright permanent non-moving well studied point-like nighttime target for cali-bration purposes. Artificial targets that meet these constraints have been dis-cussed although none have been built and put into orbit so far.

In the absence of reliable observations of the Sun itself, the astronomicalcommunity has as an alternative solution searched for reference stars repre-senting the Sun among the stars. Such stars should, depending on the calibra-tion purpose, have properties identical or very similar to the Sun if to be usedas a solar proxy. This requires a great deal of knowledge about the calibration

12

target itself in order to avoid unwanted deviations from the solar character-istics e.g. chemical composition, effective temperature etc. In addition, morethan one target is necessary to cover the Earth’s celestial hemispheres duringthe nighttime hours.

Avoiding the seemingly difficult aim to use the Sun as the primary calibra-tor, the bright, relatively nearby (∼8 pc) and well studied A0V star Vega hasbeen a popular calibration target for photometric surveys and will remain suchuntil a reliable solar source is available.

13

2. Stellar atmospheres and photometricapplications

In theory, there is no difference between theory and practice.But, in practice, there is.

/Jan L. A. van de Snepscheut/Lawrence Peter Berra

The emergent flux distribution from a stellar atmosphere is governed primar-ily by the temperature, surface gravity and chemical composition of the star.The main properties of a stellar atmosphere can therefore simplistically be de-scribed by a set of atmospheric parameters.The surface temperature, or the effective temperature, is the temperature of ablack body with an emitted flux equivalent to the total flux escaping from thestar. The effective temperature, Teff, is a function of the stellar luminosity (L)and radius (R):

Teff ≡(

L/(4 R2))1/4

, (2.1)

where is the Stefan–Boltzmann constant. The gravitational acceleration atthe surface, or the logarithmic surface gravity, logg, is given by the stellarmass M, radius R, and the gravitational constant G:

logg = log(

GMR2

)

(2.2)

The logarithmic iron-to-hydrogen ratio, often called the metallicity, as com-pared to the solar ratio is defined via the number of iron and hydrogen atomsper unit of volume:

[Fe/H]⋆ = log10(NFe/NH)⋆− log10(NFe/NH)⊙ (2.3)

The micro-turbulent parameter, t, describes the effects on the spectral linesdue to velocity changes in the gas along the photon rays with significant vari-ations within distances smaller than the mean free path of the photons. Thesefundamental characteristics are the user defined free input parameters of stel-lar atmosphere models such as MARCS (Gustafsson et al. 2008). The maingoal of the papers included in this thesis has been to describe the global prop-erties of stars via the means of atmospheric parameters and I will refer to theseas described above throughout this thesis.

15

2.1 Adding colours to the starsFilter systems for measuring magnitudes and colours in specific isolatedspectral wavelength regions, have been used throughout the years fornumerous applications. With new established photometric systems (e.g.2MASS, Sloan) and continuous developments of the already existing ones,the field continues to grow and remains an important branch in observationalas well as theoretical astronomy. The ever-growing popularity of photometricstudies may come from the fact that compared to the time-wise rather costlyspectroscopic observations, photometric observations of faint targets can beobtained on much shorter time scales. The small internal errors that can beachieved in photometric observations as compared to spectroscopic studies isanother favourable property.

In 1963 Strömgren introduced the photometric uvby filter system. The vari-ous combinations of these filters and their possible applications for describingspecific properties of stellar atmospheres were soon explored and calibrationswere established (e.g. Strömgren 1964, Crawford 1966). Compared to broad-band filter systems (e.g. Johnson 1966) this is an intermediate-band systemdesigned to be highly sensitive to specific features seen in narrow wavelengthregions. The u filter is centered around 350 nm and is located blueward of theBalmer jump. The v filter is positioned at 410 nm, and covers a region domi-nated by metal lines in solar-type stars. Finally the b and y filters are locatedon the long wavelength-side of the Planck curve. The four filters were com-bined into certain colours and indices. The (b− y) colour in the tail of theblack-body was designed to be an efficient measure of effective temperature.The c1 index encloses the discontinuity of the Balmer jump and is known tocarry information on temperature for B and A type stars and surface gravityfor later-type stars. This index is also sensitive to metallicity although this isdiminished somewhat by the twofold subtraction of the v filter. The m1 indexis designed to measure the depression in the continuum introduced by metallines (line-blanketing) in the v filter and is used to estimate the metallicity,[Fe/H].

c1 ≡ (u− v)− (v−b) (2.4)

m1 ≡ (v−b)− (b− y) (2.5)

The H index was outlined by Crawford (1958) and Crawford & Mander(1966) as the ratio of the flux measured through a narrow and broad filterprofile both centered around the hydrogen- line (486.1 nm). The Strömgrenand Crawford & Mander filter systems were soon combined and I shall referto the combined system as uvby–H throughout this thesis.

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The atmospheric parameters of stars can not be derived from photometrysolely. For this, calibration expressions need to be derived based on a com-bination of colours and indices. This can be done via the means of semi-empirical methods, an approach used by Strömgren (1964) to derive the metal-licity sensitivity of the m1 index using spectroscopically determined metallic-ities. Semi-empirical methods have been used to create calibration expres-sions often in combination with large homogeneous surveys, e.g. the Geneva-Copenhagen survey (Nordström et al. 2004, Holmberg et al. 2007, Casagrandeet al. 2011). Purley theoretical calibrations have also been developed usingmodel atmospheres (Bell 1970, Gustafsson & Bell 1979, Lester et al. 1986,Castelli & Kurucz 2006) and a combination of the two applications wheretheoretical colours are corrected using empirical data (e.g. Clem et al. 2004).

The established calibration expressions are often designed to be validin specific intervals, e.g. high and low gravities and temperatures. Whenapplying different sets of calibration expressions on a set of stars it istherefore important to investigate the possible discrepancies not to introduceunwanted inhomogenities. A recent attempt (Kim & Moon 2011) has beenmade to simultaneously estimate effective temperature, surface gravity andmetallicity, based on the Strömgren (b− y), m1 and c1 in order to mimimizethe effect of using different calibration expressions for deriving differentatmospheric parameters.

The high sensitivity of the Strömgren colours to features in isolated wave-length regions has been used to trace abundances of specific elements. Grun-dahl et al. (2002) evaluated the possibility of using the c1 index to trace nitro-gen abundances based on the presence of the NH molecule in the u filter. Thiswork resulted in a new colour index, cy = c1 − (b− y), that is sensitive to ni-trogen, but less sensitive to temperature than the c1 index (Yong et al. 2008a).The cy index was used subsequently by Lind et al. (2011) to locate differentstellar populations in a metal-poor cluster.

2.2 Synthetic coloursColours derived from purely theoretical spectra are commonly referredto as synthetic colours. Studies using calculated colours have been used,not only to explore the progress or shortcomings of model atmospheresbut to gain insights on objects where little observational data is available.The extremes of the stellar population such as very metal poor stars(V MP, e.g. Beers & Christlieb 2005) with few observed objects andstellar clusters are areas of application where synthetic photometryhas proven to be advantageous. Furthermore, the quality of largeobservational surveys often depends on the accuracy of data calibrations.Model atmospheres can be used to create large dense calibration grids

17

of synthetic colours, a task difficult to obtain based on observed colours alone.

2.2.1 Paper IIn paper I we follow a purely theoretical line of approach, using stellar modelatmospheres, MARCS (Gustafsson et al. 2008), to create a grid in the effec-tive temperature, surface gravity and metallicity parameter space for late-typestars. Based on the model atmospheres, high-resolution synthetic spectra werecalculated and convolved with the different transmission functions of the uvbyand H filters:

maguvby = −2.5log10

(∫

F Ti, d∫

Ti, d

)

(2.6)

H = −2.5

(

log

∫

F TN, d∫

TN, d− log

∫

F TW, d∫

TW, d

)

, (2.7)

where F is the flux and Ti, , TW, , TN, are the filter transmissions profiles ofthe uvby, H -wide and H -narrow filter profiles, respectively.

The main goal of this study was to investigate whether or not the observedsensitivity of the photometric indices to effective temperature, surface grav-ity and metallicity could be reproduced with synthetic colours derived fromcalculated spectra.

For a detailed comparison with observed colours a sample of starswith well determined atmospheric parameters and accurate photometricmeasurements is crucial. Such a comparison sample should ideally be basedon truly atmospheric stellar parameters from absolute fluxes combinedwith radii and masses from binary companions and not from photometriccalibrations to ensure a fully independent analysis. In paper I we establisheda stellar comparison sample based on high-accuracy literature data.

2.2.1.1 Transformations to a standard systemThe procedure in observational calibrations is mimicked in the theoretical ap-proach as the derived colours are transformed to a standard system using awell defined zero-point. In open photomeric systems like the uvby-H , this isnecessary in order to assure consistency within different photometric surveys.

The nearby (∼8pc) A0 star Vega has been studied in great detail over theyears and has been the preferred calibration target in most uvby-H surveys.Vega is however not a typical standard A0 star. It has been shown to be rapidlyrotating but with its axis close to the line of sight (Gulliver et al. 1994; Hill etal. 2004), to have non-solar abundance ratios as well as dust emission in the

18

infrared (e.g Heiter 2002). However, these departures from standard A0 stars,as well as standard model atmospheres, has been shown to produce small ef-fects on the uvby-H indices (Paunzen et al. 2002). In our theoretical approachwe therefore derived synthetic colours from a calculated synthetic spectrumof Vega based on a model with Teff = 9550 K, logg = 3.95, and [Fe/H] =−0.5,values established by observations. The derived difference between observedand synthetic colours of Vega could then be used to transform the colour gridof late-type stars to the standard system.

A second transformation is often necessary as the filter transmissionfunctions utilized in different surveys do not necessarily agree with theoriginally defined system. This departure can come from both defectsintroduced at manufacture as well as aging of the filters. Great care needsto be taken to match the different passbands not to introduce systematicvariations, especially as the Strömgren filter system has proven highlysensitive to the positioning and widths of the filters (Bessell 2005). The uvbycolours derived in this study were calculated using a set of transmissionfunctions that are thought to be equivalent to the original system defined byStrömgren. These synthetic colours can therefore be transformed directlyto the standard system based on the colours of Vega. The H index has toundergo two transformations owing to the original treatment of the filtersystem. The filter profiles utilized by Craword & Mander (1966) and used inthis study, are themselves not in the standard system. In Crawford & Manderthe observations are transformed to a set of previously observed standardstars, what is referred to as the natural system. The same transformationshould therefore be applied on synthetic H indices to ensure consistencywith observed values.

As our comparison sample was gathered from multiple sources, we werelikely to find inconsistent usage of filter functions. In paper I we thereforeinvestigated to what extent the use of slightly different filter functions wouldaffect the analysis, and found that the detected deviations are not critical forour scientific purpose. The uvby passbands used in this study and filtersemployed by recent studies can be seen in Figure 2.1.

A better zero-point than Vega perhaps, since we are testing late-type starsin the temperature regime 4500–7000 K, might have been to use the Sun.The unknown colours of the Sun makes it an impossible calibration target assuch. However, a solar-proxy, such as a solar analouge or twin, would servethe purpose as the desired zero-point. This was also tested using HR 6060 (18Scorpii), a star known to be very similar to the Sun, but as we could not re-produce the observed sensitivity of the m1 and c1 indices in a satsifactory wayfor the cooler part the model grid, Vega was chosen to be the better zero-point.

19

Figure 2.1: The filter transmission functions used in this study (solid line) comparedto the passbands of Helt et al. (1987), dashed line. As a comparison, the flux (perÅngström unit) of a model with Teff = 6000 K, logg = 4.0 and [Fe/H] = 0.0 is plottedon an arbitrary flux scale.

2.2.1.2 Calibration expressionsWe find that the sensitivity of the synthetic (b− y) and H colors is of thesame order as seen in empirical studies. The metallicity index m1 shows asomewhat larger sensitivity than observed empirically. The gravity index c1works well for stars hotter than the Sun but shows significant deviations forcooler stars. With this knowledge in hand it was interesting to test some oftenused calibration expressions for effective temperature and metalllicity basedon the same photometric systems.

Calibration expressions for effective temperature and metallicity were out-lined by Alonso et al. (1996, 1999) and Schuster & Nissen (1989), respec-tively. The form of these calibration expressions has been reused in subse-quent calibration attempts where new calibration constants are established,e.g. Ramírez & Meléndez (2005b). In the same manner we reuse the expres-sions and derive new calibration constants, but this time based on syntheticcolours.

Erroneous values of the applied zero-point would merely introduce a con-stant shift to the (b− y)− Teff, m1− [Fe/H] and c1 − logg relations, and thusdo not affect the sensitivity measure itself. This is, however, not valid forthe complex and non-linear calibration expressions based on a combinationof different colours. The derived calibration constants based on the synthetic

20

Figure 2.2: CMD of the halo cluster NGC 6397. The marked regions in the figureshow the different regions where effective temperatures where derived for a set ofstars. The figure is adapted from Korn et al. 2007.

colours were therefore used to test the status and reliability of the models,rather than to produce new calibration expressions.

The effective temperatures derived from the theoretical calibrations basedon synthetic (b− y) colours and the H index were found to compare wellwith empirical calibration expressions. We find a somewhat larger discrep-ancy when deriving a metallicity calibration. This is most noticeable in thehigh-metallicity regime. A discrepancy is maybe to be expected as the u andv filters are included in both the m1 and c1 indices. These filters cover wave-length regions heavily affected by atomic and molecular lines and the linelistsavailable are far from complete. The situation will improve as large data baseswith high-quality atomic and molecular data are generated (VALD, Kupka etal. 1999; VAMDC, Dubernet et al. 2010). However, incomplete linelists areprobably not the full answer to the discrepancies seen between the syntheticand observed colours. Other contributors to the discrepancies are non-LTEeffects and surface inhomogeneities caused by convection i.e. effects not cap-tured in one-dimensional models with mixing-length convection treatment.

2.2.1.3 Cluster applicationsAs already discussed there are several areas of application where syntheticcolours are favorable. The benefits of having a large uniform grid instead of

21

applying different calibrations valid in specific intervals is one of them. Stellarclusters are among the targets affected by these difficulties. As the stars movealong the evolutionary track, large variations in temperature and surface grav-ity can be seen. In order to describe the atmospheric parameters of the clustermembers at different evolutionary stages, different calibration expressions areoften applied. It is therefore interesting to test if synthetic colours could meetthe need of a uniform calibration. In paper I we applied the calculated colourgrid on a set of clusters, testing both the c1 sensitivity to surface gravity andthe possibility to trace nitrogen with the cy index. We found that we couldreproduce the observed m1 and c1 indices rather well by the models, whichsuggests that synthetic m1 and c1 indices can be used to estimate gravities formetal-poor giant stars. For the nitrogen sensitive cy index we found that thesynthetic index is sensitive to nitrogen abundance, althogh a little less thanwhat is seen in observations.

As we had verified that we could reproduce the empirical sensitivity of the(b− y) index to effective temperaure, testing this on a cluster was maybe themost interesting application. The metal-poor cluster NGC 6397 has been usedby Korn et al. (2007) to trace atomic diffusion i.e. effects of element separationtaking place in atmospheres of stars with weak convection. One of the criticalassumptions on which the diffusion results rely upon, are the derived effectivetemperatures. Two different calibration expressions were used to establish theeffective temperatures at specific evolutionary stages (the calibration regionsare shown in Figure 2.2). The synthetic colours were used to estimate the dif-ferences in effective temperature along the evolutionary track and we couldverify the temperature scale established by the two different calibration ex-pressions.

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3. The solar twin problem

I’ve loved the stars too fondly to be fearful of the night./Galileo Galilei

3.1 Chasing the SunIn 1978 Hardorp introduced, what would become, an extended search to findstars very similar to the Sun. As the telescopes grew larger and high-resolutionand high-quality instruments were designed, this soon developed into an in-tense search to find a star truly identical to the Sun, a solar twin. By sqrutiniz-ing stellar spectra in the optical wavelength region, of a sample of 77 stars re-sembling the Sun, Hardorp explored the solar neighbourhood. The stars werecategorized into eight groups ranked on a scale based on the detection of in-creasingly deviating features with respect to the Sun (in this case representedby a day-time sky spectrum). As many as four stars qualified into the high-est ranked group Spectra indistinguishable from solar and it was concludedthat stars very similar to Sun were rare but not absent in the solar vicinity.The finding of solar-similars encouraged a continued exploration of the fieldand the work by Hardorp was soon carried on in a series of articles (Hardorp1980a,b, 1981, 1982a, Hardorp et al. 1982b, Hardorp & Tomkin 1983). Theprogress of the field was reviewed by Cayrel de Strobel (1996) and the termi-nology defined in this review has been adapted by the stellar community andwill be used in the remaining part of this thesis.

... solar like stars form a very broad class of stars, in which is found a mixtureof late F, early, middle and, sometimes, late G type dwarfs and sub-giants. So-lar analogues are unevolved, or slightly evolved Pop I disk stars with effectivetemperatures, degree of evolution, metallicities and kinematic properties notvery different from those of the Sun. Real solar twins are ideal stars possess-ing fundamental physical parameters (mass, chemical composition, age, effec-tive temperature, luminosity, gravity, velocity fields, magnetic fields, equatorialrotation, etc) very similar, if not identical to those of the Sun.

Until a few years ago the star 18 Scorpii (HR 6060) was the only object thatcould be argued to be a real solar-twin (Porto de Mello & Da Silva, 1997,Soubiran & Triaud 2004). This star, however, has been observed to have ahigher lithium content than observed in the Sun. The Li abundance in the Sunand observed solar twins has been discussed as a low lithium content hasbeen proposed to be linked to the existence of planets (see below). Recentobservations of field stars in the solar vicinity, have confirmed the existenceof several stars very similar to the Sun (Meléndez et al. 2006, Meléndez &Ramírez 2007, Takeda et al. 2007, Takeda & Tajitsu 2009).

23

3.1.1 Solar applicationsAs has already been mentioned, the Sun is a difficult calibration object. Anapproach, avoiding the difficulties of using the Sun itself, would be to observea star very similar to the Sun. Such a stellar proxy would serve several cali-brational purposes, e.g. setting the zero points in various applications; the In-fraRed Flux Method for estimating effective temperatures (Blackwell & Shal-lis 1977, Blackwell et al. 1979, 1980, Casagrande et al. 2010), absolute fluxscales (Colina et al. 1996) and in colour-atmospheric parameters relations (seeChapter 2). An accurate temperature scale is necessary when studying e.g. theprimordial lithium abundance by comparing the level of lithium in metal-poorstars with that obtained from Big Bang Nucleosynthesis. Furthermore, solar-similars are fundamental for calibrating reflectance spectroscopy observationsof solar-system objects, where the spectral component of the Sun must be re-moved before an analysis of the spectroscopic features of the body itself canbe performed. The determinations of the true colours of the Sun, which havevaried a great deal (Cayrel de Strobel 1996, Holmberg et al. 2006, Meléndezet al. 2010), would profit from more well-determined solar twins. Finally, theuniqueness or normality of the Sun can be explored (Gustafsson 1998) underthe assumption that it is unique and too metal-rich for its age and galactic orbit(Holmberg et al. 2009).

3.2 The Li problemThe seemingly low lithium abundance of the Sun as compared to observedabundance levels in solar analogues in the solar neighborhood (e.g., Lambert& Reddy 2004), has been an intriguing issue for solar twin hunters. The spreadin Li abundance in solar-type stars is much larger than seen for other elements(Reddy et al. 2003).

Lithium is a light and easily destroyed element as it is prone to proton cap-ture and only survives at temperatures up to 2.5 million K. In solar-type starsLi is therefore only existing in the outer envelope as it burns at the higher tem-peratures in the stellar interior. If Li in the outer layers, mixed by convection,is transported inwards and thus destroyed, a depletion of Li over time wouldbe seen in the stellar photospheres. This is also one of the explanations forthe different lithium contents seen in the otherwise rather similar solar-typestars. A Li depletion over time would also explain why the amount of Li inthe Sun as, e.g., compared with Si, is lower by a factor of 160 than detected inmeteorites.

Another suggested mechanism responsible for Li depletion isrotationally-driven mixing in the interior of stars. The pre-main sequence staris coupled to its accretion disk via magnetic fields (Rebull et al. 2006, Cieza& Baliber 2007). This coupling prevents the envelope of the contracting starfrom increasing its rotational speed, while the stellar core rotates at an ever

24

increasing rate. As a result the shear velocity between the core and outerenvelope is increased. This increased degree of differential rotation enhancesthe rotationally-driven mixing, thus destroying more Li. Long-lived diskswill enhance this effect, and as planets are thought to be formed in relativelylong-lived disks, a low lithium abundance could be a signal of an interferingplanetary system. However, whether or not the star-planet interaction isstrong enough to introduce efficient rotationally-driven mixing is still to beexplored.

Recent studies of the solar neighbourhood (Baumann et al. 2010) show no ten-dencies towards a low lithium abundance - planetary system coupling. Lithiumas a possible planet tracer will continue to be explored, a real solar twin how-ever, planets or not, should show the same low lithum abundance as observedin the Sun.

3.3 Messier 67Until recently the search for solar analogues has been focused mainly to-wards the bright nearby field stars. High-accuracy abundance studies requirehigh signal-to-noise ratios and high spectral resolutions, as the lines are oftenblended and continuum placement is critical for the abundance analysis. Ob-servations of solar-type stars in clusters require a large amount of observingtime as the G dwarfs quickly become very faint at large distances.Messier 67 (M 67) is a well observed open cluster, mainly due to a numberof favourable characteristics. The cluster is relatively nearby (∼900 pc) andlocated at relatively high galactic latitudes compared to other open clustersand is therefore less effected by interstellar extinction. It also contains a largenumber of stars and has a suggested age comparable with that of the Sun(3.5–4.8 Gyr). This is unusual as the open clusters are not gravitationally wellbound and therefore tend to dissolve before reaching such old ages. Further-more, the metallicity has been estimated by observations to be close to so-lar (−0.04 to +0.03). This makes M 67 in many aspects a perfect object inthe search for a solar twin. The problems related to the apparent faintnessof G dwarfs in even nearby clusters (G2 V stars have V∼14.6 in M 67) re-mains and this requires large telescopes or otherwise rather time consumingobservations. The Very Large Telescope (VLT, ESO) meets the constraintsand intermediate-resolution observations of possible solar analogues in M 67have been carried out with the instruments at VLT (Pasquini et al. 2008, Bi-azzo et al. 2009). These studies indicate that not only do the main-sequencestars show Li depletion comparable to the abundance observed in the Sun, butseveral solar analogues are expected to be found. The most natural follow upof these prior studies would be to observe the highest-ranked solar analoguecandidate in high resolution and make a detailed analysis of the atmospheric

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parameters as well as individual abundances. This is what we did and the re-sults are presented below and in paper II.

3.4 M 67 – 1194 (Paper II)In paper II we observed the highest ranked solar analogue from previousstudies (Pasquini et al. 2008), with the multi-object spectrometerFLAMES–UVES at ESO–VLT. The fibres were positioned on differentbrighter stars in M 67, and the positions were changed from exposure toexposure, except for one fibre that was dedicated to a single object, 1194.With this setup, 18 hours of observing time was acquired at relatively highresolution (R∼47,000) of this one faint target. The observations were carriedout in the optical wavelength region, 4800–6800 Å.

We soon discovered that the post-process calibrations provided along withthe observations did not yield the desired quality. Light from the much brighterevolved stars observed in adjacent fibres, was spilling over into to the fibrededicated to the faint G dwarf. This introduced a noise pattern that, if not re-moved, would have lowered the quality of the analysis greatly. A substantialpart of the processing of the data was therefore spent on detecting and remov-ing the light contaminations to ensure a high-quality analysis.

3.4.1 Equivalent width and curve of growthAn appropriate measure of the strength of a line is the equivalent width, W.This is the integrated depression of the emergent flux profile of a spectral linenormalized with respect to the continuum.

W =∫ Fcont −F line

Fcont (3.1)

The equivalent width corresponds to the width of a rectangular portion of thespectrum completely blocking the emergent flux and an illustration of this canbe seen in Fig. 3.1.

At relatively low abundances the spectral lines are weak and the linestrength scales linearly with the number of absorbers (W N). As theabundance increases the core of the line approaches its maximum value(saturation) and the curve flattens (W

√lnN). In this case, the lines are

rather insensitive to changes in abundance. At even stronger abundancesthe equivalent width of the line increases again (W

√N). This behaviour

of spectral lines is known as the curve of growth and an illustration of thequalitative behaviour can be seen in Fig. 3.2.

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No

rmal

ized

flu

x

0

1

W

Figure 3.1: The equivalent width of a spectral line, W , corresponds to the width of arectangular portion of the spectrum completely blocking the emergent flux.

3.4.2 Deriving the atmospheric parametersThe main constraints used in the early solar twin studies have been concerningthe atmospheric parameters, effective temperature, surface gravity, metallicityand micro-turbulence. Furthermore, age, lithium abundance, activity and ro-tation has been used to verify or discard possible twins. The same approach,regarding the atmospheric parameters, was applied in the analysis of M67–1194. As we wished to determine the atmospheric parameters separately, a setof lines sensitive to mainly each one of the parameters was used. The hydro-gen line, caused by electron transitions from quantum number 2 to 3, is arelatively strong feature in solar-type stars compared to other atomic lines. Inthe temperature regime of solar-type stars, H is mainly sensitive to effectivetemperature. The core of the line, formed in layers higher up, is most likelyaffected by non-LTE. The wings of the H line, however, formed in layerswhere LTE is maintained, provides an efficient temperature measure.

As weak lines scale linearly with abundance, these are important when de-riving the metallicity. In paper II we used a set of weak Fe lines to determinethe metallicity ([Fe/H]) of M67–1194. The moderately strong Fe lines, on theother hand, are on the flat part of the curve-of-growth and are therefore littlesensitive to changes in abundance. These lines can instead be used to derivethe broadening of the line introduced by micro-turbulence.

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Figure 3.2: The curve of growth specifies the line strength (equivalent width, W ),of a spectral line as a function of elemental abundance, A. The numbers I, II and IIIplotted below the curve denote weak line, saturation and strong line, respectively. Thearrow shows an increasing micro-turbulence.

The broad wings of the strong Mg lines at 5175 Å (the Mg triplet), aresensitive to surface gravity. If the effective temperature and the Mg abundance(e.g. determined from a weak Mg line) are known, the wings can be used toestimate the surface gravity. This method was applied to determine the surfacegravity of M67-1194.

In addition to these, two characteristics of the weak Fe lines in solar-typestars can be used to estimate the effective temperature and surface gravityin a spectroscopic study. Neutral and ionized iron are relatively insensitiveand sensitive to gravity, respectively. Neutral iron lines with low and highexcitation potentials of the lower levels are rather sensitive and insensitive tochanges in effective temperature, respectively. 1

3.4.3 Equivalenth width, 2, and the spectroscopists eyeThe behaviour of spectral lines as introduced by effective temperature, surfacegravity, metallicity and micro-turbulence, can be examined by different tech-niques depending on the amount of lines, spectral region, resolution and thedesired accuracy of the analysis.

1The gravity sensitivity Fe II is on the order of +0.03 dex in abundance per -0.1 dex in surfacegravity. The temperature sensitivity of Fe I lines with low excitation potential is approximately0.06 dex in abundance per 100 K in temperature.

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Figure 3.3: The best synthetic fits to a number of lines used in the abundance analysisin paper II. The lines plotted indicates the strongest (not including H and the Mgtriplet) and the weakest lines used in the analysis.

The equivalent width, as has already been mentioned, can be used to mea-sure the strength of a line. Abundance determinations via equivalent widths,have the advantage of being essentially insensitive to broadening effects of thelines caused by e.g. rotation of the star, large scale motions as convection orbroadening of the lines caused by the instrument.

If the atomic lines are blended, adjusting a synthetic spectrum to fit theobserved line might instead be the preferred method. This is due to the equiv-alent width measuring the total depression in the selected wavelength regionregardless of blends.

Depending on the amount of lines treated in the analysis, automated pro-cedures can be used to minimize the 2 of the synthetic fit to the observedspectrum. In the case of having a large amount of lines, a line mask can beused to discard unwanted features.

On the contrary, when having a rather small amount of lines (as in paper II)using eye-judgement might be the preferred method: The experienced spec-troscopist can easily detect and discard non-relevant effects such as cosmichits and instrumental defects. A number of lines treated in paper II and theirinteractively established synthetic fits, are shown in Fig. 3.3.

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3.4.4 The peculiar composition of the SunSpectroscopic studies suffer from systematic errors such as inadequate as-sumptions in the applied model atmospheres and missing or inaccurate atomicand molecular data. Solar analogs are by definition very similar to the Sun andin a differential analysis these errors will largely cancel out. This makes highaccuracy measures of stars similar to the Sun possible, unlike other stellarobjects.

In recent studies of individual chemical elements in nearby solar twins(Meléndez et al. 2009, Ramírez et al. 2009, 2010) a distinct trend as com-pared to observed solar values has been discovered, linked to the propertiesof the elements. Refractory elements such as Ca, Ti, Al, Ni, are likely to formdust grains and are also found in the terrestrial planets. When comparing ob-servations of neighboring twins with analyses of the solar photosphere, therefractory elements seem to be somewhat underabundant in the Sun. Volatileelements, such as C, N, O, however, are more abundant in the Sun relative tothe twins.

In paper II we performed a careful line-by-line analysis of M67-1194, ex-ploring in particular the refractory and volatile elements. As the star was sus-pected to be similar to the Sun, a purely differential approach was appliedusing a solar-proxy. To minimize possible instrumental effects, a day-timesky-spectrum observed with the same instrument as our object was used. Re-markable enough, the same abundance pattern was found in the cluster star asobserved in the Sun making M67-1194 maybe the most sun-like star observedso far.

One of the suggested explanations for the seemingly peculiar compositionof the Sun as compared to nearby twins, is the formation of terrestrial plan-ets. If the Sun and the observed twins formed from a gas rather similar ininitial chemical composition, one expects to see the same abundance patternas observed in the Sun. The formation of planets will lower the amount ofrefractory elements in the protoplanetary disk, hence the material falling inon the young star will be dust-depleted. As the majority of the observed fieldtwins are not known to host planets larger abundances of refractory elementsshould be observed in their photospheres as compared to the Sun. This how-ever presumes that the stars had thin convection zones at the time of accretionfor the pattern to stay imprinted. Interesting enough, the enrichment of re-fractories compared to volatiles in the terrestrial planets and meteorites matchthe discrepancy seen in the sun relative to the solar twins rather well. If theanomalous chemical composition of the Sun is in fact due to planet formation,it could be used as a tracer to find planet host candidates.

M67-1194 is located in a rather dense cluster and it is maybe more likelythat its protoplanetary disk was cleansed by a nearby supernova or radiativepressure from brilliant stars rather than planet formation.

Finally it is interesting to ask whether or not it is possible that the Sun wasonce formed in M 67 and has evaporated from the cluster. One question is if a

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planetary system like ours can survive in a cluster environment on a timescalelong enough for the star to evaporate. It can be shown that the planetary systemcould in fact survive, however the Oort cloud will not (private communication,H. Rickman, B. Gustafsson & A. Korn). Whether or not it is possible or likelythat the Oort cloud could have formed at a later stage will have to be exploredfurther.

The fact that M67-1194 seems to be very similar to the Sun, also makes ita perfect calibration target, not the least in large upcoming surveys like Gaia(ESA).

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4. M dwarfs

My goal is simple. It is a complete understanding of the universe,why it is as it is and why it exists at all

/Steven Hawkins

The solar neighborhood is mainly populated by stars less massive than theSun. As much as 50–70% of the Galactic population is thought to consist ofM dwarfs (Chabrier 2003). Despite this, little is known about the numerous Mdwarfs due to the intrinsic faintness characterising the stars at the bottom ofthe main sequence in the HR diagram.

The large amount of M dwarfs also makes detailed knowledge of these starsessential for describing quantities such as the initial mass function (Salpeter1955) and the present day mass function. The distribution of stellar mass givesimportant insights into the evolution and chemical enrichment of the Galaxy.As there are no direct observational determinations of the mass functions,they must be derived via the observed brightness of the objects, the luminos-ity function. The transformation from brightness to mass is based on stellarmodels, that are sensitive to e.g. chemical composition.

The faintness of the M dwarfs have made detailed analyses difficult andthe field of research is therefore relatively young. The first attempts to deter-mine metallicities for M dwarfs were carried out during the seventies (Mould1976, 1978) in line-by-line analyses of atomic lines in the near infrared wave-lengths with intermediate resolution. Later M dwarfs were divided into threebroad categories based on metallicity, dwarfs, subdwarfs and extreme subd-warfs (Gizis 1997), using low resolution optical spectra and synthetic spec-tra. Although the first attempts to analyse M dwarfs were merely indica-tive, the opportunity to perform a careful abundance analysis has improvedgreatly. Large-aperture telescopes and instruments designed to yield high ac-curacy measurements in specific wavelength regions have improved the sit-uation greatly. Furthermore, the improved computer capacity making high-resolution synthetic spectra possible as well as the continuous updates ofatomic and molecular data used in the modelling, have made detailed anal-yses possible.

Abundance analyses of known solar-type planetary hosts have revealed acorrelation between super solar metallicity and the frequency of planets (San-tos et al. 2004, Fischer & Valenti 2005). It is therefore interesting to investi-gate whether or not the same relation holds for M dwarfs. Recent photometricabundance determinations of M dwarfs with and without planets yield contra-dictory results as both subsolar metallicities (Bonfils 2005) are derived as wellas super solar abundances (Johnson & Apps 2009) for known planet hosts.

The search for extra solar planets has been focused mainly towards solartype stars (F,G,K), a maybe preferred starting-point considering the one con-

33

firmed habitable planet so far, the Earth. Recent discoveries of planets aroundM dwarfs and notably a planetary system around an M dwarf, GJ 581(bcde)(Bonfils et al. 2005b, Udry et al. 2007, Mayor et al. 2009) have given rise to anincreased effort towards finding planets around M dwarfs. There are severalongoing observational surveys with the main aim to detect planets around Mdwarfs (e.g. MErth Nutzman & Charbonneau 2008).

4.1 The M dwarf spectrumAccurate metallicity determinations of M dwarfs have proven difficult. In thelow temperature regimes covered by these objects, 2000–4000 K, molecularbands dominate the spectrum. In the optical wavelength region absorption bymainly TiO but also VO, CaH and MgH (early-type), give rise to heavy de-pressions in the continuum. Further out in the near to intermediate infraredwavelengths, FeH and H2O are the dominant absorbers with contributionsfrom also CrH. The pseudo-continuum introduced by molecules in the opti-cal wavelength region makes a precise continuum placement in these regionsdifficult and abundance determinations uncertain. The dominant TiO featurescan on the other hand be used as an efficient measure of effective temperatureand are also rather sensitive to metallicity.

The near infrared to infrared is mainly characterized by a growing absorp-tion by water with later spectral types. The large amount of water lines in thisregion makes abundance determinations based on atomic lines difficult due tothe many blends by water lines. The large amount of absorption lines causedby water increases the computational time of synthetic spectra considerably.The uncertainties in the abundance analysis also increase due to inadequate orinaccurate water line lists.

In early type M dwarfs, M0–M4.5, FeH is a main molecular feature in thenear infrared. Its absorption is sparse enough to make a reliable continuumplacement possible and an accurate abundance determination feasible. In pa-per III we performed a high-resolution spectroscopic abundance analysis ofa number of early type M dwarfs. In Fig. 4.1 the observations of one of thetargets (GJ876) is shown together with an optical comparison spectrum of thesame star.

4.2 The metal content of M dwarfs (Paper III)Stellar formation theories tell us that stars in binary systems have most likelybeen formed out of the same molecular cloud. The members in a binary systemshould therefore also have the same chemical composition. Binary systemsare common among low mass dwarfs and many systems containing a solar-type primary and an M dwarf secondary are known. These particular systems

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Figure 4.1: The M dwarf star GJ876. The observations are marked with a gray shade.Upper panel: Observations from paper III and the best fit synthetic spectrum. Lowerpanel: Observations in the optical wavelength region and a synthetic fit. 1% of theTiO lines are labled. Atomic lines are marked as as arrows and the wavelength scaleis in nm.

provide an important opportunity to explore the accuracy of M dwarf modelatmospheres. Solar-type stars are well observed and model atmospheres de-scribing these are well explored. The spectral dominance of molecules seenin M dwarfs is also a lot less prominent in the hotter solar-type stars, makinginaccurate molecular line data less critical. Calibration attempts using a solar-type primary and an M dwarf component have been made to verify the relia-bility of metallicity determinations of M dwarfs (Bonfils 2005a, Bean 2006b)and we applied the same calibration technique in paper III. We observed threewide binary systems and eight single M dwarfs with the aim to validate abun-dance determinations techniques based on spectroscopic observations and toestablish a reliable basis for a new metallicity scale of M dwarfs.

4.2.1 Less molecular features – more telluric linesTo avoid the heavy blends of TiO in the optical wavelength region, the nearinfrared J-band (1100–1400 nm) was observed. The M dwarfs were chosen tobe early type, making FeH the main molecular absorber in the spectral region.

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0.0

0.2

0.4

0.6

0.8

1.0

1175 1176 1177 1178 1179 1180Wavelength [nm]

0.0

0.2

0.4

0.6

0.8

1.0

N

orm

aliz

ed f

lux

K

Ca

K

Ti

Fe

CaTi

Ca

Figure 4.2: Telluric removal in the M dwarf GJ436. Upper panel: Observed stellarspectrum including telluric lines (black) and observed telluric lines via a rapidly ro-tating early-type star (gray). Lower panel: The telluric-corrected spectra of the star(black) and the best-fit synthetic spectra (gray).

Early type M dwarfs have been shown to be little affected by dust comparedto later spectral types (≥M6, Jones & Tsuji 1997; Tsuji 2002) and dust wastherefore not included in the atmospheric models.

The observed wavelength region was selected to contain little molecularabsorption and mainly atomic lines, but a majority of the prominent lines ob-served were of telluric origin. To represent the telluric lines a rapidly rotatingearly type star, essentially free from atomic and molecular lines was observed.A common procedure for calibrating the wavelength scale is to observe tho-rium and argon (Th-Ar) lines produced by a calibration lamp and adjust theseto fit measured laboratory wavelengths. In the infrared the number of Th-Arcalibration lines declines and it was clear in a comparison of the pipe-line pro-cessed data and tabulated spectral lines that the wavelength calibration did notproduce the desired outcome. A new wavelength calibration was therefore es-tablished using the telluric lines in the observed spectrum and tabulated wave-

36

lengths for these. In Fig. 4.2 a representative wavelength region is shown toillustrate the amount of telluric lines and their successful removal.

4.2.2 The unknown infraredThe infrared wavelength region is still rather unexplored compared to the opti-cal region. The available line lists of atomic and molecular data in the infraredsuffer from missing or inaccurate line parameters.

To test the quality of present atomic line data we used the latest version ofthe VALD database (VALD3) to compose a line list in the J-band. A syntheticspectrum of the Sun based on the composed data was calculated and comparedto high-quality high-resolution solar observations. The comparison showedthat inaccuracies in atomic line data in the J-band do exist as a number of linesdid not match the observed line strengths. The solution to this problem wasto create astrophysically determined quantities, i.e. by adjusting the tabulatedline parameters1 as well as the micro and macro-turbulence parameters to fitthe observed spectrum of the Sun.

We noted that some of the atomic lines with line parameters calibrated onthe solar fit, grew too strong in the cold M dwarfs. Potassium is known tobe affected by non-LTE in the Sun (Zhang et al. 2006) and the synthetic fitof these lines was too strong in the M dwarfs. As the non-LTE effect in theM dwarfs could not be verified, the four K lines in the observed wavelengthregions were excluded from the analysis.

For a given set of atmospheric parameters, effective temperature, surfacegravity and the micro-turbulence parameter, the best-fit synthetic spectrabased on a 2 minimization was established by adjusting the metallicity,[Fe/H]. To verify the convergence of the abundance determinations, a set ofinitial starting parameters was used in the calculations. The respective 2

and derived metallicities could then be used to locate the global minimum.The atomic lines present in the observed spectral regions were too few toallow determination of all atmospheric parameters simultaneously. Thereforephotometric calibrations were used to determine the effective temperatureand surface gravity. The unknown micro-turbulence parameter was set to1 km/s.

In paper III we determined new and accurate metallicities for 14 M dwarfs.When comparing with previous studies of stars in common, we found that ourdeterminations confirm higher metallicity values rather than lower ones. Thisis the first time a high resolution spectroscopic analysis has been carried outfor M dwarfs in the J-band. The key advantages of this method compared to

1 The line parameters determined, were logg f , where g is the statistical weight and f the oscilla-tor strength, and a parameter specifying the line broadening by collisions with neutral particles(van der Waals broadening). Atomic hydrogen was assumed to be the main source for colli-sional broadening.

37

spectral index methods or photometric calibrations is its high accuracy andthe possibility to derive individual elemental abundances.

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5. Perspectives for the future

In this thesis tests of stellar atmosphere analysis techniques as well as newdiscoveries are presented. The work described can be improved and continuedin several directions. The validation of stellar atmospheres via uvby–Hphotometry is interesting as it indicates the progress and shortcomings ofpresent-day 1D models. The successful effective temperature calibrationsbased on synthetic (b − y) colours and H indices and their possible usein cluster applications should be tested further. The origin of the somewhatdifferent sensitivities in the synthetic m1 and c1 indices as compared to theobserved values, and in particular for the cooler models, needs to be exploredfurther. New and more accurate atomic and molecular data will indeedimprove the situation although this will probably not fully correct for thediscovered discrepancies. It is also interesting to discuss the limitations of the1D assumptions such as the description of convection via the mixing-lengthrecipe and its effect on the synthetic colours in the uvby–H filter system,and the effects of the LTE assumption.

The proposed solar twin, M67–1194, and its surprising similarities to the Sunshould be explored further. Whether or not the volatile/refractory pattern seenin both the twin and the Sun is in fact a tracer for the formation of planetsor a characteristic seen in cluster environments and/or specifically M 67 arequestions to be answered. Further observations of suggested solar analogs inM 67 will help to answer the latter. Time has been awarded to the project forcontinued high-resolution spectroscopic observations of G dwarfs in M 67,and a number of solar analogs will hopefully be observed in the spring of2012.

The possible calibration applications of M67-1194 for studies in the 15magnitude regime should also be explored. The upcoming satellite missionGaia will observe a large number of stars and minor bodies in the solarsystem. M 67–1194 is a suitable calibration target for investigating theperformance of the instruments as its low magnitude compared to observedfield twins coincides with the magnitude range of the sources that Gaia willobserve. A technical note to the Gaia community suggesting M67–1194 asthe preferred calibration target is currently being written.

The metallicity scale for M dwarfs has been uncertain. The lack of conver-gence in abundance determinations using different methods such as photo-

39

metric calibrations or spectroscopic indices suggest more high-quality obser-vations. We have shown that abundance determinations based on high resolu-tion spectroscopic observations in the near infrared provides a robust methodfor deriving metallicities. A follow up study based on the same technique andcovering a larger sample of M dwarfs with both higher and lower metallici-ties will provide important information on the metallicity scale. New instru-ments, such as SIMPLE (Origlia et al. 2010), designed for high-resolutionspectroscopy covering wide spectral ranges in the near-infrared at the largesttelescopes, will undoubtedly improve the accuracies and efficiency of abun-dance determinations.

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6. My contributions to the includedpapers

Paper II carried out the computation of the grid of synthetic spectra and calculatedthe corresponding synthetic colours. I established a large part of the stellarcomparison sample and performed the cluster tests, tests with different filtertransmission functions. I established the Vega transformation calibration,derived the calibration expressions, and performed most of the sensitivitycalculations. Wrote most of the paper.

Paper III carried out parts of the post-processing of the data. I performed the analysisof the atmospheric parameters as well as individual atomic elements. Wrotemost of the paper.

Paper IIII carried out the post-processing of the data and the calibration of the atomicline data. I carried out the computation of the synthetic spectra and performedthe analysis. Wrote parts of the observing proposal (was P.I. for the secondproposal) and most of the paper.

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7. Swedish summary – Svensksammanfattning

Solen är vår närmaste stjärna. Blott åtta minuter bort mätt med ljusetshastighet förser solen oss med mer information än någon annan stjärna. Detär därför naturligt att använda solen som referens när vi observerar ochanalyserar andra stjärnor. Detta har dock visat sig vara svårt i praktiken.Den stora skillnaden i ljusstyrka mellan solen och andra stjärnor gör detoftast omöjligt att observera solen och de mycket ljussvagare stjärnorna medsamma instrument. Att använda samma instrument är kritiskt för att uppnåhög noggrannhet. En lösning på problemet är att istället observera objekt somär så lika solen som möjligt. Dessa är i regel ljussvaga och kan därför ocksåobserveras med ljuskänsliga instrument. Exempel på objekt som används föratt representera solen är dagshimlen, det reflekterade ljuset från en asteroideller månen och ljuset från andra stjärnor som påminner om solen. I densenare kategorin finner vi också de mest intressanta kalibreringsobjektendå det har visat sig vara svårt att hitta stjärnor som är mycket lika solen.Generellt delas sollika stjärnor in i tre kategorier. Soltypsstjärnor ärstjärnor som påminner om solen men kan avvika något i temperatur,grundämnessammansättning, storlek och ålder. Solanaloger är mycket likasolen och soltvillingar är identiska. Det är främst den senare kategorin somhar visat sig vara mycket ovanlig, åtminstonde i solens omedelbara närhet.

7.1 Stjärnatmosfärsmodeller och fotometri (Artikel I)Stjärnljuset vi observerar kommer till största delen från stjärnatmosfären.För att tolka den information om stjärnor vi erhåller från utsänt ljuskrävs teoretiska stjärnatmosfärsmodeller. Dessa används för att härledafundamentala egenskaper hos stjärnan som yttemperatur, ytgravitation ochgrundämnessammansättning. Det är därför av största vikt att de modeller vianvänder är så lika verkligheten som möjligt.

Genom att observera stjärnljus genom olika färgfilter kan man särskiljautsänt ljus i specifika våglängdområden, så kallade magnituder. Inomfotometrin placeras filter ut i våglängdsområden i stjärnspektrat som ärspeciellt känsliga för till exempel ändringar i temperatur. Det fotometriskauvby-H (Strömgren–Crawford) filtersystemet används ofta för att beräknaspecifika egenskaper hos stjärnor.

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För att undersöka tillförlitligheten hos befintliga stjärnatmosfärsmodellerkan teoretiska färger beräknas från modellatmosfären. En jämförelse medobserverade färger påvisar tillförlitligheten eller eventuella avvikelser hosde beräknade färgerna. I artikel I användes datorprogrammet MARCS föratt undersöka teoretiska uvbyH -färger beräknade från teoretiska spektrabaserade på stjärnatmosfärsmodeller. I en jämförelse med ett stort antalobserverade stjärnor vars färger och parametrar (yttemperatur, ytgravitationoch grundämnessammansättning) är kända, kunde vi sedan dra slutsatserom modellernas överensstämmelse med verkligheten. Det visade sig att deberäknade (b− y) och H färgerna, som framförallt är temperaturkänsliga,uppvisar näst intill samma känslighet som hos observerade färger. Deberäknade färgindexen c1 och m1 visade vissa avvikelser gentemotmotsvarande observerade index och i synnerhet för de kallaste modellerna.Orsaken till avvikelsen är ej ännu fastslagen men tros till stor del bero påinkorrekt och ofullständig information om de molekyl- och atomlinjer sompåverkar filtersystemet främst i den ultravioletta till blåa delen av spektrumet.

7.2 Solen och dess tvillingar (Artikel II)Observationer av närbelägna stjärnor har visat att solen är unik menockså relativt vanlig. Flera stjärnor som är näst intill identiska med solen,soltvillingar, har observerats i solens närområde. Vid en närmre, merdetaljerad undersökning av individuella grundämnen, har det dock visat sigatt få av dessa soltvillingar verkligen uppvisar de karaktärsdrag vi ser hossolen. Stoftbildande grundämnen såsom Fe, Ni och Al, finns till exempel ilägre halt i solens atmosfär. Andelen gasbildande grundämnen som C, N,O och S, finns i högre halt i solen jämfört med soltvillingarna. En möjligförklaring till den besynnerliga skillnaden mellan solen och tvillingarna kanvara förekomsten av planetsystem. Om planeter bildas i stoftskivan hos ungastjärnor kommer skivan till stor det att rensas på stoftbildande grundämnen.Resterna av skivan som sedan faller in på stjärnan kommer då att innehållamindre stoftbildande grundämnen jämfört med stoftskivor där inga planeterbildats. En annan förklaring skulle kunna vara att den protosolära nebulosanrensats på stoftbildande grundämnen på grund av en närbelägen supernova.

Messier 67, M 67, är en välobserverad gammal öppen stjärnhop. Hopenhar visat sig vara av ungefär samma ålder som solen och har en metallhaltliknande solens. På grund av det stora antalet stjärnor i M 67 utgör hopenett utmärkt område för att söka efter soltvillingar. I artikel II undersöktes ensoltvilling i M 67 genom högupplösta spektra. Stjärnan, M67–1194, visade sigi en noggrann jämförelse besitta näst intill identiska atmosfäriska parametrar(yttemperatur, ytgravitation och grundämnessammansättning) som solen. Enundersökning av specifika grundämnen visade också att stjärnan har sammahalter av stoftbildande- och flyktiga ämnen som solen. Huruvida dessa likheter

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härstammar från bildandet av planeter eller snarare påvisar andra förhållandenvid stjärnans bildande, återstår att undersöka. Den senare möjligheten skullekunna antyda att solen härstammar från en tät stjärnhop, kanske till och medfrån M 67.

7.3 Grundämnessammansättningen hos M-dvärgar(Artikel III)Observationer i solens omedelbara närhet har visat att stjärnor kallareän solen är mycket vanliga. Stjärnor av typen M, med temperaturermellan 2000 och 4000 Kelvin, kan utgöra så mycket som 70 % av denobserverbara baryoniska massan. De kalla M-dvärgarna är mycket ljussvaga.Högkvalitativa spektroskopiska analyser av dessa objekt kräver därför långaexponeringstider, vilket har gjort sådana studier relativt ovanliga. Studierav grundämnessammansättningen hos M-dvärgar har resulterat i varierandemetallhalter. Fler högkvalitativa undersökningar krävs därför för att etableranya tillförlitliga resultat.

De kalla M-dvärgarna bildar en mängd molekyler i sina atmosfärer. Dåfullständig information saknas för dessa molekyler, är teoretiska spektra förM-dvärgar relativt osäkra. Det infraröda J-bandet, 1100–1400 nm, innehålleri huvudsak svaga absorptionslinjer av FeH. Det låga antalet molekyläraabsorptionslinjer i detta våglängdsområde underlättar därmed en grundäm-nesanalys baserad på atomära absorptionslinjer och minskar osäkerhetenhärrörande från ofullständiga molekyldata. Stjärnor i dubbelstjärnesystem harmed största sannolikhet bildats ur samma stoftmoln och bör därför uppvisaliknande grundämnessammansättning. Soltypsstjärnor är, jämfört medM-dvärgar, välstuderade. Högkvalitativa observationer och välutvecklademodellatmosfärer gör grundämnesanalyser av soltypsstjärnor relativttillförlitliga. Genom att observera ett dubbelstjärnesystem bestående av ensoltypsstjärna och en M-dvärg kan tillförlitligheten hos modellatmosfärerna,det beräknade spektrumet och analysen i stort undersökas.

I artikel III analyserades den grundämnesammansättningen hos åttaM-dvärgar. Tre dubbelstjärnesystem innehållande både en soltypsstjärna ochen M-dvärg användes för att undersöka analysens tillförlitlighet. De nyametallhalterna överensstämmer med senare tidens studier och stjärnornasom observerats i samma dubbelstjärnesystem uppvisar liknande metallhalt.De framgångsrika resultaten av studien visar att analyser av högupplöstaspektra i det infraröda J-bandet är både tillförlitliga och att rekommenderaför framtida studier av M-dvärgar.

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8. Acknowledgements

I would first like to thank my terrific supervisors Ulrike Heiter, Andreas Kornand Bengt Gustafsson for all your time spent listening, encouraging andteaching. Without you this thesis would not have been the same. You haveinspired and guided me through my years as a PhD student.

My gratitude also goes to:Kjell Eriksson and Bengt Edvardsson, for your high spirits. Talking to youalways makes me smile. Johan Warell for being a great source of inspirationand for taking me to Hawaii. Nikolai Piskunov for being annoyinglyintelligent and always helpful.

Samuel for being my direct information link to the latest scientificachievments and for being the unbeatable squash partner. Thomas fordragging me out on necessary breaks and evenings at Uplands. My family fortheir support, encouragement and for always being there.Emma P for being the fantastic friend that always listen. Anders and Fredrikfor all the laughs and crazy times during the early part of my education.Johanna for all your support and encouraging postcards. Wlad, not only didyou introduce me to the Karaoke scene in Uppsala, you have been my rolemodel as a scientist. I will never forget your pedagogical skills, That’s theWindows way of doing it.... Thank you Stuart.Bettan, Erik, and all the other people at the division of astronomy and spacephysics.

Finally, Kristina. You came into my life when I needed you the most and Ikeep needing you. Your endless support and faith in me has kept me going. Iknow noone else who would stay up all night knitting just to keep me companywhile working. This thesis is for you.

Uppsala, 19 September 2011

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