M dwarf stars make up over 70% of stars by number in the Milky Way Galaxy and are known to host at least two exoplanets per star on average. Using mutually eclipsing double-lined spectroscopic binary stars (SB2 EBs), astronomers can empirically measure stellar properties of M dwarf stars including mass and radius. However, empirical measurements systematically differ from the predictions of stellar evolutionary models and show large scatter. Some M dwarf stars are outliers, with radii that are a factor of 2-to-3 larger than model predictions, assuming they were measured accurately. In this dissertation, I investigated whether the outliers, systematic offset, and the scatter seen in the mass-radius diagram are physical, using SB2 EBs with photometry from NASA's Kepler Mission and high-resolution near-infrared ground-based spectroscopy. Empirical measurements using space-based photometry and high-resolution near-infrared ground-based spectroscopy, together with Bayesian model-fitting techniques, provide significant advancements over previous measurements. For this dissertation work, a sample of Kepler EBs were carefully chosen to be detached and non-interacting. I conducted a radial velocity survey of the sample using Immersion GRating INfrared Spectrometer (IGRINS) with the Discovery Channel Telescope (DCT) and iSHELL with NASA's Infrared Telescope Facility (IRTF). Combined with high-precision Kepler data, I determined the masses and radii of the component stars in the sample. I also determined a new mass-radius relationship of M dwarf stars using the sample of Kepler EB systems. My investigation showed that the outliers in the mass-radius diagram of M dwarf stars are not physical and they are due to the quality of data and from analysis using different pipelines. I also showed that the offset and scatter in the mass-radius diagram are persistent, which are not from the measurement uncertainties. This suggests the need for an extra degree of freedom to accurately capture the discrepancies between the empirical measurements and model predictions. Lastly, I showed that reduced convective heat flow due to enhanced magnetic fields from rapid stellar rotation can account for the offset and scatter in the measurements.

M dwarfs are abundant and long-lived stellar objects. The formation of planets around stars in stellar systems is believed to be metallicity dependent. To determine the metallicity with synthetic spectrum analysis, the elements producing the absorption lines ofthe spectra first have to be identified. The aim of this thesis is to identify and list the elements or molecules that produce the absorption lines in the spectra of Barnard's star. This thesis was done at the Division for Astronomy and Space Physics at Uppsala University. High resolution infrared spectral data recorded in the J band 1.1–1.4 μm was downloaded from the CRIRES-POP database. The data had to be wavelength corrected due to the effects of Doppler shift. A modified IDL program was used to read the data files,normalize the flux to unity and plot the spectra. This procedure was also done with the telluric spectra using data from a solar flux atlas. The IDL program plotted the normalized spectra together in the same plot. With this procedure the absorption features originating from the earth’s atmosphere could be identified and discarded. The analysis of the spectral lines resulted in wavelength values which were tested against the VALD3 database to determine what elements were possibly responsible for the absorption features. The results are presented in a line list. It can be used with other software programs to determine the metallicity. The identified elements and molecules agrees in part with earlier measurements of stellar spectra from M dwarf stars except for a number of lines where no matching elements were found in the VALD3 database. A line list with possible elements in the photosphere of Barnard’s star can be constructed from the spectra using high-resolution infrared spectroscopy. / M dvärgstjärnor är de mest förekommande stjärnorna i vår galax. De har en mycket långlivslängd, vissa tusen gånger längre än vår sol. Det finns teorier om att planetbildning runt stjärnor styrs av halten av ämnen som inte är väte eller helium. Denna halt kallas metallicitet. För att på konstgjord eller syntetisk väg bestämma metalliciteten i Barnard’s stjärna, en M dvärg, behöver de ämnen som bidrar till absorptionslinjerna i fotosfären först identifieras. Målsättningen med detta arbete var att identifiera de grundämnen och eventuella molekyler som skapar absorptionslinjerna i spektrumet till Barnard’s stjärna. Detta arbete utfördes på institutionen för fysik och astronomi. Metoden använde ett modifierat IDL program för att läsa och plotta data. Högupplöst infraröd spektraldata från Jbandet (1.1–1.4 μm) till Barnard’s stjärna hämtades från CRIRES-POP databasen och data för det telluriska spektrumet från en databas med telluriska linjer. Därefter plottades de samtidigt i ett våglängdsöverlappande normaliserat spektra. I programmet gick absorptionslinjer som inte hade sitt ursprung i jordens atmosfär att urskilja manuellt. Då våglängderna för absorptionlinjerna bestämts, matades värden in i databasen VALD3. Analysen av de returnerade värdena från VALD3 genererade en resultatlista med de mest sannolika elementen för de olika absorptionsvåglängderna. Resultatlistan kan användas som ingångsvärde till program som syntetiskt beräknar metalliciteten. Resultaten överensstämmer till viss del med tidigare mätningar. Slutsatsen är att metoden med högupplöst infraröd spektral data kan användas för att bestämma en lista med element och molekyler från fotosfären i Barnard’s stjärna.