Desplazamiento forzado en San Miguel

For the collection of spectroscopic data of the sample, we performed high resolution spec- troscopy using the 2.2 m telescope at Calar Alto, Spain equipped with the fiber coupled ´echelle spectrograph FOCES (Fiber Optics Cassegrain ´Echelle Spectrograph). The performance of the spectrograph allows a resolving power of ∆λ/λ= 60,000. This and the well defined con- tinuum throughout the orders (Korn, 2002) enables us to perform spectral synthesis analysis of the F-, G-, and late K-stars of the sample. Especially the continuum can be extrapolated from one order to the other. We also know the position and the curvature of the continuum at lines which span more than one order like the Balmer-, magnesium-, or calcium lines. To know the exact shape of the continuum at these lines is required to measure e.g. the effective temperature using the Hα- and Hβ-line profiles, or to confirm the surface gravity using the magnesium Ib line profiles.

Additionally, M-stars of the Gershberg FSs sample which could not be observed at Calar Alto because of bad weather and technical problems, high resolution ´echelle spectroscopy was performed using the Tautenburg 2 m multipurpose Schmidt-telescope equipped with a short slit ´echelle spectrograph. The resolving power of the instrument is ∆λ/λ= 67,000, but the continuum is not as well defined as for the FOCES spectrograph. This is mainly due to the way flat field images are taken. Anyway, for the M-stars the spectral synthesis analysis cannot be performed, because the input of opacities for molecules and the atmospheric LTE model might not be sufficient.

FOCES observation and data reduction

The FOCES data were reduced using a dedicated software package implemented in IDL (In- teractive data language) which was developed by the construction team of the FOCES spec- trograph and provided by Thomas Gehren and Klaus Fuhrmann, but it is also available at the Calar Alto Observatory. Each afternoon bias, flat field and thorium argon images were taken. For the flat field images the internal flat field lamp was used which is located close above the fiber entrance and the light is projected onto the entrance diaphragm by moving a mirror into the light path. A series of three flats were taken, where the first image was well exposed in the red wavelength regime, the second image was well exposed in the green wavelength regime and the red wavelength regime was overexposed and in the third flat field image, the blue wavelength regime was well exposed while the red part of the spectrum was overexposed. After these three images the telescope was moved to another position in the dome simulating the movement of the telescope as during the observations in the night. This

2.4. OBSERVATION AND DATA REDUCTION 27

procedure was repeated ten times each afternoon. During all the calibration and science ex- posures the so called ’fiber shaker’ was active, which shakes the fiber close to the entrance of the spectrograph. This reduces the noise which is introduced onto the spectrum by the fiber, as was shown by empirical test. An idea why this ’fiber noise’ is introduced if the fiber is not moved is the following: The fiber is connected at the upper and lower end to a fiber head which is mounted to the telescope and the spectrograph, respectively. This coupling squeezes the fiber. When the fiber lies in a certain position, some wavelengths are transmitted through the fiber well and others are absorbed or scattered in the fiber. These specific wavelengths which are not transmitted through the fiber but scattered depend on the curvature of the fiber. Shaking it only slightly will remove this effect because the curvature of the fiber is changed permanently. Additionally, the movement of the telescope during the acquisition of the flat field images simulates the position of the fiber during observations. Also the position of the fiber while the telescope is moved changes the performance, because the great overall curvature of the fiber is changed. The points of the fiber which are squeezed have a different diffraction index than the free fiber. The fiber cladding and the core are deformed at these two positions which can introduce scattering of light through the cladding.

The bias and thorium-argon images (arcs) were taken at the beginning and the end of the night. Wavelength calibration during the night is not necessary because the instrument is mechanically decoupled from the telescope by the fiber and therefore mechanically very stable, meaning the spectrograph does not move when the telescope is pointed. It is located in a dedicated room below the telescope. The temperature in this room does not change appreciably during the night, even though it is not especially temperature stabilized. For the spectral synthesis analysis, we do not need a subpixel precision for the wavelength calibration. We are not measuring high precision radial velocity variations which can be caused by the presence of planets or (sub)stellar companions. For this kind of observation a long time baseline is required in any case. For our purpose the precision is sufficient and we did not want to lose observing time, because each thorium argon image takes about five minutes including the movement of the lamps and mirrors as well as the warming up of the lamp.

The bias of each science and flat field image was subtracted using a mean bias image created of all acquired bias images in the observing run. As a next step the spectra, the flat field, and the arc image were extracted and the corresponding rows of the CCD of each order were coadded after applying a weight to each row of the extracted order depending on the count rate. After that each coadded order of the flat field image is normalized to one and the coadded orders of each science image are divided by the corresponding flat field order. This is necessary, because the fiber illuminates the central rows of each order much stronger than the rows on the edge. Dividing the rows on the edge which have a pixelcount close to zero by a flat field, that also has a pixelcount close to zero, will result in an unreliable pixelcount number. For a description of the implemented method, see Horne (1986).

After the flat fielding the wavelength calibration is assigned. To check if major shifts of the wavelength have occurred we compare the different thorium argon images acquired in the beginning and at the end of each observing night first. In case of shifts, the wavelength calibration is done using the thorium argon image which was taken closest to the observing date.

Reduction of the Tautenburg data

For the Tautenburg data the situation is slightly different. The spectrograph is located in the Cassegrain focus of the multipurpose Schmidt telescope, which means that the lightpath leads across a mirror which is inserted instead of the Schmidt camera and which reflects the light through the axis of the telescope onto the entrance slit of the spectrograph. This mirror has

28 2 THE SAMPLE

a curvature the way that the short focal length of the Schmidt telescope is prolonged, so that spectroscopy in the Cassegrain focus is possible. This configuration of a Schmidt Telescope is not very typical. †

This setup means the spectrograph is mechanically decoupled from the telescope as FOCES and indeed it is also located in a climate controlled room at a stable temperature. The light is projected directly onto the entrance slit of the spectrograph, so that the star can move along the slit during the night. Each star, therefore, has an individual aperture. The light of the lamp used for flat fielding is projected directly onto the slit by a mirror so the illumination of the slit is different for the flat field images and the science targets. This results in a very unreliable flat field correction as the light paths of the lamps and the stars are different. The data cannot be used for spectral synthesis analysis, yet. Attempts are made to change the flat fielding procedure and to use a flat field screen mounted inside the dome. First tests performed with this setup by Matthias Ammler show that the flat field correction has improved and that now the spectra look promising for the spectral synthesis analysis. In the future the Tautenburg staff plans to equip the spectrograph with an optical fiber.

The data reduction and calibration of the science targets was performed similar to the procedure described for DFOSC (see Section 2.4.1).

The spectrograph is temperature stabilized and therefore does not change its instrument characteristics during the night. Additionally, it is equipped with an iodine cell which can be used as a stable wavelength reference for radial velocity planet or companion star search down to a radial velocity signal of 3 m/s. In Chapter 5 we will describe the radial velocity measurements with this equipment which are currently still ongoing for the most promising young stars of the flare star sample.

†_{This design was chosen because of the special conditions in Tautenburg. The original design was made}

following the construction plans of the Palomar survey telescope with a closed metal tube to block the stray light. But in Tautenburg they desired to be able to perform spectroscopy in bright time when the moon is up. So they designed the Schmidt Telescope with a Cassegrain focus. The Schmidt camera is removed and a mirror is inserted instead.

Also it is remarkable how the location was chosen: At the time when the telescope was built, the scientists were convinced that the best seeing conditions could be found on a small hill located in a forest. Bearing this in mind, Tautenburg is perfect.

The third remarkable feature of the Tautenburg telescope is the dome heating. To avoid having fog settle on the cooler mirrors, one has two possibilities: One cools the telescope during daytime or night fall with an air condition or a big fan to the temperature which is present in the night. Or you heat up the dome and telescope. For Tautenburg, the second possibility was chosen. (Dr. Eike Guenther, private communications)

Chapter 3

Stellar atmospheres models

The stellar light observed on earth or from space is emitted from the outer regions of the star, the atmosphere. The atmosphere can be divided into the photosphere and the chromosphere. The inner section of the star where the energy is produced, cannot be observed directly because photons which are generated in the center of the star interact with material of the lower sections and the atmosphere. The atmosphere of the star is the region where the energy coming from the center of the star is absorbed and reemitted, and finally escapes the star. We will formulate the mathematical equations to describe the physics of the observed phenomena. In this chapter we will give the basic ideas of the model atmospheres of late F-, G-, and early K-type stars. After this it will be explained how to calculate model spectral lines and compare with observed lines in order to derive the physical parameters of the stars.

The easiest case would be that the star emits as a black body. But as very early spectro- scopic observations of stars have shown, this is not true. Already in 1814 Fraunhofer observed absorption lines in the spectrum of the sun and later on around 1823 in other stars as well. He already knew that the overall emission does not follow a simple black body curve. The development of ’real physics’ began with Kirchhoff and Bunsen (1859) in Heidelberg. During that time the beginning of spectral analysis was set with the interpretation of the Fraunhofer lines. 1860 Kirchhoff formulated Kirchhoff’s law, which gives the relation between emission and absorption of radiation in thermodynamical equilibrium.

3.1

Assumptions

When observing stars from the earth, we perceive all stars except the sun to be point sources. So in principal we do not observe a spatially resolved object but only the integrated light from the surface pointed towards us. Surface features like stellar spots, plage regions, convection and granulation are not resolved.

Assuming that the height of the atmosphere is small compared to the radius of the star, we can describe the atmosphere to be plane-parallel. This simplifies the equations a lot. Observations of the sun show that the atmosphere is about 400 km deep whereas the radius of the sun is 700,000 km. The assumption that the atmosphere is small holds for the sun and we can assume that it is the same for stars which are comparable to the sun.

For young stars or M-, L-, or T-type stars, the convection layer might be deeper or even reach to the center. For these stars Ludwig et al. (2002) have simulated the convection with their three dimensional hydrodynamical computer model of the atmosphere (Allard et al., 2001). The chemical composition of these stars also plays a major role, because the atmo- spheres are cool so that two and three atomic molecules are stable and can be observed. The chemistry of these cool stars poses a huge problem since opacity functions are not yet well

30 3 STELLAR ATMOSPHERES MODELS

Figure 3.1: A schematic view of the different layer in the sun. For the modeling of the star only the atmosphere is important. The atmosphere includes the photosphere and the chromosphere.

calculated. Measurements in the laboratory of the emission and absorption of these molecules must be determined at these temperatures and pressure conditions of a star. Having this in mind, we will not try to model these cool objects with our model atmosphere code.

The next assumption would be that the star is in thermal equilibrium (TE). In this case the star is a closed system and isothermal object, not losing energy or material to the surrounding medium, especially not radiating. The energy of the system in TE is distributed equally among the different degrees of freedom. Of course we describe the gas of the atmosphere as an ideal gas. The intensity distribution of the spectrum of such a system is a Planck distribution:

B_ν(T) = 2hν3 c2 1 exp¡hν kT ¢ −1 (3.1)

whereh is Planck’s constant (h= 6.62618×1034Js),kBoltzmann’s constant (k= 1.38066×

10−23_JK−1 _{= 8.61733×10}−5_{eV),cis the speed of light (c= 2.99792458×10}8_ms−1_{), T is the} effective temperature of the star, andν denotes the frequency of the emitted light. It is clear that a real star is not in thermodynamic equilibrium. The ratio of particles with a velocity vr to the total number of particles follows a Maxwell distribution

dN(vr) Ntot = ³ _m 2πkT ´3 2 exp µ −mv2_r 2kT ¶ dvr. (3.2)