EVALUACIÓN 5 METODOLOGÍA

The temperature is the parameter with the largest influence on the silver and palladium abundances. This parameter is in general seen to affect (0.01 to 0.14 dex depending on the element) the abundances of lighter elements (Cayrel et al. 2004). For silver I found the effect of changing the temperature by 100 K to be slightly larger (0.05 to 0.2 dex). Different colour calibrations from various groups were tested confirming a difference in the temperature scale as is mentioned in Section 3.2.1.

Consistently too high or low temperatures cause offsets in abundances, and in order not to predict too high abundances by adopting a temperature scale that predicts high temperatures, I selected a scale that predicts intermediate temperatures (see Section 3.2.1 and Figure 3.1). This places my determinations of the stellar parameters in the mid range of the stellar parameters compared to other studies. There are several ways to determine the temperature of a star, one method is by fitting synthetic spectra with known temper- ature to temperature sensitive lines (such as H lines), another method to determine the temperature is via excitation potentials and a third method is to adopt calibrations that relate the star’s colour and metallicity to the temperature. Not all methods can be applied to all types of stars. For instance horizontal branch stars, which have anti-symmetric lines making line fitting very difficult, and due to their very blue colour they fall outside the allowed calibration ranges, which leaves the excitation potentials as the only temperature determination method. This method can lead to large uncertainties depending on the accuracy of the excitation potentials of the selected Fe lines. Therefore I chose the most accurate T-colour calibration (as done in high accuracy abundance studies Mel´endez et al. (2010)) and supplemented with excitation temperatures only when necessary. There ex- ist several such colour-T calibrations and in order to avoid inhomogeneities and method dependent offsets in the colour calibrations it is important to stick to one calibration.

The colour of a star is sensitive to its temperature and metallicity. Photometry, colour indices and extinction are necessary input for this colour calibration as is the metal- licity. Colour-Teff calibrations from Alonso et al. (1996b), Ram´ırez & Mel´endez (2005),

¨

Onehag et al. (2009) and Masana et al. (2006) were applied for V,K and Str¨omgrem pho- tometry. Alonso et al. (1994, 1996b) noted that the V-K colour is a good choice because it is almost insensitive to metallicity and includes infra-red magnitudes which are gener- ally less affected by reddening (less dust absorbed) compared to the visual magnitudes. However, according to L. Casagrande (priv. comm.) this colour calibration is far from being flawless, since it spans over a wide flux range, in which case the Infra Red Flux Method (IRFM) (Alonso et al. 1996a; Casagrande 2008) has difficulties fitting the entire black body curve. A purely infrared colour is preferred, but for our data sample it is not available for all the stars. Therefore, the V-K colour calibration had to be adopted:

θef f = 0.555 + 0.195(V −K) + 0.013(V −K)2−0.008(V −K)[Fe/H]

+ 0.009[Fe/H]−_0.002[Fe/H]2 _(3.1)

3.2 Temperature 31

(see Alonso et al. 1996b) e.g. 1.1 ≤ _(V −_K) ≤ _{1.6 for -1.5} ≥ _{[Fe/H] > -3.5 and the}

lower limit for (V-K) decreases with increasing metallicity. This agrees with the fact that for a fixed temperature the colour of a star will become more red the more metal-rich it is. The impact the metals have on the colour can be explained by the line blanketing from all the metallic lines. The UV and blue continuum will be reduced and the star will experience a flux distribution to the red wavelengths (Ram´ırez & Mel´endez 2005). In order to apply the colour-Teff formula for the dwarf stars from Alonso et al. (1996b), the colour terms need to be de-reddened and converted to the TCS (The Carlos Sanches Telescope) filter system from which this calibration was derived. Our infra-red magnitudes are taken from 2MASS2 _{and the visual magnitudes are from the Johnson-Cousins (Johnson) filter} system3_{. Thus, to apply the formulas from Alonso et al. (1996b, 1999) we need to convert} the 2MASS to Johnson and then to TCS following Bessell (2005). Ram´ırez & Mel´endez (2005) is on the other hand adjusted to deal directly with 2MASS-Johnson colours so no conversion is needed here. An example of calculating the temperature for a dwarf star is given below. According to Bessell (2005) the K magnitudes can be converted from 2MASS to the Johnson (J) filter system via the following:

K2M ASS =KJ −0.04 (3.2)

and converting the V-K colour from Johnson to TCS can be carried out via this relation: (V −K)T CS = 0.05 + 0.994(V −K)J (3.3)

The above mentioned filter relation is taken from Alonso et al. (1994) (to keep the calibration as homogeneous as possible) and the two filters are seen to be very similar for this colour. The difference between TCS and Johnson filter system is on average 0.04 magnitudes. This indicates that the filter conversion from Johnson to 2MASS would almost cancel out the conversion from Johnson to TCS. Nissen et al. (2002) note that the error on the V - K colour might be 0.05 mag, similar to the colour difference from the filter conversion, would lead to an error of± 50 K in the temperature. I found that a 0.04 mag increase in V - K could lead to a 100 K decrease in temperature for a few of the dwarfs, but generally agree with the estimate from Nissen et al. (2002), and would furthermore only imply a decrease of 30 K for the giants. To limit the errors and uncertainties the filter conversion was implemented.

The reddening has a much larger effect on the temperature than the filter conversion. The values for the reddening have generally been taken from Nissen et al. (2002, 2004, 2007) for the dwarfs and otherwise estimated from the Schlegel dust maps4 _{(Schlegel et al. 1998)} for the giants. It is well known that these dust maps tend to overestimate the extinction for stars close to the plane, and for a few stars the reddening values E(B - V) had to be rescaled by multiplying with an empirical adjusted factor according to Bonifacio et al.

2

http://www.ipac.caltech.edu/2mass/

3

Taken from the General Catalogue of Photometric Data http://obswww.unige.ch/gcpd/gcpd.html

4

32 3. Stellar Parameters

(2000) in order to obtain reasonable temperatures. Figure 3.1 shows the different colour– temperature calibrations, and for e.g. HD298986 a wrong E(B-V) of 0.52 would lead to a too high temperature (10100 K). The value of the temperature is much too high to match the values of F and G stars (∼ _{6000 K), and by applying the rescaling of the dereddening}

the values predicted become acceptable for these types of stars.

E(B−V)true=E(B−V)Schlegel,if ≤0.1, else 0.1 + 0.65(E(B−V)Schlegel−0.1) (3.4)

Since the derivation of the majority of our stars is based on V - K colours, the reddening needs to be transformed to this colour as well. For consistency the transformation from Alonso et al. (1996b) was chosen:

E(V −K) = 2.72·E(B−V) (3.5) The derived stellar parameters can be found in Table 3.1 and 3.2 for giants and dwarfs, respectively. In these tables an ’a’ indicates that the temperature was derived from excita- tion potentials either because photometry or extinction (E(V-K)) was missing, or because the metallicity or colour fell outside the allowed calibration ranges. For the gravities the ’a’ indicates that I did not have parallaxes and therefore had to resort to ionisation balance of Fe I and II to determine log g. The ’b’ implies that the stars are r-process enhanced and the ’c’ shows that the stellar parameters had their values altered in order to provide flat trends for either temperature, gravity or microturbulent velocities.

3.2.1

Comparing temperature scales

I determined the temperature based on several colour–Tef f calibrations, applying two dif-

ferent colours V–K and b–y (Str¨omgren photometry). The calibrations considered here are based on Masana et al. (2006), ¨Onehag et al. (2009) (only b–y)), Alonso et al. (1996b), Alonso et al. (1999), Ram´ırez & Mel´endez (2005) and Casagrande et al. (2010) (combined with L. Casagrande priv. comm.). The derived temperatures based on these studies scale slightly different between the dwarfs and giants, and they will therefore be discussed sep- arately. Generally the Str¨omgren photometry for the dwarfs predicts higher temperatures than the V–K colour. The difference between the five mentioned colour calibration studies can span several hundreds of Kelvin, but can in other cases all agree within∼_{50 K (see Fig-}

ure 3.1). The studies tend to predict temperatures, where Casagrande et al. (2010) yield the lowest values and ¨Onehag et al. (2009) and Ram´ırez & Mel´endez (2005) the highest. All the temperature predictions are mentioned in increasing order for the more metal-rich stars as well as shown in Figure 3.1:

Casagrande et al. (2010), Masana et al. (2006), Alonso et al. (1996b), Ram´ırez & Mel´endez (2005) and ¨Onehag et al. (2009)

However, for the very metal-poor stars the studies predict different temperatures (starting with the lowest temperature and ending with the highest):

3.2 Temperature 33

Ram´ırez & Mel´endez (2005).

The predicted temperatures of Alonso et al. (1996b) and Masana et al. (2006) generally

Figure 3.1: Temperatures for nine stars calculated with formulas from five different studies (as indicated in the figure legend). Alonso et al. (1996b) is seen to predict temperatures located in the middle of the temperature range for the more metal-rich stars ([Fe/H]>-2.0) and yields temperatures in the lower parts of the range for stars with lower metallicity. Generally, the b-y (Str¨omgren colour) predicts a higher temperature than V-K does. agree, often within 30 - 40 K, whereas the derived temperatures from Str¨omgren pho- tometry from Alonso et al. (1996b) and ¨Onehag et al. (2009) are higher and agree within 100 - 150 K. The temperatures derived from Ram´ırez & Mel´endez (2005) are always in the high end of the temperature range. The temperatures provided by L. Casagrande (Casagrande et al. 2010) can deviate by 240 K compared to the values derived by Alonso et al. (1996b), but are mainly 100 - 140 K lower than the temperatures derived using their calibra- tions. This changes for the most metal-poor stars where the temperatures from Casagrande can be 30 - 140 K higher than those derived by the use of calibrations from Alonso et al. (1996b) (see Figure 3.1).

The overall view of these calibrations is that the temperature estimates based on the calibrations from Alonso et al. (1996b) tend to be around the mid range of the estimated temperatures, which was another reason to select these calibrations despite not being the most recent ones. Additionally, Nissen et al. (2007) showed the excellent agreement

34 3. Stellar Parameters

of the temperatures derived by Hβ line fitting and temperatures derived by Tef f–colour

calibration using the V–K colour (Alonso et al. 1996b), supporting my choice of this colour– Tef f calibration.

For the giants, calibrations from Alonso et al. (1999) tend to predict lower temperatures than those from Ram´ırez & Mel´endez (2005). There are several cases however, where temperatures derived based on the calibrations from ¨Onehag et al. (2009) are lower than the Str¨omgren colour calibrations from both Ram´ırez & Mel´endez (2005) and Alonso et al. (1999), and where the temperatures derived from the V–K calibrations from Alonso et al. (1999) are higher than the temperatures derived from the V–K colour calibrations from Ram´ırez & Mel´endez (2005). Generally the temperatures derived from my samples giants agree within 80 - 150 K when derived from Tef f–(V–K) calibration from Alonso et al.

(1999) and Ram´ırez & Mel´endez (2005). To have one consistent temperature scale for both dwarfs and giants, the calibration from Alonso et al. (1999) was chosen for the giants.