4 The observed wavelength dependence

It was noticed by Serkowski (1973) that observations of linear interstellar polarization follows the same curve when the ratio of polarizations ${P}(\lambda)/{ P}(\lambda_{\rm max})$ is plotted against the ratio of the wavelength $\lambda_{\rm max}$ of the maximum polarization for a given star to the wavelength $\lambda$ at which polarization is measured. The Serkowski's empirical relationship is given by

$${ P}(\lambda)/{ P} (\lambda_{\rm max}) = {\rm exp} [-K\ln^2(\lambda_{\rm max}/\lambda)], \hskip.5cm K=1.15.$$

The wavelength of maximum polarization varies from star to star and is typically in the range 0.45 $\mu$m to 0.8 $\mu$m, with a median value of 0.545 $\mu$m (Serkowiski et al.1975).

Least squares fit were applied to the 40 stars showing degree of polarization greater than 0.5% in the UBV passbands. From the obtained fit, the $P_{\rm max}$ and $\lambda_{\rm max}$ were found for each of these stars. Figure 4 gives a comparison between the obtained normalized wavelength dependence of the observed linear polarization (dots) with the Serkowski's formula (solid line).

Figure 5 shows the distribution of the obtained $\lambda_{\rm max}$. The diagram shows a maximum in the range $0.50 < \lambda_{\rm max} \le 0.55\,\mu$m. The median value for the obtained $\lambda_{\rm max}$ values is 0.534 $\mu$m, in agreement with what is observed for the typical interstellar medium. There are two stars (315 - HD79936 and 317 - HD80085) showing rather small $\lambda_{\rm max}$ values, and since their lines-of-sight sit in the same region of the sky, the abnormal values may be characteristic of this direction. However, due to the uncertainties in the measurements, mainly for 315 (HD79936), this hypothesis requires further confirmation.

 

Figure 8: Observed polarization (B-band) and colour excess E(b-y) up to 100 pc. The estimated colour excess are indicated by the small squares as: (Empty Square) E(b-y) < 0$.\!\!^{\rm m}$017. (Light Grey Square) 0$.\!\!^{\rm m}$017 $\le$ E(b-y) < 0$.\!\!^{\rm m}$030. ( Darker Grey Square) 0$.\!\!^{\rm m}$030 $\le$ E(b-y) < 0$.\!\!^{\rm m}$050. (Grey Square) 0$.\!\!^{\rm m}$050 $\le$ E(b-y) < 0$.\!\!^{\rm m}$100. (Dark Grey Square)) 0$.\!\!^{\rm m}$100 $\le$ E(b-y) < 0$.\!\!^{\rm m}$200. (Black Square) E(b-y) $\ge$ 0 $.\!\!^{\rm m}$200

 

Figure 9: Same as Fig. 8. Stars in the range $100 \le d < 150$ pc

 

Figure 10: Same as Fig. 8. Stars in the range $150 \le d < 250$ pc

 

Figure 11: Same as Fig. 8. Stars in the range $250 \le d < 400$ pc