G3 - reddening and extinction laws

• measuring extinction $A_{\lambda }$ across the spectrum is challenging
• thus, the relative extinction, or reddening is measured:

• the $B$ and $V$ bands are centred arounf $440$ nm and $540$ nm respectively

• it can be expressed as a function of any other couple of bands

• a simple parameter $K_{\lambda }$ can link the reddening to the extension in any other band $A_{\lambda }:$

• this is called an extinction law

• the special case in $V$ band is $R_V=A_V/E(B-V)$

• in the MW, $R_V\approx 3.1$ and $A_V\approx 1$ mag kpc${}^{-1}$ on the galactic plane

• this is an average, with the total extinction towards the centre $\sim 30$ mag

in different galaxies

image: H Cegla, lecture notes

• in most $\lambda$, the law follows ${\lambda }^{-1}$, ie. Mie scattering

• $K_{\lambda }$ becomes steeper at short wavelengths due to Rayliegh scattering

• this is also due to the prevalence of smaller grains

• LMC and SMC have a steeper dependence, indicating compositional differences in particle sizes

• MW and LMC both have a bump around $220$ nm, which is a well recognised spectral feature of graphite

• the shape of the extinction law is driven by:

  • formation which drives the size
  • metallicity which drives the composition