I have developed a new general-purpose deterministic 2D radiative transfer code for astrophysical dusty environments named LELUYA (www.leluya.org). It can provide the solution to an arbitrary axially symmetric multi-grain dust distribution around an arbitrary heating source. By employing a new numerical method, the implemented algorithm automatically traces the dust density and optical depth gradients, creating the optimal unstructured triangular grid. The radiative transfer equation includes dust scattering, absorption and emission. Unique to LELUYA is also its ability to self-consistently reshape the sublimation/condensation dust cavity around the source to accommodate for the anisotropic diffuse radiation. LELUYAs capabilities are demonstrated in the study of the asymptotic giant branch (AGB) star IRC+10011. The stellar winds emanating from AGB stars are mostly spherically symmetric, but they evolve into largely asymmetric planetary nebulae during later evolutionary phases. The initiation of this symmetry breaking process is still unexplained. IRC+10011 represents a rare example of a clearly visible asymmetry in high-resolution near-infrared images of the circumstellar dusty AGB wind. LELUYA shows that this asymmetry is produced by two bipolar cones with 1/r0.5 density profile, imbedded in the standard 1/r2 dusty wind profile. The cones are still breaking though the 1/r2 wind, suggesting they are driven by bipolar jets. They are about 200 years old, thus a very recent episode in the final phase of AGB evolution before turning into a proto-planetary nebula, where the jets finally break out from the confining spherical wind. IRC+10011 provides the earliest example of this symmetry breaking thus far.

The use of Type Ia supernovae (SNe Ia) as distance indicators is essential for studying the expansion history of the Universe and for exploring the nature of dark energy. However, a lack of understanding of the progenitor systems and the empirically derived colour-brightness corrections represent severe limitations for SNe Ia as cosmological probes. In this thesis, we study how dust along the line of sight towards SNe Ia affects the observed light over a wide range of wavelengths; from X-rays to infrared. Unless properly corrected for, the existence of intergalactic dust will introduce a redshift dependent magnitude offset to standard candle sources and bias the cosmological parameter estimates as derived from observations of SNe Ia. We model the optical extinction and X-ray scattering properties of intergalactic dust grains to constrain the intergalactic opacity using a combined analysis of observed quasar colours and measurements of the soft X-ray background. We place upper limits on the extinction AB(z = 1) &lt; 0.10 - 0.25 mag, and the dust density parameter Ωdust &lt; 10−5 − 10−4 (ρgrain/3 g cm−3), for models with RV &lt; 12 − ∞, respectively. Dust in the host galaxies, and dust that may reside in the circumstellar (CS) environment, have important implications for the observed colours of SNe Ia. Using the Hubble Space Telescope and several ground based telescopes, we measure the extinction law, from UV to NIR, for a sample of six nearby SNe Ia. The SNe span a range of E(B − V ) ≈ 0.1 − 1.4 mag and RV  ≈ 1.5 − 2.7, showing a diversity of dust extinction parameters. We present mid- and far-infrared (IR) observations for a number of SNe Ia, obtained with the Herschel Space Observatory and Spitzer Space Telescope, addressing CS dust as an explanation for “peculiar” extinction towards some SNe Ia. No excess IR emission is detected, limiting CS dust masses, Mdust &lt; 10−5 solar masses. In particular, the timely appearance of SN 2014J in M82 - the closest SN Ia in several decades - allows for detailed studies, across an unprecedented wavelength range, of its lightcurve and spectral evolution along with the host galaxy and CS environment. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 5: Manuscript. Paper 6: Manuscript.</p>