Monte Carlo Radiative Transfer Research Articles

On the impact of radiative transfer in fluorescence imaging of bacterial films and suspensions

Fluorescence imaging and spectroscopy are convenient, rapid, and simple methods to analyze chemical samples including biological materials such as bacterial biofilms and suspensions. In principle, these techniques could be used to diagnose or discriminate between infectious bacteria in infections of the skin or ocular surface (microbial keratitis, MK). However, the extension of these techniques to macroscopic turbid media that strongly absorb and scatter light is difficult. Radiative transfer effects obscure the relationship between microscopic scattering and absorption properties and macroscopically observable quantities such as fluorescence intensity, transmission, and reflection. A combination of experimental measurements of aqueous bacteria cell suspensions and Monte Carlo radiation transfer simulations are performed to better understand these effects. Several general observations, e.g., that fluorescence intensity is maximized in scattering-dominated media, are discussed in detail. It was found that wavelength-dependent radiative transfer effects are observable even at moderate optical densities (OD ∼ 1; well below the diffusion limit). Careful consideration of radiative transfer effects using physically rigorous models is needed to determine single-cell scattering and absorption properties and interpret quantitative fluorescence measurements accurately in most cases of interest. A detailed discussion of radiative transfer effects and analytical models is provided. In the context of surface infections and MK, it was found that radiative transfer effects may be negligible for the model bacteria E. coli in some cases; however, more accurate measurements of microbe optical properties are needed to confirm and extend this conclusion to other species. Overall this work demonstrates that quantitative fluorescence imaging and spectroscopy of bacterial films and suspensions is feasible, but requires detailed sample characterization and careful consideration of radiative transfer effects.

Probing the eccentricity in protostellar discs: Modelling kinematics and morphologies

Protostellar discs are mostly modelled as circular structures of gas and dust orbiting a protostar. However, a number of physical mechanisms, for example, the presence of a (sub)stellar companion or initial axial asymmetry, can cause the gas and dust orbital motion to become eccentric. Theoretical studies have revealed that, when present, disc eccentricity is expected to occur with predictable profiles that can be long-lasting and potentially observable in protostellar systems. We construct an analytical model predicting the typical features of the kinematics and morphology of eccentric protostellar discs, with the final goal of characterising the observational appearance of eccentricity in discs. We validate the model using a numerical simulation of a circumbinary disc (where the binary makes the disc eccentric). We finally post-process the simulation with Monte Carlo radiative transfer to study how eccentric features would appear through the 'eyes' of ALMA. Besides the motion of the material on eccentric Keplerian orbits in the disc orbital plane, the most characteristic eccentric feature emerging from the analytical model is strong vertical motion with a typical anti-symmetric pattern (with respect to the disc line of pericentres). A circumbinary disc with a $ 40$ au eccentric cavity cav =0.2$), carved by an $a_ bin =15$ au binary, placed at a distance $d=130$ pc, is expected to host in its upper emission surface vertical oscillations up to $v_ z ms $ close to the cavity edge, that is to say, well within ALMA spectral and spatial resolution capabilities. A residual spiral pattern in the vertical velocity $ z ms $ of the simulation cannot be captured by the theoretical model, we speculate it to be possibly linked to the presence of a companion in the system.

High Accuracy Photodissociation Rates in VULCAN with MCRT

Photochemical processing is a key influence on the chemical compositions of exoplanet atmospheres. We develop a 1D plane-parallel Monte Carlo radiative-transfer (MCRT) path length method to calculate actinic fluxes for photochemical modeling, which we couple to the VULCAN photochemical model. Due to the flexible nature of MCRT methods, this enables accurate calculation of photodissociation rates for complex multiple scattering scenarios encountered in exoplanet atmospheres such as high altitude haze layers.

Accuracy of ALMA estimates of young disk radii and masses

Context. Protoplanetary disks, which are the natural consequence of the gravitational collapse of the dense molecular cloud cores, host the formation of the known planetary systems in our universe. Substantial efforts have been dedicated to investigating the properties of these disks in the more mature Class II stage, either via numerical simulations of disk evolution from a limited range of initial conditions or observations of their dust continuum and line emission from specific molecular tracers. The results coming from these two standpoints have been used to draw comparisons. However, few studies have investigated the main limitations at work when measuring the embedded Class 0/I disk properties from observations, especially in a statistical fashion. Aims. In this study, we provide a first attempt to compare the accuracy of some critical disk parameters in Class 0/I systems, as derived on real ALMA observational data, with the corresponding physical parameters that can be directly defined by theoreticians and modellers in numerical simulations. The approach we follow here is to provide full post-processing of the numerical simulations and apply it to the synthetic observations the same techniques used by observers to derive the physical parameters. Methods. We performed 3D Monte Carlo radiative transfer and mock interferometric observations of the disk populations formed in a magnetohydrodynamic (MHD) simulation model of disk formation through the collapse of massive clumps with the tools RADMC-3D and CASA, respectively, to obtain their synthetic observations. With these observations, we re-employed the techniques commonly used in disk modelling from their continuum emissions to infer the properties that would most likely be obtained with real interferometers. We then demonstrated how these properties may vary with respect to the gas kinematics analyses and dust continuum modelling. Results. Our modelling procedure, based on a two-component model for the disk and the envelope, shows that the disk sizes can be properly recovered from observations with sufficient angular resolutions, with an uncertainty of a factor ≈1.6–2.2, whereas their masses cannot be accurately measured. Overall, the masses are predominantly underestimated for larger, more massive disks by a median factor of ≈2.5, and even up to 10 in extreme cases, with the conversion from flux to dust mass under the optically thin assumption. We also find that the single Gaussian fittings are not a reliable modelling technique for young, embedded disks characterised by a strong presence of the envelopes. Thus, such an approach is to be used with caution. Conclusions. The radiative transfer post-processing and synthetic observations of MHD simulations offer genuine help in linking important observable properties of young planet-forming disks to their intrinsic values in simulations. Further extended investigations that tackle the caveats of this study, such as the lack of variation in the dust composition and distribution, dust-to-gas ratio, and other shortcomings in the numerical models, would be essential for setting constraints on our understanding of disk and planet formations.

Feasibility of detecting shadows in disks induced by infall

Observations performed with high-resolution imaging techniques have revealed the existence of shadows in circumstellar disks that can be explained by the misalignment of an inner disk with respect to an outer one. The cause of misalignment, however, is still a matter of debate. In this study, we investigate the feasibility of observing shadows induced by one prominent scenario that may lead to misalignment, which involves the late infall of material onto a protostellar system. In particular, we used previously performed hydrodynamical simulations of such events and we generated flux maps in the visible, near-infrared, submillimeter, and millimeter wavelength ranges using Monte Carlo radiative transfer. Based on those results, we derived synthetic observations of these systems performed with the instruments SPHERE/VLT and ALMA, which we used as a basis for our subsequent analysis. We find that near-infrared observations with SPHERE are particularly well suited for detecting shadows via direct imaging alongside other features such as gaps, arcs, and streamers. On the contrary, performing a shadow detection based on reconstructed ALMA observations is very challenging due to the high sensitivity that is required for this task. Thus, in cases that allow for a detection, sophisticated analyses may be needed, for instance by the utilization of carefully constructed azimuthal profiles, aiding the search for potentially shallow shadows. Lastly, we conclude that a late infall-induced disk misalignment offers a plausible explanation for the emergence of shadows observed in various systems.

Feasibility study on retrieving exoplanetary cloud cover distributions using polarimetry

As a new growing field, exocartography aims to map the surface features of exoplanets that are beyond the resolution of traditional observing techniques. While photometric approaches have been discussed extensively, polarimetry has received less attention despite its promising prospects. We demonstrate that the limb polarization of an exoplanetary atmosphere offers valuable insights into its cloud cover distribution. Specifically, we determine an upper limit for the polarimetric precision, which is required to extract information about the latitudinal cloud cover of temperate Jovian planets for scenarios of observations with and without host stars. To compute the scattered stellar radiation of an exoplanetary atmosphere and to study the polarization at various planetary phase angles, we used the three-dimensional Monte Carlo radiative transfer code POLARIS. When the planetary signal can be measured separately from the stellar radiation, information about the latitudinal cloud cover for polar cap models is accessible at polarimetric sensitivities of percent . In contrast, a precision of about e-3 ppm is required when the stellar flux is included to gain this information.

On the evolution of the observed mass-to-length relationship for star-forming filaments

ABSTRACT The interstellar medium is threaded by a hierarchy of filaments from large scales (∼100 pc) to small scales (∼0.1 pc). The masses and lengths of these nested structures may reveal important constraints for cloud formation and evolution, but it is difficult to investigate from an evolutionary perspective using single observations. In this work, we extract simulated molecular clouds from the ‘Cloud Factory’ galactic-scale ISM suite in combination with 3D Monte Carlo radiative transfer code polaris to investigate how filamentary structure evolves over time. We produce synthetic dust continuum observations in three regions with a series of snapshots and use the filfinder algorithm to identify filaments in the dust derived column density maps. When the synthetic filaments mass and length are plotted on an mass–length (M–L) plot, we see a scaling relation of L ∝ M0.45 similar to that seen in observations, and find that the filaments are thermally supercritical. Projection effects systematically affect the masses and lengths measured for the filaments, and are particularly severe in crowded regions. In the filament M–L diagram we identify three main evolutionary mechanisms: accretion, segmentation, and dispersal. In particular we find that the filaments typically evolve from smaller to larger masses in the observational M–L plane, indicating the dominant role of accretion in filament evolution. Moreover, we find a potential correlation between line mass and filament growth rate. Once filaments are actively star forming they then segment into smaller sections, or are dispersed by internal or external forces.

Improving Monte Carlo radiative transfer in the regime of high optical depths: The minimum scattering order

Radiative transfer simulations are a powerful tool that enables the calculation of synthetic images of a wide range of astrophysical objects. These simulations are often based on the Monte Carlo method, as it provides the needed versatility that allows the consideration of the diverse and often complex conditions found in those objects. However, this method faces fundamental problems in the regime of high optical depths which may result in overly noisy images and severely underestimated flux values. In this study, we propose an advanced Monte Carlo radiative transfer method, namely, an enforced minimum scattering order that is aimed at providing a minimum quality of determined flux estimates. For that purpose, we extended our investigations of the scattering order problem and derived an analytic expression for the minimum number of interactions that depends on the albedo and optical depth of the system, which needs to be considered during a simulation to achieve a certain coverage of the scattering order distribution. The method is based on the utilization of this estimated minimum scattering order and enforces the consideration of a sufficient number of interactions during a Monte Carlo radiative transfer simulation. Moreover, we identified two notably distinct cases that shape the kind of complexity that arises in such simulations: the albedo-dominated case and the optical depth-dominated case. Based on that, we analyzed the implications related to the best usage of a stretching method as a means to alleviate the scattering order problem. We find that its most suitable application requires taking into account the value of the albedo as well as the optical depth. Furthermore, we argue that the derived minimum scattering order can be used to assess the performance of a stretching method with regard to the scattering orders its usage promotes. Finally, we stress the need for developing advanced pathfinding techniques to fully solve the problem of Monte Carlo radiative transfer simulations in the regime of high optical depths.

Changing streetlighting schemes and the ecological availability of darkness.

Artificial light at night (ALAN), from streetlights and other sources, has a wide variety of impacts on the natural environment. A significant challenge remains, however, to predict at intermediate spatial extents (e.g. across a city) the ALAN that organisms experience under different lighting regimes. Here we use Monte Carlo radiative Transfer to model the three-dimensional lighting environment at, and just above, ground level, on the spatial scales at which animals and humans experience it. We show how this technique can be used to model a suite of both real and hypothetical lighting environments, mimicking the transition of public infrastructure between different lighting technologies. We then demonstrate how the behaviour of animals experiencing these simulated lighting environments can be emulated to probe the availability of darkness, and dark corridors, within them. Our simulations show that no single lighting technology provides an unmitigated alleviation of negative impacts within urban environments, and that holistic treatments of entire lighting environments should be employed when understanding how animals use and traverse them.

Numerical Simulation of Photospheric Emission in Long Gamma-Ray Bursts: Prompt Correlations, Spectral Shapes, and Polarizations

We explore the properties of photospheric emission in the context of long gamma-ray bursts (GRBs) using three numerical models that combine relativistic hydrodynamical simulations and Monte Carlo radiation transfer calculations in three dimensions. Our simulations confirm that photospheric emission gives rise to correlations between the spectral peak energy and luminosity that agree with the observed Yonetoku, Amati, and Golenetskii correlations. It is also shown that the spectral peak energy and luminosity correlate with the bulk Lorentz factor, as indicated in the literature. On the other hand, synthetic spectral shapes tend to be narrower than those of the observations. This result indicates that an additional physical process that can provide nonthermal broadening is needed to reproduce the spectral features. Furthermore, the polarization analysis finds that, while the degree of polarization is low for the emission from the jet core (Π < 4%), it tends to increase with viewing angle outside of the core and can be as high as Π ∼ 20%–40% in an extreme case. This suggests that the typical GRBs show systematically low polarization compared to softer, dimmer counterparts (X-ray-rich GRBs and X-ray flashes). Interestingly, our simulations indicate that photospheric emission exhibits large temporal variation in the polarization position angle (Δψ ∼ 90°), which may be compatible with those inferred in observations. A notable energy dependence of the polarization property is another characteristic feature found in the current study. Particularly, the difference in the position angle among different energy bands can be as large as ∼90°.

A Morphokinematic Study of the Enigmatic Emission Nebula NGC 6164/5 Surrounding the Magnetic O-type Star HD 148937

HD 148937 is a peculiar massive star (Of?p) with a strong magnetic field (1 kG). The hourglass-shaped emission nebula NGC 6164/5 surrounds this star. This nebula is presumed to originate from episodic mass-loss events of the central O-type star, but the detailed formation mechanism is not yet well understood. Grasping its three-dimensional structure is essential to uncovering the origin of this nebula. Here we report the high-resolution multiobject spectroscopic observations of NGC 6164/5 using the GIRAFFE on the 8.2 m Very Large Telescope. Integrated intensity maps constructed from several spectral lines delineate well the overall shape of this nebula, such as the two bright lobes and the inner gas region. The position–velocity diagrams show that the two bright lobes are found to be redshifted and blueshifted, respectively, while the inner region has multiple layers. We consider a geometric model composed of a bilateral outflow harboring nitrogen-enriched knots and expanding inner shells. Its spectral features are then simulated by using a Monte Carlo radiative transfer technique for different sets of velocities. Some position–velocity diagrams from simulations are very similar to the observed ones. According to the model that best reproduces the observational data, the two bright lobes and the nitrogen-enriched knots are moving away from HD 148937 at about 120 km s−1. Their minimum kinematic age is estimated to be about 7500 yr. We discuss possible formation mechanisms of this nebula in the context of binary interaction.

Diagnosis of Circumstellar Matter Structure in Interaction-powered Supernovae with Hydrogen Line Features

Some supernovae (SNe) are powered by the collision of the SN ejecta with dense circumstellar matter (CSM). Their emission spectra show characteristic line shapes of combined broad emission and narrow P Cygni lines, which should closely relate to the CSM structure and the mass-loss mechanism that creates the dense CSM. We quantitatively investigate the relationship between the line shape and the CSM structure by Monte Carlo radiative transfer simulations, considering two representative cases of dense CSM formed by steady and eruptive mass loss. Comparing the Hα emission between the two cases, we find that a narrow P Cygni line appears in the eruptive case but does not appear in the steady case due to the difference in the velocity gradient in the dense CSM. We also reproduce the blueshifted photon excess observed in some Type IIn SNe, which is formed by photon transport across the shock wave, and find the relationship between the velocity of the shocked matter and the amount of blueshift of the photon excess. We conclude that the presence or absence of narrow P Cygni lines can distinguish the mass-loss mechanism and suggest high-resolution spectroscopic observations with λ/Δλ ≳ 104 after the light-curve peak for applying this diagnostic method.

Improving Monte Carlo radiative transfer simulations: A shift of framework

Monte Carlo radiative transfer (MCRT) simulations are a powerful tool for determining the appearance of astrophysical objects, analyzing the prevalent physical conditions within them, and inferring their properties on the basis of real observations. Consequently, a broad variety of codes has been implemented and optimized with the goal of solving this task efficiently. To that end, two distinct frameworks have emerged, namely, the extinction and the scattering framework, which form the basis of the path determination procedures of those codes. These procedures affect the step length of simulated photon packages and are used for determining flux estimates. Despite the fact that these simulations play an important role at present and thus require significant computational resources, little attention has been paid to the benefits and the drawbacks of both frameworks so far. In this study, we investigate their differences and assess their performance with regard to the quality of thereby obtained flux estimates, with a particular focus on the required computational demand. To that end, we use a testbed composed of an infinite plane-parallel slab, illuminated from one side, and we determine transmitted intensity using MCRT simulations for both frameworks. We find that there are vast differences between the frameworks with regard to their convergence speed. The scattering framework outperforms the extinction framework across all considered optical depths and albedos when solving this task, particularly in the regime of high optical depths. Its implementation can therefore greatly benefit all modern MCRT codes as it has the potential to significantly reduce required computation times. Thus, we highly recommend its consideration for various tasks that require MCRT simulations.

Shaping the CO snowline in protoplanetary disks

Context. Characterizing the dust thermal structure in protoplanetary disks is a fundamental task because the dust surface temperature can affect both the planetary formation and the chemical evolution. Because the temperature depends on many parameters, including the grain size, it can be challenging to properly model the grain temperature structure. Many chemistry disk models usually employ a sophisticated single dust structure designed to reproduce the effect of a realistic population presumably composed of a large diversity of sizes. This generally represents a good approximation in most cases. Nonetheless, it dilutes the effects of the complex radiative interactions between the different grain populations on the resulting dust temperature, and thus, the chemistry. Aims. We seek to show that the radiative interactions between dust grains of different sizes can induce a nontrivial dust temperature structure that cannot be reproduced by a single dust population and that can significantly affect the chemical outcome. Methods. The disk thermal structures were computed using the Monte Carlo radiative transfer code RADMC-3D. The thermal structures were postprocessed using the gas-grain code NAUTILUS to calculate the evolution of the chemical abundance. Results. We find that simultaneously using at least two independent dust grain populations in disk models produces a complex temperature structure due to the starlight that is intercepted by the upper layers of the disk. In particular, we find that micron-sized dust grains are warmer than larger grains and can even show a radial temperature bump in some conditions. This dust temperature spread between the grain populations results in the segregation of the CO snowline and in an unexpected CO gas hole in the midplane. We compare the results with observed close to edge-on class I/II disks. Conclusions. Our study shows that the size dependence of the dust temperature significantly impacts the chemistry, and that two dust populations at least are required to account for this property of the thermal structure in protoplanetary disk models over a wide range of disk masses and dust properties.

Disc Tearing in a Be Star: Predicted 3D Observations

Abstract We build on our previous work involving smoothed particle hydrodynamic simulations of Be stars, by using the model that exhibited disc tearing as input into the three-dimensional Monte Carlo radiative transfer code hdust to predict observables from a variety of viewing angles throughout the disc tearing process. We run one simulation at the start of each orbital period from 20 to 72 orbital periods, which covers two complete disc tearing events. The resulting trends in observables are found to be dependent on the relative position of the observer and the tearing disc. The H$\rm \alpha$ equivalent width, V magnitude, and polarization can all increase or decrease in any combination depending on the viewpoint of the observer. The H$\rm \alpha$ line profile also displays changes in strength and peak separation throughout the tearing process. We show how the outer disc of the torn system can have a large effect on the H$\rm \alpha$ line profile, and also contributes to a wavelength-dependent polarization position angle, resulting in a similar sawtooth shape to the polarization percentage. Finally, we compare our predictions to Pleione (28 Tau) where evidence has suggested that a disc tearing event has occurred in the past. We find that our tearing disc model can broadly match the trends seen in Pleione’s observables, as well as produce the two-component H$\rm \alpha$ lines observed in Pleione. This is the strongest evidence, thus far, of Pleione’s disc having indeed experienced a tearing event.

Monte Carlo radiative transfer peel off mechanism for spatially extended detectors

We present an extension to the well-known peel off optimization for Monte Carlo radiative transfer simulations. The classical method is only applicable when the distance between the detector and the peel off event is much bigger than the size of the detector. We use two alternatives to the classical method and calculate the peel off intensity via a subdivision and an integration method. We compare their performance for a realistic scenario and derive guidelines for a general treatment. This allows for precise peel off calculations at any distance to the detector surface.

Synthetic light curves and spectra from a self-consistent 2D simulation of an ultra-strippped supernova

ABSTRACT Spectroscopy is an important tool for providing insights into the structure of core-collapse supernova explosions. We use the Monte Carlo radiative transfer code artis to compute synthetic spectra and light curves based on a two-dimensional explosion model of an ultra-stripped supernova. These calculations are designed both to identify observable fingerprints of ultra-stripped supernovae and as a proof of principle for using synthetic spectroscopy to constrain the nature of stripped-envelope supernovae more broadly. We predict characteristic spectral and photometric features for our ultra-stripped explosion model, and find that these do not match observed ultra-stripped supernova candidates like SN 2005ek. With a peak bolometric luminosity of $6.8\times 10^{41}\, \mathrm{erg}\, \mathrm{s}^{-1}$, a peak magnitude of $-15.9\, \mathrm{mag}$ in R band, and Δm15,R = 3.50, the model is even fainter and evolves even faster than SN 2005ek as the closest possible analogue in photometric properties. The predicted spectra are extremely unusual. The most prominent features are Mg ii lines at $2 {,}800\, {\mathring{\rm A}}$ and $4 {,}500\, {\mathring{\rm A}}$ and the infrared Ca triplet at late times. The Mg lines are sensitive to the multidimensional structure of the model and are viewing-angle dependent. They disappear due to line blanketing by iron group elements in a spherically averaged model with additional microscopic mixing. In future studies, multi-D radiative transfer calculations need to be applied to a broader range of models to elucidate the nature of observed Type Ib/c supernovae.

A disc wind model for blueshifts in quasar broad emission lines

ABSTRACT Blueshifts – or, more accurately, blue asymmetries – in broad emission lines such as C iv λ1550 are common in luminous quasars and correlate with fundamental properties such as Eddington ratio and broad absorption line (BAL) characteristics. However, the formation of these blueshifts is still not understood, and neither is their physical connection to the BAL phenomenon or accretion disc. In this work, we present Monte Carlo radiative transfer and photoionization simulations using parametrized biconical disc-wind models. We take advantage of the azimuthal symmetry of a quasar and show that we can reproduce C iv blueshifts provided that (i) the disc-mid-plane is optically thick out to radii beyond the line formation region, so that the receding wind bicone is obscured; and (ii) the system is viewed from relatively low (that is, more face-on) inclinations (≲40°). We show that C iv emission-line blueshifts and BALs can form in the same wind structure. The velocity profile of the wind has a significant impact on the location of the line formation region and the resulting line profile, suggesting that the shape of the emission lines can be used as a probe of wind-driving physics. While we are successful at producing blueshifts/blue asymmetries in outflows, we struggle to match the detailed shape or skew of the observed emission-line profiles. In addition, our models produce redshifted emission-line asymmetries for certain viewing angles. We discuss our work in the context of the C iv λ1550 emission blueshift versus equivalent-width space and explore the implications for quasar disc wind physics.

Modelling variable linear polarization produced by Co-rotating Interaction Regions (CIRs) across optical recombination lines of Wolf–Rayet stars

ABSTRACT Massive star winds are structured both stochastically (‘clumps’) and often coherently (Co-rotation Interaction Regions, or CIRs). Evidence for CIRs threading the winds of Wolf–Rayet (WR) stars arises from multiple diagnostics including linear polarimetry. Some observations indicate changes in polarization position angle across optical recombination emission lines from a WR star wind but limited to blueshifted Doppler velocities. We explore a model involving a spherical wind with a single conical CIR stemming from a rotating star as qualitative proof-of-concept. To obtain a realistic distribution of limb polarization and limb darkening across the pseudo-photosphere formed in the optically thick wind of a WR star, we used Monte Carlo radiative transfer (MCRT). Results are shown for a parameter study. For line properties similar to WR 6 (EZ CMa; HD 50896), combining the MCRT results, a simple model for the CIR, and the Sobolev approximation for the line formation, we were able to reproduce variations in both polarization amplitude and position angle commensurate with observations. Characterizing CIRs in WR winds has added importance for providing stellar rotation periods since the vsin i values are unobtainable because the pseudo-photosphere forms in the wind itself.

Non-LTE Monte Carlo radiative transfer – III. The thermal properties of tilted and warped Be star discs

ABSTRACT We use the three-dimensional Monte Carlo radiative transfer code hdust to model Be stars where the disc is tilted from the equatorial plane of the star. We compute 128 models across four spectral types, B0, B2, B5, and B8, tilting the disc by 0, 10○, 20○, and 40○, respectively, while varying disc density according to spectral type. We also compute every model for an average and high stellar rotation rate. We first discuss non-tilted disc temperatures and show its nonlinear dependence on stellar and disc parameters. We find that tilting the disc minimally affects the density-weighted average disc temperature, but tilting does create a temperature asymmetry in disc cross-sections, which is more pronounced for a faster rotation rate. We also investigate the effect tilting has on V-band magnitude, polarization, and the H$\rm \alpha$ line. Tilting the disc does affect these observables, but the changes are entirely dependent on the position of the observer relative to the direction of tilt. We find the observables that distinguish tilting from a change in density or geometry are the H$\rm \alpha$ line shapes, where it can transition between single-peaked and double-peaked, and the polarization position angle, whose value is dependent on the projected major elongation axis of the disc on the sky. We also present one early- and one late-type model with warped discs. We find their temperature structure varies a small amount from the uniformly tilted models, and the different observables correspond to different tilt angles, consistent with their expected volume of origin within the disc.