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The SKIRT project
advanced radiative transfer for astrophysics
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The SKIRT project
advanced radiative transfer for astrophysics
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This page describes how SKIRT handles wavelengths during a simulation. The discussion is organized as follows:
Other topics with related information include:
With few exceptions, the interactions between matter and radiation depend heavily on the radiation's wavelength. Furthermore, some processes affect the wavelength of an interacting photon (e.g. Doppler shifts caused by relative motion) or drastically "convert" a fraction of radiative energy from one wavelength to another (e.g. absorption and re-emission by dust grains). As a result, wavelength plays an important role in a radiative transfer simulation code such as SKIRT.
The physical processes are emulated by a stream of discrete photon packets. When a photon packet is emitted, it receives a certain amount of energy at a given wavelength. While the packet moves through the spatial domain of the simulation, some of its energy is absorbed by the transfer medium, and its wavelength may be adjusted by interactions with the medium. At each scattering event, a special photon packet is peeled-off towards each instrument to record the observed flux. The energy absorbed by the medium is re-emitted at a later stage by launching new photon packets at different wavelengths.
This brief summary passes over a lot of details and complexities, but even so it hints at the many areas in the simulation where wavelength-related aspects need to be handled and configured. On the other hand, not every simulation requires this full general treatment. For example, when studying dust extinction in the optical wavelength range, there is no need for handling dust emission.
With respect to the treatment of wavelengths, SKIRT has two distinct simulation modes called panchromatic and oligochromatic. One of these modes must be selected early on in the simulation configuration process, and the choice affects many of the other options in the configuration.
Panchromatic simulation mode is the most powerful and commonly used mode in SKIRT. A panchromatic simulation operates with a continuous range of wavelengths that often spans X-ray, ultraviolet, optical, infrared and/or submillimeter bands. Such a simulation supports the full SKIRT feature set, including for example thermal emission by dust grains and the effects of kinematics. If the range is limited to optical or shorter wavelengths, it obviously doesn't make sense to include thermal emission, but the other features such as kinematics remain available.
In panchromatic mode, the user must specify a primary source wavelength range in which the spectrum assigned to each source must be considered. Individual photon packets can receive any wavelength in that continuous range, sampled from the source spectrum. On the other hand, accumulated (and thus stored) spectral quantities such as the radiation field or observed fluxes must necessarily be discretized on some wavelength grid. Similarly, the calculation of a secondary emission spectrum of a medium such as dust requires spectral discretization. Therefore, the user must configure the appropriate wavelength grids for storing the radiation field and fluxes detected by instruments, and for calculating secondary emission where applicable.
Oligochromatic simulation mode can be used for studying extinction effects (i.e. absorption and scattering) at a limited number of specific wavelengths (or just a single wavelength) in the ultraviolet and/or optical spectrum. The simulation operates at these discrete wavelength values only, and is therefore unable to calculate wavelength-integrated quantities such as dust temperatures or thermal emission, or to properly handle wavelength shifts such as those caused by kinematics. On the other hand, because of the small number of wavelengths in use, the total number of photon packets launched can usually be substantially smaller than for panchromatic simulations. In other words, one trades speed for a reduction of the supported feature set.
In oligochromatic mode, the user must specify the list of discrete wavelengths to be used in the simulation. The luminosity of each source is still derived from its associated SED or SED family, and luminosity normalization proceeds as usual (and may even happen at wavelengths that differ from the oligochromatic wavelengths). However, newly emitted photon packets are automatically assigned one of the distinct oligochromatic wavelengths. Furthermore, all instruments are forced to use a special wavelength grid with narrow bins around the oligochromatic wavelengths.
The description in this section assumes panchromatic simulation mode.
The fundamental properties of a photon packet include its wavelength and its weight. The wavelength property specifies the wavelength of all photons in the packet. The weight property specifies the number of photons carried by the packet, or more precisely the number of photons per unit of time (because SKIRT solves the time-independent radiation transfer equation). Refer to the PhotonPacket class for more details.
At launch (from a primary or secondary source), a photon packet receives a wavelength sampled from the source spectrum and a luminosity, i.e. its share of the total luminosity of the source. The wavelength is stored as given. The luminosity is converted to a weight (number of photons) for storage in the photon packet.
During a photon packet’s life cycle, updates can occur to both its weight, e.g. because of absorption, and its wavelength, e.g. after being scattered by a moving medium. Because these updates can be fractional, both wavelength and weight are stored as floating-point values. Adjusting a photon packet's wavelength indirectly affects the luminosity represented by the packet, because the latter is inversely proportional to the wavelength.
Each radiation source provides a mechanism to sample a random wavelength from its spectral energy distribution (see the SED and SEDFamily classes and their subclasses) and assign a corresponding luminosity such that the bolometric luminosity of the source is properly distributed across the photon packets. Analytically defined SEDs could in principle employ a specialized sampling routine. However, the current implementation always samples from a tabulated source spectrum. The procedure properly interpolates the tabulated values so that the sampled wavelengths can take any value rather than being restricted to some discrete grid.
It is important that all features in the spectrum are properly sampled, including narrow lines or wavelength ranges with low luminosities. To this end, the sampling procedure employs composite biasing to combine sampling from two distributions: the SED itself (favoring wavelengths that carry a lot of energy) and a custom bias distribution (favoring specific wavelength areas). Both the composite bias factor and the bias distribution are user-configurable. See the WavelengthDistribution class and its subclasses. By default, the procedure has a bias factor of 0.5 and a bias distribution that is logarithmic in wavelength.
The default scheme ensures that the low-luminosity tails of a typical spectrum are properly sampled, while still favoring the higher-luminosity areas. Even narrow spectral features are properly sampled because half of the wavelengths are selected from the source SED at full spectral resolution. Lowering the bias fraction focuses more photon packets into high-luminosity areas because the composite distribution more closely follows the source spectrum. Vice versa, a bias fraction close to unity causes the source spectrum to be essentially ignored for the purpose of wavelength sampling. For more information, see Configuring wavelength grids.
The wavelength of a photon packet is defined relative to the model coordinate system. In other words, a medium at rest relative to the model coordinate system sees this wavelength. Velocities of sources and media are also defined relative to the model coordinate system. The bulk velocity of the aggregate medium in a spatial grid cell is determined by averaging the bulk velocities of all media components weighed by density. Instruments are considered to be at rest relative to the model coordinate system except for models placed at non-zero redshift; see Nonzero redshift & CMB dust heating.
When a photon packet is launched, its wavelength is Doppler shifted according to the component of the source velocity in the photon packet’s direction. When a photon packet interacts with a medium, the perceived wavelength is derived by Doppler shifting the packet’s wavelength according to the component of the medium velocity in the photon packet’s incoming direction. Specifically, registration of a photon packet’s contribution to the radiation field uses this perceived wavelength. After a scattering interaction, the photon packet’s wavelength is replaced by the perceived wavelength, Doppler shifted according to the component of the medium velocity in the photon packet’s outgoing direction.
When a random-walk photon packet traverses a spatial cell in the simulation domain, its contribution to the radiation field is accumulated according to the photon packet's perceived wavelength. Similarly, when a peel-off photon packet arrives at one of the instruments, its contribution to the observed flux is accumulated according to the photon packet's wavelength, possibly redshifted if the model is placed at non-zero redshift (see Nonzero redshift & CMB dust heating).
Because wavelength is a continuous quantity and the available memory is finite, the stored data must be spectrally discretized. The appropriate wavelength grid depends on the model and on the desired resolution and accuracy, and may even differ between instruments. These wavelength grids must therefore be configured by the user; see Configuring wavelength grids.