Knowledge of the output and three dimensional distribution of all constituents of galaxies (stars of all ages, gas, dust, cosmic rays) is a prerequisite for understanding the process of star-formation along the cosmic time, and ultimately the formation and evolution of galaxies. However, what we measure is the spatial and spectral energy distribution (SED) of galaxies. In this chapter we describe self-consistent modeling of the SED involvingradiative transfer (RT) calculations that follow the interaction between stellar photons and dust particles, and make predictions for all emission mechanisms involved. Tracing the energy flow and accounting for the anisotropy of the problem requires modelling of SEDs spanning a broad range in wavelengths and the spatial distribution of the emission. A RT modelaccurately calculates the stellar SEDs emitted by the newly-formed stars by both calculating the effect of dust attenuation throughout the galaxy, and by providing a three dimensional picture of the stellar emission of these stars. This way it produces a solution for the SFR, and the 3D distributions of all stellar components of a galaxy (stars of all ages and from different morphological components, like disks, bulges, and bars) and of the dust distribution, giving us a detailed understanding of the make up of a galaxy, both of its stellar content and of the interstellar medium structure.

Everything we know about galaxies and the stars that form within them comes from the photons we detect across the electromagnetic spectrum. Gaining the greatest possible knowledge from the light we detect is thus key to understanding young stellar populations. To do this requires a detailed model of the physical processes producing the luminous signal we detect and quantify. In this chapter we will concentrate on the details of stars and stellar populations. We will address how we can model stars and predict how they appear, and thus how we derive the star-formation rate of observed galaxies by comparing theoretical predictions to observations. We will discuss the current understanding in this area and highlight significant recent advances that have modified this understanding. First we discuss the evolution of stars, followed by modelling of their atmospheres. Then we consider how we can combine these to create model stellar populations and eventually synthesize a predicted spectrum. Finally we discuss other factors and caveats that must be considered in spectral synthesis, before looking towards the future of this field.

Recipes for the determination of SFRs of and within galaxies have enabled many advances in understanding the properties and physics of stellar and galaxy populations. However, like all recipes, they have significant limitations, and they are usually only applicable within the luminosity and physical range where they have been calibrated. Outside this range, they can under/overestimatethe true SFR up to factors of several. Recipes are based on the assumption of a constant SFR over some period of time. For practical reasons, the `mass of newly formed stars' is typically extrapolated from the sum of the mass of massive stars, and the `period of time' is the lifetime of those massive stars. These choices are dictated by purely observational constraints and the cumulative light from the massive stars is used for the purpose of measuring SFRs. Analysis of large samples of star-forming regions within galaxies can average out variations in physical properties, enabling the calibration of `local' SFR indicators. In this chapter single-band SFR indicators in the mid- and far-infrared arepresented and discussed as a function of region size. The need to account for both dust attenuated and unattenuated star formation has led to the formulation of SFR indicators that combine an optical or UV tracer with an infrared or radio tracer, both for galaxies and star–forming regions. We discuss these calibrations and the main limitations of these recipes when they are applied within galaxies.

Addressing the question of the formation and the evolution of galaxies in a cosmological context implies that we must understand their emission over the broadest electromagnetic spectrum. Using multi-wavelength data consistently enables to measure reliable physical parameters like star-formation rates and stellar masses.However, the drawback of this approach is that we do need more information in terms of data. We also need to handle them by using powerful computers and smart codes that are able to run ina reasonable amount of time and deal with a wealth of data and a huge number of models. A statistical approach is also mandatory to estimate the reliability of the results. In this chapter I will describe the different components and physical processesthat leave their imprints in the distribution of energy of galaxiesandhow physicalparameters related to their star formation history can be extracted from the fit of their spectral energy distribution. I willpresent physically-motivated codes which assume an energy balance between dust stellar absorption and re-emission

Observations of the high-energy (X-ray, γ-ray) emission for galaxies opens a new window to study star-forming activity through the detection of the remnants of massive stars. In this chapter we discuss the use of X-ray binaries, supernovae and supernova remnants,γ-ray emission, and γ-ray burstsas star-formation rate indicators. We give an introduction to the different types of X-ray binaries, recent efforts to model their population, and wepresent our current understanding of the scalling relations between populations of X-ray binaries, or their integrated X-ray emission, and the star-formation rate or stellar mass of their host galaxies. Special attention is given on the dependence of these scaling relations and the formation efficiency of X-ray binaries on the age and metallicity of the stellar populations.We also discuss the use of supernovae,supernova remnants, and γ-ray emission (γ-ray bursts and total γ-ray emission) as probes of star-forming activity, recent results and the limitations of these methods. Finally we discuss how gravitational wave sources can be used in order to probe the star-formation history of the Universe.

Stars play such a fundamental role in the evolution of galaxies, some of the key-questions in the field of galaxy evolution and cosmology are related to the history of their formation in galaxies. How do star formation and its history depend on the environment or on the mass of galaxies? When do stars form globally in the history of the universe ? When and how does starlight contribute to the re-ionization phase in the early universe?The goal of this book is to provide the reader an overall presentation of the theoretical and observational backgrounds about the definition and measurement of Star-Formation Rates in galaxies

The measured star-formation rates (SFRs) of galaxies comprise an important constraint on galaxy evolution and also on their cosmological boundary conditions. Any available tracer of the SFR depends on the shape of the mass-distribution of formed stars, i.e. on the stellar initial mass function(IMF). The luminous massive stars dominate the observed photon flux while the dim low-mass stars dominate the mass in the freshly formed population. Errors in the number ratio of the massive to low-mass stars lead to errors in SFR measurements and thus to errors concerning the gas-accretion ratesand the gas-consumption time-scales of galaxies. The stellar IMF has traditionally been interpreted to be a scale-invariant probability density distribution function (PDF), but it may instead be an optimal distribution function. In the PDF interpretation, the stellar IMF observed on the stales of individual star clusters is equal to the galaxy-wide IMF (gwIMF) which, by implication, would be invariant. In this chapter we discuss the fundamental properties of the IMF and of the gwIMF, the nature of both and their systematic variability as indicated by measurements and theoretical expectations, and we discuss the implications for the SFRs of galaxies.

We can trace star formation through a broad variety of observations: photospheric emission from massive stars in the ultraviolet, dust emission in the infrared from grains heated and excited by energetic photons, hydrogen and metal recombination lines from the optical to the infrared, and even free-free continuum and synchrotron emission in the radio domain. The first and foremost constraint for astronomers in estimating SFRs is the ability to obtain adequate observations. For instance, distant galaxies may have emission lines shifted beyond the near-infrared, making them inaccessible from the ground, or the object may be too faint for its free-free emission to be detected. The nature of the observed galaxy and the available instruments therefore strongly guide how we can measure star formation. In the context of this chapter we concentrate on detailing how we can use any observation in star formation tracing bands to measure the SFR as reliably as possible. We will start with theoretical considerations to understand the impact if the assumptions behind each SFR estimator and then discuss the observational constraints.

Dust impacts observations of stars and gas in galaxies by absorbing and scattering photons. Correctly accounting for the effects of dust allows for more accurate studies of a galaxy's stars and gas while also enabling the study of the dust grains themselves.The impact of dust on measurements of individual stars in a galaxy can be straightforwardly modeled as extinguishing the stellar light. Dust extinction towards a star is defined as the combined effect of absorption of photons and scattering of photons out of the line-of-sight towards the star. For integrated measurements of regions of galaxies or whole galaxies that contain multiple stars intermixed with dust, the effects of dust are termed attenuation and are harder to model. Integrated measurements include stars extinguished with different amounts of dust and scattering of photons into the measurement aperture. The infrared dust emission powered by the absorbed photons provides a vital measurement of the amount of energy absorbed by dust. This infrared measurement is not possible for individual stars butprovides an important constraint in modeling the effects of dust on integrated measurements. The aim of this chapter is to provide the details of dust extinction, attenuation, and emission and recommendations for how to model the effects ofdust on observations.