Evolution stellar populations in galaxies is one of the key ingredients of our understanding of galaxy evolution in general. If we look at colors of galaxies nearby we can immediately see that there is a bimodel distribution. There is a fairly narrow red, peak, which is due to the elliptical galaxies and bulges. And there is a fairly broad blue distribution, that corresponds to the discs of spirals. In more modern renderings, you can plot colors as a function of intrinsic luminosity. And you still see those same two blobs. But they're a little tilted. In the case of elliptical galaxies that ridge line. [inaudible] is really mass[INAUDIBLE]. The more luminous the. The ellipticals retain more of their, chemical evolution products. Their more metal rich metals absorb more like in the ultraviolet galaxy look redder. So this is largely mass metallicity sequence. For spirals there isn't a very simple relation like that. Their colors are combination of mixture of stellar ages. Star formation rates as well as extinction by dust. So we can produce predicted theoretical spectra of evolving galaxies in the following fashion. We have to make an assumption of what the star formation history is. This is a purely pre-parametering the model, but we can make reasonable guesses. We need to know what is the initial mass function, the distribution of stars by mass when they're formed, because stars of different masses can be involved in very different[UNKNOWN]. Then for each stellar mass and, and, and age we need a spectrum. So we need libraries of stellar spectra that can be associated with all components of the stellar population at any given age. This is actually not an easy thing to do, because we can observe a lot near us. But for example, we have no spectra of very metal poor very massive stars, because those have burnt out long time ago. And, again from theory, tested by observations of star clusters and so on, we need stellar population evolution tracks. How does distribution of stars and color magnitudes space the HR Diagram changes the function of time for a given amount of. Chemical enrichment and so on. You take a quantity of gas and turn it all into stars instantaneously. A delta function star formation rate distributed according to your initial mass function. And then follow it's evolution in time. This is what's known as a simple stellar population. There is no such thing in reality, although globular clusters come close. And then it can represent net total star formation history of a galaxy is a collection of these, and follow the map. One popular way of expressing star formation histories is a exponentially declining rate. Which is probalby not a bad overall assumption Average or many galaxies. In this case, for early type galaxies there is a lot of star formation early on. The exponential very steep. For this galaxy very shallow. For irregular galaxies may be essentially flat or even rising. Stellar evolution is one of the best understood Segments of astrophysics. We really do know how stars work and evolve. And that's been confirmed again and again through many decades of observations. There are certainly details that still need to be ironed out. But at the level that we care about here, we really do understand that. An important thing to remember is that more massive stars They are much faster, they are more luminous, they are also hotter, so they are[UNKNOWN] more important but not for long. Thus, spectrum of an evolving galaxy will change more rapidly in the blue parts of the spectrum, thanks to the short life times of these massive stars. And will be changing relatively slowly in the red parts of the spectrum where the most of the light may be coming from well of all slowly evolving population of red giants. There are many stellar populations indices methods out there. And they sometimes disagree on some details. But by and large the agreement's pretty good. One popular set is called Giselle. Which is a library of The galaxy evolution spectra by[UNKNOWN] and[UNKNOWN]. We know how stars evolve. We even have spectra of lots of different kinds of stars. And we have some idea of the initial mass function. At least we measure it locally in the milky way. And then we have to make assumptions what it's saying in all galaxies at all times. We can test some of those assumptions. But then we have to assume star formation rate which again is a completely free parameter in this exercise. This is what stellar evolution tracks look like. They're computed from stellar evolution models. And a star evolves it moves in the color magnitude space. How and where depends very much or almost entirely on its mass with minor dependence on its metallicity. So we get these stellar evolutionary tracks from theory, our understanding of stellar structure and evolution it's pretty solid. Then, we need to have their spectra. And for kinds of stars that we can observe near us, that's an easy thing to acquire. For kinds of stars that are no longer with us, say, very young, metal poor, very high mass stars. This will require some theoretical modeling, and stripulation. We make an assumption about initial mass function, and again we understand that in the local Milky Way condition, but it would be very different in the early universe where, say, stars were made out of, Of hydrogen and helium, and hardly anything else. In fact, we believe that was the case, that the initial mass function of primordial stars was very different. And then again, we have to assume star formation history. In reality, we assume some types of star formation histories. Compute the consequences, compared it to iterations and iterate until we have a model that seems to fit observations and that's telling us what the likely star formation history of these galaxies was. So stars evolve, the blue ones keep disappearing faster. Galaxies will be changing their colors and here in color, color space you can follow the, theoretical behavior of evolving stellar populations. You can also see where the galaxies are, and indeed they form something of a. Sequence that corresponds to the younger, hotter stars on late Hubble types, older, redder stars for the early Hubble types. Here is a comparison of predictions of three different types of stellar population and synthesis models by different groups. And it shows predicted colors and mass to light ratios for model galaxies. By and large they agree very well. The minor disagreements usually are very young ages and there is some debate actually what is the correct thing to assume but. Qualitatively at least, we understand very well how things are working. And so this is what evolving spectra of stellar populations look like. This is for a simple stellar population. Remember this is a scoop of stars made all at once, and let go. Note, these are logarithmic plots of log flux versus log wavelength. So. They really hide the strong contrast. And if you stare at curves which are labeled by their age, those near the top tends to be youngest because younger stars are more luminous. You find out that in the ultraviolet, blue part of the spectrum, the flux will plummet very quickly. Whereas it would be changing in the red part of the spectrum, but much slower which is exactly what we expect. Here is a comparison of predicted model spectral of different ages assuming different libraries of stellar population evolution tracs and spectra. And again you see that. Different models seem to be in an excellent mutual agreement. Which is giving us some confidence that we actually do understand how this works. Another kind of models that they are now more popular are so called, semi-analytical, or hybrid models, where one can use telepopulation synthesis models. Associate them with galaxies that they're being assembled through hierarchical structure formation. Either from a numerical simulation, or from some statistical description thereof. And make predictions of how will they ch, colors change and so on. There are unfortunately way too many two level parameters in these models. And so they have some modest success, but they illustrate of all different things that have to be taken into account, and a lot of assumptions that have to be made. Next time we will turn to the actual observations of galaxy evolution.