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ASTR 5610, Majewski [SPRING 2018]. Lecture Notes

ASTR 5610 (Majewski) Lecture Notes


References: See Binney & Merrifield, Section 5.4, and the Renzini & Buzzoni (1986) article placed in the reading list.

Spectral Energy Distributions

Even with HST, we can only resolve individual stars and create system color-magnitude diagrams for star clusters and galaxies within approximately the Local Group.

Thus, the question arises, what information can we derive from the Spectral Energy Distribution (SED) of a galaxy, as gauged by colors or integrated spectra?

The SED of a galaxy must evolve:

Passive Evolution of an SSP

Because of its relative simplicity, we start with passive evolution of an SSP.

Of course, the driving timescale in the evolution is that set by the Main Sequence turnoff mass, which is a function of the age of the SSP.

Some simple observations:

Relative Timescales of MS and Post-MS Phases

We have already seen that the age of a main sequence star is given by:

With the Main Sequence mass-luminosity relationship incorporated:

we obtain a rapid decrease in MS lifetime with increasing mass.

We also previously estimated that the HB phase was typically much shorter.

Main Sequence Luminosity Evolution

The integrated luminosity of a system is the sum of the luminosities of all stars.

Clearly, the total luminosity from Main Sequence stars is given by:

But there is a subtlety that the above procedure ignores:

Clearly the total brightness of MS stars is dictated by the shape of the IMF.

We see from this exercise that for a passively evolving system (or a system with no recent -- less than a fraction of a Gyr -- star formation) the integrated light from the system is dominated by the evolved stars.

Post-MS Luminosity Evolution and The Fuel Consumption Thereom

The evolutionary flux of a population -- the rate at which stars leave the MS and venture into Post-MS phases and die -- is given by:

b(t ) = (TO) (d TO / dt ),


Again, because of the shortness of Post-MS phases, all phases after the MSTO contain stars coming from more or less the same ZAMS mass.

Fuel Consumption Evolution, Phase Transitions, and Luminosity Evolution for an SSP

The fuel consumption for stars in different evolutionary phases, Fj , is directly related to the initial mass, age and chemical composition of a star, and can be determined in most cases by stellar evolutionary theory.

For an SSP, the fuel consumption for Post-MS stars is simply given by the j of the MSTO stars.

The total fuel consumption for stars through all phases of Post-MS evolution, Ftot = j Fj , as a function of MSTO mass, and therefore population age, is shown below:

From Renzini & Buzzoni (1986, in The Spectral Evolution of Galaxies, eds. C. Chiosi & A. Renzini, Reidel Publishing, pp. 201).
Several discontinuities are seen in the fuel consumption versus age (or MSTO mass) plot (actual positions depend on composition):

Despite the phase transitions we see, the overall amount of fuel burned on the Post-MS does not vary too greatly with turnoff mass.

While the fuel consumption discontinuities have little affect on the luminosity evolution, on the other hand, the distribution of stars in the CMD suffer nearly discontinuous readjustments as the age of an SSP reaches the ages of the transition masses.

Color Evolution of an SSP

The SED is actually sensitive to the temperature distribution of the constituent stars, and, in turn, the temperature distribution is a function of age (or of the age distribution in a complex population).

Clearly the redistribution of the types of stars that contribute large fractions of the bolometric luminosity in an SSP will leave different imprints on the luminosity in different specific filters, and, therefore, we can increase sensitivity to specific stellar types by clever choice of appropriate color indices.

Considering the above color characteristics for Post-MS stars and their relative contributions according to the Fuel Consumption Thereom, we can make the following general comments about the evolution of an SSP's SED:

  1. The 20 Myr transition should herald a sudden increase in NIR luminosity from He-core burning stars, with little effect on the NUV-blue light.
  2. The 0.5 Gyr transition should affect the visual to NIR part of the SED, with little effect on NUV-blue light.

    This transition can be seen in the model shown below, where:

    • the U-B flux steadily drops (as a reflection of the burn-off of the MSTO) at all times.
    • the B-V color also reddens for this reason until about 0.5 Gyr when additional V flux from late type AGB stars accelerates the B-V reddening.
    • U-B

      The evolution of the colors of a galaxy experiencing a starburst lasting 20 Myr. The left-most dashed line shows the evolution if the burst is the dominant stellar population in the galaxy, and ages are marked along the line. From Larson & Tinsley (1978, ApJ, 219, 46).
  3. The width of the composite optical-NIR SED shrinks with age, because both the MS gets redder and the AGB/RGB gets shorter with age (transition from a "bowl-shaped" vs. "hump-shaped" SED).

    From Binney & Merrifield, Figure 5.2.

    In addition, if a population is older and more metal poor, the AGB and RGB are bluer.
    • A ``wide" SED would have lots of blue/UV and NIR flux.

      Thus, it would have, e.g., blue U-B or U-V colors and red V-K colors.
    • A narrowing of the width of an SED would be expressed by a decrease in the difference between U-V and V-K colors.

      Plot showing the distribution of star clusters in the Magellanic Clouds, which are well known to have a large spread in ages. The ages of clusters generally increases (not linearly) towards the right in the figure. As may be seen, the youngest MC clusters show wide SEDs (red V-K and blue U-V), but with time the U-V and V-K colors become more similar. The red light in the V-K is from very luminous stars in red supergiant phases in the youngest clusters. From Persson et al. (1983, ApJ, 266, 105).
  4. For the oldest populations, the contribution of PAGB stars, though small in terms of bolometric luminosity, may make a significant contribution to the UV and NUV flux of the SSP with no effect on the red/NIR.

    • Elliptical galaxies and the bulges of spiral galaxies, in particular, are well known to exhibit a UV-upturn in their SEDs:

    • These upturns indicate the presence of very hot stars:

      From Renzini & Buzzoni (1986, in The Spectral Evolution of Galaxies, eds. C. Chiosi & A. Renzini, Reidel Publishing, pp. 223).
    • ...and had earlier been discussed as possibly reflecting the rise of PAGB stars in these old systems.
    However, more recent work (e.g., Dorman, O'Connell & Rood 1995), suggests that old HB and post-ZAHB, evolved HB stars are more likely to be the dominant UV sources in stellar populations.

    • If true, this is an important development, because the UV flux can then provide important leverage on ages for older systems for ages when the age-sensitivity of the optical-NIR colors has greatly coarsened (i.e., after a few Gyr).
    In either case, the UV flux of a system, once calibrated (see Yi et al. 1999, ApJ, 513, 128), may lead to a powerful tool for aging older systems, since once stars are older than a few Gyr, the UV to V flux ratio increases monotonically with time.

    A comparison of four different models -- including different mixes of HB types/metallicities and PAGB stars -- for the evolution of the (1500A - V) color in a simplistic stellar population resembling those in early type galaxies. The figure shows the current disagreement of various synthetic population models, but also the potential for age dating once the correct model is clarified. From Yi et al. (1999, ApJ, 513, 128).
    Note the bluer (1500A - V) color in both young (<1-2 Gyr) and old populations.
  5. Given the UV and NIR sensitivity to various population phase transitions, one may conclude that the wings of a galaxy SED are much more sensitive to age than are the optical part of the SED.

Comments on the Spectral Classification of Galaxies

The SEDs of galaxies have been described with a variety of (similar) classification schemes:

It is clear that what such schemes are characterizing is the dominant contributing sources to the SED, and are sensitive to things like the relative mix of late and early type stars, and, for the latter, the relative youth of the youngest strong population.

Galaxies with Complex SFHs

Real galaxies tend not to be SSPs.

As we have seen, passive evolution of an SSP quickly becomes rather slow and monotonic for luminosity and mean color.

On the other hand, if anything interesting happens to the SFR along the way of passive evolution, the SED can respond dramatically.

Redshift Effects

A complication not even included in the above diagrams are redshift effects, which will be an important contributor to the appearance of a source's broadband magnitudes and colors.

Two redshift effects must be accounted for and corrected in the colors of high redshift sources:

Real Codes

Among the components that real population synthesis/evolution codes must include:

...and the above only pertains to the integrated light from an unresolved source.

A number of people make careers out of developing such codes. Among the more familiar ones are:

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All material copyright 2003,2006 ,2008,2010,2012,2016,2018 Steven R. Majewski. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 551 and Astronomy 5610 at the University of Virginia.