Stellar Populations - Lecture II - Durham Universityastro.dur.ac.uk/~rjsmith/stelpop19_lec2.pdf ·...

Russell Smith Stellar Populations 2019 / II

Stellar Populations - Lecture IIRUSSELL SMITH

Ogden Centre West 129

[email protected]

http://astro.dur.ac.uk/~rjsmith/stellarpops.html

Slides from Lec 1 now posted

mailto:[email protected]

http://astro.dur.ac.uk/~rjsmith/stellarpops.html

Russell Smith Stellar Populations 2019 II

1. Introduction - Phases of stellar evolution

- Simple Stellar Populations

2. Resolved Stellar Populations - Cluster CMDs

- SSP fitting: age, metallicity, IMF

- Complex populations: SFH, MDF

- Exotica

- Limitations

Course outline

3. Population synthesis - Principles and caveats

- Temperature, metallicity and gravity effects on stellar spectra.

- Flux contribtions

- Colours

Optical age-metallicity degeneracy

Beyond the optical

- Spectral synthesis

Empirical and theoretical stellar libraries

Spectroscopic age/metallicity indicators.

IMF indicators

4. Applications - Abundance ratios and chemical evolution.

- Star-formation histories and stellar masses.


Tool: simulated CMDs

Random extraction of:– mass(IMF)– age(SFR) – metallicity(Z(t))

• Interpolation of the extracted star (m,t,Z) on the HRD (log L, log Teff)

• Determination and application of bolometric corrections: BC(T, g, Z)

• Application of observational uncertainties: – photometric error – incompleteness

Composite stellar population

Aparicio & Gallart 2004

Age & metallicity histories

General methods for fitting multiple populations in resolved populations.

Recover stellar mass formed in a range of age bins.

Can also fit the metallicity in each age bin.

More ambitiously, can aim to recover fraction of stars formed on a grid of age and metallicity.


Age & metallicity histories

Gallart et al. (2007) Local Group Dwarf Galaxies


Selection criteria

y J-H ≥ 0.72

y K ≤ 17.41

y J-K ≥ 0.74

y J-K =1.20

y No sources selected beyond ~

4kpc from the galactic centre

y [Fe/H] = -1.29 ± 0.07

y Results published in Sibbons et al.

(2012)

Oldest white-dwarfs are fainter and cooler in older populations.

Some other age / metallicity tracersSibbons et al. 2012

Carbon stars (where C dredged to surface in late AGB, affecting IR colours) are more common at low metallicity, so C/M ratio is a metallicity indicator using only very luminous stars.

J-K

K

M-type (oxygen-rich AGBs)

C-type (carbon-rich AGBs)

NGC 6822

NGC6397 Hansen et al.

(2007)

10 Gyr

11.5 Gyr

13 Gyr


Direct constraints on low-mass (~0.5 Msun) end of the IMF.

Requires very faint photometry so possible only in nearby LG dwarfs.

Initial Mass Function 3

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Fig. 1.— The HST/ACS CMDs of two UFD galaxies, Hercules (left) and Leo IV (right). For the IMF analysis, we include stars belowthe sub-giant branch and above the 66% and 75% completeness limits for Hercules and Leo IV, respectively (green points). The axes arelabeled in both STMAG and Vega magnitudes. The blue line is a representative isochrone of 13.6Gyr and the mean metallicity of eachgalaxy (Table 1). Blue crosses indicate stellar mass in units of M⊙ on the main sequence.

for Leo IV. All images were dithered to mitigate detec-tor artifacts and enable resampling of the point spreadfunction (PSF). Our image processing includes the lat-est pixel-based correction for charge-transfer inefficiency(Anderson & Bedin 2010). We co-added the images foreach filter in a given tile using the IRAF DRIZZLE pack-age (Fruchter & Hook 2002), with masks for cosmic raysand hot pixels derived from each image stack, resulting ingeometrically-correct images with a plate scale of 0.03′′

pixel−1 and an area of approximately 210′′ × 220′′.We performed both aperture and PSF-fitting photome-

try using the DAOPHOT-II package (Stetson 1987), as-suming a spatially-variable PSF constructed from iso-lated stars. The final catalog combined aperture pho-tometry for bright stars with photometric errors < 0.02mag and PSF-fitting photometry for the rest, all nor-malized to an infinite aperture. Due to the scarcityof bright stars, the uncertainty in the normalization is0.02 mag. Our photometry is in the STMAG system:mλ = −2.5× log10fλ − 21.1, except where we explicitlystate Vega magnitudes (Figure 1). The catalogs werecleaned of stars with poor photometry and backgroundgalaxies. Sources were rejected based on photometricerrors (< 0.1mag) and the DAOPHOT χ and sharp pa-rameters. We also reject stars with bright neighbors andthose falling within the profiles of extended backgroundgalaxies because these are noisier than isolated stars ofcomparable magnitude. We apply the same rejection cri-teria in determining the completeness of our data de-scribed below. For more details on the data reductionsee Brown et al. (2009).We performed extensive artificial star tests to evalu-

ate the photometric scatter and completeness for each

galaxy. These tests employed the same PSF model andPSF-fitting routines used in the construction of the ob-served catalogs, including the algorithms for culling poor-quality stars, image artifacts and corrections for chargetransfer efficiency. Artificial stars were inserted intothe image with appropriate reductions in signal (andnoise) due to charge transfer inefficiency. Stars werethen blindly recovered and corrected for charge transfer(Anderson & Bedin 2010). The artificial stars were in-serted over a wide range of color (−1.3 ≤ m606−m814 ≤0.5) and magnitude (32 ≥ m814 ≥ 16) with most of thestars falling near the observed stellar locus and biased to-ward fainter magnitudes, thus providing the most fidelityin the analysis region. A total of 5,000,000 artificial starswere inserted into each image, spread over thousands ofpasses in order to avoid significantly altering the level ofcrowding and the associated photometric scatter. Thenumber of stars recovered from all passes sets the com-pleteness fractions given in Table 2. For this analysis,we include stars fainter than the red giant branch andbrighter than the magnitude where photometric errorsapproach the main-sequence width and photometric ar-tifacts begin to contribute significantly to the catalog(green region in Figure 1, see Table 2). The faint cutoffcorresponds to the 66% and 75% completeness limits forHercules and Leo IV, respectively. This magnitude re-gion corresponds to a stellar mass range of 0.52−0.77M⊙

and includes 2380 stars in Hercules and 1054 stars in LeoIV.

2.1. Constructing the Model IMFs

We analyze our observed luminosity functions by for-ward modeling stellar evolutionary tracks with an ana-

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0.764 0.747 0.698 0.617 0.521mass (MO .)

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Salpeter (1955; α=2.35)

Bottom-light power law (α=0.5)

25 26 27 28m814 (STMAG)

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Leo IV

Best-fit power law (α=1.31)

Salpeter (1955; α=2.35)

Bottom-light power law (α=0.5)

Fig. 3.— The observed luminosity function for Hercules (left) and Leo IV (right). Errors bars are computed from the observed numberof stars in each luminosity bin. For comparison, we plot three theoretical power law IMFs, convolved with our observational errors andphotometric completeness. The fits were normalized to reproduce the number of stars in the observed luminosity function, but here theyhave been normalized at the bright end for clarity. We compare our best-fitting model (green) to a Salpeter IMF (α = 2.35, blue) and anextremely bottom-light IMF (α = 0.5, red).

Fig. 4.— Stellar mass functions for the five galaxies in whichthe IMF has been measured via direct star counts: the MilkyWay (blue, Bochanski et al. 2010), the SMC (light blue, Kaliraiet al. 2012), Ursa Minor dSph (green; Wyse et al. 2002), Leo IV(orange; this work) and Hercules (red; this work). Except for Her-cules, the vertical normalization is arbitrary. For reference, thepublished power law slopes are shown for each dataset, normalizedat 0.75M⊙. We note that a power law slope of α = 1 is a flatline in this log-log plot. The UFD galaxies show noticeably flattermass functions in this mass range.

The presence of unresolved binary stars can mimica flattening of the IMF at low masses (Kroupa et al.1991; Bochanski et al. 2010). On the main sequence,

Kroupa et al. (1991) first demonstrated that unresolvedbinary systems widen the main sequence beyond observa-tional errors, with binary systems brighter and redwardof the single star main sequence. Our best-fitting single-power law IMF is degenerate between steeper IMF slopeswith high binary fractions and shallower (more bottom-light) IMF slopes with lower binary fractions (Figure 2).For Hercules, the binary fraction is constrained to befbinary = 0.48+0.20

−0.12 for a single power law or 0.47+0.16−0.14

for a log-normal IMF. The binary fractions for Leo IVare similar, but far less constrained due to the smallernumber of observed stars (Table 1). While binary starswere known to exist in the UFDs based on repeatedspectroscopic measurements of red giant branch stars(Simon et al. 2011; Koposov et al. 2011), these observa-tions did not strongly constrain the binary fraction itself(Martinez et al. 2011). Our results are the first quanti-tative constraints on the binary fraction in the UFDs.The binary fractions inferred for the UFDs pertain to

stars in the mass range 0.52 − 0.77M⊙, predominantlyK-dwarf stars. In the solar neighborhood, the multi-plicity of stars decreases with decreasing stellar mass(Kraus & Hillenbrand 2012), with more massive OB-type stars having binary fractions upwards of fbinary =0.7 (Peter et al. 2012), down to M-stars with binary frac-tions between 0.2-0.3 (Janson et al. 2012). This trendmay be the result of intrinsic differences in the binaryfraction as a function of stellar mass, the consequence of asingle overall binary fraction and random pairings acrossthe mass spectrum, or possibly due to binary disruptionover time combined with ages differences between spec-tral populations (Kroupa et al. 1993; Marks & Kroupa2011). For K-dwarfs, Duquennoy & Mayor (1991) sug-

Geha et al. (2013) Best-fit slope is 1.16

(cf Salpeter 2.35)

Updates: Gennaro et al. 2018(a,b)


CMD exotica: blue stragglers

Why haven’t these stars evolved off the main sequence like others of similar mass?

Not thought to be young, but rather “delayed” evolution.

Most likely due to stellar collisions or mass transfer in binary stars: “stellar re-fuelling”.

Note: We don’t know how to predict from first principles the number of BS stars formed in a population…

Two sequences of BS matching collisional and mass-transfer models.

Evolutionary models of COL-BSS (Sills et al. 2009): • collisions between two MS stars (0.4 - 0.8 M) • Z = 10-4 (ZM30 = 2.5 10-4)

• blue-BSS sequence well reproduced by collisional isochrones of 1-2 Gyr

• red-BSS sequence too red to be reproduced by collisional isochrones of any age

Ferraro (2009)

Sandage (1953) (!)

Globular cluster M3


CMD exotica: multiple Main-Seq in GCsMultiple populations in globular clusters 9

Fig. 1 The triple MS of NGC 2808 (Piotto et al. 2007) and the position of the two MSstars, one on the bMS, one on the rMS, analysed by Bragaglia et al. (2010b).

.

In the case of ω Cen, the SGB had been known to present a large spread(e.g., Hilker & Richtler 2000), possibly implying a spread in age. The firstindication of an actual split was shown by Ferraro et al. (2004), who founda fainter SGB, connected to the highest metallicity RGB. This split was con-firmed (e.g., Bedin et al. 2004; Sollima et al. 2005) and a more complicatedstructure was detected. For instance, Villanova et al. (2007) identified at leastfour distinct SGBs and explained them with differences in metallicity and inage (but the large age spread, > 4 Gyr, is controversial) trying also to under-stand how they connect to the multiple MSs and RGBs. Detailed abundanceanalysis, such as the one in Pancino et al. (2011), but on larger samples ofSGB stars in each of the sub-sequences is required to settle the problem.

Impressive evidence of multiple populations comes from the very precisephotometry of an increasing number of lower-mass clusters, obtained mainlywith HST: NGC 1851 (Milone et al. 2008; in this globular cluster also ground-based data show a split, see Zoccali et al. 2009, Milone et al. 2009), NGC 6388(Moretti et al. 2009, combining optical HST and infrared ground-based adap-tive optic data), 47 Tuc (Anderson et al. 2009), M 22, and M 54 (Piotto et al.2009).

NGC 1851 is the best studied of all these. As already indicated by thediscovery paper (Milone et al. 2008), the split SGB can be explained by adifference in age (∼ 1 Gyr) or in C+N+O content (He has a small effect and therequired difference in [Fe/H] would show up elsewhere in the colour-magnitudediagram). An enhanced CNO abundance was explored e.g., by Cassisi et al.(2008) and Ventura et al. (2009a), finding it a viable explanation. Indeed, Yonget al. (2009) proposed a variable CNO in a small sample of RGB stars (notfound by Villanova et al. 2010, but apparently confirmed on a larger sample,Yong, still unpublished). Also debated is the radial distribution of the two sub-branches (e.g., Zoccali et al. 2009 and Milone et al. 2009); a more concentrateddistribution is expected for the second generation. The split, however, appears

Many (all?) globular clusters now show evidence for multiple populations. (Not such good SSP approximations after all!)

Relative size of populations is a long-standing and continuing puzzle.

Surprisingly, the blue MS is more metal rich than the red MS: Interpreted as evidence for increased Helium abundance in 2nd-generation stars.

Piotto et al. (2007)


CMD exotica: horizontal branch

HORIZONTAL BRANCH MORPHOLOGY

Temperature of HB stars depends on how much mass was lost on the RGB. Difficult to model.

The temperature distribution on the HB in globular clusters depends on mostly on their metallicity.

But some differences not attributable to metallicity: what is the “second parameter” that determines HB form at given Fe/H?

Classic High-Fe/H “Red Clump” Classic Low-Fe/H Blue HB

Famous “2nd parameter” pair with same Fe/H but very different HB


Multiple populations in GCs

UV photometry from HST for ~60 GCs. Filters optimized to maximize split between multiple sequences (sensitive to CN, CH, NH bands in UV/blue).



Discrete populations traceable through MS/RGB/HB phases.

1st generation: “normal” abundances

2nd generation: polluted by CNO-processed material.

(But 2nd-gen is large compared to 1st-gen… how?)


Multiple populations in GCs

Review: Bastian & Lardo (2018)


Practical limitations

Figure 2: The distribution of galaxies in the nearby universe (yellow points), deprojected

to indicate true distances from the Milky Way (center). Spirals brighter than -17 mag and

ellipticals brighter than -19 mag are highlighted (green symbols). Concentric circles

indicate the volume of space that can be surveyed in 10, 100, and 1000 hours with JWST

(red) and HST (blue), reaching 0.5 mag below the turnoff in a 12 Gyr population. HST

can survey a few Local Group sightlines, while JWST can survey many Local Group

galaxies and also reach the Sculptor Group (e.g., NGC300 and NGC55).

4. Bright Red Stars in Nearby Galaxies

The bright region of the Color-Magnitude Diagram (CMD) of external galaxies carries

information on their Star Formation History, albeit with a lesser degree of detail than the

turn off region. Indeed the portion of the CMD brighter than MJ ≈ -4 contains in their

evolved evolutionary stages stars formed since one Hubble time. Decoding the stellar

counts in this part of the CMD in terms of SFH is complicated by several effects, which

include the relatively low number of stars per unit mass of the parent stellar population,

the less accurate color temperature transformations, and the uncertain modelling of the

Asymptotic Giant Branch (AGB) evolutionary phase. Still, it is possible to derive a

robust measurement of the mass in stars within broad age ranges, which corresponds to a

Galaxies with 12-Gyr MSTO accessible to HST/JWST in 10, 100, 1000 hours. (Brown et al. 2008)

Difficulties for resolved photometry in more distant galaxies:

* Faintness (limited information if MSTO not reached)

* Crowding (forces observations into outer halo - unrepresentative?)

Improving on this situation a major low-z science goal for 30m-class telescopes and JWST.


Practical limitationsMetallicity gradients in Virgo Ellipticals with E-ELTs 15

Figure 18. Output (J, I − J) CMDs in the same crowding conditions (µB = 21.64 mag arcsec−2) assuming three different input PSFs.The color reflects the metallicity bin of the object with the same encoding as on Fig. 1. The metallicity of the output stars is identified onthe basis of the positional coincidence with input objects on the J band image. The dashed lines highlight the 50 per cent completenessin the two colors.

Figure 20. Input (red filled histogram) and recovered (black thick histogram) metallicity distributions for the non-optimal PSFs casesconsidered and µB = 21.64 mag arcsec−2. The [Fe/H] histogram bin widths for which the input and output metallicity distributions arein best agreement are 0.18 and 0.19 dex for cases B and C respectively, c.f. the 0.18 bin width of case A (Fig. 16).

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Girardi L., Bertelli G., Bressan A., et al., 2002, A&A, 391,195

Gilmozzi R., Spyromilio J., 2007, The Messenger, 127, 11

Gullieuszik M., Greggio L., Held E. V., et al., 2008, A&A,483, L5

Greggio L., Renzini A., 2011, Stellar Populations. A UserGuide from Low to High Redshift., Wiley-VCH Verlag-GmbH & Co. KGaA, Weinheim, Germany

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c⃝ 2002 RAS, MNRAS 000, 1–16

Simulated RGB for Virgo ellipticals (~15 Mpc) at Reff/2 with E-ELT. (Schreiber et al. 2013).

Still in the limited-information regime!

We will not resolve centres of giant ellipticals any time soon…

A. Deep et al.: Colour–magnitude diagrams in Virgo

Fig. 19. Here we plot the surface brightness profile of NGC 4472 (fromKormendy et al. 2009), a “typical” giant elliptical galaxy in the Virgocluster. There is a vertical line placed at the distance from the centreof the galaxy at the highest surface brightness for which CMDs canbe made and photometered with E-ELT and JWST (coming from thisstudy), and HST/ACS (Durrell et al. 2007).

as has been presented now. The PSF from MAORY has beenprovided on a “best effort” basis, and it is at the limits of whatis thought to be possible given the current technical specifica-tions of both MAORY and the telescope adaptive mirror (M 4).In conclusion the I filter should remain part of the “standard” fil-ter set of any MCAO system for the E-ELT, even with a minimalAO performance.

A possible upgrade path for the telescope may allow betterAO performance in the optical which could lead to deep I lumi-nosity functions, which can also be used to interpret the prop-erties of distant stellar populations. If the sensitivity of the I fil-ter can be pushed to reach the Horizontal Branch limit in Virgo(I ∼ 31), then it will be possible to directly and unambiguouslydetermine the presence of an ancient and/or metal-poor stellarpopulations in elliptical galaxies in the Virgo cluster.

A good observing strategy for studying elliptical galaxieswill be to use three filters, namely I, J and Ks. The I−K com-bination will be most useful for studying the metal poor popu-lation, or to determine if one is present. The J−K colour willbe more revealing about the presence of extremely red evolvedstars, such as carbon stars and metal rich AGB stars.

5.2. What we may learn about elliptical galaxies

The centre of a giant elliptical galaxy in Virgo typically has acentral surface brightness, µv ∼ 16 mag/arcsec2. Our simula-tions suggest MICADO/MAORY will be able to detect individ-ual stars, even old, metal poor stars, close to the central regionsof such a galaxy. It will be possible to make CMDs within 5 arc-sec of the centre, of even the largest elliptical galaxies, comparedto 250 arcsec for JWST, as is shown in Fig. 19.

Of course, as can be seen from Fig. 7, the amount of informa-tion that can be extracted from a CMD at a surface brightness,

µv = 17 mag/arcsec2 is likely to minimal. Assuming that thedistance to the galaxy is very well known, then it will be pos-sible to tell if we are looking at the AGB star population. If thedistance is uncertain, and it is not known a priori if a stellar pop-ulation contains AGB stars or not, then there will be no clearway of deciding if AGB or RGB stars are being detected fromthis kind of CMD.

All the CMDs in Fig. 7 are still only of the upper region ofthe RGB in a Virgo galaxy, so it is not always going to be possi-ble to disentangle the complex star formation histories. However,a much longer exposure time will of course improve the faintlimit for accurate photometry. Even though these CMDs of theRGB are not the ideal CMDs to make a unique interpretation(e.g., Gallart et al. 2005), it should also be possible to determinethe age and metallicity spread (see Fig. 5). In the case of distinctage or metallicities differences, such as we used for our simula-tions, it may often be possible to infer their presence.

Well populated CMDs will allow accurate studies of the rela-tive properties within galaxies, and how galaxies may vary com-pared to each other. This means comparative studies of how thenumbers of stars of different colours and luminosity vary withposition, and the relative importance of different types of starson the RGB at different positions. This will provide valuable in-formation as to how the stellar population was built up. It willbe interesting to compare the stellar populations in low surfacebrightness regions (where the photometry is more accurate) withhigher surface brightness regions in the same galaxies, or lowsurface brightness dwarf galaxies with the giants. This will re-quire a detailed understanding of the crowding and incomplete-ness properties of the CMDs.

It should not be forgotten that the CMDs presented, in Fig. 7are for extremely small fields of view (0.75 arcsec squared), andwhen the full field of MICADO is considered 5000 times morestars will be included in each CMD. These cover a range of sur-face brightness going from the inner to the outer regions of atypical elliptical galaxy. The surface brightness variation is typ-ically very smooth for elliptical galaxies, but for theses typesof stars, a global colour and luminosity can hide a lot of varia-tion (e.g., Monachesi et al. 2011). Comparing the resolved stellarpopulations of the inner and outer regions of elliptical galaxieswill have important implications for formation scenarios.

For these kinds of relative studies a large field view (com-pared to the size of the galaxy being studied) is required. Themajor advantage of an MCAO imager for this science case, is thewide field of view that is possible (∼53 arcsec square), with uni-form AO correction. This allows an accurate and detailed com-parative study of a significant area of most elliptical galaxies atthe distance of Virgo.

Figure 20 shows, from the surface brightness limits ofMICADO/MAORY imaging, how many galaxies in Virgo (fromKormendy et al. 2009) can be studied in detail, to which dis-tance from the centre, in a one hour exposure. We can see that itwill be possible to resolve the entire stellar population of dwarfspheroidal galaxies, as they are uniformly low surface bright-ness systems. It should be realised that most of the central re-gions of galaxies in Virgo are no more than 1−3 arcmin across,at a surface brightness of ∼22 mag/arcsec2. The wide field ofMICADO/MAORY will thus efficiently allow the sampling of arange of surface brightness across each galaxy.

Of course MICADO/MAORY will also be able to make moredetailed CMDs of closer by giant elliptical galaxies, such asNGC 3379 (M 105) the dominant member of the Leo group, ata distance of 10.5 Mpc (Salaris & Cassisi 1998). This is thus0.7 mag closer than the simulations at the distance of Virgo

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Review of stellar evolution. Population model inputs: isochrones and initial mass function. Observed cluster colour magnitude diagrams. Isochrone fitting methods: ages, metallicities. (We can learn a lot from this kind of data, if we can get it.) More complicated cases & exotica. (Could be more common than we would like to think.) Practical limitations. (Resolved studies cannot fairly sample the population of galaxies.)

To go beyond the resolved populations in and near the LG, we need to understand how to learn from unresolved stellar pops.

Resolved stellar pops : summary


Unresolved populationsOur aim is to learn about galaxies!

Specifically to “measure” their stellar ages and metallicities (or more generally SFH and MDF), and their stellar masses.

“Easy” when individual stars can be measured and placed on CMD.

But of all the galaxies in the universe, only a few dozen can be resolved...

(And those that are resolved are not a fair sample of the universe - no giant ellipticals.)

So what about the rest?

What do we do when we can’t see the individual stars?


Even unresolved galaxies are made of stars. So if we know the properties of their stars

- i.e. if their stars are similar to MW stars - or their stars can be modelled from first principles

then we can “add up the stars” to build a model, and test this against the properties of an observed galaxy.

Early spectral synthesis models attempted to do just that: combine individual stars in varying proportion to match observed spectrum of a galaxy... ... but such models very under-constrained, as well as quite uninformative.

Building galaxies from stars?


Modern methods take advantage of the “fundamental principle of stellar populations”: regularity in stellar content.

Building galaxies from SSPsC

onroy (2013)

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Figure 1:

Overview of the stellar population synthesis technique. The upper panels highlight the ingredientsnecessary for constructing simple stellar populations (SSPs): an IMF, isochrones for a range ofages and metallicities, and stellar spectra spanning a range of Teff , Lbol, and metallicity. Themiddle panels highlight the ingredients necessary for constructing composite stellar populations(CSPs): star formation histories and chemical evolution, SSPs, and a model for dust attenuationand emission. The bottom row shows the final CSPs both before and after a dust model is applied.

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M4III

G2V

A0V

O5V

SF and Chem Evol

0 5 10 1505

101520

SFR

0 5 10 15t (Gyr)

-2.0-1.5-1.0-0.50.0

log

Z/Z O

•

SSPs

0.01 0.10 1.00λ (µm)

-20

-18

-16

-14

-12

log

f ν

1010 yr

106 yr

Dust

0.10 0.25 0.50 1.00

12345

τ/τ V

attenuation

1 10 100 1000λ (µm)

-19

-18

-17

-16

log νf

ν

emission

CSP

0.01 0.10 1.00 10.00 100.00 1000.00λ (µm)

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

log νf

ν

dust-free

dusty

Figure 1:


5

Instead of building unresolved galaxy from individual stars, use SSPs as the building blocks.


From ingredients:

- IMF

- isochrones

- stellar spectra,

we generate spectra of SSPs over range of age and metallicities.

Later, we can combine SSPs to generate composite stellar populations, and/or introduce effects of dust if necessary.

Spectral synthesis: SSPsIMF

0.1 1.0 10.0 100.0M (MO •)

10-410-3

10-2

10-1

100

101

102

103

dn/d

M


Isochrones

3.54.04.5log Teff

-2

0

2

4

6

log

L bol

106 yr

1010 yr

Stellar Spectra

0.1 1.0λ (µm)

-3

-2

-1

0

1

2

log

f ν +

C

M4III

G2V

A0V

O5V

SF and Chem Evol

0 5 10 1505

101520

SFR

0 5 10 15t (Gyr)

-2.0-1.5-1.0-0.50.0

log

Z/Z O

•

SSPs

0.01 0.10 1.00λ (µm)

-20

-18

-16

-14

-12

log

f ν

1010 yr

106 yr

Dust

0.10 0.25 0.50 1.00

12345

τ/τ V

attenuation

1 10 100 1000λ (µm)

-19

-18

-17

-16

log νf

ν

emission

CSP

0.01 0.10 1.00 10.00 100.00 1000.00λ (µm)

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

log νf

ν

dust-free

dusty

Figure 1:


5

Conroy (2013)

IMF

0.1 1.0 10.0 100.0M (MO •)

10-410-3

10-2

10-1

100

101

102

103

dn/d

M


Isochrones

3.54.04.5log Teff

-2

0

2

4

6

log

L bol

106 yr

1010 yr

Stellar Spectra

0.1 1.0λ (µm)

-3

-2

-1

0

1

2

log

f ν +

C

M4III

G2V

A0V

O5V

SF and Chem Evol

0 5 10 1505

101520

SFR

0 5 10 15t (Gyr)

-2.0-1.5-1.0-0.50.0

log

Z/Z O

•

SSPs

0.01 0.10 1.00λ (µm)

-20

-18

-16

-14

-12

log

f ν1010 yr

106 yr

Dust

0.10 0.25 0.50 1.00

12345

τ/τ V

attenuation

1 10 100 1000λ (µm)

-19

-18

-17

-16

log νf

ν

emission

CSP

0.01 0.10 1.00 10.00 100.00 1000.00λ (µm)

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

log νf

ν

dust-free

dusty

Figure 1:


5


General principle:

1) Assign a spectrum Sλ to each point on the isochrone.

[Sλ is physically determined by temperature, composition and surface gravity. Isochrone tells us which Teff and Z to assign for each mass].

2) Sum spectra of stars, weighted by the IMF, N(M) along the isochrone.

Other approaches possible (e.g. “fuel consuption theorem” method - Renzini, Maraston)

SSP spectra: ingredients

Fλ(t, Z) = ∫ Sλ(Teff(M),g(M) | t, Z) . N(M) dM

Mup(t)

Mlo

IMF

0.1 1.0 10.0 100.0M (MO •)

10-410-3

10-2

10-1

100

101

102

103

dn/d

M


Isochrones

3.54.04.5log Teff

-2

0

2

4

6

log

L bol

106 yr

1010 yr

Stellar Spectra

0.1 1.0λ (µm)

-3

-2

-1

0

1

2

log

f ν +

C

M4III

G2V

A0V

O5V

SF and Chem Evol

0 5 10 1505

101520

SFR

0 5 10 15t (Gyr)

-2.0-1.5-1.0-0.50.0

log

Z/Z O

•

SSPs

0.01 0.10 1.00λ (µm)

-20

-18

-16

-14

-12

log

f ν

1010 yr

106 yr

Dust

0.10 0.25 0.50 1.00

12345

τ/τ V

attenuation

1 10 100 1000λ (µm)

-19

-18

-17

-16

log νf

ν

emission

CSP

0.01 0.10 1.00 10.00 100.00 1000.00λ (µm)

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

log νf

ν

dust-free

dusty

Figure 1:


5

IMF

0.1 1.0 10.0 100.0M (MO •)

10-410-3

10-2

10-1

100

101

102

103

dn/d

M


Isochrones

3.54.04.5log Teff

-2

0

2

4

6

log

L bol

106 yr

1010 yr

Stellar Spectra

0.1 1.0λ (µm)

-3

-2

-1

0

1

2

log

f ν +

C

M4III

G2V

A0V

O5V

SF and Chem Evol

0 5 10 1505

101520

SFR

0 5 10 15t (Gyr)

-2.0-1.5-1.0-0.50.0

log

Z/Z O

•

SSPs

0.01 0.10 1.00λ (µm)

-20

-18

-16

-14

-12

log

f ν

1010 yr

106 yr

Dust

0.10 0.25 0.50 1.00

12345

τ/τ V

attenuation

1 10 100 1000λ (µm)

-19

-18

-17

-16lo

g νf

ν

emission

CSP

0.01 0.10 1.00 10.00 100.00 1000.00λ (µm)

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

log νf

ν

dust-free

dusty

Figure 1:


5

IMF

0.1 1.0 10.0 100.0M (MO •)

10-410-3

10-2

10-1

100

101

102

103

dn/d

M


Isochrones

3.54.04.5log Teff

-2

0

2

4

6

log

L bol

106 yr

1010 yr

Stellar Spectra

0.1 1.0λ (µm)

-3

-2

-1

0

1

2

log

f ν +

C

M4III

G2V

A0V

O5V

SF and Chem Evol

0 5 10 1505

101520

SFR

0 5 10 15t (Gyr)

-2.0-1.5-1.0-0.50.0

log

Z/Z O

•

SSPs

0.01 0.10 1.00λ (µm)

-20

-18

-16

-14

-12

log

f ν

1010 yr

106 yr

Dust

0.10 0.25 0.50 1.00

12345

τ/τ V

attenuation

1 10 100 1000λ (µm)

-19

-18

-17

-16

log νf

ν

emission

CSP

0.01 0.10 1.00 10.00 100.00 1000.00λ (µm)

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

log νf

ν

dust-free

dusty

Figure 1:


5


Conceptually simple, but many challenges in detailed application. At a general level, we need to worry about:

Are the isochrones correct, for stellar phases that contribute a lot of light? Do we have spectra for all the relevant phases / parameters that will be present in the galaxies we’re going to model? Can we attach the right spectra to the right point on the isochrones (i.e. are the stellar parameters known)? Regimes of age/metallicity/wavelength where poorly-modelled stellar phases contribute a lot of flux.

Caveats

Fλ(t, Z) = ∫ Sλ(Teff(M),g(M) | t, Z) . N(M) dM

Mup(t)

Mlo


Effective temperature Teff : the dominant influence on stellar spectra.

Traditionally denoted by spectral type (OBAFGKM).

Continuum shape from black-body behaviour.

Modified by atomic/molecular processes in the stellar atmosphere.

Stellar parameters: Temperature

Peak in UV, all lines weak

H-lines strongest

Peak in blue, atomic metal lines.

Peak in red, metal lines and molecular bands

Peak in IR, strong molecular bands

H (Balmer series)

Mgb

CH

TiO

Balmer break

4000A break

Ca H+K

↝

↝↝ ↝↝

↝

↝

⚛↝ ↝↝

⚛↝


(1) Increasing metallicity shifts the isochrone to lower temperature (change in opacities in stellar interior).

The temperature effect changes the broad-band shape of the spectrum.

(2) Increasing metallicity also increases absorption in atomic/molecular transitions in the atmosphere.

Line absorption affects narrow intervals for strong lines, but combined effect of many weak metal lines changes the broad-band shape too (“line-blanketing” strongest in the blue).

Metallicity effects (stars)F stars from SDSS/SEGUE (Yanny et al. 2009)

CH (“G-band”)

Hydrogen Balmer lines


Aside: what exactly is metallicity?“METAL” CONTENT OF THE GAS THE STARS FORMED FROM Core composition changes as the star evolves, but the surface layers reflect the original composition (at least until late evolutionary phases).

EMPIRICAL NOTATION For measurements of metallicity in stellar atmospheres, we usually express abundances in terms of number density (not mass fractions).

Total metallicity is often expressed as [Z/H] = log10(NZ/NH) - log10(NZ/NH)sun. Then:

[Z/H]=0 is solar metallicity, [Z/H]=+0.3 is twice-solar, [Z/H] = -1 is one tenth solar, &c.

When talking about the interiors of stars, modellers express chemical mixture of material as mass fractions:

X or H = mass fraction of H , Y = mass fraction of HeZ = mass fraction of everything else = “metals”

astronomers’ periodic table


Aside: what exactly is metallicity?

BUT WHAT IS COMPOSITION OF “Z” ?

Note that O is the most important element for stellar evolution: it is abundant and a big contributor to the opacities. Unfortunately it is hard to measure O from stellar spectra!

Much easier to measure Fe which has lots of absorption lines in the optical.

So we often talk about [Fe/H] instead. This is equivalent to [Z/H] or [O/H] if the abundance of all elements is varied proportionately. (We’ll come back to this...)

x1000

atomic number

mas

s fr

acti

onsolar composition


Giants and dwarfs of same temperature and metallicity have similar mass (e.g. factor 2-3) but very different radius (e.g. factor 20-100)

Hence differ in their surface gravity / pressure.

Traditionally referred to through luminosity classes I-V.

Gravity effects on spectra

– 16 –

40005000600070008000

Effective Temperature (K)

-2

-1

0

1

2

3

Log(

L/L Su

n)

300040005000600070008000

C N

Fig. 6.— Comparisons between scaled-solar (solid lines) and the enhanced elements C and

N at constant Z (dashed lines) and [Fe/H]=0 (dot-dashed lines) for ages 1 and 8 Gyr.

Effective Temperature

Lum

inos

ity

1 Gyr

8 Gyr

A F G K

K III (giant)

K V (dwarf)


Affects balance between ionization states of atoms, and also the molecular equillibrium.

Prominent gravity indicators in IR:

Stronger in dwarfs:

- Wing-Ford band (FeH)

- Neutral alkali metal lines (Na, K)

- water bands (hard to measure!)

Stronger in giants:

- CO and CN bands

- Ionized metal lines (Ca triplet - but not in M stars)

Gravity effects on spectra

Na

COCO

M5 III

M5 V

CN

Rayner et al. 2009

(dwarf)

(giant)


Luminosity contributions and colours– 16 –

40005000600070008000

Effective Temperature (K)

-2

-1

0

1

2

3

Log(

L/L Su

n)

300040005000600070008000

C N

Fig. 6.— Comparisons between scaled-solar (solid lines) and the enhanced elements C and

N at constant Z (dashed lines) and [Fe/H]=0 (dot-dashed lines) for ages 1 and 8 Gyr.

Effective Temperature

Lum

inos

ity

1 Gyr

8 Gyr

A F G K

For overall flux contributions and broad-band colours, can ignore details of the spectral features.

Transformation from Lbol to band luminosities: “bolometric corrections”

Most massive stars are few in number, but each is very luminous.

Low-mass stars are numerous, but individually very faint.

Which group contributes most of the light? Which group carries most of the mass?

Balance depends on the IMF...


For old ages, solar metallicity, Chabrier IMF. Optical flux dominated by MS and RGB: the best understood phases.

(Balance to RGB in redder bands, MS in bluer.)

AGB at ~few per cent.

Luminosity contributions: optical

0.2 0.3 0.5 1.0 2.0λ (µm)

0.01

0.10

1.00

frac

tion

of to

tal f

lux

SFR∝ e−t/0.1 Gyr

pAGB/bHB

AGB

RGB+rHB

MS

steeply falling SFH

0.2 0.3 0.5 1.0 2.0λ (µm)

0.01

0.10

1.00

frac

tion

of to

tal f

lux

SFR∝ e−t/10 Gyr

AGB

RGB+rHBMS

typical SF galaxy at z~0

0.2 0.3 0.5 1.0 2.0λ (µm)

0.01

0.10

1.00

frac

tion

of to

tal f

lux

SFR∝ t

AGB

RGB+rHB

MS

rising SFH

0.05 0.1 0.2 0.5 1.0 2.0λ (µm)

0.01

0.10

1.00

frac

tion

of to

tal f

lux

M>60 MO •

M>20 MO •

SFR∝ e-t/10 Gyr

@ 13.5 Gyr

0.05 0.1 0.2 0.5 1.0 2.0λ (µm)

106

107

108

109

1010

light

-wei

ghte

d ag

e (y

r)

<age>m

SFR∝ e-t/10 Gyr

@ 13.5 Gyr

ioni

zing

pho

tons

ultra

viol

et

Figure 5:

Top Panels: Fractional contribution to the total flux from stars in various evolutionary phases, forthree different SFHs. The left panel is representative of a galaxy that formed nearly all of its starsvery rapidly at early times, the middle panel is representative of a typical star-forming galaxy atz ∼ 0, and the right panel may be representative of the typical galaxy at high redshift. Fluxcontributions are at 13 Gyr (solid lines) and 1 Gyr (dashed lines) after the commencement of starformation; all models are solar metallicity, dust-free, and are from FSPS (v2.3;Conroy, Gunn & White 2009). Labeled phases include the main sequence (MS), red giant branch(RGB), asymptotic giant branch (AGB, including the TP-AGB), post-AGB (pAGB), and the blueand red horizontal branch (bHB and rHB). Bottom Left Panel: Fractional flux contributions forstars more massive than 20M⊙ and 60M⊙ for the SFH in the middle panel of the top row.Bottom Right Panel: Light-weighted age as a function of wavelength for the same SFH. Thedashed line indicates the corresponding mass-weighted age.

practice.

2.3 Composite Stellar Populations

The simple stellar populations discussed in Section 2.1 are the building blocks for more

complex stellar systems. Composite stellar populations (CSPs) differ from simple ones inthree respects: (1) they contain stars with a range of ages given by their SFH; (2) they

17

RGB

AGB

Conroy (2013)

(solid lines: age=13 Gyr)

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