Modeling Tracers of Young Stellar Population Age in Star-Forming Galaxies
aa r X i v : . [ a s t r o - ph . GA ] N ov Modeling Tracers of Young Stellar Population Age in Star-Forming Galaxies
Emily M. Levesque CASA, Department of Astrophysical and Planetary Sciences, University of Colorado 389-UCB,Boulder, CO 80309
Claus Leitherer
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
ABSTRACT
The young stellar population of a star-forming galaxy is the primary engine drivingits radiative properties. As a result, the age of a galaxy’s youngest generation of starsis critical for a detailed understanding of its star formation history, stellar content,and evolutionary state. Here we present predicted equivalent widths for the H β , H α and Br γ recombination lines as a function of stellar population age. The equivalentwidths are produced by the latest generations of stellar evolutionary tracks and theStarburst99 stellar population synthesis code, and are the first to fully account for thecombined effects of both nebular emission and continuum absorption produced by thesynthetic stellar population. Our grid of model stellar populations spans six metallicities(0 . < Z < . M ⊙ instantaneousburst and a continuous star formation rate of 1 M ⊙ yr − ), and two different treatmentsof initial rotation rate ( v rot = 0 . v crit and 0.4 v crit ). We also investigate the effects ofvarying the initial mass function. Given constraints on galaxy metallicity, our predictedequivalent widths can be applied to observations of star-forming galaxies to approximatethe age of their young stellar populations.
1. Introduction
The radiative properties of a star-forming galaxy are generated by its young stellar population.Young hot massive stars are the primary source of ionizing radiation in these galaxies, poweringtheir emission spectra. Supernova and gamma-ray burst progenitors in these galaxies are membersof this same massive star sample. The lower-mass members of this young stellar population willoften dominate the galaxy’s continuum emission. As a result, the age of the newest generationof stars is a crucial factor in determining the origins of a star-forming galaxy’s spectral signature.Well-developed age diagnostics for star-forming galaxies therefore allow us to better understand Hubble Fellow;
[email protected] β , H α , and Br γ –are all expected to be excellent indicators of young stellar population age. The steady decreaseof the ionizing photon flux as the youngest and hottest massive stars die will deplete the nebularcomponent of the hydrogen lines, while the underlying absorption will decrease at a much slowerrate due to the substantial contribution from cooler lower-mass stars. As a result, the equivalentwidths of these features will directly measure the ratio of the young ionizing population over theolder non-ionizing population (Stasi´nska & Leitherer 1996, Leitherer 2005).Dottori (1981) was the first to predict that the equivalent width of H β (W(H β )) should decreasewith the age of a starburst. Soon after, Copetti et al. (1986) modeled a starburst HII region andfound that W( Hβ ) decreased almost monotonically with age. The first in-depth analysis of this andother similar age diagnostics was presented in Stasi´nska & Leitherer (1996). While the nature ofthe hydrogen recombination lines is complicated by other parameters such as metallicity, the natureof the initial mass function (IMF), stellar mass loss rates, and older underlying stellar populations,both Copetti et al. (1986) and Stasi´nska & Leitherer (1996) concluded that the primary determiningfactor in these line widths was starburst age. Finally, Schaerer & Vacca (1998) presented a suiteof evolutionary synthesis model outputs that illustrated the evolution of W( Hβ ) with age for avariety of different metallicities, clarifying the abundance dependence of this age diagnostic. Thismetallicity-dependent W( Hβ )-age relation was recently quantified in Levesque et al. (2010a). Basedon these theoretical relations, W( Hβ ) has since been used as a direct proxy for starburst age (e.g.Stasi´nska et al. 2001).More recently, Fernandes et al. (2003) were the first to verify from observations that W(H β )does indeed decrease with starburst age, combining empirical determinations of starburst age withobservations and synthetic galaxy spectra. Mart´ın-Manj´on et al. (2008) further extended theseage diagnostics to more complex star formation histories; while W(H β ) is a reliable gauge of asingle coeval burst’s stellar population, most realistic galaxy models much account for multiple starformation episodes. They concluded that even when modeling multiple starbursts, W( Hβ ) servedas a good age indicator out to ∼
10 Myr.Applying model-based age diagnostics to observations of star-forming galaxies requires accom-modating for several complicating factors. Underlying continuum absorption from the lower-massmembers of the young stellar population will decrease the observed value of the W( Hβ ) equivalentwidths, making calibrations based only on the nebular emission features uncertain by as much as afactor of 2 at later ages and weaker nebular equivalent widths (Fernandes et al. 2003). Gonz´alez-Delgado (1999, 2005) present detailed examinations of how equivalent widths for the H α and H β absorption features evolve with time for a starburst. Effectively accounting for this absorption com-ponent is crucial when developing a calibration meant to be applied to observations. Furthermore, apure starburst model lacks any contribution from an older stellar population, which yields a much 3 –redder continuum and disproportionately dilutes observed equivalent widths for lines at shorterwavelengths; for further discussion of dilution effects see Fernandes et al. (2003) and Section 4.Finally, while stellar mass loss rates were found to be a secondary effect by Copetti et al. (1986),subsequent generations of stellar evolutionary models have newly emphasized the critical role thatmass loss and other physical properties such as rotation and binarity can have on the lifetimes ofstellar populations and even the particular phases predicted at a given mass by evolutionary tracks(e.g. Meynet et al. 1994, Vanbeveren et al. 1998Eldridge & Stanway 2009, Ekstr¨om et al. 2012,Levesque et al. 2012, Georgy et al. 2013).Here we present our theoretical relations between W( Hβ ), W(H α ), W(Br γ ), and age. Ourresults are based on the latest generation of stellar evolutionary tracks and the Starburst99 stellarpopulation synthesis code, and are the first to account for the combined effects of nebular emis-sion and continuum absorption in our measurements of equivalent widths. In Section 2 we presentthe parameters adopted in our stellar population synthesis models and describe the analyses usedto calculate our final equivalent widths. In Section 3 we illustrate the age evolution of W( Hβ ),W(H α ), W(Br γ ) in our models and consider the effects produced by different star formation his-tories, variations to the IMF, and treatments of stellar rotation. Finally, in Section 4 we discusspersisting challenges for age diagnostics in observed spectra of star-forming galaxies as well asfuture improvements and analyses that could improve these diagnostics.
2. Model Grid Parameters
For our analysis of the W(H β ), W(H α ), and W(Br γ ) evolution with age, we use modelsproduced by the Starburst99 evolutionary synthesis code (Leitherer et al. 1999, 2010; Leitherer& Chen 2009; V´azquez & Leitherer 2005). The Starburst99 code initially generates the massdistribution of a stellar population for a given metallicity Z and following a specified initial massfunction (IMF). Stellar evolutionary tracks are then used to assign fundamental stellar parameters(e.g. luminosity, effective temperature, etc.) and their variation with time commencing on thezero-age main-sequence and terminating when the end-point of stellar evolution is reached. Foreach time step during the evolution and for each mass interval, the code assigns properties such asthe resulting energy distribution, color, chemical yields, and others. Integration over all masses andall stellar generations then provides the synthetic properties of the full population. The adjustableinput parameters of the models are the initial chemical composition, the IMF as specified via theslope α and the upper and lower mass limits, and the star formation history. The stellar evolutionmodels are fixed and considered well calibrated. It is important to realize that evolution modelsfor massive stars are not derived from first principles but have built-in adjustable parameters, suchas the mixing length and the mass loss rates, which were previously calibrated via observations ofresolved stellar populations in the Local Group of galaxies. The main constraints are provided bythe width of the main-sequence, ratios of various stellar types, and determinations of individualstellar parameters (e.g. Massey 2013). In order to produce realistic equivalent widths for H β and 4 –H α , we require models that account for the combined effects of the nebular emission and continuumas well as underlying stellar absorption, which becomes significant at 6-8 Myr in the optical regime(see Gonz´alez Delgado et al. 2005). We therefore use optical high-resolution output spectra fromStarburst99 produced using the latest improvements in stellar atmosphere models, accommodatingkey components such as non-LTE effects and line blanketing (for a detailed discussion of thesehigh-resolution models, see Martins et al. 2005).Starburst99 computes the ionizing fluxes from the set of model atmospheres published bySmith et al. (2002), which are assigned to each data point provided by the evolutionary tracks.The atmospheres are based on the WM-Basic (Pauldrach et al. 2001) and CMFGEN (Hillier &Miller 1998) codes, which are generally considered the most appropriate for massive O- and Wolf-Rayet (WR) stars, respectively. Both sets of atmospheres are spherically extended and account forthe hydrodynamics of the outflow (see the discussion in Smith et al. 2002 for a comparison of theirmain features). Both models sets were tailored by Smith et al. (2002) to match the properties of theGeneva evolutionary tracks and are therefore directly compatible with these evolution models. TheWM-Basic O-stars models are used along the main-sequence and early post-main-sequence untilthe surface hydrogen abundance by mass reaches 0.4. Stars with lower hydrogen abundance areconsidered WR stars and are modeled with the CMFGEN atmospheres. The surface abundancesof the major elements change drastically during the WR phase, and the CMFGEN atmosphereabundances are modified accordingly. While there is consistency between the CMFGEN abundancesand the chemical composition of the tracks, this is not the case for the WM-Basic O-star models. Inparticular, the decrease of the hydrogen abundance is not accounted for. Fortunately, Starburst99allows us to investigate whether the variable hydrogen abundance along the main-sequence tracksaffect the emergent Lyman continuum. The Starburst99 code incorporates an additional set ofWM-Basic models as part of a high-resolution UV library (Leitherer et al. 2010). These modelscover the spectral region 900-3000˚A and do in fact account for the hydrogen and helium variationalong the main-sequence. Comparison of the Smith et al. (2002) and Leitherer et al. (2010) modelsshortward of the Lyman edge suggest negligible differences.The emergent fluxes of spherical, expanding atmospheres are sensitive to the wind densities,and therefore to the mass-loss rates. This sensitivity is particularly pronounced at the shortestwavelengths in the ionized helium continuum below 228˚A. The mass-loss rates of the atmospheremodels adopted by Smith et al. (2002) are calibrated via observed values. In contrast, the mass-loss rates in the stellar evolution models are initially based on observations but then are adjustedto enforce agreement between the observed and theoretical upper Hertzsprung-Russell diagram.Generally, the rates in the evolution models are higher than those used for the atmospheres. How-ever, this is not a concern for the hydrogen Lyman continuum, for which wind effects are almostnegligible. This can be appreciated in Fig. 3 of Smith et al. (2002) where the UV part of thespectrum of a WM-Basic model is compared to a static plane-parallel Kurucz model (Lejeune etal. 1997). The latter can be thought of an atmosphere with zero mass loss. As expected, there arelarge differences below 228˚A, whereas the two models are identical (except for line-blanketing) in 5 –the hydrogen Lyman continuum.We include seven different sets of stellar evolutionary tracks in our models spanning six differentmetallicities. We begin with the set of non-rotating stellar evolutionary tracks presented in Meynetet al. (1994) that adopt a “high” mass loss rate enhanced to approximate rotation effects. Thesetracks are calculated at metallicities of Z = 0 . , . , . , . Z as the mass-weighted heavy element abundance where the Sun has Z = 0 .
014 on the scale discussedby Asplund et al. 2005). Note that the high-resolution stellar spectra in Starburst99 are availableat metallicities of Z = 0 . , . , . Z = 0 . Z = 0 . Z = 0 .
008 spectra. We also include the two new sets ofstellar evolutionary tracks at Z = 0 .
014 presented in Ekstr¨om et al. (2012). Both included updatedopacities, nuclear reaction rates, and mass-loss treatments as compared to the previous generationof models. Most importantly, one set of the new tracks models the evolution of non-rotating stars(initial v rot = 0 . v crit ), while the other models the evolution of stars with an initial rotation velocityof v rot = 0 . v crit (where v crit is the break-up speed at the equator). For more discussion of theseevolutionary tracks, see Ekstr¨om et al. (2012).We adopt two different treatments of the SFH in our models: a zero-age instantaneous burst ofstar formation with a fixed mass of 10 M ⊙ , and continuous star formation with a constant rate of1 M ⊙ yr − , starting from an initial time of 0 Myr and assuming a stellar population large enoughto fully sample the upper end of the IMF. Modeling an instantaneous burst of star formationallows us to clearly trace the effects of a single coeval stellar population, while a continuous starformation treatment represents the other extreme of a stellar population that reaches and sustainsequilibrium after the first 3-4 Myr. In reality, most star-forming galaxies occupy a middle groundbetween the two extreme star formation histories that we model here, showing evidence of severalshort bursts of star formation interleaved with quiescent periods (see, for example, Terlevich et al.2004, Mart´ın-Manj´on et al. 2008). Starting with an initial 0 Myr age, we simulate the evolutionof our synthetic stellar populations up to 20 Myr in 0.5 Myr increments. At ages >
20 Myr for theinstantaneous burst stellar populations, the galaxy spectrum becomes dominated by lower-massstars and the nebular emission features disappear as the hot ionizing massive star population diesout. Our initial grid of Starburst99 outputs was run with a Kroupa IMF, with α = 1 . ⊙ -0.5M ⊙ mass range and α = 2 . ⊙ -100M ⊙ (Kroupa 2001). However, in order toexplore the effects of the IMF on our age diagnostic lines, we also ran models for the Z = 0 . α = 1 . α = 3 . ⊙ -100M ⊙ mass range (the regime of interest for our work given the dominance of massive stars at these earlyages) to examine the impact of varying IMFs. All three IMFs have a mass range of 0.1 M ⊙ -100M ⊙ .The combined nebular emission and continuum components of W(H β ), W(H α ), and W(Br γ )were determined directly from the ewidth output file of the Starburst99 code, which includes theresults of the code’s determinations of continuum luminosities, line luminosities, and equivalent 6 –widths for the nebular hydrogen features (for more discussion on the importance of the nebularcontinuum, particularly at early ages and longer wavelengths, see Leitherer & Heckman 1995).The stellar absorption components were calculated based on the hires Starburst99 output file.These data include the code’s calculation of a high-resolution theoretical spectrum from 3000-7000˚A . For our calculations we used the normalized spectra from this file to fit the stellar H β andH α absorption features and determine an equivalent width. Combining these (negative) values ofabsorption equivalent widths with the nebular components at each timestep produced final values ofW(H β ) and W(H α ) for our models. This correction for stellar absorption is particularly importantin the case of our instantaneous burst star formation history models at later ages, where thenebular emission components are depleted and the stellar absorption increases (for more discussionsee Gonz´alez Delgado et al. 2005). In the case of Br γ , the stellar absorption in this wavelengthregime is insignificant at early ages; the continuum is dominated by red supergiants, which do nottypically show hydrogen in their spectra (see, for example, Levesque et al. 2005), at later ages( &
10 Myr). As a result we simply calculate W(Br γ ) as the nebular components with no additionalcontribution from stellar absorption.
3. Evolution of the Hydrogen Recombination Lines
Figure 1 shows the evolution of W(H β ), W(H α ), and W(Br γ ) with time for our models adoptingan instantaneous burst star formation history. All three spectral features show a similar evolutionwith time and a metallicity-driven spread, comparable to the results of Schaerer & Vacca (1998)and Leitherer et al. (1999). Their evolution is best characterized by a sharp drop in the first 2-5 Myrfollowed by a significantly more graduate decrease to a ≤ Z = 0 . , .
020 and 0 .
040 models show a rapid decrease beginning at 0 Myr and diminishto ≤ ≤ Z = 0 .
001 models,which shows a persistent emission component in all three line features that is present up to ∼ β ) and W(H α ) and ∼
18 Myr for W(Br γ ).Our models with Z = 0 . , . β ),W(H α ), and W(Br γ ) beginning at 3-3.5 Myr and lasting 0.5-1Myr (interestingly, the evolution of For more information on the output products of Starburst99 please see . β ), W(H α ), and W(Br γ ) illustrated in Leitherer et al. 1999 also shows this small increase,but only in the higher -metallicity cases). The rotating Z = 0 .
014 models include a second 0.5-1Myr increase in the equivalent widths at 5.5 Myr, and predict larger equivalent widths than thenon-rotating Z = 0 .
014 models between 1-10.5 Myr. From our past work on the ionizing spectraproduced by rotating and non-rotating stellar populations (Levesque et al. 2012) we can attributethese small increases in equivalent width to the onset and duration of the Wolf-Rayet phase in ourmodeled stellar populations. Non-rotating models of stellar evolution predict Wolf-Rayet stars anage of 3-5 Myr, while rotating models permit lower-mass stars to evolve to the Wolf-Rayet phase,maintaining a higher ionizing flux for longer and showing a later increase in equivalent widthscorresponding to the age of the lower-mass Wolf-Rayet population.The exception to this very similar evolution of the hydrogen recombination lines with time isthe Z = 0 .
001 model. At this metallicity we see a slower overall decrease in W(H β ) and W(H α )with time and a significant resurgence in the value of W(Br γ ) beginning at 5.5 Myr and lastinguntil 7 Myr. This demonstrates that Br γ may not be a robust indicator of young stellar populationage at very low metallicities due to its double-valued nature of behavior. The unique behavior at Z = 0 .
001 can be attributed to the effects of low metallicity on the red supergiant population. Athigh metallicities the ionizing fluxes decrease nearly monotonically after 3 Myr and the near-IRcontinuum increases at > ⊙ ) stars. Combined, this leads to a steep decline in equivalent width. At Z = 0 . Z = 0 .
004 models at 5.5Myr. It is worth noting that, as described in Section 2, our Z = 0 .
004 models were produced bycombining Z = 0 .
004 stellar evolutionary tracks with Z = 0 .
008 atmosphere models; therefore, itis possible that a model run with Z = 0 .
004 stellar atmospheres would in fact present a clearermissing link between the predictions of our Z = 0 .
001 and Z = 0 .
004 models.In Figure 2, we plot W(H β ), W(H α ), and W(Br γ ) as a function of time for models that adopta continuous star formation rate. While our instantaneous burst models are the best means ofexamining the equivalent widths produced by a single coeval stellar population - making them thepreferred models for applications for starburst galaxies - our continuous star formation models rep-resents the opposing “extreme” of star formation history. With all star-forming galaxies occupyingsome middle ground between these two assumptions, the equivalent widths produced by both setsof models effectively serve as lower (instantaneous) and upper (continuous) limits on the youngstellar population age associated with an observed equivalent width. Like the instantaneous burstmodels, our continuous star formation models show a similar metallicity-dependent evolution withtime for W(H β ), W(H α ), and W(Br γ ); however, in the continuous star formation case the modelsinstead approach constant > β ),W(H α ), and W(Br γ ) for our rotating and non-rotating Z = 0 .
014 models. As previously illustratedby Leitherer et al. (1999), changes in α can have a strong effect on the predicted equivalent widthsof the hydrogen recombination lines; steeper IMFs consistently produce smaller equivalent widthsat all ages and the difference appears to become more pronounced at higher values of α . A KroupaIMF and shallower ( α = 1 . β ), W(H α ),and W(Br γ ) for the non-rotating instantaneous burst models, but otherwise the differences areconsistent for both star formation histories and rotation treatments. Based on a similar analysisin Leitherer et al. (1999), these IMF effects should not be metallicity-dependent.
4. Discussion
We have illustrated the predicted evolution of W( Hβ ), W(H α ), W(Br γ ) as a function of agefor our grid of stellar population synthesis models. These predictions are the first to accommodatethe combined effects of nebular emission and continuum absorption produced by a stellar popula-tion, and also include models that span multiple metallicities, star formation histories, and stellarrotation treatments, offering improvements over previous work (e.g. Leitherer et al. 1999, Schaerer& Vacca 1998, Mart´ın-Manj´on et al. 2008, Levesque et al. 2010a). Given constraints on metallic-ity, these predicted equivalent widths can be applied to observations of star-forming galaxies toapproximate the age of their young stellar populations.However, it is important to note several shortcomings of these models that may limit the effi-cacy of our predicted equivalent widths when applied to observations. Like many stellar populationsynthesis codes (e.g. Bruzual & Charlot 2003), Starburst99 does not account for the destructiveeffects of dust, instead assuming that 100% of the ionizing photons produced by the stellar popula-tion make it to recombination. Accounting for dust effects in typical star-forming galaxies shouldyield values for W(H α ) and W(H β ) that are ∼
30% lower to account for the absorption of Ly-man continuum photons (e.g. DeGioia-Eastwood 1992, Fioc & Rocca-Volmerage 1997, Inoue et al.2001). Similarly, the use of hydrogen recombination lines as age indicators is rendered ineffectivefor very high-metallicity or dusty galaxies where the bulk of the ionizing photons will be destroyedbefore they can recombine.The predicted W(H α ) and W(H β ) equivalent widths can also potentially suffer from the effectsof dilution, as described in Fernandes et al. (2003) and Section 1. The presence of a significantlyolder ( & ≥ U − V colors for star-forming galaxies to effectively characterize the presence of olderunderlying stellar populations.Finally, it is clear that treatments of stellar rotation and mass loss in the evolutionary trackscan have a significant effect on the predicted equivalent widths produced by stellar populations.Levesque et al. (2010b) highlighted the insufficient ionizing fluxes produced by Starburst99 whenadopting the non-rotating stellar evolutionary tracks of Meynet et al. (1994). Subsequently, inLevesque et al. (2012) we examined the ionizing continuum produced by a rotating stellar popu-lation in detail, and conclude that the rotation rates modeled by the Geneva evolutionary tracks(Ekstr¨om et al. 2012, Georgy 2012) may now lead to an overproduction of high-energy ionizingphotons. The treatment of rotation itself presents an important source of uncertainty that mustbe considered in such work (e.g. Meynet et al. 2013, Chieffi & Limongi 2013). Finally, current evo-lutionary tracks, both rotating and non-rotating, have highlighted several uncertainties concerningmass loss rates, particularly during the red supergiant phase (Georgy et al. 2012). Even so, it isclear that rotation directly yields larger equivalent widths for the hydrogen recombination lines.Furthermore, binary stellar evolution also has a significant impact on the ionizing flux; similar to arotation stellar population, models of binary stellar evolution produce significantly larger equivalentwidths (Eldridge & Stanway 2009). These comparisons highlight the importance of stellar evolu-tionary models, and their treatments of crucial properties such as rotation and binary, in modelingstellar populations.EML is supported by NASA through Hubble Fellowship grant number HST-HF-51324.01-Afrom the Space Telescope Science Institute, which is operated by the Association of Universities forResearch in Astronomy, Incorporated, under NASA contract NAS5-26555. Support for Programnumber AR-12824 was provided by NASA through a grant from the Space Telescope Science Insti-tute, which is operated by the Association of Universities for Research in Astronomy, Incorporated,under NASA contract NAS5-26555. REFERENCES
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12 –Fig. 1.— The evolution of W(H β ) (top), W(H α ) (center), and W(Br γ ) (bottom) with age for ourmodels adopting an instantaneous burst star formation history (with an initial mass of 10 M ⊙ ) anda Kroupa IMF ( alpha = 2.3 for 0.5M ⊙ -100M ⊙ ). The models span the five metallicities availablefrom the Meynet et al. (1994) stellar evolutionary tracks as well as the z = 0 .
014 evolutionarytracks of Ekstr¨om et al. (2012), and adopt rotation rates of v rot = 0 (solid lines) and v rot = 0 . v crit (dashed line). 13 –Fig. 2.— As in Figure 1, but for models adopting a continuous star formation history with a starformation rate of 1 M ⊙ yr − . 14 –Fig. 3.— The evolution of W(H β ) (top), W(H α ) (center), and W(Br γ ) (bottom) with age forour instantaneous burst (left) and continuous star formation (right) models, demonstrating theeffects of varying the IMF. The models shown here adopt the z = 0 . v rot = 0 (solid lines)and v rot = 0 . v crit (dashed lines) evolutionary tracks of Ekstr¨om et al. (2012) and IMFs with a0.5M ⊙ -100M ⊙ mass range exponent of α = 1 . α = 2 . α = 3 ..