arXiv subjects

Charlie Conroy

Publications and source records attributed to Charlie Conroy.

At least 217 records · Page 12Linked to original sources

arXiv2017

The Stellar Initial Mass Function in Early-Type Galaxies From Absorption Line Spectroscopy. IV. A Super-Salpeter IMF in the center of NGC 1407 from Non-Parametric Models

It is now well-established that the stellar initial mass function (IMF) can be determined from the absorption line spectra of old stellar systems, and this has been used to measure the IMF and its variation across the early-type galaxy population. Previous work focused on measuring the slope of the IMF over one or more stellar mass intervals, implicitly assuming that this is a good description of the IMF and that the IMF has a universal low-mass cutoff. In this work we consider more flexible IMFs, including two-component power-laws with a variable low-mass cutoff and a general non-parametric model. We demonstrate with mock spectra that the detailed shape of the IMF can be accurately recovered as long as the data quality are high (S/N$\gtrsim300$) and cover a wide wavelength range (0.4um-1.0um). We apply these flexible IMF models to a high S/N spectrum of the center of the massive elliptical galaxy NGC 1407. Fitting the spectrum with non-parametric IMFs, we find that the IMF in the center shows a continuous rise extending toward the hydrogen-burning limit, with a behavior that is well-approximated by a power-law with an index of -2.7. These results provide strong evidence for the existence of extreme (super-Salpeter) IMFs in the cores of massive galaxies.

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arXiv2017

The Evolution and Properties of Rotating Massive Star Populations

We investigate the integrated properties of massive (>10 Msun), rotating, single-star stellar populations for a variety of initial rotation rates (v/vcrit=0.0, 0.2, 0.4, 0.5, and 0.6). We couple the new MESA Isochrone and Stellar Tracks (MIST) models to the Flexible Stellar Population Synthesis (FSPS) package, extending the stellar population synthesis models to include the contributions from very massive stars (>100 Msun), which can be significant in the first ~4 Myr after a starburst. These models predict ionizing luminosities that are consistent with recent observations of young nuclear star clusters. We also construct composite stellar populations assuming a distribution of initial rotation rates. Even in low-metallicity environments where rotation has a significant effect on the evolution of massive stars, we find that stellar population models require a significant contribution from fast-rotating (v/vcrit>0.4) stars in order to sustain the production of ionizing photons beyond a few Myr following a starburst. These results have potentially important implications for cosmic reionization by massive stars and the interpretation of nebular emission lines in high-redshift star-forming galaxies.

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arXiv2017

Halo Histories vs. Galaxy Properties at z=0 II: Large-Scale Galactic Conformity

Using group catalogs from the SDSS DR7, we attempt to measure galactic conformity in the local universe. We measure the quenched fraction of neighbor galaxies around isolated primary galaxies, dividing the isolated sample into star-forming and quiescent objects. We restrict our measurements to scales $>1$ Mpc to probe the correlations between the formation histories of distinct halos. Over the stellar mass range $10^{9.7} \le M_\ast/M_\odot \le 10^{10.9}$, we find minimal statistical evidence for conformity. We further compare these data to predictions of the halo age-matching model, in which the oldest galaxies are associated with the oldest halos at fixed $M_\ast$. For models with strong correlations between halo and stellar age, the conformity signal is too large to be consistent with the data. For weaker implementations of age-matching, galactic conformity is not a sensitive diagnostic of halo assembly bias, and would not produce a detectable signal in SDSS data. We reproduce the results of Kauffmann et al 2013, in which the star formation rates of neighbor galaxies are significantly reduced around primary galaxies when the primaries are themselves low star formers. However, we find this result is mainly driven by contamination in the isolation criterion, when using our group catalog to remove the small fraction of satellite galaxies in the sample, the conformity signal largely goes away. Lastly, we show that small conformity signals, i.e., 2-5% differences in the quenched fractions of neighbor galaxies, can be produced by mechanisms other than halo assembly bias. For example, if passive galaxies occupy more massive halos than star forming galaxies of the same stellar mass, a conformity signal that is consistent with recent measurements from PRIMUS (Berti et al 2016) can be produced.

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arXiv2016

Future Prospects: Deep Imaging of Galaxy Outskirts using Telescopes Large and Small

The Universe is almost totally unexplored at low surface brightness levels. In spite of great progress in the construction of large telescopes and improvements in the sensitivity of detectors, the limiting surface brightness of imaging observations has remained static for about forty years. Recent technical advances have at last begun to erode the barriers preventing progress. In this Chapter we describe the technical challenges to low surface brightness imaging, describe some solutions, and highlight some relevant observations that have been undertaken recently with both large and small telescopes. Our main focus will be on discoveries made with the Dragonfly Telephoto Array (Dragonfly), which is a new telescope concept designed to probe the Universe down to hitherto unprecedented low surface brightness levels. We conclude by arguing that these discoveries are probably only scratching the surface of interesting phenomena that are observable when the Universe is explored at low surface brightness levels.

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arXiv2016

A massive, quiescent, population II galaxy at a redshift of 2.1

Unlike spiral galaxies such as the Milky Way, the majority of the stars in massive elliptical galaxies were formed in a short period early in the history of the Universe. The duration of this formation period can be measured using the ratio of magnesium to iron abundance ([Mg/Fe]), which reflects the relative enrichment by core-collapse and type Ia supernovae. For local galaxies, [Mg/Fe] probes the combined formation history of all stars currently in the galaxy, including younger and metal-poor stars that were added during late-time mergers. Therefore, to directly constrain the initial star-formation period, we must study galaxies at earlier epochs. The most distant galaxy for which [Mg/Fe] had previously been measured is at z~1.4, with [Mg/Fe]=0.45(+0.05,-0.19). A slightly earlier epoch (z~1.6) was probed by stacking the spectra of 24 massive quiescent galaxies, yielding an average [Mg/Fe] of 0.31+/-0.12. However, the relatively low S/N of the data and the use of index analysis techniques for both studies resulted in measurement errors that are too large to allow us to form strong conclusions. Deeper spectra at even earlier epochs in combination with analysis techniques based on full spectral fitting are required to precisely measure the abundance pattern shortly after the major star-forming phase (z>2). Here we report a measurement of [Mg/Fe] for a massive quiescent galaxy at z=2.1. With [Mg/Fe]=0.59+/-0.11, this galaxy is the most Mg-enhanced massive galaxy found so far, having twice the Mg enhancement of similar-mass galaxies today. The abundance pattern of the galaxy is consistent with enrichment exclusively by core-collapse supernovae and with a star-formation timescale of 0.1-0.5 Gyr - characteristics that are similar to population II stars in the Milky Way. With an average past SFR of 600-3000 Msol/yr, this galaxy was among the most vigorous star-forming galaxies in the Universe.

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arXiv2016

Nebular Continuum and Line Emission in Stellar Population Synthesis Models

Accounting for nebular emission when modeling galaxy spectral energy distributions (SEDs) is important, as both line and continuum emission can contribute significantly to the total observed flux. In this work, we present a new nebular emission model integrated within the Flexible Stellar Population Synthesis code that computes the total line and continuum emission for complex stellar populations using the photoionization code Cloudy. The self-consistent coupling of the nebular emission to the matched ionizing spectrum produces emission line intensities that correctly scale with the stellar population as a function of age and metallicity. This more complete model of galaxy SEDs will improve estimates of global gas properties derived with diagnostic diagrams, star formation rates based on H$α$, and stellar masses derived from NIR broadband photometry. Our models agree well with results from other photoionization models and are able to reproduce observed emission from H II regions and star-forming galaxies. Our models show improved agreement with the observed H II regions in the Ne III/O II plane and show satisfactory agreement with He II emission from $z=2$ galaxies when including rotating stellar models. Models including post-asymptotic giant branch stars are able to reproduce line ratios consistent with low-ionization emission regions (LIERs).

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arXiv2016

Are the Formation and Abundances of Metal-Poor Stars the Result of Dust Dynamics?

Large dust grains can fluctuate dramatically in their local density, relative to gas, in neutral, turbulent disks. Small, high-redshift galaxies (before reionization) represent ideal environments for this process. We show via simple arguments and simulations that order-of-magnitude fluctuations are expected in local abundances of large grains under these conditions. This can have important consequences for star formation and stellar abundances in extremely metal-poor stars. Low-mass stars could form in dust-enhanced regions almost immediately after some dust forms, even if the galaxy-average metallicity is too low for fragmentation to occur. The abundances of these 'promoted' stars may contain interesting signatures, as the CNO abundances (concentrated in large carbonaceous grains and ices) and Mg and Si (in large silicate grains) can be enhanced or fluctuate independently. Remarkably, otherwise puzzling abundance patterns of some metal-poor stars can be well-fit by standard core-collapse SNe yields, if we allow for fluctuating dust-to-gas ratios. We also show that the observed log-normal-like distribution of enhancements in these species agrees with our simulations. Moreover, we confirm Mg and Si are correlated in these stars, with abundance ratios similar to those in local silicate grains. Meanwhile [Mg/Ca], predicted to be nearly invariant from pure SNe yields, shows large enhancements as expected in the dust-promoted model, preferentially in the [C/Fe]-enhanced metal-poor stars. This suggests that (1) dust exists in second-generation star formation, (2) dust-to-gas ratio fluctuations occur and can be important for star formation, and (3) light element abundances of these stars may be affected by the chemistry of dust where they formed, rather than directly tracing nucleosynthesis.

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arXiv2016

Exploring Systematic Effects in the Relation Between Stellar Mass, Gas Phase Metallicity, and Star Formation Rate

There is evidence that the well-established mass-metallicity relation in galaxies is correlated with a third parameter: star formation rate (SFR). The strength of this correlation may be used to disentangle the relative importance of different physical processes (e.g., infall of pristine gas, metal-enriched outflows) in governing chemical evolution. However, all three parameters are susceptible to biases that might affect the observed strength of the relation between them. We analyze possible sources of systematic error, including sample bias, application of signal-to-noise ratio cuts on emission lines, choice of metallicity calibration, uncertainty in stellar mass determination, aperture effects, and dust. We present the first analysis of the relation between stellar mass, gas phase metallicity, and SFR using strong line abundance diagnostics from Dopita et al. (2013) for ~130,000 star-forming galaxies in the Sloan Digital Sky Survey and provide a detailed comparison of these diagnostics in an appendix. Using these abundance diagnostics yields a 30-55% weaker anti-correlation between metallicity and SFR at fixed stellar mass than that reported by Mannucci et al. (2010). We find that, for all abundance diagnostics, the anti-correlation with SFR is stronger for the relatively few galaxies whose current SFRs are elevated above their past average SFRs. This is also true for the new abundance diagnostic of Dopita et al. (2016), which gives anti-correlation between metallicity and SFR only in the high specific star formation rate (sSFR) regime, in contrast to the recent results of Kashino et al. (2016). The poorly constrained strength of the relation between stellar mass, metallicity, and SFR must be carefully accounted for in theoretical studies of chemical evolution.

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arXiv2016

Redshift Measurement and Spectral Classification for eBOSS Galaxies with the Redmonster Software

We describe the redmonster automated redshift measurement and spectral classification software designed for the extended Baryon Oscillation Spectroscopic Survey (eBOSS) of the Sloan Digital Sky Survey IV (SDSS-IV). We describe the algorithms, the template standard and requirements, and the newly developed galaxy templates to be used on eBOSS spectra. We present results from testing on early data from eBOSS, where we have found a 90.5% automated redshift and spectral classification success rate for the luminous red galaxy sample (redshifts 0.6$\lesssim z \lesssim$1.0). The redmonster performance meets the eBOSS cosmology requirements for redshift classification and catastrophic failures, and represents a significant improvement over the previous pipeline. We describe the empirical processes used to determine the optimum number of additive polynomial terms in our models and an acceptable $Δχ_r^2$ threshold for declaring statistical confidence. Statistical errors on redshift measurement due to photon shot noise are assessed, and we find typical values of a few tens of km s$^{-1}$. An investigation of redshift differences in repeat observations scaled by error estimates yields a distribution with a Gaussian mean and standard deviation of $μ\sim$0.01 and $σ\sim$0.65, respectively, suggesting the reported statistical redshift uncertainties are over-estimated by $\sim$54%. We assess the effects of object magnitude, signal-to-noise ratio, fiber number, and fiber head location on the pipeline's redshift success rate. Finally, we describe directions of ongoing development.

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arXiv2016

Halo Histories vs. Galaxy Properties at z=0, I: The Quenching of Star Formation

We test whether halo age and galaxy age are correlated at fixed halo and galaxy mass. The formation histories, and thus ages, of dark matter halos correlate with their large-scale density $ρ$, an effect known as assembly bias. We test whether this correlation extends to galaxies by measuring the dependence of galaxy stellar age on $ρ$. To clarify the comparison between theory and observation, and to remove the strong environmental effects on satellites, we use galaxy group catalogs to identify central galaxies and measure their quenched fraction, $f_Q$, as a function of large-scale environment. Models that match halo age to central galaxy age predict a strong positive correlation between $f_Q$ and $ρ$. However, we show that the amplitude of this effect depends on the definition of halo age: assembly bias is significantly reduced when removing the effects of splashback halos---those halos that are central but have passed through a larger halo or experienced strong tidal encounters. Defining age using halo mass at its peak value rather than current mass removes these effects. In SDSS data, at M$_{\rm gal}\gtrsim 10^{10.0}$ M_sol/h$^2$, there is a $\sim 5\%$ increase in $f_Q$ from low to high densities, which is in agreement with predictions of dark matter halos using peak halo mass. At lower stellar mass there is little to no correlation of $f_Q$ with $ρ$. For these galaxies, age-matching is inconsistent with the data across the wide range the halo formation metrics that we tested. This implies that halo formation history has a small but statistically significant impact on quenching of star formation at high masses, while the quenching process in low-mass central galaxies is uncorrelated with halo formation history.

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arXiv2016

A High Stellar Velocity Dispersion and ~100 Globular Clusters for the Ultra Diffuse Galaxy Dragonfly 44

Recently a population of large, very low surface brightness, spheroidal galaxies was identified in the Coma cluster. The apparent survival of these Ultra Diffuse Galaxies (UDGs) in a rich cluster suggests that they have very high masses. Here we present the stellar kinematics of Dragonfly 44, one of the largest Coma UDGs, using a 33.5 hr integration with DEIMOS on the Keck II telescope. We find a velocity dispersion of 47 km/s, which implies a dynamical mass of M_dyn=0.7x10^10 M_sun within its deprojected half-light radius of r_1/2=4.6 kpc. The mass-to-light ratio is M/L=48 M_sun/L_sun, and the dark matter fraction is 98 percent within the half-light radius. The high mass of Dragonfly 44 is accompanied by a large globular cluster population. From deep Gemini imaging taken in 0.4" seeing we infer that Dragonfly 44 has 94 globular clusters, similar to the counts for other galaxies in this mass range. Our results add to other recent evidence that many UDGs are "failed" galaxies, with the sizes, dark matter content, and globular cluster systems of much more luminous objects. We estimate the total dark halo mass of Dragonfly 44 by comparing the amount of dark matter within r=4.6 kpc to enclosed mass profiles of NFW halos. The enclosed mass suggests a total mass of ~10^12 M_sun, similar to the mass of the Milky Way. The existence of nearly-dark objects with this mass is unexpected, as galaxy formation is thought to be maximally-efficient in this regime.

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arXiv2016

Accelerated Fitting of Stellar Spectra

Stellar spectra are often modeled and fit by interpolating within a rectilinear grid of synthetic spectra to derive the stars' labels: stellar parameters and elemental abundances. However, the number of synthetic spectra needed for a rectilinear grid grows exponentially with the label space dimensions, precluding the simultaneous and self-consistent fitting of more than a few elemental abundances. Shortcuts such as fitting subsets of labels separately can introduce unknown systematics and do not produce correct error covariances in the derived labels. In this paper we present a new approach -- CHAT (Convex Hull Adaptive Tessellation) -- which includes several new ideas for inexpensively generating a sufficient stellar synthetic library, using linear algebra and the concept of an adaptive, data-driven grid. A convex hull approximates the region where the data lie in the label space. A variety of tests with mock datasets demonstrate that CHAT can reduce the number of required synthetic model calculations by three orders of magnitude in an 8D label space. The reduction will be even larger for higher-dimensional label spaces. In CHAT the computational effort increases only linearly with the number of labels that are fit simultaneously. Around each of these grid points in label space an approximate synthetic spectrum can be generated through linear expansion using a set of "gradient spectra" that represent flux derivatives at every wavelength point with respect to all labels. These techniques provide new opportunities to fit the full stellar spectra from large surveys with 15-30 labels simultaneously.

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arXiv2016

Constructing Polynomial Spectral Models for Stars

Stellar spectra depend on the stellar parameters and on dozens of photospheric elemental abundances. Simultaneous fitting of these $\mathcal{N}\sim 10-40$ model labels to observed spectra has been deemed unfeasible, because the number of ab initio spectral model grid calculations scales exponentially with $\mathcal{N}$. We suggest instead the construction of a polynomial spectral model (PSM) of order $\mathcal{O}$ for the model flux at each wavelength. Building this approximation requires a minimum of only ${\mathcal{N}+\mathcal{O}\choose\mathcal{O}}$ calculations: e.g. a quadratic spectral model ($\mathcal{O}=2$) to fit $\mathcal{N}=20$ labels simultaneously, can be constructed from as few as $231$ ab initio spectral model calculations; in practice, a somewhat larger number ($\sim 300-1000$) of randomly chosen models lead to a better performing PSM. Such a PSM can be a good approximation only over a portion of label space, which will vary case by case. Yet, taking the APOGEE survey as an example, a single quadratic PSM provides a remarkably good approximation to the exact ab initio spectral models across much of this survey: for random labels within that survey the PSM approximates the flux to within $10^{-3}$, and recovers the abundances to within $\sim 0.02$ dex rms of the exact models. This enormous speed-up enables the simultaneous many-label fitting of spectra with computationally expensive ab initio models for stellar spectra, such as non-LTE models. A PSM also enables the simultaneous fitting of observational parameters, such as the spectrum's continuum or line-spread function.

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arXiv2016

MESA Isochrones and Stellar Tracks (MIST). I: Solar-Scaled Models

This is the first of a series of papers presenting the Modules for Experiments in Stellar Astrophysics (MESA) Isochrones and Stellar Tracks (MIST) project, a new comprehensive set of stellar evolutionary tracks and isochrones computed using MESA, a state-of-the-art open-source 1D stellar evolution package. In this work, we present models with solar-scaled abundance ratios covering a wide range of ages ($5 \leq \rm \log(Age)\;[yr] \leq 10.3$), masses ($0.1 \leq M/M_{\odot} \leq 300$), and metallicities ($-2.0 \leq \rm [Z/H] \leq 0.5$). The models are self-consistently and continuously evolved from the pre-main sequence to the end of hydrogen burning, the white dwarf cooling sequence, or the end of carbon burning, depending on the initial mass. We also provide a grid of models evolved from the pre-main sequence to the end of core helium burning for $-4.0 \leq \rm [Z/H] < -2.0$. We showcase extensive comparisons with observational constraints as well as with some of the most widely used existing models in the literature. The evolutionary tracks and isochrones can be downloaded from the project website at http://waps.cfa.harvard.edu/MIST/.

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arXiv2016

The MOSDEF Survey: The strong agreement between H-alpha and UV-to-FIR star formation rates for z~2 star-forming galaxies

We present the first direct comparison between Balmer line and panchromatic SED-based SFRs for z~2 galaxies. For this comparison we used 17 star-forming galaxies selected from the MOSFIRE Deep Evolution Field (MOSDEF) survey, with $3σ$ detections for H$α$ and at least two IR bands (Spitzer/MIPS 24$μ$m and Herschel/PACS 100 and 160$μ$m, and in some cases Herschel/SPIRE 250, 350, and 500$μ$m). The galaxies have total IR (8-1000$μ$m) luminosities of $\sim10^{11.4}-10^{12.4}\,\textrm{L}_\odot$ and star-formation rates (SFRs) of $\sim30-250\,\textrm{M}_\odot\,\mathrm{yr^{-1}}$. We fit the UV-to-far-IR SEDs with flexible stellar population synthesis (FSPS) models - which include both stellar and dust emission - and compare the inferred SFRs with the SFR(H$α$,H$β$) values corrected for dust attenuation using Balmer decrements. The two SFRs agree with a scatter of 0.17 dex. Our results imply that the Balmer decrement accurately predicts the obscuration of the nebular lines and can be used to robustly calculate SFRs for star-forming galaxies at z~2 with SFRs up to $\sim200\,\textrm{M}_\odot\,\mathrm{yr^{-1}}$. We also use our data to assess SFR indicators based on modeling the UV-to-mid-IR SEDs or by adding SFR(UV) and SFR(IR), for which the latter is based on the mid-IR only or on the full IR SED. All these SFRs show a poorer agreement with SFR(H$α$,H$β$) and in some cases large systematic biases are observed. Finally, we show that the SFR and dust attenuation derived from the UV-to-near-IR SED alone are unbiased when assuming a delayed exponentially declining star-formation history.

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arXiv2016

Pixel Color Magnitude Diagrams for Semi-Resolved Stellar Populations: The Star Formation History of Regions within the Disk and Bulge of M31

The analysis of stellar populations has, by and large, been developed for two limiting cases: spatially-resolved stellar populations in the color-magnitude diagram, and integrated light observations of distant systems. In between these two extremes lies the semi-resolved regime, which encompasses a rich and relatively unexplored realm of observational phenomena. Here we develop the concept of pixel color magnitude diagrams (pCMDs) as a powerful technique for analyzing stellar populations in the semi-resolved regime. pCMDs show the distribution of imaging data in the plane of pixel luminosity vs. pixel color. A key feature of pCMDs is that they are sensitive to all stars, including both the evolved giants and the unevolved main sequence stars. An important variable in this regime is the mean number of stars per pixel, $N_{\rm pix}$. Simulated pCMDs demonstrate a strong sensitivity to the star formation history (SFH) and allow one to break degeneracies between age, metallicity and dust based on two filter data for values of $N_{\rm pix}$ up to at least $10^4$. We extract pCMDs from Hubble Space Telescope (HST) optical imaging of M31 and derive non-parametric SFHs from $10^6$ yr to $10^{10}$ yr for both the crowded disk and bulge regions (where $N_{\rm pix}\approx30-10^3$). From analyzing a small region of the disk we find a non-parametric SFH that is smooth and consistent with an exponential decay timescale of 4 Gyr. The bulge SFH is also smooth and consistent with a 2 Gyr decay timescale. pCMDs will likely play an important role in maximizing the science returns from next generation ground and space-based facilities.

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arXiv2015

APOGEE chemical tagging constraint on the maximum star cluster mass in the $α$-enhanced Galactic disk

Stars born from the same molecular cloud should be nearly homogeneous in their element abundances. The concept of chemical tagging is to identify members of disrupted clusters by their clustering in element abundance space. Chemical tagging requires large samples of stars with precise abundances for many individual elements. With uncertainties of $σ_{[X/{\rm Fe}]}$ and $σ_{\rm [Fe/H]} \simeq 0.05$ for 10 elements measured for $>10^4$ stars, the APOGEE DR12 spectra may be the first well-suited data set to put this idea into practice. We find that even APOGEE data offer only $\sim 500$ independent volume elements in the 10-dimensional abundance space, when we focus on the $α$-enhanced Galactic disk. We develop and apply a new algorithm to search for chemically homogeneous sets of stars against a dominant background. By injecting star clusters into the APOGEE data set we show that chemically homogeneous clusters with masses $\gtrsim 3 \times 10^7 \, {\rm M}_\odot$ would be easily detectable and yet no such signal is seen in the data. By generalizing this approach, we put a first abundance-based constraint on the cluster mass function for the old disk stars in the Milky Way.

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arXiv2015

Ubiquitous Time Variability of Integrated Stellar Populations

Long period variable stars arise in the final stages of the asymptotic giant branch phase of stellar evolution. They have periods of up to ~1000d and amplitudes that can exceed a factor of three in the I-band flux. These stars pulsate predominantly in their fundamental mode, which is a function of mass and radius, and so the pulsation periods are sensitive to the age of the underlying stellar population. The overall number of long period variables in a population is directly related to their lifetime, which is difficult to predict from first principles because of uncertainties associated with stellar mass-loss and convective mixing. The time variability of these stars has not been previously taken into account when modeling the spectral energy distributions of galaxies. Here we construct time-dependent stellar population models that include the effects of long period variable stars, and report the ubiquitous detection of this expected `pixel shimmer' in the massive metal-rich galaxy M87. The pixel light curves display a variety of behaviors, including linearly rising and falling curves, semi-periodic curves, and sudden increases or decreases in the flux level. The observed variation of 0.1-1% is very well matched to the predictions of our models. The data provide a strong and novel constraint on the properties of variable stars in an old and metal-rich stellar population, and we infer that the lifetime of long period variables in M87 is shorter by approximately 30% compared to predictions from the latest stellar evolution models.

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