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On the importance of the few most massive stars: the ionizing cluster of NGC 588. L. Jamet 1 , E. Pérez 2 , M. Cerviño 2 , G. Stasinska 1 , R.M. González Delgado 2 , J.M. Vílchez 2 1 LUTH, Observatoire de Meudon, France 2 Instituto de Astrofísica de Andalucía, Granada, Spain. H  + continuum.

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On the importance of the few most massive stars: the ionizing cluster of NGC 588

L. Jamet1, E. Pérez2, M. Cerviño2, G. Stasinska1, R.M. González Delgado2, J.M. Vílchez2

1 LUTH, Observatoire de Meudon, France

2 Instituto de Astrofísica de Andalucía, Granada, Spain

H + continuum

HST - F439W

  • Observational material
  • Long-slit optical spectra (3595-9805 Å) obtained with the 3.5m telescope of CAHA Observatory (Calar Alto, Almería, Spain) on 1998/08/27-28
  • IUE large-aperture spectrum: SiIV 1400, CIV 1550, HeII 1640 stellar lines (low quality spectrum)
  • HST-STIS spectrum of the brightest star
  • HST-WFPC2 high-resolution images in five bands (F170W, F336W, F439W, F547M, F469N)
  • Ground-based images through H, H and H continuum filters


We present the results of a double analysis of the central cluster of NGC 588, a giant HII region located in the outskirts of the nearby spiral galaxy M33, 800 kpc away from us. We first used integrated observational data to constrain a model based on the standard assumptions of an instantaneous star formation and of a continuous power-law IMF. This analysis led to unsatisfactory results, and we decided to proceed to a second modeling, based on the photometry of the individual stars in a series of HST images. This model resulted in a good fit of its observational constraints, inferring however a cluster age of 4.2 Myr, significantly larger than the 2.8 Myr age found with the “classical” analysis. We interpret the discrepancy between the two models as the result of the discreteness of the actual IMF of the cluster, and discuss the uncertainties due to IMF sampling in models of unresolved and moderately massive clusters, where assumptions must be done regarding the IMF.

50 pc

  • “Classical” model
  • Code: Starburst99 (Leitherer et al., 1999)
  • Continuous IMF dN/dm  m-, 1
  • instantaneous formation, age 
  • metallicity Z=0.004 or Z=0.008
  • Constraints: fully integrated properties: W(H)=330±30 Å, L(F439W)=4.721035 erg s-1 Å-1, IUE spectrum, at least one WN star (N(WN)1)
  • Best fit: Z=0.008, =2.8 Myr, =2.35 (Salpeter slope), mup=120 M, Mtot=3000 Mbut this model predicts:
  • W(H)=247 Å
  • N(WN)=0.03
  • 12 O stars, and 0.80 blue supergiant (BSG) with T<3 104 K
  • This “classical” model fails to reproduce W(H) and N(WN) simultaneously, because it predicts the simultaneous presence of WN stars and non-ionizing but optically very luminous BSGs. What if the IMF is not fully sampled?

Star-by-star model

  • 173 stars detected in HST-WFPC2 images
  • The 1st and 3rd brightest stars are of WNL type
  • 56 brightest stars compared to theoretical isochrones in the (MF439W,MF170W-MF547M) color-magnitude diagram (CMD)
  • A model (mass, temperature, luminosity, spectrum…) is associated with each star for a given tested isochrone, and the model spectrum of the cluster is computed from the individual model spectra of the 173 detected stars
  • The constraints are the (MF439W,MF170W-MF547M) CMD, W(H), the Balmer jump (seen in the CAHA data), and the UV lines seen in the IUE spectrum.
  • All the constraints are very well fitted, excepting the SiIV 1400 line, for an age of 4.2 Myr (the 90% confidence interval is 3.6-4.4 Myr).

Real IMF and distribution of the stars; importance of the few most massive stars

A few Monte-Carlo simulations

In the star-by-star analysis of the cluster, each star was assigned an initial mass and a position in the HR and (MF439W,log Q(H0)) diagrams.

The initial mass histogram is statistically compatible with a Salpeter IMF with a total mass of 5800 M (integrated above 1 M), though the branch of non-ionizing BSGs is entirely empty, and the WR branch is more populated than what would be predicted by integrating the power-law IMF fitted on the initial mass histogram (2 stars vs. 0.51 star).

The two plots on the right show the results of Monte-Carlo simulation of random discrete sampling of the average IMF of NGC 588, with a fix number of stars given by the integral of this IMF, and an age of 4.2 Myr. The first panel shows the histogram of log W(H) for 106 realizations, and the second panel, the distribution of 104 realizations in the (Q(O+)/Q(H0),W(H)) diagram.

In the case of a cluster with the same IMF, age and metallicity as NGC 588, the 90% likelihood interval for W(H) is as wide as 40-244 Å. Furthermore, the (Q(O+)/Q(H0),W(H)) diagram suggests that the hardness of ionizing radiation of a cluster of moderate mass may be very uncertain if the sampling of its IMF is unknown, with exception of the case where there is WR.


By exploiting a varied set of data, we were able to infer a realistic model of the ionizing cluster of NGC 588, and to compare it to a model based on the common assumption of a continuous IMF, used to analyze unresolved clusters. We could establish that the discreteness of the IMF sampling has dramatic consequences both on the integrated diagnostics of the cluster and on the unobservable Lyman continuum. This observation can be naturally explained by the following statement: the radiation of a young cluster of moderate mass is dominated by the few most massive stars, that show a wide variety of photometric and spectral properties and are subject to strong population fluctuations. We suggest that whenever the stars of a cluster are resolved, they should be individually processed when modeling the cluster. In the contrary case, care must be taken when inferring the properties (age, mass…) studied cluster or when deriving its ionizing flux for modeling of the GHR it ionizes.

A general formalism on the effects of IMF random sampling has been developed since 2002 by Cerviño et al., and needs further detailed work. Additional issues, especially the evolution of massive stars (Massey 2003) and the duration of star formation in clusters (Tenorio-Tagle 2003), also deserve to be addressed.

The brightest 6 stars alone, that sparsely occupy the most evolved parts of the diagrams shown above, produce as much as half the optical flux and two thirds of the ionizing photons of the whole cluster. An IMF sampling with a few BSGs would have made the cluster ~2 times brighter in the optical range, but W(H) would have been much smaller. Furthermore, an artificial shift of the two WR stars along the WR branch causes quite significant changes in the hardness of the Lyman continuum, one of the main elements driving the temperature and the ionization structure of the surrounding nebula.