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Stellar Populations in the Galactic Center

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Cosmic Rays in Star-Forming Environments

Part of the book series: Astrophysics and Space Science Proceedings ((ASSSP,volume 34))

Abstract

We discuss the stellar content of the Galactic Center, and in particular, recent estimates of the star formation rate (SFR). We discuss pros and cons of the different stellar tracers and focus our attention on the SFR based on the three classical Cepheids recently discovered in the Galactic Center. We also discuss stellar populations in field and cluster stars and present some preliminary results based on near-infrared photometry of a field centered on the young massive cluster Arches. We also provide a new estimate of the true distance modulus to the Galactic Center and we found 14. 49 ± 0. 02(standard) ± 0.10(systematic) mag (7. 91 ± 0. 08 ± 0. 40 kpc). Current estimate agrees quite well with similar photometric and kinematic distance determinations available in the literature. We also discuss the metallicity gradient of the thin disk and the sharp change in the slope when moving across the edge of the inner disk, the Galactic Bar and the Galactic Center. The difference becomes even more compelling if we take into account that metal abundances are based on young stellar tracers (classical Cepheids, Red Supergiants, Luminous Blue Variables). Finally, we briefly outline the possible mechanisms that might account for current empirical evidence.

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Notes

  1. 1.

    The interested reader is referred to http://albione.oa-teramo.inaf.it/

  2. 2.

    The interested reader is referred to the Table 2 of [17] for a detailed list of the most recent metallicity estimates of the Galactic Center.

  3. 3.

    http://www.eso.org/public/teles-instr/e-elt.html

  4. 4.

    http://www.tmt.org/

  5. 5.

    http://www.gmto.org/

  6. 6.

    http://ircamera.as.arizona.edu/nircam/

References

  1. Allard, E. L.; Knapen, J. H.; Peletier, R. F.; Sarzi, M.: The star formation history and evolution of the circumnuclear region of M100. Mont. Notic. Royal Astron. Soc. 371, 1087 (2006)

    Article  ADS  Google Scholar 

  2. Andrievsky, S. M.; et al.: Using Cepheids to determine the galactic abundance gradient. III. First results for the outer disc. Astron. & Astroph. 392, 491 (2002)

    Google Scholar 

  3. Andrievsky, S. M.; Luck, R. E.; Martin, P.; Lépine, J. R. D.: The Galactic abundance gradient from Cepheids. V. Transition zone between 10 and 11 kpc. Astron. & Astroph. 413, 159 (2004)

    Google Scholar 

  4. Athanassoula, E.: The existence and shapes of dust lanes in galactic bars. Mont. Notic. Royal Astron. Soc. 259, 345 (1992)

    ADS  Google Scholar 

  5. Barbuy, B.; et al.: VLT-FLAMES analysis of 8 giants in the bulge metal-poor globular cluster NGC 6522: oldest cluster in the Galaxy?. Analysis of 8 giants in NGC 6522. Astron. & Astroph. 507, 405 (2009)

    Google Scholar 

  6. Brand, J., & Blitz, L.: The Velocity Field of the Outer Galaxy. Astron. & Astroph. 275, 67 (1993)

    ADS  Google Scholar 

  7. Bono, G.; Marconi, M.; Stellingwerf, R. F.: Classical Cepheid Pulsation Models. I. Physical Structure. Astroph. J. Suppl. 122, 167 (1999)

    Article  ADS  Google Scholar 

  8. Bono, G.; Marconi, M.; Cassisi, S.; Caputo, F.; Gieren, W.; Pietrzynski, G.: Classical Cepheid Pulsation Models. X. The Period-Age Relation. Astroph. J. 621, 966 (2005)

    ADS  Google Scholar 

  9. Bono, G.; Caputo, F.; Marconi, M. & Musella, I.: Insights into the Cepheid Distance Scale. Astroph. J. 715, 277 (2010)

    Article  ADS  Google Scholar 

  10. Carraro, G.; et al.: Old open clusters in the outer Galactic disk. Astron. & Astroph. 476, 217 (2007)

    Article  ADS  Google Scholar 

  11. Carraro, G.; Costa, E.; Ahumada, J. A.: Photometric Characterization of the Galactic Star Cluster Trumpler 20, Astron. J. 140, 954 (2010)

    Article  ADS  Google Scholar 

  12. Caputo, F.; Marconi, M.; Musella, I.; Pont, F.: Pulsational constraints to the metallicity gradient in the Galactic disk. Astron. & Astroph. 372, 544 (2001)

    Article  ADS  Google Scholar 

  13. Cescutti, G.; Matteucci, F.; François, P.; Chiappini, C.: Abundance gradients in the Milky Way for α elements, iron peak elements, barium, lanthanum, and europium. Astron. & Astroph. 462, 943 (2007)

    Article  ADS  Google Scholar 

  14. Chiappini, C.; Matteucci, F.: A new Picture for the Galaxy Formation. Astrophysics and Space Science, 265, 425 (1999)

    Article  ADS  Google Scholar 

  15. Chiappini, C.; Matteucci, F.; Romano, D.: Abundance Gradients and the Formation of the Milky Way. Astroph. J. 554, 1044 (2001)

    Article  ADS  Google Scholar 

  16. Cunha, K.; et al.: Chemical Abundances of Luminous Cool Stars in the Galactic Center from High-Resolution Infrared Spectroscopy. Astroph. J. 669, 1011 (2007)

    Article  ADS  Google Scholar 

  17. Davies, B.; et al.: The Chemical Abundances in the Galactic Center from the Atmospheres of Red Supergiants. Astroph. J. 694, 46 (2009a)

    Article  ADS  Google Scholar 

  18. Davies, B.; et al.: Chemical Abundance Patterns in the Inner Galaxy: The Scutum Red Supergiant Clusters. Astroph. J. 696, 2014 (2009b)

    Article  ADS  Google Scholar 

  19. Davies, B.; et al.: A newly discovered young massive star cluster at the far end of the Galactic Bar. Mont. Notic. Royal Astron. Soc. 419, 1860 (2012)

    Article  ADS  Google Scholar 

  20. Debattista, V. P.; Mayer, L.; Carollo, C. M.; Moore, B.; Wadsley, J.; Quinn, T.: The Secular Evolution of Disk Structural Parameters. Astroph. J. 645, 209 (2006)

    Article  ADS  Google Scholar 

  21. Deharveng, L.; Peña, M.; Caplan, J.; Costero, R.: Oxygen and helium abundances in Galactic HII regions - II. Abundance gradients. Mont. Notic. Royal Astron. Soc. 311, 329 (2000)

    Google Scholar 

  22. Espinoza, P.; Selman, F. J.; Melnick, J.: The massive star initial mass function of the Arches cluster. Astron. & Astroph. 501, 563 (2010)

    Google Scholar 

  23. Figer, D. F.; McLean, I. S.; Morris, M.: Massive Stars in the Quintuplet Cluster. Astroph. J. 514, 202 (1999)

    Article  ADS  Google Scholar 

  24. Figer, D. F.; et al.: Massive Stars in the Arches Cluster. Astroph. J. 581, 258 (2002)

    Article  ADS  Google Scholar 

  25. Figer, D. F.; Rich, R. M.; Kim, S. S.; Morris, M.; Serabyn, E.: An Extended Star Formation History for the Galactic Center from Hubble Space Telescope NICMOS Observations. Astroph. J. 601, 319 (2004)

    Article  ADS  Google Scholar 

  26. Figer, D. F.; et al.: Discovery of an Extraordinarily Massive Cluster of Red Supergiants. Astroph. J. 643, 1166 (2009)

    Article  ADS  Google Scholar 

  27. Friedli, D.; Benz, W.: Secular evolution of isolated barred galaxies. II. Coupling between stars and interstellar medium via star formation. Astron. & Astroph. 301, 649 (1995)

    Google Scholar 

  28. Friel, E. D.; et al.: Metallicities of Old Open Clusters. AJ 124, 2693 (2002)

    Google Scholar 

  29. Fritz, T. K.; Gillessen, S.; Dodds-Eden, K., et al.: Astroph. J. 737, 73 (2011)

    Google Scholar 

  30. Genzel, R.; Eckart, A.; Ott, T.; Eisenhauer, F.: On the nature of the dark mass in the centre of the Milky Way. Mont. Notic. Royal Astron. Soc. 291, 219 (1997)

    Article  ADS  Google Scholar 

  31. Gillessen, S.; et al.: Monitoring Stellar Orbits Around the Massive Black Hole in the Galactic Center. Astroph. J. 692, 1075 (2009)

    Article  ADS  Google Scholar 

  32. Graham, A. W., & Guzmán, R.: HST Photometry of Dwarf Elliptical Galaxies in Coma, and an Explanation for the Alleged Structural Dichotomy between Dwarf and Bright Elliptical Galaxies. Astronomical Journal. 125, 2936 (2003)

    Article  ADS  Google Scholar 

  33. Hill, V.; et al.: The metallicity distribution of bulge clump giants in Baade’s window. Astron. & Astroph. 534, 80 (2011)

    Article  ADS  Google Scholar 

  34. Honma, M., & Sofue, Y.: Rotation Curve of the Galaxy. Publications of the Astronomical Society of Japan, 49, 453 (1997)

    ADS  Google Scholar 

  35. Inno, L.; et al.: On the distance of the Magellanic Clouds using Cepheid NIR and optical – NIR period – Wesenheit relations. Astroph. J. 764, 84 (2013)

    Article  ADS  Google Scholar 

  36. Inno, L.; et al.: The Classical Cepheid Distance scale in the NIR bands. Journal of Physics: Conference Series. 383, 012008 (2012)

    Article  ADS  Google Scholar 

  37. Kim, S. S.; et al.: The Arches Cluster Mass Function. Astroph. J. 653, 113 (2006)

    Article  ADS  Google Scholar 

  38. Kim, S. S.; Saitoh, T. R.; Jeon, M.; Figer, D. F.; Merritt, D.; Wada, K.: Nuclear Star-forming Ring of the Milky Way: Simulations. Astroph. J. 735, 11 (2011a)

    Article  ADS  Google Scholar 

  39. Kim, J.; et al.: Galaxy Formation with Self-consistently Modeled Stars and Massive Black Holes. I. Feedback-regulated Star Formation and Black Hole Growth. Astroph. J. 738, 54 (2011b)

    Google Scholar 

  40. Kormendy, J.; Kennicutt, R. C.: Secular Evolution and the Formation of Pseudobulges in Disk Galaxies. Ann. Rev. Astron & Astroph. 42, 603 (2004)

    Article  ADS  Google Scholar 

  41. Kormendy, J.; Fisher, D. B.; Cornell, M. E.; Bender, R.: Structure and Formation of Elliptical and Spheroidal Galaxies. Astroph. J. Suppl. 182, 216 (2009)

    Article  ADS  Google Scholar 

  42. Kovtyukh, V. V.; Wallerstein, G.; Andrievsky, S. M.: Galactic Cepheids. I. Elemental Abundances and Their Implementation for Stellar and Galactic Evolution. Publ. Astron. Soc. Pacific 117, 1173 (2005)

    Google Scholar 

  43. Lagioia, E.P.; et al.: Deep and accurate near infrared photometry of the young massive cluster Arches. in preparation

    Google Scholar 

  44. Launhardt, R.; Zylka, R.; Mezger, P. G.: The nuclear bulge of the Galaxy. III. Large-scale physical characteristics of stars and interstellar matter. Astron. & Astroph. 384, 112 (2002)

    Google Scholar 

  45. Lemasle, B.; François, P.; Bono, G.; Mottini, M.; Primas, F.; Romaniello, M.: Detailed chemical composition of Galactic Cepheids. A determination of the Galactic abundance gradient in the 8–12 kpc region. Astron. & Astroph. 467, 283 (2007)

    Google Scholar 

  46. Lemasle, B.; François, P.; Piersimoni, A.; Pedicelli, S.; Bono, G.; Laney, C. D.; Primas, F.; Romaniello, M.: Galactic abundance gradients from Cepheids. On the iron abundance gradient around 10–12 kpc. Astron. & Astroph. 490, 613 (2008)

    Google Scholar 

  47. Liermann, A.; et al.: The Quintuplet cluster. II. Analysis of the WN stars. Astron. & Astroph. 524, 82 (2010)

    Google Scholar 

  48. Lubowich, D. A.; et al.: Deuterium in the Galactic Centre as a result of recent infall of low-metallicity gas. Nature 405, 1025 (2000)

    Article  ADS  Google Scholar 

  49. Luck, R. E.; et al: The galactic abundance gradient from Cepheids. IV. New results for the outer disc. Astron. & Astroph. 401, 939 (2003)

    Google Scholar 

  50. Luck, R. E.; Kovtyukh, V. V.; Andrievsky, S. M.: The Distribution of the Elements in the Galactic Disk. AJ 132, 902 (2006)

    Article  ADS  Google Scholar 

  51. Luck, R. E.; et al.: The Distribution of the Elements in the Galactic Disk. II. Azimuthal and Radial Variation in Abundances from Cepheids. AJ 142, 51 (2011a)

    Google Scholar 

  52. Luck, R. E.; Lambert, D. L.: The Distribution of the Elements in the Galactic Disk. III. A Reconsideration of Cepheids from l = 30 ∘  to 250 ∘ . AJ 142, 136 (2011b)

    Google Scholar 

  53. Marconi, M.; Musella, I.; & Fiorentino, G.: Cepheid Pulsation Models at Varying Metallicity and ΔY ∕ ΔZ. Astroph. J., 632, 590 (2005)

    Article  ADS  Google Scholar 

  54. Martins, F.; et al.: Stellar and wind properties of massive stars in the central parsec of the Galaxy. Astron. & Astroph. 468, 233 (2007)

    Article  ADS  Google Scholar 

  55. Martins, F.; et al.: The most massive stars in the Arches cluster. Astron. & Astroph. 478, 219 (2008)

    Article  ADS  Google Scholar 

  56. Matsunaga, N.; Kawadu, T.; Nishiyama, S.; Nagayama, T.; Kobayashi, N.; Tamura, M.; Bono, G.; Feast, M. W.; Nagata, T.: Three classical Cepheid variable stars in the nuclear bulge of the Milky Way. Nature 477, 188 (2011)

    Article  ADS  Google Scholar 

  57. Matsunaga, N.; et al.: Cepheids another short period variables near the Galactic centre. Mont. Notic. Royal Astron. Soc. submitted (2012)

    Google Scholar 

  58. Mezger, P. G.; Zylka, R.; Philipp, S.; Launhardt, R.: The nuclear bulge of the Galaxy. II. The K band luminosity function of the central 30 PC. Astron. & Astroph. 348, 457 (1999)

    Google Scholar 

  59. Najarro, F.; et al.: Metallicity in the Galactic Center: The Arches Cluster. Astroph. J. 611, 105 (2004)

    Article  ADS  Google Scholar 

  60. Najarro, F.; et al.: Metallicity in the Galactic Center: The Quintuplet Cluster. Astroph. J. 691, 181 (2009)

    Article  Google Scholar 

  61. Nishiyama, S.; et al.: Interstellar Extinction Law in the J, H, and Ks Bands toward the Galactic Center. Astroph. J. 638, 839 (2006)

    Article  ADS  Google Scholar 

  62. Nishiyama, S.; et al.: Interstellar Extinction Law Toward the Galactic Center III: J, H, KS Bands in the 2MASS and the MKO Systems, and 3.6, 4.5, 5.8, 8.0 ?m in the Spitzer/IRAC System. Astroph. J. 696,1407 (2009)

    Google Scholar 

  63. Pedicelli, S.; Bono, G.; Lemasle, B.; et al.: On the metallicity gradient of the Galactic disk. Astron. & Astroph. 504, 81 (2009)

    Article  ADS  Google Scholar 

  64. Pedicelli, S.; et al.: New Baade-Wesselink distances and radii for four metal-rich Galactic Cepheids. Astron. & Astroph. 518, 11 (2010)

    Article  ADS  Google Scholar 

  65. Philipp, S.; et al.: The nuclear bulge. I. K band observations of the central 30 PC. Astron. & Astroph. 348, 768 (1999)

    Google Scholar 

  66. Pietrinferni, A.; Cassisi, S.; Salaris, M.; Castelli, F.: A Large Stellar Evolution Database for Population Synthesis Studies. I. Scaled Solar Models and Isochrones. Astroph. J. 612, 168 (2004)

    Google Scholar 

  67. Pietrinferni, A.; Cassisi, S.; Salaris, M.; Castelli, F.: A Large Stellar Evolution Database for Population Synthesis Studies. II. Stellar Models and Isochrones for an α-enhanced Metal Distribution. Astroph. J. 642, 797 (2006)

    Google Scholar 

  68. Portinari, L.; Chiosi, C.: On radial gas flows, the Galactic Bar and chemical evolution in the Galactic Disc. Astron. & Astroph. 355, 929 (2000)

    ADS  Google Scholar 

  69. Prada Moroni, P. G.; et al.: On the Evolutionary and Pulsation Mass of Classical Cepheids. III. The Case of the Eclipsing Binary Cepheid CEP0227 in the Large Magellanic Cloud. Astroph. J. 749, 108 (2012)

    Google Scholar 

  70. Reid, M. J.; Menten, K. M.; Zheng, X. W. et al.: Trigonometric Parallaxes of Massive Star-Forming Regions. VI. Galactic Structure, Fundamental Parameters, and Noncircular Motions. Astroph. J. 700, 137 (2009)

    Google Scholar 

  71. Reid, M. J.; Menten, K. M.; Zheng, X. W. et al.: A Trigonometric Parallax of Sgr B2. Astroph. J. 705, 1548 (2009)

    Article  ADS  Google Scholar 

  72. Selman, F.; Melnick, J.; Bosch, G.; Terlevich, R.: Astron. & Astroph. 341, 98 (1999)

    ADS  Google Scholar 

  73. Serabyn, E.; Morris, M.: Sustained star formation in the central stellar cluster of the Milky Way. Nature 382, 602 (1996)

    Article  ADS  Google Scholar 

  74. Sharples, R.; Bender, R.; Agudo Berbel, A.; et al.: Recent Progress on the KMOS Multi-object Integral Field Spectrometer. The Messenger, 139, 24 (2010)

    ADS  Google Scholar 

  75. Stetson, P. B.: The center of the core-cusp globular cluster M15: CFHT and HST Observations, ALLFRAME reductions PASP 106, 250 (1994)

    Article  Google Scholar 

  76. Stolte, A.; et al.: The Arches Cluster: Evidence for a Truncated Mass Function? Astroph. J. 628, 113 (2005)

    Article  ADS  Google Scholar 

  77. Soszyński, I.; Dziembowski, W. A.; Udalski, A. et al.: The Optical Gravitational Lensing Experiment. The OGLE-III Catalog of Variable Stars. XI. RR Lyrae Stars in the Galactic Bulge. Acta Astronomica. 61, 1 (2011)

    Google Scholar 

  78. Twarog, B. A.; et al.: Some Revised Observational Constraints on the Formation and Evolution of the Galactic Disk. AJ 114, 2556 (1997)

    Article  ADS  Google Scholar 

  79. Vallée, J. P.: The Spiral Arms and Interarm Separation of the Milky Way: An Updated Statistical Study. AJ 130, 569 (2005)

    Article  ADS  Google Scholar 

  80. van Loon, J. T.; et al.: Infrared stellar populations in the central parts of the Milky Way galaxy. Mont. Notic. Royal Astron. Soc. 338, 857 (2003)

    Article  ADS  Google Scholar 

  81. Wakker, B. P.; et al.: Accretion of low-metallicity gas by the Milky Way. Nature 402, 388 (1999)

    Article  ADS  Google Scholar 

  82. Yong, D.; et al.: Elemental Abundance Ratios in Stars of the Outer Galactic Disk. III. Cepheids. AJ 131, 2256 (2006)

    Article  Google Scholar 

  83. Yuan, C.: Relationships Between Active Galactic Nuclei and Starburst Galaxies.ASP Conference Series. 31, 127 (1992)

    Google Scholar 

  84. Yuan, C. & Kuo, C.-L.: Bar-driven Spiral Density Waves and Accretion in Gaseous Disks.Astroph. J. 486, 750 (1997)

    Article  ADS  Google Scholar 

  85. Yusef-Zadeh, F.; et al.: Star Formation in the Central 400 pc of the Milky Way: Evidence for a Population of Massive Young Stellar Objects. Astroph. J. 702, 178 (2009)

    Article  ADS  Google Scholar 

  86. Zánmar Sánchez, R.; Sellwood, J. A.; Weiner, B. J.; Williams, T. B.: Modeling the Gas Flow in the Bar of NGC 1365. Astroph. J. 674, 797 (2008)

    Article  ADS  Google Scholar 

  87. Zaritsky, D.; Kennicutt, R. C.; Huchra, J.P.: H II regions and the abundance properties of spiral galaxies. Astroph. J. 420, 87 (1994)

    Article  ADS  Google Scholar 

  88. Zoccali, M., Renzini, A., Ortolani, S., et al.: Age and metallicity distribution of the Galactic bulge from extensive optical and near-IR stellar photometry. Astron. & Astroph. 399, 931 (2003)

    Article  ADS  Google Scholar 

  89. Zoccali, M.; et al.: The metal content of bulge field stars from FLAMES-GIRAFFE spectra. I. Stellar parameters and iron abundances. Astron. & Astroph. 486, 177 (2008)

    Google Scholar 

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Acknowledgements

It is a pleasure to thank M. Fabrizio for a detailed and critical reading of an early version of this manuscript. One of us GB thanks ASTROMUNDUS and the Department of Astronomy, University of Belgrade for their warm hospitality. We are indebted to the great patience and the constant support from the editors. This work was partially supported by the PRIN MIUR 2011 (P.I. M. Marconi). We are grateful to Jorgen Melnik for the detailed reading of an early draft of this manuscript, and in particular for drawing to our attention the thorny problems connected with NIR photometric calibration.

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Authors and Affiliations

  1. Dipartimento di Fisica, Universita’ di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133, Roma, Italy

    G. Bono (Science visitor), L. Inno, E. P. Lagioia & K. Genovali

  2. INAF– Osservatorio Astronomico di Roma, via Frascati 33, 00040, Monte Porzio Catone, Italy

    G. Bono (Science visitor)

  3. European Souther Observatory, Karl-Schwarzschild-Str. 2, 85748, Garching bei München, Germany

    G. Bono (Science visitor)

  4. Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    N. Matsunaga

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  1. G. Bono
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  1. , (IEEC-CSIC) Campus UAB, Fac. de Ciències, ICREA & Institute of Space Sciences, Torre C5, parell, 2a planta, Barcelona, 08193, Spain

    Diego F. Torres

  2. , Leopold-Franzens-Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstraße 25/8, Innsbruck, 6020, Austria

    Olaf Reimer

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Bono, G., Matsunaga, N., Inno, L., Lagioia, E.P., Genovali, K. (2013). Stellar Populations in the Galactic Center. In: Torres, D., Reimer, O. (eds) Cosmic Rays in Star-Forming Environments. Astrophysics and Space Science Proceedings, vol 34. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35410-6_9

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