The Stellar IMF at High Redshift

1. STScI, March 30, 2005 The Stellar IMF at High Redshift Long Ago and far Away: The Fossil Record in an External Galaxy Rosemary Wyse

2. The Fossil Record • Stars of mass like the Sun live for the age of the Universe – studying low-mass old stars allows us to do Cosmology locally. • Complementary approach to direct study at high redshift. • Stars retain some memory of initial conditions – age, chemical abundances (modulo mass transfer), orbital angular momentum (modulo resonances, torques)

3. Clues from the Fossil Record • Resolved stars – Local Group galaxies • Star formation history • Chemical evolution • Merging history: for which system have we derived SFH? Match CDM? • Stellar Initial mass function Today’s talk

4. CDM simulation of the Local group Moore et al. 2001 6Mpc box 300kpc box Left : z=10, small haloes dominate. Red indicates possible site of star formation at this time (very dense regions). Right: Present time, many of the small haloes have merged into the model Milky Way halo; oldest stars found throughout the Milky Way and in satellitesgalaxies.

5. The IMF Long Ago & Far Away: Faint Stars in the UMi dSph Galaxy • Dwarf spheroidal in Ursa Minor is apparently dark-matter dominated, of very low surface brightness, and total luminosity equal to a globular cluster • Stars are all old, and metal-poor • Fossil record of long-lived, low-mass stars yields luminosity function via star counts • High-mass IMF leaves signature in elemental abundances of stars they enriched

6. A Typical Satellite Galaxy: Leo I Dwarf spheroidal Umi dSph is ~3 mag lower central surface brightness and a factor of ten lower luminosity

7. The Ursa Minor Dwarf Spheroidal • Distance ~ 70kpc • Total luminosity ~ 3 x 105 LV, ~ that of a globular cluster • Central surface brightness ~ 25.5 V-mag/sq • Stellar velocity dispersion ~ 10km/s • Mass-to-V-band light ratio 10–70M/L,significantly above a globular cluster (~ 2) • Most stars are very old, as old as halo globulars • Stars are metal-poor, [Fe/H] ~ –2 dex Mateo 98; Kleyna et al 98, 01, 04; Bellazzini et al 02; Carrera et al 02; Palma et al 03; Gomez-Flechoso et al 03; Winnick 03

8. Stars in UMi dSph are OLD Hernandez et al 00 Most stars formed at early times , 12Gyr ago, or redshifts > 2

9. Most stars in Umi dSph formed at redshift z ~ 2  = 0.7, M =0.3  = 0, M = 0.3

10. Faint Stellar Luminosity Function • The dominant stellar population in the UMi dSph is old and metal-poor, similar to a halo globular cluster, a system with no dark matter • Most robust result is direct comparison between luminosity function of stars in UMi dSph and in globular clusters of same age and metallicity, observed in same bandpasses, same telescope/ detector. Same stellar populations, equivalent to comparison of mass functions.

11. Deep Imaging with Hubble Space Telescope • Deep images of a field close to the centre of the Ursa Minor dwarf spheroidal (extant WFPC2 data); STIS as primary (optical LP filter), WFPC2 (V606 & I814) and NICMOS (NIC2/H) in parallel. ~30,000s total. • Off-field at 2—3 tidal radii, same exposure • Globular clusters M15 ([Fe/H] ~ –2 dex) and 47 Tuc ([Fe/H] ~ –0.7 dex) with extant WFPC2 V & I, new data in STIS/LP and NIC2/H. Wyse, Gilmore, Houdashelt, Feltzing, Hebb, Gallagher & Smecker-Hane 2002

12. V-band WFPC2 Umi dSph center Crowding not an issue even at faint magnitudes (hindsight..)

13. WFPC2 V, V-I CMD plus selection for LFs V606 All

14. Very few unresolved objects in off field meet  and sharpness criteria. Broad colour range, little contamination of Umi dSph main sequence.

15. UMi dSph V-band LF  M92 M15  Piotto et al 97; Shifted and renormalised 50% completeness V=28.35 M606 =+9.1 V-band luminosity functions of UMi dSph and of globular clusters are indistinguishable.

16. UMi dSph I-band LF M92  M15  Piotto et al 97; Shifted and renormalised 50% completeness I=27.2 M814 =+8.1 I-band luminosity functions are indistinguishable. STIS/LP data provide independent check – agree.

17. UMi dSph STIS LP LF Single-band data, used offset field to correct (lower panel). M15, shifted & scaled.  Again, indistinguishable luminosity functions

18. STIS LP transformed to I-band: Histogram is derived from STIS LP data, using M15 data, open points are the directly observed I-band data.

19. …….and Statistics Various statistical tests were employed to quantify the agreement of the various datasets: • Linear, least-square fits to Log N vs Mag over ranges of magnitude and various bin choices gave agreement to better than 2 • K-S tests on unbinned data for a variety of magnitude ranges; rather sensitive to systematics such as relative distance moduli, but again general agreement at better than 5% significance level • -square tests on binned data, again range of bin centers and magnitude ranges; agree better than 5% significance

20. NICMOS Data • The NICMOS images are extremely sparse and not very deep (NB this program took several years to complete due to successive STIS failures and NIC2 was the best camera at the time initiated). • No new information on stars with normal main sequence colours • Excludes a hypothetical population of extremely red stars just below WFPC2 and STIS limits

21. Possible Complications • Has mass segregation affected the LF in the comparison globular clusters? – not significantly at these magnitudes at these radii, as estimated through modeling data in annuli • Is the binary population the same in UMi and in the comparison globular clusters? – see evidence for normal binary sequence in UMi, plus blue stragglers, so probably OK. • Reddening, relative distance moduli? – large bins, as adopted, lessen sensitivity to errors in these • Is Umi dSph relaxed? – several fields, same results

22. Invariant mass function • Indistinguishable luminosity functions in two systems of same (narrow) age and metallicity distributions • Same underlying stellar mass functions, despite very different in most other ways e.g. different galaxy, different dark matter content, different mean stellar densities…. • Stellar density in UMi probably significantly lower now than when stars formed, but likely still much less than a globular cluster

23. Same low-mass IMF in Galactic Bulge Zoccali et al 2002 M15 High metallicity, -0.3 dex; old, ~ 12Gyr

24. Mass Functions • If adopt Baraffe et al models, our 50% completeness limits all correspond to ~0.3M and a power-law slope somewhat flatter than Salpeter over the range 0.3M–0.8M: consistent with local disk (Kroupa 03) • But M-L transformation not well-defined for K/M dwarfs, especially as function of age and metallicity • Find eclipsing low-mass binary systems in open clusters of known age and metallicity (Hebb, Wyse & Gilmore 2004; 2005..)

25. Photometric Monitoring of Open Clusters • Selected six nearby open clusters, old enough to have low-mass stars on the main sequence • Age and metallicity from brighter member stars • Age range 0.2–4Gyr, metallicity –0.2 dex to solar • Monitored 1 degree FOV, well beyond nominal cluster radii • Survey designed to detect eclipse events in low-mass systems, primary 0.3M  – 0.5M  , with periods of hours to days

26. Expected detection efficiency (percentage) for low-mass systems with adopted survey parameters, from Monte Carlo simulations (two different mass ratio distributions assumed, solid and dotted lines)

27. Six observing runs 2002-03, KPNO 4m + INT For example, DSS image of NGC 6633 plus INT pointings

28. Montage of differential light curves Useful to check for systematics

29. Standard deviation in lightcurves vs I-band mag for all non-blended objects in M67 field (KPNO)

30. Detection of Eclipse Signal • Simple rms of light curve fails to distinguish • Observing strategy used pairs of observations; Stetson J-index designed for such programs. Measures the residuals of pairs, but also in fact no great improvement in finding (simulated) eclipses • Box-fitting algorithm (Tingley 03; Kovacs et al 02) designed to detect periodic signals which alternate between two discrete levels best

31. Signal Detection Efficiency vs I-mag Output by box-fitting algorithm for a set of simulated lightcurves with sampling rate and rms values chosen to match real data: open circles no eclipse, stars with eclipse added. Algorithm recovers correct eclipse period for I < 20, where rms = signal

32. Eclipse candidates found! M35  J Solid: single M3 ~0.4M Dashed: binaries Empirical SEDs from Leggett (92) V Spectroscopic & high-frequency photometric follow-up planned. Phase

33. NGC1647  Solid: M2V 0.5M Unequal mass binary Empirical SEDs from Leggett (92)

34. Heliocentric Radial Velocity (km/s) ~ ~ ~ ~ ~ ~ Julian Date - 2450000 NGC 1647 candidate M2V from TiO km/s TiO Fe I TiO Na I TiO CaH TiO K I H TiO CaH TiO TiO Radial velocity ~0.2M ~0.5M Period of model radial velocity curves taken from light curves.

35. Data also ideal for : • Studies of mass segregation and dynamical evolution in clusters • Calibrate metallicity scale of K/M dwarfs • ‘G-dwarf problem’ with K/M dwarfs, true unevolved stars… • Field Galactic structure….lines of sight include the outer disk…

36. Massive Star IMF at High Redshift • Type II supernovae have progenitors > 8 M and explode on timescales ~ 107 yr, less than dynamical timescale of typical dwarf galaxy, and less than duration of star formation • Low mass stars enriched by only Type II SNe show enhanced ratio of -elements to iron, with value dependent on mass distribution of SNe progenitors – if well-mixed system, see IMF-average • Type Ia SNe produce very significant iron, on longer timescales, few x 108 – 109 yr

37. Type II Supernova yields Ejecta Gibson 1998 Progenitor mass

38. Schematic [O/Fe] vs [Fe/H] Wyse & Gilmore 1993 IMF biased to most massive stars Type II only Plus Type Ia Fast Slow enrichment Self-enriched star forming region. Assume good mixing so IMF-average yields

39. Gilmore & Wyse 1991 Schematic of expected pattern of [O/Fe] in stars for system with continuous star formation. The plateau reflects enrichment by a massive-star-IMF-average and value will vary with IMF;  slope =1.2 [O/Fe]=0.3 The turn-down is due to input of iron from Type Ia SNe which starts at some delay, 1—2 Gyr (?), after birth of progenitor binary system. The [Fe/H] reached by this time depends on SFH.

40. Cosmic scatter in elemental abundances of metal poor halo stars is extremely low, 0.05 dex – fully sampled IMF of massive stars? Invariant IMF! Nucleosynthesis implies slope similar to Salpeter, same as local disk, gives [/Fe] Cayrel et al. 2004

41. Different symbols for different stellar populations: Filled circles are thick disk (kinematically), open circles are thin disk: both consistent same IMF Local F/G dwarfs Edvardsson et al 1993; Nissen 2004

42. LMC stars show sub-solar ratios of [/Fe], consistent with expectations from extended star formation. Hiatus then burst gas Continuous star formation Smith et al 2003 Gilmore & Wyse 1991

43. Tolstoy et al 2003 Large open colored symbols are stars in dSph galaxies, black symbols are Galactic stars: the stars in typical dSph tend to have lower values of [a/Fe] at a given [Fe/H], consistent with fixed IMF and extended SFH, plus perhaps α-enhanced winds

44. Massive Star IMF: Elemental Abundances Open symbols, UMi dSph Filled symbols, M92, M3 Shetrone et al 01 UMi and globular stars show Type II plateau, with value as expected for approx Salpeter IMF. UMi perhaps downturn to higher [Fe/H]; some iron from Type I supernovae, expected if star formation duration  1–2 Gyr?  UMi distribution ~

45. Same Massive IMF in Bulge McWilliam & Rich 04 Oxygen???

46. Conclusions and Future Work • The low-mass stellar IMF is remarkably invariant, over a range of metallicities, age, star-formation rates, surface densities, dark matter content, formation epoch…..most of the parameters that might have thought important – not Jeans mass fragmentation? • High mass IMF also apparently invariant, with close to Salpeter slope • Calibrate M/L for low-mass stars • Understand how dSph evolve (ongoing VLT/Flames/UVES project)

47. Evolution of Dwarf Spheroidals • Expectation of simplest theory is that initial burst of star formation drives a powerful wind that quenches subsequent star formation (e.g. Larson 1974; Dekel & Silk 1987; Wyse & Silk 1986) • Does not agree with spread in ages of dSph stars, or with modest derived rates of star formation • CDM models with star formation suppressed by reionization have similar problem with age range • Re-accretion of gas?? (Silk, Wyse & Shields 1987) • Trend with distance, but why each dSph so different? • Dark haloes accrete too and would light up..

48. Carina dSph metallicity distribution Data Koch et al 2004 (inc. Wyse) Left, stochastic model Right, model from Lafranchi & Matteucci 2003

49. Stochastic Enrichment model Searle 1977 • Independent star-forming regions, each with identical ‘enrichment events’ occuring at a fixed mean rate • Enrichment is then a Poisson process • For constant overall star formation rate, metallicity distribution of long-lived stars given by integral over events • Model parameter is the mean number of enrichment events per region – changes shape. Adopted value of 2 here.

50. Open Questions and Future Work • What was the star formation history of the disk of the Milky Way? • Was the merger history of the Milky Way mostly quiecsent since z ~ 2 (gas, fluffy old satellites..) • Same questions for all galaxies! • How important are flows of gas in evolution of different galaxies? Out and/or in? • How did the dSph evolve? What are the parameters of their dark matter haloes? Need self-consistent model matching star- formation input to CMD, gas flows to dark halo etc.