The Star Formation History of the Carina Dwarf Galaxy

We have analyzed deep B and V photometry of the Carina dwarf spheroidal reaching below the old main-sequence turnoff to about V = 25. Using simulated color-magnitude diagrams to model a range of star formation scenarios, we have extracted a detailed, global star formation history. Carina experienced three significant episodes of star formation at about 15 Gyr, 7 Gyr, and 3 Gyr. Contrary to the generic picture of galaxy evolution, however, the bulk of star formation, at least 50%, occured during the episode 7 Gyr ago, which may have lasted as long as 2 Gyr. For unknown reasons, Carina formed only 10-20% of its stars at an ancient epoch and then remained quiescent for more than 4 Gyr. The remainder (~30%) formed relatively recently, only 3 Gyr ago. Interest in the local population of dwarf galaxies has increased lately due to their potential importance in the understanding of faint galaxy counts. We surmise that objects like Carina, which exhibits the most extreme episodic behavior of any of the dwarf spheroidal companions to the Galaxy, are capable of contributing to the observed excess of blue galaxies at B = 24 only if the star formation occurred instantaneously.Comment: 23 pages of text, 20 figures, 8 tables. AJ, in pres

WFPC2 Observations of Star Clusters in the Magellanic Clouds: I. The LMC Globular Cluster Hodge 11

We present our analysis of Hubble Space Telescope Wide Field Planetary Camera 2 observations in F555W (broadband V) and F450W (broadband B) of the globular cluster Hodge 11 in the Large Magellanic Cloud galaxy. The resulting V vs. (B-V) color-magnitude diagram reaches 2.4 mag below the main-sequence turnoff (which is at V_TO = 22.65 +- 0.10 mag or M_V^TO = 4.00 +- 0.16 mag). Comparing the fiducial sequence of Hodge 11 with that of the Galactic globular cluster M92, we conclude that, within the accuracy of our photometry, the age of Hodge 11 is identical to that of M92 with a relative age-difference uncertainty ranging from 10% to 21%. Provided that Hodge 11 has always been a part of the Large Magellanic Cloud and was not stripped from the halo of the Milky Way or absorbed from a cannibalized dwarf spheroidal galaxy, then the oldest stars in the Large Magellanic Clouds and the Milky Way appear to have the same age.Comment: 14 pages (LaTeX+aaspp4.sty), 3 tables and 4 figures (Postscript, gzipped tar file). Postscript version of paper, tables, and full-resolution figures available at http://www.astro.columbia.edu/~mighell/hodge11.html To appear in the Astronomical Journa

The Star Formation History of the Local Group dwarf galaxy Leo I

We present a quantitative analysis of the star formation history (SFH) of the Local Group dSph galaxy Leo I, from the information in its HST [(V-I),I] color-magnitude diagram (CMD). The method we use is based in comparing, via synthetic CMDs, the expected distribution of stars in the CMD for different evolutionary scenarios, with the observed distribution. We consider the SFH to be composed by the SFR(t), the Z(t), the IMF, and a function $\beta(f,q)$, controlling the fraction $f$ and mass ratio distribution $q$ of binary stars. The comparison between the observed CMD and the model CMDs is done through chi-square minimization of the differences in the number of stars in a set of regions of the CMD. Our solution for the SFH of Leo I defines a minimum of chi-square in a well defined position of the parameter space, and the derived SFR(t) is robust, in the sense that its main characteristics are unchanged for different combinations of the remaining parameters. However, only a narrow range of assumptions for Z(t), IMF and $\beta(f,q)$ result in a good agreement between the data and the models, namely: Z=0.0004, a Kroupa et al. (1993) IMF or slightly steeper, and a relatively large fraction of binary stars. Most star formation activity (70% to 80%) occurred between 7 and 1 Gyr ago. At 1 Gyr ago, it abruptly dropped to a negligible value, but seems to have been active until at least ~ 300 Myr ago. Our results don't unambiguously answer the question of whether Leo I began forming stars around 15 Gyr ago, but it appears that the amount of this star formation, if existing at all, would be small.Comment: 25 pages + 14 figures. Accepted by The Astronomical Journa

Clues on the evolution of the Carina dwarf spheroidal galaxy from the color distribution of its red giant stars

The thin red giant branch (RGB) of the Carina dwarf spheroidal galaxy appears at first sight quite puzzling and seemingly in contrast with the presence of several distinct bursts of star formation. In this Letter, we provide a measurement of the color spread of red giant stars in Carina based on new BVI wide-field observations, and model the width of the RGB by means of synthetic color-magnitude diagrams. The measured color spread, Sigma{V-I}=0.021 +/- 0.005, is quite naturally accounted for by the star-formation history of the galaxy. The thin RGB appears to be essentially related to the limited age range of its dominant stellar populations, with no need for a metallicity dispersion at a given age. This result is relatively robust with respect to changes in the assumed age-metallicity relation, as long as the mean metallicity over the galaxy lifetime matches the observed value ([Fe/H] = -1.91 +/- 0.12 after correction for the age effects). This analysis of photometric data also sets some constraints on the chemical evolution of Carina by indicating that the chemical abundance of the interstellar medium in Carina remained low throughout each episode of star formation even though these episodes occurred over many Gyr.Comment: 4 pages, 3 figures, accepted for publication in the Astrophysical Journal Letter

Parameter Estimation in Astronomy with Poisson-Distributed Data. I. The Chi-Square-Gamma Statistic

Applying the standard weighted mean formula, [sum_i {n_i sigma^{-2}_i}] / [sum_i {sigma^{-2}_i}], to determine the weighted mean of data, n_i, drawn from a Poisson distribution, will, on average, underestimate the true mean by ~1 for all true mean values larger than ~3 when the common assumption is made that the error of the ith observation is sigma_i = max(sqrt{n_i},1). This small, but statistically significant offset, explains the long-known observation that chi-square minimization techniques which use the modified Neyman's chi-square statistic, chi^2_{N} equiv sum_i (n_i-y_i)^2 / max(n_i,1), to compare Poisson-distributed data with model values, y_i, will typically predict a total number of counts that underestimates the true total by about 1 count per bin. Based on my finding that the weighted mean of data drawn from a Poisson distribution can be determined using the formula [sum_i [n_i + min(n_i,1)] (n_i+1)^{-1}] / [sum_i (n_i+1)^{-1}], I propose that a new chi-square statistic, chi^2_gamma equiv sum_i [n_i + min(n_i,1) - y_i]^2 / [n_i + 1], should always be used to analyze Poisson-distributed data in preference to the modified Neyman's chi-square statistic. I demonstrate the power and usefulness of chi-square-gamma minimization by using two statistical fitting techniques and five chi-square statistics to analyze simulated X-ray power-law 15-channel spectra with large and small counts per bin. I show that chi-square-gamma minimization with the Levenberg-Marquardt or Powell's method can produce excellent results (mean slope errors <=3%) with spectra having as few as 25 total counts.Comment: 22 pages (LaTeX+aaspp4.sty), 6 tables (PostScript format) and 12 figures (PostScript format). The PostScript version of the paper, tables, and full-resolution color figures are available at http://www.noao.edu/staff/mighell/chi-square-gamma/ To appear in the Astrophysical Journal (accepted 1998 November 20

Dwarf Cepheids in the Carina Dwarf Spheroidal Galaxy

We have discovered 20 dwarf Cepheids (DC) in the Carina dSph galaxy from the analysis of individual CCD images obtained for a deep photometric study of the system. These short-period pulsating variable stars are by far the most distant (~100 kpc) and faintest (V ~ 23.0) DCs known. The Carina DCs obey a well-defined period-luminosity relation, allowing us to readily distinguish between overtone and fundamental pulsators in nearly every case. Unlike RR Lyr stars, the pulsation mode turns out to be uncorrelated with light-curve shape, nor do the overtone pulsators tend towards shorter periods compared to the fundamental pulsators. Using the period-luminosity (PL) relations from Nemec et al. (1994 AJ, 108, 222) and McNamara (1995, AJ, 109, 1751), we derive (m-M)_0 = 20.06 +/- 0.12, for E(B-V) = 0.025 and [Fe/H] = -2.0, in good agreement with recent, independent estimates of the distance/reddening of Carina. The error reflects the uncertainties in the DC distance scale, and in the metallicity and reddening of Carina. The frequency of DCs among upper main sequence stars in Carina is approximately 3%. The ratio of dwarf Cepheids to RR Lyr stars in Carina is 0.13 +/- 0.10, though this result is highly sensitive to the star-formation history of Carina and the evolution of the Horizontal Branch. We discuss how DCs may be useful to search effectively for substructure in the Galactic halo out to Galactocentric distances of ~100 kpc.Comment: 20 pages of text, 7 figure

The Effect of Star Formation History on the Inferred Initial Stellar Mass Function

Peaks and lulls in the star formation rate (SFR) over the history of the Galaxy produce plateaux and declines in the present day mass function (PDMF) where the main-sequence lifetime overlaps the age and duration of the SFR variation. These PDMF features can be misinterpreted as the form of the intrinsic stellar initial mass function (IMF) if the star formation rate is assumed to be constant or slowly varying with time. This effect applies to all regions that have formed stars for longer than the age of the most massive stars, including OB associations, star complexes, and especially galactic field stars. Related problems may apply to embedded clusters. Evidence is summarized for temporal SFR variations from parsec scales to entire galaxies, all of which should contribute to inferred IMF distortions. We give examples of various star formation histories to demonstrate the types of false IMF structures that might be seen. These include short-duration bursts, stochastic histories with log-normal amplitude distributions, and oscillating histories with various periods and phases. The inferred IMF should appear steeper than the intrinsic IMF over mass ranges where the stellar lifetimes correspond to times of decreasing SFRs; shallow portions of the inferred IMF correspond to times of increasing SFRs. If field regions are populated by dispersed clusters and defined by their low current SFRs, then they should have steeper inferred IMFs than the clusters. The SFRs required to give the steep field IMFs in the LMC and SMC are determined. Structure observed in several determinations of the Milky Way field star IMF can be accounted for by a stochastic and bursty star formation history.Comment: accepted by ApJ for 1 Jan 2006, Vol 636, 12 pages + 6 figure

Deep HST-WFPC2 photometry of NGC 288. II. The Main Sequence Luminosity Function

The Main Sequence Luminosity Function (LF) of the Galactic globular cluster NGC 288 has been obtained using deep WFPC2 photometry. We have employed a new method to correct for completeness and fully account for bin-to-bin migration due to blending and/or observational scatter. The effect of the presence of binary systems in the final LF is quantified and is found to be negligible. There is a strong indication of the mass segregation of unevolved single stars and clear signs of a depletion of low mass stars in NGC 288 with respect to other clusters. The results are in good agreement with the prediction of theoretical models of the dynamical evolution of NGC 288 that take into account the extreme orbital properties of this cluster.Comment: 16 pages, 6 .ps figures. Low resolution version of fig. 1; full resolution figure soon available at http://www.bo.astro.it/bap/BAPhome.html l. Latex. emulateapj5.sty macro included. Accepted for publication by The Astronomical Journa