A New Way with Old Stars: Fluctuation Spectroscopy

Astronomers use models to derive properties of individual stars that we cannot directly observe, such as mass, age, and radius. This is also the case for a group of stars (a galaxy or a star cluster). How do we test how accurate these models are? Well, we compare model predictions against observations. One problem with current stellar population models is that they remain untested for old populations of stars (because they are rare). These old stars are important because they produce most of the light from massive elliptical galaxies. So a wrong answer from model means a wrong answer on various properties of massive elliptical galaxies such as their age and metallicity. (Houstan, we have a problem.)

Fear not — this paper introduces fluctuation spectroscopy as a new way to test stellar population models for elliptical galaxies. It focuses on a group of stars known as red giants, stars nearing the end of their lives. The spectra of red giants have features (TiO and water molecular bands) that can be used to obtain the chemical abundances, age, and initial mass function (IMF) of a galaxy. Red giants are very luminous. For instance, once our beloved Sun grows into old age as a red giant, it will be thousands of times more luminous than today. As such, red giants dominate the light of early-type galaxy (another name for elliptical galaxy). By looking at an image of an early-type galaxy, we can infer that bright pixels contain more red giants than faint pixels. Figure 1 illustrates this effect. Intensity variations from pixel-to-pixel are due to fluctuations in the number of red giants. By comparing the spectra of pixels with different brightness, one can isolate the spectral features of red giants. Astronomers can then analyse these spectral features to derive galaxy properties to be checked against model predictions.

The top panel shows brightness \textit{variations} in a model elliptical galaxy based on the observed light distribution of NGC 4472. The bottom panel shows a bright (left) and a faint  (right) pixel, while the inset figures are color versus magnitude diagrams of the stars in these pixels. The bright pixel contains many more bright giants than the faint pixel. SBF stands for surface brightness fluctuation.

FIG. 1 – Top left figure shows a model elliptical galaxy based on observation of NGC 4472. The right figure zooms in on a tiny part of the galaxy, and shows the pixel-to-pixel brightness variations within that tiny region. Figures on the bottom panel further zoom in on a bright (white) and a faint (black) pixel. The bright pixel (bottom left) contains many more bright red giant stars, represented as red dots, compared to the faint pixel (bottom right). The inset figures are color versus magnitude diagrams of the stars in these pixels, where there are more luminous giant stars (open circles) in the bright pixel.

The authors applied fluctuation spectroscopy on NGC 4472, the brightest galaxy in the Virgo cluster. They obtained images of the galaxy at six different wavelengths using the narrow-band filters (filters that allow only a few wavelengths of light, or emission lines, to pass through; see this or this) in the Advanced Camera for Surveys aboard the Hubble Space Telescope. In addition, they acquired deep broad-band images (images obtained using broad-band filters that allow a large portion of light to go through) of the galaxy. These broad-band images, because of their high signal-to-noise compared to the narrow-band images (broad-band images receive more light than narrow-band images and so have higher signals), are used to measure the flux in each pixel in order to measure how brightness changes. Next, the authors divided narrow-band images in two adjacent narrow-band filters. Recall that since narrow-band filters allow only certain emission lines to get through, the ratio of flux in two narrow-band filters –an “index image”– is a proxy to the distribution of stellar types in each pixel because different stars produce different emission lines. The money plot of this paper, Figure 2, shows the relation between the averaged indices of index image and surface brightness fluctuation; it illuminates the fact that pixels with more red giants (larger SBF) produce a different spectrum (indices of index images) than pixels with less giants (lower SBF).

By fitting observed index variations with models, we can obtain a predicted spectrum. The authors compared observed index variations of NGC 4472 with modeled index variations derived from Conroy & van Dokkum (2012) stellar population synthesis models, shown in Figure 3, which performs well in characterizing the galaxy.

The last thing that the authors analysed are the effects of changing model parameters on the indices of index images, in particular by varying age, metallicity, and the IMF. They found that the indices are sensitive to age and metallicity, thereby enabling them to exclude models that produce incompatible ages and metallicities with observations. One interesting result is that the indices are also sensitive to the presence of late M giant stars, which allows one to constrain their contribution to the total light from a galaxy. This is useful because standard stellar population synthesis models for early-type galaxies do not include the presence of these cool giants.

In conclusion, the authors introduced fluctuation spectroscopy as a probe of stellar type distributions in old populations. They applied this method to NGC 4472 and found that results of observation agree very well with model predictions. Various perturbations are introduced into the model with the most important result being that one can quantify the contribution of late M giants to the integrated light of early-type galaxies. Before ending, the authors propose directions for future work, which include obtaining actual spectra rather than narrow-band images and studying larger ranges of surface brightness fluctuations.

Averaged indices of index images for different narrow-band filter combinations versus surface brightness fluctuation for NGC 4472. In this paper, the authors focus on an SBF range from 0.95 (low fluctuation) to 1.05 (high fluctuation). Most of the filter combinations exhibit a clear relation between index values and the SBF.

FIG. 2 – Vertical axis is the flux ratio in a narrow-band filter and the adjacent band. It is a measure of the different number of different stars present. The horizontal axis is surface brightness fluctuation, SBF. SBF = 1 is the mean, while SBF < 1 represents little fluctuation and SBF > 1 represents high fluctuation. There is a trend between index and SBF because red giants produce a larger-than-average brightness and a different spectrum that changes the index of different index images.

This figure compares observed indices (dots) with model indices (lines). The model predictions agree amazingly well with observations. The bottom panel is the residual, or the difference between observed and predicted indices.

FIG. 3 – The top panel compares observed indices (dots) of NGC 4472 with model indices (lines). The vertical and horizontal axes are the same as Figure 2. The bottom panel shows the differences between observed and predicted indices. These figures suggest that model predictions agree amazingly well with observations.


About Suk Sien Tie

I am a third year PhD student at the Department of Astronomy at The Ohio State University. I am currently working on quantitative analyses of various quasar selection methods using the Dark Energy Survey (DES) and quasar variability via microlensing.

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