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In-depth information: Making (galactic) history with big data: First global age map of the Milky Way

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In the last two decades, astronomy has entered the realm of big data, with surveys tracking and analyzing millions of astronomical objects, both distant galaxies and stars within our home galaxy, the Milky Way. The Sloan Digital Sky Survey (SDSS), which started systematic observations with a dedicated 2.5 meter telescope at Apache Point Observatory in New Mexico in 2000, has played a key role in this development. The Max Planck Institute for Astronomy (MPIA) was a partner in the original SDSS and in the ongoing fourth incarnation SDSS IV, and MPIA research has made ample use of data from all the four SDSS surveys so far.

Two of the SDSS observational programs, APOGEE and APOGEE-2, target stars within the Milky Way. APOGEE stands for Apache Point Observatory Galactic Evolution Experiment, and the specific goal of these two surveys is a better understanding of how our Milky Way has come into being, and evolved over the past billions of years.

Survey data and astronomical rainbows

From telescope observations, astronomers obtain a rich data set describing the light emitted by the star. The most complete data of this kind is obtained in spectroscopic surveys, such as the various SDSS surveys: for each object under study, a spectrum is obtained, that shows precisely how the light emitted by the object is distributed over the various possible wavelengths - how much light is emitted in some narrow range of blue light, or red light, or any of the thousands of different color shades distinguished by astronomers in between. The result is a highly differentiated rainbow of colors stretching from radio waves and infrared colors below the red end of the spectrum to purplish blue, representing the shortest-wavelength light that can propagate through the Earth's atmosphere, and to high-energy radiation that is only accessible to space telescopes.

In practice, any one survey can only observe a portion of the entire spectrum. The APOGEE survey concentrates on near-infrared observations at high resolutions and high sensitivity; at such wavelengths, the dust obscuring large parts of the Milky Way from the sight of optical telescopes is practically invisible, allowing for a clear view of the Milky Way as a whole. The APOGEE spectrograph takes spectra in the wavelength range between 1.52 and 1.69 μm (H band), dividing this narrow range into nearly 2300 distinctive "colors" (corresponding to a spectral resolution of R=22 500, at a typical signal-to-noise ratio S/N > 100).

APOGEE targeted over 100,000 red giant stars. A star becomes a red giant after having fused the hydrogen in its core to helium; red giants are typically luminous, and thus visible out to great distances. A typical red giant is observable for APOGEE out to distances of around 80 000 light-years, which allows the survey to detect such stars throughout the whole of the Milky Way galaxy, providing for comprehensive coverage. Also, red giant luminosity depends very little on the star's age or its chemical composition. Hence, a study of red giants does not run the risk of being biased towards stars of certain ages or compositions - it has a good chance of providing a fair sample.

Big data is only as good as its tools

Big data is only as useful as the available analysis tools. The need for specific tools is defined by the question one intends to answer. In particular, in order to understand the evolution of the Milky Way, you need to extract from your data the ages of our galaxy's various stars. Models of galaxy evolution predict particular distributions for stars of various ages: Stellar disks, the dominant stellar component of galaxies like the Milky Way, should have formed from the inside out: so, one would expect to find the older stars closer to the galactic center, and the younger stars at the outside.

Also, the thickness of the galactic disk is thought to have increased with age. Specifically, as one moves outward from the galactic center, one would expect to find more and more younger stars at greater distances from the plane of the disk. In order to test these predictions, and with them our current understanding of galactic evolution, one needs to determine the ages for a large sample of stars, covering a substantial range of distances from the galactic center, and of distances above and below the galactic plane.

Dating stellar clusters

Unfortunately, stars do not readily show their age. Age estimates need to rely on a combination of stellar modeling and observations, exploiting correlations between the age of a star and other more readily measurable properties.

Previously, most age estimates for red giants relied on one of three methods of limited reach. Stars within one and the same (open) stellar cluster can reasonably be assumed to have formed at the same time, and thus have the same age. They will also have formed from the same cloud of interstellar material, and thus have very similar chemical compositions. In a diagram plotting color vs. brightness, such stars show a characteristic distribution, including a linear structure ("main sequence") containing those stars that are burning hydrogen in their cores ("main sequence stars"). Red giants are found in another characteristic section of this diagram.

Main sequence star luminosity correlates with a star's temperature (effective temperature), so such diagrams allow for the determination of stellar luminosities and, in comparison with the observed brightness, for a determination of the distance of the stars in question. From the same plot, it is also possible to deduce the age of the cluster: High-mass stars turn into red giants sooner than lower-mass stars; on the other hand, high mass main sequence stars are also more luminous than low-mass star. Combining these two pieces of information, cluster age can be inferred from the "turn-off point" of the diagram, namely the point separating higher-mass stars that have already become red giants from lower-mass stars still part of the main sequence.

Unfortunately, such clusters are comparatively rare; also, as clusters disperse on a time-scale of billions of years, this method will not produce results for red giants beyond a certain age.

Alternative dating: sub-giants and chemistry

An alternative method allows for age estimates for so-called sub-giants: stars that have just finished burning hydrogen in their cores (have just left the main sequence) and are on their way to becoming red giants. For such stars, parameter such as the (effective) temperature, the gravitational acceleration at the star's surface (surface gravity) and chemical composition (notably iron abundance, [Fe/H]), all of which are comparatively simple to determine from the star's spectrum, can be combined to give a fairly reliable estimate of the star's age.

Unfortunately, such sub-giants are much less luminous than red giants, and thus more difficult to observe out to greater distances. With the current state of telescopes available for survey duty, it wouldn't be possible to detect sub-giants at sufficiently large distances to cover the whole Milky Way.

The third method is more qualitative than quantitative. Over time, stars produce more and more heavier elements within their core. Massive stars produce and spread some of the heaviest elements around when, at the end of their lives, they explode as supernovas. Stars whose atmospheres contain only a tiny proportion of these heaviest elements are bound to have formed early on in galactic history, before a significant number of supernovae had occured, and thus should be very old. Such estimates, however, effectively only quantify how many earlier generations of stars there were, a qualitative, but not a quantitative estimate of birth epoch, or age.

Spectroscopic dating techniques

Neither of these earlier methods provide the tool that would be needed to take full advantage of spectroscopic surveys such as APOGEE - neither allows astronomers to determine the age of red giant stars simply by looking at their spectra!

This is where the new analysis tools come in: Two complementary spectral dating methods for red giants, developed by the two MPIA postdoctoral researchers Marie Martig and Melissa Ness and their collaborators, respectively.

Both methods make use of a treasure trove of data that has become available thanks to measurements by the European (CNES/ESA) satellite mission CoRoT and the NASA mission Kepler. Both satellites have gained wide recognition for their detections of numerous extrasolar planets. But through the same type of measurement, namely the ultra-precise tracking of minute stellar brightness variations, they have also provided with researchers with accurate data about stellar oscillations.

Stars are not static balls of gas (or, more accurately, plasma) - instead, they oscillate, changing slightly in size and, consequently, in brightness, over time scales of hours, minutes and seconds. Just as the sound produced by a bell allows you to infer some of the bell's properties (including constraints on its size and shape), observation of stellar oscillations allows astronomers to infer some of the star's properties, including stellar masses. In particular, recent analyses of Kepler measurements have yielded masses for almost 2000 red giant stars which have also been observed as part of the APOGEE survey, published in 2014 as the so-called APOKASC catalogue as the result of a collaboration between the APOGEE team and the Kepler Asteroseismic Science Consortium.

This sample provides ideal conditions for studying correlations between stellar masses and spectral features - which could then, in turn, be used to estimate stellar masses from spectral data alone! In turn, for red giants, knowledge of a star's mass allows astronomers to estimate its age. The star's mass determines how long the star will spend as a main sequence star, burning hydrogen in its core. The time spent in the red giant phase is much shorter than the star's time on the main sequence; hence, knowing the star's mass, and thus the age at which it began to turn into a red giant, gives an excellent approximation for the red giant's actual age.

Age dating via the stellar mixmaster

The approach by Martig et al. is to link spectral features and red giant age is physics-based. Stars with a mass of more than about 1.3 times that of our Sun fuse hydrogen to helium through intermediate stages involving carbon (C), nitrogen (N) and oxygen (O) nuclei in what is known as the CNO cycle. In consequence, the inner regions where CNO fusion happens will contain more nitrogen-14 (14N) and less carbon-12 (12C) than otherwise. Stars with a higher mass have a higher core temperature, allowing for CNO fusion over a larger volume; the higher the mass, the more pronounced the chemical changes involving nitrogen and carbon.

Stars with masses up to ten times that of our Sun have what is known as convective outer layers, in which the star's matter is constantly on the move, hotter material moving up, cooler material down, in a process akin to that of water virulently boiling in a pot or kettle. When those stars leave the main sequence to become red giants, their structure changes, and lower and lower layers participate in the convection. For stars undergoing CNO fusion, this results in what is known as the "first dredge-up", in which the chemical composition of the star's outermost layers changes as material changed by the CNO processes, rich in nitrogen and low in carbon-12, is dredged up from the inner regions.

But the chemical composition of the outermost regions can be observed via the star's spectrum: chemical elements typically absorb and scatter light close to characteristic, very specific wavelengths, creating a "chemical fingerprint" of dark spectral lines (absorption lines) in the star's spectrum. This points towards a way of deducing red giant ages from spectra: use the spectra to determine the carbon-12 and nitrogen-14 abundances, most importantly the ratio of nitrogen to carbon; from this, deduce the star's mass and hence its age.

This possibility was first noted in APOGEE data by Thomas Masseron and Gerry Gilmore from Cambridge University in 2015. Marie Martig took this a crucial step further, using 1475 red giants from the APOKASC sample, for which Kepler measurements had provided mass values, to derive a quantitative relation between nitrogen/carbon abundances and stellar age. The correlation is clearly visible in figure 2, which plots the carbon-nitrogen ratio [C/N] against the total amount [M/H] of elements heavier than helium detectable in the star's atmosphere. Age is color-coded, from median ages around 1 billion years in blue to 12 billion years in dark red.

Letting the data speak (almost) for itself

An alternative approach to derive stellar ages from spectral features was taken by Melissa Ness and colleagues. They have called their approach The Cannon, after the US astronomer Annie Jump Cannon (1863-1941) who devised a pioneering way of classifying stars using their spectra, laying the groundwork for our modern view of stellar structure and evolution.

The Cannon is a two-step process that can be applied to any stellar survey in which data for each star was taken using the same instrument and reduction procedure. In the first step, a training set of objects for which both the spectra and the quantities of interests (such as temperature, surface gravity or, most importantly in our example, stellar mass) are known. Using a well-defined procedure, the training set is used to generate a general and highly flexible statistical model, which does not require knowledge of the underlying physical processes, linking spectral data as input with stellar parameters (more precisely, probability density functions for such parameters).

Figure 3 shows a small part of two sample spectra created using the resulting model, which shows the kind of spectral changes to expect for stars of different mass.

After using 1639 red giants from the APOKASC data set, Ness et al. obtained a model expected to be able to estimate stellar mass from spectral data with an accuracy of about 20%. The astronomers validated their approach by using only part of the training set to define their model, using the remaining stars for testing.

Mapping the Milky Way

With a relationship between spectral data and stellar masses/ages and the APOGEE spectral data for about 100 000 red giants, it proved possible to produce comprehensive maps of the age distribution of stars in the Milky Way. Since the stars' parameters (notably its temperature and mass) also allow for an estimate of their absolute brightness, stellar distances can be calculated, and the resulting map is three-dimensional.

Such maps were constructed based on the methods of Martig et al. and of Ness et al. The Ness et al. map, shown in figure 4, covers a large region within our galaxy, including the galactic center and reaching out to distances of around 65 000 light years from the center, making for a comprehensive map of one radial section of the Milky Way. Figure 4 shows the map embedded in a simulation of our galaxy as a whole.

For comparison: the best previous survey of stars with known ages, the Geneva-Copenhagen Survey, had only covered the wider solar neighborhood, namely stars closer than about 330 light-years. This had severely limited tests of galactic evolution.

The new, comprehensive map by Ness et al. already allows for much wider-ranging tests of our current understanding of the evolution of our Milky Way. Crucially, the map shows that when we move outward from the center, we find younger and younger stars in the galactic plane. This confirms current models that have the Milky Way's disk grow inside out, with the disk starting small at an earlier age and growing outward as more and more additional stars are created.

Also, at any given radius, the younger stars are typically found closer to the galactic plane than their older cousins. It is unclear whether the larger vertical motion of older stars, which has moved them away from the plane, is due to the circumstances under which these stars were born or due to later interactions ("kinematic heating").

Will we eventually be able to write a complete history of the Milky Way?

The results by Martig et al. and by Ness et al. are important steps within a wider development. Over the next years, surveys such as the APOGEE-2 spectroscopic survey and the precise measurements of stellar positions and motions provided by ESA's Gaia satellite will provide data about our galaxy's stars that is of unprecedented quality and comprehensiveness.

Using analysis methods such as the ones presented here, as well as their counterparts e.g. for determining the abundances of various elements in stellar atmosphere, to determine fundamental stellar parameters ("labels"), this survey data can be used to make a census of stars, listing their ages, masses and compositions.

When combined with simulations of galaxy and star formation, astronomers might be able to use such a census to reconstruct the star formation history of our galaxy: how many stars within our galaxy were formed at different times of galactic history, and in which regions, and how these stars have enriched our galaxy's raw material with the various elements they produce via nuclear fusion (thus enabling the production of heavier elements, of planets and, eventually, of living beings).

While this reconstruction of galactic history, and of our own galactic origins, certainly is of interest in its own right, its impact will be far wider than our galaxy-scale cosmic neighborhood: Most stars in the universe form in galaxies with masses comparable to that of the Milky Way. Learning about our own galactic history, structure and evolution provides a sound foundation for understanding star formation, galaxy evolution and chemical evolution in the wider universe, as well.

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