FAQ

As the time pass-by, all around us evolve. Aging tries to order and measure this change, and therefore a stellar age is something intuitive. It is the time spent from the stellar birth to the present day. The problem is that the stellar birth is something ill-defined, that is, when is t=0? In the literature, there are some definitions, from the moment when the hydrostatic equilibrium is established to the deuterium-burning phase and when a photosphere appears. All these definitions place t=0 at different moments. The good news is: compared with the complete life of a star, this uncertainty is usually really small.

During its evolution, every star spends most of its life in two stages: 1) Burning Hydrogen into Helium, called Main-Sequence, and 2) Cooling slowly at the end of its life, as a White Dwarf or a Neutron star. If its end is to be a black hole, who knows what it is really happening. The question, in our case, is that during the Main-Sequence stage stars are almost unaltered. For example, the Sun will spend 10Gyrs in this phase, and no clear indicators of its real age within this phase are accessible.

That is, there is a lack of a direct indicator for measuring the stellar age. The only option is using indirect methods. We estimate the age of a star: 1) Because, for a given temperature, luminosity, and chemical composition, models predict that the only option is a certain range of ages; 2) Because we have measured all the rotational periods of the rest of stars that berth with it (if this is the case) and their values are compatibles with previous determinations; 3) Because we have measured the surface chemical content of some elements and we have observed that some abundances are correlated with age; 4) Etc. All are indirect and sometimes very model dependent.

On the other hand, there is also a lack of a dating technique suitable for every star and evolutionary stage. What we have is a list of techniques that can be applied only for certain cases, with not much overlap among them and with important bias.

To complete the picture, we must keep in mind that we don’t know indubitably the age of any star only by analyzing the light we receive from them. The only stellar age we really know with a large accuracy is the age of the Sun, and not because we have analyzed its light, but because we live in its planetary system and we have analyzed the most ancient rocks. This is something impossible to do, nowadays, for any other star. The Sun is our real benchmark, and having only one element accurately known is not a great starting point.

I will only add the stellar dating using chemical abundances, not only lithium, with labels PMS: -, ZAMS: E, I, Main Sequence: E, I, Pop II: -.

If I try to describe them with only one small paragraph, I would say:

• Nucleocosmochronometry: Measuring the ratio of two radioactive elements with different decay times we can estimate how much time has passed-out. Suitable for old stars.
• Kinematics: If you have the velocity and position of a group of stars and, if moving backward all of them, you find a common origin at the same time, we can measure where all they berth and when. Suitable for stars in clusters.
• Isochrones: Using models we can draw in the HR diagram the lines of stars with the same age and different masses. When we have an observation, placing it in the same HR diagram we can compare it with these isochrones and estimate the age of the star. Suitable almost for every star.
• Lithium depletion boundary: Lithium is destroyed and converted into Barium when a certain temperature is reached. This happen when very-low-mass stars are young, and following models, we can calculate the moment when this temperature is reached. Suitable for very-low-mass and young stars in clusters.
• Asteroseismology: Some stars have seismic periodic waves traveling inside them. If these variations are observed, we can characterize the star with an enormous precision, in particular, its age. Suitable for almost any pulsating star, but especially useful for FGK solar-like stars.
• Stellar spin down or gyrochronology: The rotational velocity of FGK stars decreases with time. The exact mechanism of this process is unknown. Work in progress. But magnetic break-down is the main suspect. Suitable for FGK star in clusters, but sometimes it is applied to field stars.
• Decay of activity: It is somehow linked to the stellar spin down. Stellar activity also decreases with time, maybe because this activity is linked to the stellar rotation and the stellar spin-down impacts on the stellar mean activity.
• Decline in Lithium: Don’t confuse with the Lithium Depletion Boundary. In stellar clusters we have seen that the surface Lithium decreases with the age. The exact mechanism of this slow depletion is still poorly understood. Suitable for young stars in clusters.
• Chemical abundance: Most of the chemical elements different from H and He are created by the stars during their late evolutionary stages, prior to becoming a White Dwarf, a Neutrons star or a black hole depending on the stellar initial mass. With the time, when more and more stars die, the abundances of certain elements increase in the Galaxy. Therefore, the chemical abundance of some elements within a star is a measurement of the abundance of these elements at the time of its birth. Therefore, they are a stellar clock.

Some of the techniques for stellar dating are model dependent and some other have a background theoretical equation. In both cases, the estimation of the stellar mass and radius improves the accuracy of these techniques. For example 1) by adding a data driving prior to the Bayesian inference for fitting evolutionary tracks or isochrones, or 2) by providing real values to this background equation (as it is the case of gyrochronology, for example).

On the other hand, and as an additional benefit, a precise estimation of the stellar mass and radius has an impact in other astrophysical fields such as exoplanets. Therefore, a tool for estimating stellar masses and radii is a necessary first step for THOT.

We are planning to develop one main tool for the estimation of the most probable age of a star using all the techniques available for every particular case. This general tool will have some subtools that can be also used separately, such as the estimation of stellar masses and radii, or the model fitting using spectroscopic and/or asteroseismic observables, for example.