Draft:Kippenhahn Diagram

• Comment: rather thin on independent sources? Theroadislong (talk) 19:24, 9 May 2024 (UTC)

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A Kippenhahn diagram, introduced by  Rudolf Kippenhahn is a 2D diagram which shows how the structure of a star changes through its lifetime, specifically allowing for graphical representation of the boundaries between distinct areas of the star as a function of the time remaining in the stellar life. A Kippenhahn diagram can be thought of as a stellar spacetime diagram, plotting the change in various stellar quantities locations over time.

Kippenhahn diagrams contain a tremendous amount of information about a star, and as such can be visually overwhelming when initially seen. Following is a step-by-step build up of an example Kippenhahn Diagram, generated using the stellar evolution code MESA and a plotting software designed specifically for producing such diagrams using MESA output

Enclosed Mass

Beginning of a Kippenhahn Diagram, showing the line for total mass over time

X Axis - Time

The x-axis plots time, often presented as the time remaining until star 'death'. When used with a stellar evolution simulation code, the x-axis may list the 'Model Number' where increasing model number is related to later models produced of the star. As such, model number can be considered directly analogous to remaining stellar lifetime, where higher model numbers indicate larger stellar age and thus smaller time remaining until death.

Y axis - Enclosed Mass

Often reported in Solar Mass units, a value close to zero would indicate that at that point, very little of the star's mass is enclosed, while the maximum value indicates the surface of the star, at which point all of the star's mass is being considered. For this example, the maximum is 20 Solar masses, the total Mass of the Star at ZAMS.

Black Line - Change of total mass over time

The black line, indicated on the plot, traces the total mass of the star over time. It begins at 20, the initial mass of the example star, and stays there for the main sequence lifetime, evidenced by the horizontal area of the black line at small model numbers (corresponding to earlier times of the star's life). As the star evolves, stellar winds will blow mass away, which is where the negative slope begins, at intermediate mass numbers. Following the black line across the plot through 'time' (technically model number) indicates what the total mass of the star is at a particular time, and how it changes.

Energy Generation Regions

Second step of a Kippenhahn Diagram, with shaded areas representing net energy generation

Next, the diagram adds colored, shaded areas representing areas of the star that are actively producing energy. These regions indicate net energy generation, so the combined effects of nuclear energy generation and neutrino energy losses. The shading gradients are in a logarithmic scale, where each hue represents an order of magnitude change in net energy generation.

Focusing first on one vertical slice, at model number 250 for example, there is a gradient of color beginning at 0 enclosed mass, becoming lighter with larger enclosed mass,. The color scheme, indicated by the color bar to the right of the figure, is set to show areas where more energy is being generated per second as darker, getting lighter as less energy is being produced. For this particular example, at model number 250, the energy is being produced entirely in the inner half of the star's mass, within 10 solar masses. The shading is darkest underneath 2.5 solar masses, meaning that in the stellar core area, the innermost 2.5 ${\rm {M_{\odot }}}$ worth of the star, the largest amount of energy is being produced.

These shaded areas change over time, describing the star's evolution to shell burning energy generation. White areas indicated sections of the star that are not producing energy, but may be transporting it via a range of mechanisms.

Elemental Core Locations

Core locations of different elements over time, as dotted lines

As a star evolves, it can burn elements heavier than Hydrogen in it's core. A Kippenhahn diagram can describe this as well.

The dotted blue line indicates the mass contained in the He core for this example star. For the earliest model numbers/times, this dotted blue line remains at zero, meaning the core is composed of H. When the H is exhausted and the core is now composed of He, the line jumps up to encompass roughly 7 solar masses worth of the innermost part of the star. Following this line across describes the elemental composition of the stellar core over time. We can also use this to inform what shell burning is happening as the star evolves. Near model number 200, where the He core mass has jumped up, we see energy generation happening above this core line, meaning that a Hydrogen shell outside of the core has begun fusing.

Kippenhahn diagrams can be made to include a number of core element masses. In this example, locations of the Carbon core and Oxygen core are included.

Energy Transfer

Kippenhahn Diagram showing areas of convection

Kippenhahn Diagrams also provide information about the method of energy transfer happening in different areas of the star at different stages of its life.

First, lime green hatching indicates areas of the star where convection is happening.

Red areas indicate where the primary method of heat transfer is semi-convective

Semi-Convective mixing areas marked

Further mixing and heat transfer processes can be included, with thermohaline mixing shown in gold

Thermohaline mixing areas marked