ATRONOMY – COMOLOGY (42) CALCULATOR
Merger Tree Timescale
A precise tool.
What is the Merger Tree Timescale & How does it work?
In the hierarchical model of structure formation, darkβmatter haloes grow by accreting smaller companions. The time it takes for a satellite halo to spiral into the centre of a more massive host β the merger timescale β governs the buildup of galaxies, the triggering of starbursts, and the evolution of cluster substructure.
The merger timescale depends on the masses of the two haloes, the cosmic epoch (redshift), and the orbital configuration of the infalling satellite. Dynamical friction, which drains orbital energy, is stronger for more massive satellites and for orbits that are more circular. Halo concentration also modulates the density profile that the satellite experiences, subtly altering the decay rate.
A widely used analytic approximation combines these dependencies into a compact expression. Below is the formula employed by the widget, together with a legend that defines each symbol.
t_{mathrm{merge}} = 0.1,mathrm{Gyr},left(frac{M_{1}}{10^{12},M_{odot}}right)^{1.3},frac{1}{mu},(1+z)^{-2},epsilon^{-0.5},left(frac{c}{10}right)^{0.2}
t_{mathrm{merge}} = merger timescale (Gyr)
M_{1} = primary halo mass (M_β)
mu = mass ratio M_{2}/M_{1}
z = redshift
epsilon = orbital circularity (0β1)
c = halo concentration
M_{1} = primary halo mass (M_β)
mu = mass ratio M_{2}/M_{1}
z = redshift
epsilon = orbital circularity (0β1)
c = halo concentration
Parameters
Result
β
Frequently Asked Questions
What is the merger timescale in astrophysics?
The merger timescale is the time it takes for a smaller satellite halo to spiral into the center of a larger host halo, influencing galaxy growth and evolution.
How does cosmic epoch affect the merger timescale?
The merger timescale depends on the cosmic epoch (redshift), with different epochs affecting how quickly haloes merge due to varying cosmological conditions.
What role does orbital configuration play in the merger timescale?
The orbital configuration of the infalling satellite, including its eccentricity and inclination, significantly impacts the merger timescale by influencing the dynamical friction experienced by the halo.
How is dynamical friction related to the merger timescale?
Dynamical friction slows down the orbital motion of a satellite halo as it interacts with stars in the host galaxy, increasing the time it takes for the satellite to merge.
Why is the merger timescale important in astrophysics?
The merger timescale is crucial for understanding galaxy formation, starburst activity, and the evolution of cluster substructure, as it governs how haloes grow and interact over cosmic time.
Can you explain the relationship between halo masses and the merger timescale?
The merger timescale is inversely proportional to the mass ratio of the satellite to the host halo; larger mass differences lead to faster mergers due to stronger gravitational forces.
How do I input the parameters for a specific merger scenario in this calculator?
To calculate the merger timescale, input the masses of the two haloes, the redshift (cosmic epoch), and the orbital parameters such as eccentricity and inclination into the calculator.
Results are for informational purposes only and do not constitute professional advice.