3. Evolution of Matter Perturbations Flashcards
Describe the relationship between overdense regions and dark matter and how they evolve over time
Overdense regions have higher dark matter densities than their surroundings
- More dark matter will fall into their potential well
- These overdense regions grow over time
Describe the potential of the overdense region, and state how they evolve
Gravitational potential = Grav potential of the universe + grav potential of overdense region
- Each potential evolves according to GR
What is a pocket universe?
A small region of space time and we look as to how it evolves over time by solving the Friedmann equations
- Matter dominated, positively curved and closed
Explain why a total matter collapse due to gravity is prevented from overdense regions over time
Due to the interactions between particles
- Friction, collisions, pressure etc. redistribute energy according to the Virial theorem 2K + U = 0
Describe how the virial theorem explains that there is not a total collapse due to gravity
2K + U = 0
- Gravitational potential coverted to KE
- Outward pressure
- Collapse is halted
Describe our explanation as to why dark matter doesnt have total collapse
We say dark matter follows a “collisionless relaxation” to a Virialised state as we don’t know what happens
- Gravitationally bound over dense regions are dominated by dark matter which we call Halos
- Baryonic matter falls into DM halos which are the site of galaxy formation
What is the scale for defining a halo/overdensity?
Any region around 200 times denser than the critical density
How are galaxies formed in relation to the overdensities of the Universe?
Baryons are carried along with the gravity of the dominant dark matter
- Baryons then condense to form galaxies
Describe how galaxies collapse in the Universe
Matter never collapses purely radially
- First collapses on 1st axis. Sphere -> sheet
- Then collapses on the 2nd axis. Sheet -> filament
- Finally that collapses. Filament -> spheroid
What do we need to know in order to model the cosmic web (collapse of galaxies)?
Fluid mechanics, gas interaction, DM assumptions, gravity
What are the two types of cosmological simulations?
- N Body simulations
- Hydrodynamic simulations/Smoothed particle hydrodynamics
Describe N body simulations
- Particles placed in a box and interact under gravity. Assume only gravity matters (good for DM, less for baryons.
- Want to predict the position at a later time
- Calculation scales as N^2, clever algorithms get to NlogN. Computationally difficult for large boxes. Need GPUs and supercomputers
Describe hydrodynamic simulations
- Need to solve continuity equations for baryon interactions
- Divide a box into a grid. At each time step, solve for the density at each point (computationally intensive)
- Simulations use active grid refinement (AGR) or mesh (AMR)
- Dense regions evolve quickly in space-time, so grid must be denser and vv
When considering numerical simulations, what are the 3 elements we must find the optimal combination of?
- Mass resolution
- Length resolution
- Time resolution
What is meant by mass resolution?
- Each particle in a N body simulation or fluid element represents much more than 1 star
- Often on the scales of 10^6 solar masses
