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Beschreibung
Karteikarten von Daniel Torres, aktualisiert vor 6 Monate
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Erstellt von Daniel Torres
vor 6 Monate
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| Frage | Antworten |
| E^2(z) (k=0) |
Image:
Hubble (binary/octet-stream)
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| Convective Derivative | |
| Contuity Equation | |
| Euler Equation |
Image:
Euler (binary/octet-stream)
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| Poisson Equation | |
| At early times or small fluctuations | P=0 |
| Eulerian vs Lagrangian | Eulerian fixed in space, Lagrangian moves with fluid |
| Comoving Gradient | |
| Growth of structures when delta is small | |
| EdS | |
| Linear Growth Factor D(a) | |
| Form of D | a in EdS, smaller later in other cosmologies |
| Potential Evolution | |
| ZA | Extrapolation of linear growth into the non-linear regime when δ is not small. Particles move in straight lines. Breaks down when shell crossing occurs; particle trajectories intersect and the local density becomes infinite. |
| ZA comoving position | |
| Initial Displacement Field | |
| EdS radius growth of sphere at mean density | t^(2/3) |
| Radius of slightly overdense sphere | |
| Linear sol to radius of overdense sphere | |
| Mean vs overdense sphere | |
| Overdensity linear approx |
Image:
Me (binary/octet-stream)
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| Overdensity Values | |
| Virial Theorem | 2K+V=0 |
| Virial radius for Spherical Tophat | r_vir = r_ta/2 |
| Mass of virialised Perturbation |
Image:
Vir M (binary/octet-stream)
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| Value of Delta_c | 18 pi^2 =178 EdS, sometimes 200, 500. |
| Gaussian Random Field | Initial overdensity field. The phases of the individual Fourier Modes are random, all info withing the amplitudes. |
| Average of the Gaussian Random Field | 0 |
| Vairance of Gaussian Random Field | |
| Usual Power Spectrum and Inflation Prediction | P(k) = k^n, n~1 |
| Meszaros Effect | Supresses growth on small scales (large k) due to radiation |
| Linear power spectrum | P(k) = D^2(a) |
| Smoothed overdensity field (variance on a certain scale) | |
| What is filtered by the smoothing? | lambda << R, R comoving radius of top-hat sphere. |
| Ergodic principle | Ensemble average over many independent universes is equivalent to one over well separated points. |
| Characteristic comoving scale of dark matter halo definition | delta_C=sigma_R |
| Characteristic radius for k^n power spectrum |
Image:
Rstar (binary/octet-stream)
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| When is sigma_8 evaluated | a=1 |
| Rstar Mstar relation, Mstar definition |
Image:
Mstar (binary/octet-stream)
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| Behaviour of characteristic halo mass | For n>-3, grows with time |
| Local gradient of CDM power spectrum | d ln P/d ln k >-3 |
| Halo mass function and cumulative mass function | |
| Press-Schechter ansatz | |
| Peak height | nu = delta_C/sigma_R |
| PS mass function behaviours | Power-law like at low masses (common), exponential at large masses (rare). |
| Dynamical timescale | Time taken for a halo to collapse. Timescales over which gravity can react to changes in the system |
| Dynamical timescale formula |
Image:
Dyntim (binary/octet-stream)
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| Relaxation timescale | Time taken for two-body encounters to drive a collisionless sytem to collisional. For real galaxies and DM haloes, much logner than the age of the universe, so collisionless. |
| Relaxation timescale formula |
Image:
Reltim (binary/octet-stream)
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| Singular Isothermal Sphere grav potential | |
| SIS velocity dispersion | sigma^2, constant |
| Hernquist model grav potential | |
| SIS density | |
| Hernquist Density | |
| Navarro, Frenk and White (NFW) | rho goes as r^-3 at large radius, usually used for haloes in cosmological simulations |
| Jean Length | Distance a sound wave can propagate in a crossing time. Perturbations with larger radius collapse, smaller are stable. |
| Jeans Length Formula | |
| Adiabatic Sound Speed | |
| gamma for monoatomic ideal | 5/3 |
| Jeans Mass (If greater, Collapse) | |
| Temperature- DM velocity dispersion relation for isothermal sphere in hydrostatic equilibrium | |
| Virial Temperature | |
| Spherical top hat definition of halo | |
| Cooling time | u/udot, measures how fast can hydrostatic gas radiate its thermal E |
| Specific thermal energy | |
| Emissivity (Power radiated per unit volume) | |
| Cooling time with cooling function | |
| Cooling to dynamical time relations | If cooling time lower, gas falls to the centre and forms a galaxy, if not, hydrostatic atmosphere at virial T |
| Cooling radius | Where the dynamical and cooling time meet. Gas within it forms a galaxy |
| When the virial radius is the cooling one | At 12 solar masses, so mass scale of galaxies. Higher are groups or clusters. |
| How do DM haloes acquire spin ang mom? | Torques from the surrounding structures (tidal) |
| Time evolution of ang mom of proto-halo region, EdS case | J(t)=a^2 Ddot, just t for EdS |
| Spatial evolution of ang mom of proto-halo | Depends on inertia tensor of proto-halo and tidal tensor |
| Halo spin parameter | |
| Typical halo spin param | 0.04 |
| Exponential surface density of disks | |
| Halo vs disk | M_d=f_dM; J_d=j_dJ |
| Isothermal halo disk central surface density | |
| Isothermal halo disk central length scale | |
| Model ISM | Three phases: Cold clouds 100 K, warm gas 10^4 K, hot gas 10^6 K. In approximate pressure equilibrium and polytropic equation of state, P proportional a rho^gamma_eff |
| Kennicut-Schmidt Law |
Image:
Ks (binary/octet-stream)
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| Parameters of KS law | Sigma gas greater than critical, n ~1.4 |
| Feedback processes | Reduces accretion of cold gas and subsequent SF. Main two supernova explosions from massive stars and AGN. Supernova affect dwarf and galaxy scales, AGN galaxy, group and cluster scales. |
| Galactic wind speed due to supernovae | |
| Parameters of wind speed | Epsilon efficiency parameter, eta mass loading parameter. |
| Galaxy velocity dispersion-Halo mass relation | |
| Hot clusters thermal emission | Bremsstrahlung, Lambda(T)=sqrt(T) |
| X-ray luminosity-mass |
Image:
Lm (binary/octet-stream)
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| Real LM relation | Steeper: Feedback processes heats gas in low mass clusters and groups, so lower luminosity |
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