Individual Star Formation and Feedback: Parameters
About
The tables below list all parameters relevant to the formation and feedback associated with our individual star methods. Included at the very bottom are input parameters to set specific to chemical evolution and certain problem types, related to these methods.
Star Formation and Supernova Feedback
Enzo Name | Description | Value(s) | Notes | Refs. |
IndividualStarIMFUpperMassCutoff | Upper limit of IMF | 100.0 M_{⊙} | ||
IndividualStarIMFLowerMassCutoff | Lower limit of IMF | 1.0 M_{⊙} | ||
IndividualStarVelocityDispersion | At formation, stars are given random velocity from Guassian distribution with mean velocity determined by the local gas velocity and dispersion set by this parmeter | 1.0 km s^{−1} | T.B.D, but 1.0 km s^{−1} is reasonable | |
IndividualStarIMFSeed | random number seed | (arbitrary) | ||
0 = Salpeter | ||||
IndividualStarIMF | 1 = Kroupa | 0 | ||
2 = Chabrier | ||||
IndividualStarIMFCalls | Number of calls to IMF to reset rnum generator on restart | – | Not to be set by user, but saved at each dump file | |
IndividualStarSalpeterSlope | α for Salpeter | 2.35 | ||
IndividualStarKroupaAlpha1 | α for first mass bin | 1.3 | ||
IndividualStarKroupaAlpha2 | α for second mass bin | 1.3 | ||
IndividualStarKroupaAlpha3 | α for third mass bin | 2.3 | ||
IndividualStarMassFraction | Maximum fraction, $f_{\rm gas \to *}$, of baryon mass in cell that can be converted to stars in a single timestep. If $M_{\rm IMF,min} < f_{\rm gas \to *} M_{\rm gas} < M_{\rm IMF,max}$, then IMF is truncated for that cell such that $M_{\rm IMF,max} = f_{\rm gas \to *} M_{\rm gas}$ | 0.5 | Proper value requires testing and discussion | From method used in Goldbaum et. al. 2015 |
IndividualStarSNIIMassCutoff | Stellar mass above which star produces CC SN | 8.0 M_{⊙} | T.B.D | |
IndividualStarWDMinimumMass | Lower mass limit for stars that turn into WD | 1.7 M_{⊙} | 1.7 M_{⊙} is lower limit of empirical intiial to final mass relation used to set WD masses | Salaris et. al. 2009 for DTD |
IndividualStarWDMaximumMass | Upper mass limit for stars to turn into WD | 8.0 M_{⊙} | Dahlen et. al. 2004, Mannuci et. al. 2006, Maoz & Mannucci 2012 | |
IndividualStarUseSNIa | Switch to enable SN Ia and turn on / of WD formation | 0 or 1 | Default ON | |
IndividualStarSNIaMinimumMass | Lower mass limit of a WD’s progenitor star that is capable of going SN Ia | 3 M_{⊙} | Not well understood value, but default is what is typically assumed | |
IndividualStarSNIaMaximumMass | Maximum mass limit “ ” | 8.0 M_{⊙} | “” | |
IndividualStarSNIaFraction | Normalizes probability distribution for SNIa rates, and is the fraction of stars in the above mass range that will explode as SN Ia given a Hubble time | 0.043 | Fraction is on order of a few percent, but depends on choice of IMF and normalization of the delay time distribution (DTD) | |
IndividualStarDTDSlope | β in power law decay (t^{−β}) of DTD that sets the decay of probabilty as a function of time for our WD’s to explode as SNIa | 1.07 | Mean from Cote et. al. 2015. Values vary, but around 1.0-1.3 | Maoz et. al. 2012 , Maoz et. al. 2014 and Cote et. al. 2015 for compilation |
IndividualStarStellarWinds | Turn stellar winds on or off | 1 | Winds not yet coded | |
IndividualStarRadiationMinimumMass | Stars above this value are radiation sources if radiation is ON | 8.0 M_{⊙} | Used value is T.B.D. | |
IndividualStarBlackBodyOnly | Radiation is (by default) calulated using OSTAR2002 grid for stars with $T_{\rm eff}$ and g on the grid. When off the grid, a black body curve is used. This turns off OSTAR2002 for all stars if ON | 0 | 0 or 1 | |
IndividualStarFollowStellarYields | If ON, and MultiMetals enabled, this tags stars with chemical abundances of their formation cells AND enables chemical ejection during feedback modes | 1 | Feedback of metals not in place | |
IndividualStarWindTemperature | Temperature ceiling for injection region in stellar wind model. Exceeding this temperature engages wind mass loading | 1.0E6 | A few million is ideal | Weaver 1977, Koo & McKee 1992 a,b |
IndivudalStarUseWindMixingModel | On or Off - If on, mass loads winds with grid averaged metal abundances in order to maintain IndividualStarWindTemperature winds | 1 | Strong recommendation to leave on | |
IndividualStarFeedbackOverlapSample | Number of sampling points per cell in volume overlap calculation | 20 | 10-20 seems to produce reasonable spherical winds with few zone radius injection regions - much higher is expensive |
Cosmic Rays
Cosmic rays are controlled by the adopted diffusion coefficient, the adiabatic index, maximum sound speed, and fraction of SN energy deposited into cosmic rays (and subtracted from the total thermal energy input). There will be an initial cosmic ray energy density that we need to decide what to do with... possibly we should just set it to be dynamically insigificant initially....
Enzo Name | Description | Value(s) | Notes | Refs. |
CRModel | CR’s on or off | 1 | likely test on and off | |
CRDiffusion | Diffusion on or off | 1 | test on and off | |
CRkappa | Cosmic ray diffusion coefficent | ?? | This will require testing and conversation | |
CRFeedback | Fraction of SN energy converted into CR’s rather than thermal | 0.25 | Again, testing needed | |
GalaxySimulationCR | Sets initial CR energy density as fraction of thermal energy | ?? |
Radiation
Below are new radiation parameters:
Enzo Name | Description | Value(s) | Notes | REfs. |
self_shielding_method | Switch between self shielding approximations in GRACKLE | 0 = no shielding, 1 = e^{−τ}, 2 = Rahmati et. al. 2013 in HI, e^{−τ} in HeI and HeII , 3 = Rahmati et. al. 2013 in HI and HeI, none in HeII | Rahmati et. al. 2013 | |
IndividualStarBlackBodyq0Factors | Fit factors to smooth HI ionzing radiation | 0.1, 3.2 | ||
IndividualStarBlackBodyq1Factors | ” | 0.001, 4.0 | ||
IndividualStarBlackBodyFUVFactors | ” | 10^{−4}, 2.3×10^{−5} | ||
IndividualStarBlackBodyLWFactors | ” | 5.0×10^{−5}, 5.0×10^{−6} |
The radiation parameters specific to my stars are discussed above (i.e. how the ionizing rate is calculated for each star). These are the radiative transfer parameters relevant to our simulation.
Enzo Name | Description | Value(s) | Notes | Refs. |
RadiativeTransfer | On or Off | On | Test both | |
RadiativeTransferRadiationPressure | Compute radiation pressure. Currently ONLY handles pressure felt by hydrogen (on or off) | 1 | ||
RadiativeTransferRaysPerCell | Number of photon rays computed in each cell (effectively a photon resolution) | 5 | may need to play with this, 5 is default | |
RadiativeTransferSourceRadius | Radiation sources are considered point sources, but will radiate as uniform sphere of desired value if > 0 | 0 | I don’t think we need this, and i think it fixes the radius to a single value, not a value per star. But if we have R for each star anyway, this might be useful? Not sure if its relevant | |
RadiativeTransferPropogationSpeedFraction | Photon speed as fraction of c | 1 | Lower number is less accurate but computationally easier, ideally stick with 1 |
Multi species and Chemistry
General parameters for turning multispecies and chemistry on / off for our simulations. The chemistry parameters (multi metals) are new.
ProblemType 260: ChemicalEvolutionTest
A new problem type was created that was meant to be used to test the physics associated with both the individual star formation / feedback as well as the chemical evolution. This initializes a star at the center of a uniform box of gas and lets it evolve. If one is impatient, one can manually set the star lifetime to an arbitrarily small value if one is concerned only with end-of-life (i.e. supernova) effects.
This star is deposited within the first timestep, and is not present at t = 0. Star formation is turned off for the remainder of the simulation.
Enzo Name | Description | Value(s) | Notes | Refs. |
ChemicalEvolutionTestStarMass | Mass of star | (arbitrary) | ||
ChemicalEvolutionTestStarMetallicity | Metal fraction of star | (arbitrary) | ||
ChemicalEvolutionTestStarLifetime | Manually set star lifetime | 0 | Value of 0 turns this off and lifetime is calculated as normal from stellar properties. > 0 is lifetime in Myr | |
ChemmicalEvolutionTestStarPosition | Coordinates of position in code units | 0.5 0.5 0.5 | center |
ProblemType 31: GalaxySimulation
A few parameters were added to the galaxy simulation problem type to set initial values for disk / halo chemical properties. A few of these new parameters below are stored in the TestProblemData struct that can be used in most simulations (see the next section) TestProblemData is used to set initial metal fractions for all species, and is coded to set two values per species for use with two different regimes in a given initial conditions set up. This is simple, but coding this for arbitrary locations is not trivial. For reading GalaxySimulation code, any TestProblemData with XX is used to set the disk initial values, and any with XX is used to set the halo / ambient medium initial values. If nothing is specified, the default is to set everything as primordial with the various metal fractions set to “tiny_number”.
I’ve also added a bunch of parameters to set MultiSpecies initial conditions following IC’s in other problem types for doing so.
Enzo Name | Description | Value(s) | Notes | Refs. |
TestProblemUseMetallicityField | Enables metallicity tracking | 1 | This is unfortunate, but there is a GalaxySimulationUseMetallicityField parameter that already exists, but DOES NOT actually enable metallicity fraction tracking, but a different tracer field (disk, not disk). I made this parameter as to not break previous functionality, but naming is unfortunate | |
GalaxySimulationInitialDiskMetallicity | Metal fraction of disk | |||
GalaxySimulationInitialHaloMetallicity | Metal fraction of halo |
Astrobites: Galaxies May Be Eating Gas All the Time!
Spiral galaxies, like our own Milky Way , are continuously forming stars from molecular hydrogen stored in the disks. Without additional gas supply from outside of the disks, galaxies’s star-forming activities would be halted in a few billion years due to the shortage of molecular gas – so called the gas consumption problem. To alleviate the crisis, both theories and simulations suggest that there may exist large amount of gas surrounding the disks of galaxies, which could potentially be accreted onto the disks to form stars (see other solutions in Putman+2012). Astronomers intensively search the evidence of the existence of such gas in the vicinity of galaxies – the circumgalactic medium (CGM). The CGM is loosely defined as the gas confined within the virial radius of a galaxy; i.e., gas is gravitationally bound to the central galaxy. Thus far, observers have found that for galaxies that are as luminous as the Milky Way, their CGM could contain as much gas as the stellar mass of the disks (e.g., Werk+2014), serving as gas reservoirs that would keep fueling the disks and maintain the star-forming activities.
If the galaxies were able to accrete gas from their CGM to feed their disks’ star formation, one might expect some correlation between the properties of the CGM gas and that of the disk gas. The authors of this paper performed a statistical study on a sample of galaxies to search for such correlation. Specifically, they aimed to understand the difference/similarity between the neutral hydrogen (H $\rm \scriptstyle I$) in the CGM and that in the disks.
The First Distance Constraint on the Renegade High Velocity Cloud Complex WD
and 5 collaborators
Low-Noise Frequency Translation of Single Photons via Four Wave Mixing Bragg Scattering
CE245 HW2
Homework 2
(Due on: Wed, April 15, 8:00PM)
Problem 1. A stochastic process is defined as \begin{equation}
x_{k}=x_{k-1}+m_k,\ \ \ x_{0}=0
\end{equation} Find the expected value E{x_{k}} and the variance $E\{(x_k-\overline{x}_k)^2\}$ of this process.
ANS:
equation 1. can rewrite as: \begin{equation}
x_{k}=x_{k-1}+m_k=x_{k-2}+m_k+m_k=x_{k-2}+2(m_k) \\
x_{k}=x_{k-3}+m_k+2(m_k)=x_{k-3}+3(m_k) \\
x_{k}=...=x_{0}+k(m_k), \ \ \ where\ x_{0}=0 \\
x_{k}=k(m_k)
\end{equation}
Therefore, the expected value can compute as: \begin{equation} E\{x_{k}\}=E\{x_{k-1}+m_k\}=E\{k(m_k)\}=k*E\{m_k\}=k*\int_{-\infty}^\infty m_k\ p(m_k)\ dm_k \\ E\{x_{k}\}=k\ \int_{-1/2}^{1/2} m_k\ p(m_k)\ dm_k=k\ \int_{-1/2}^{0} m_k\ 4\ (m_k+1/2)\ dm_k+\int_{0}^{1/2} m_k\ (2-4m_k)\ dm_k \\ E\{x_{k}\}=k\ (\frac{4}{3}m_k^3+m_k^2 \left| {_{-1/2}^{0} } \right.+\frac{-4}{3}m_k^3+m_k^2 \left| {_{0}^{1/2} } \right.)=k\ \frac{1}{6}\\ \end{equation} And, the variance can compute as: \begin{equation} E\{(x_k-\overline{x}_k)^2\}=\int_{-\infty}^\infty (x_k-\overline{x}_k)^2\ p(x)\ dx, \ \ \ where\ x_k=k\ m_k\ and\ \overline{x}_k=E\{x_{k}\}=k\ \frac{1}{6} \\ E\{(x_k-\overline{x}_k)^2\}=\int_{-\infty}^\infty k\ (m_k-\frac{1}{6})^2\ p(m_k)\ dm_k\\ E\{(x_k-\overline{x}_k)^2\}=k(\ \int_{-1/2}^{0} (m_k-\frac{1}{6})^2\ 4\ (m_k+1/2)\ dm_k+\int_{0}^{1/2} (m_k-\frac{1}{6})^2\ (2-4m_k)\ dm_k) \\ E\{(x_k-\overline{x}_k)^2\}=k\ (m_k^4+\frac{2}{9}m_k^3-\frac{5}{18}m_k^2+18m_k \left| {_{-1/2}^{0} } \right.-m_k^4+\frac{10}{9}m_k^3-\frac{7}{18}m_k^2+18m_k \left| {_{0}^{1/2} } \right.)\\ E\{(x_k-\overline{x}_k)^2\}=k\ \frac{1}{18} \\ \end{equation}
The Rainfall Annual Cycle Bias over East Africa in CMIP5 Coupled Climate Models
East Africa has two rainy seasons: the long rains (March–May, MAM) and the short rains (October–December, OND). Most CMIP3/5 coupled models overestimate the short rains while underestimating the long rains. In this study, the East African rainfall bias is investigated by comparing the coupled historical simulations from CMIP5 to the corresponding SST-forced AMIP simulations. Much of the investigation is focused on the MRI-CGCM3 model, which successfully reproduces the observed rainfall annual cycle in East Africa in the AMIP experiment but its coupled historical simulation has a similar but stronger bias as the coupled multimodel mean. The historical−AMIP monthly climatology rainfall bias in East Africa can be explained by the bias in the convective instability (CI), which is dominated by the near surface moisture static energy (MSE) and ultimately by the MSE’s moisture component. The near surface MSE bias is modulated by the sea surface temperature (SST) over the western Indian Ocean. The warm SST bias in OND can be explained by both insufficient ocean dynamical cooling and latent flux, while the insufficient short wave radiation and excess latent heat flux mainly contribute to the cool SST bias in MAM.
Circum-Binary Barn-oulli
Since I am not going to upgrade yet, I will make these notes public.
The non-viscous Bernoulli equation
The steady-state Euler equation reads \begin{equation} \left(\mathbf{v} \cdot \nabla \right)\mathbf{v} + \frac{1}{\rho}\nabla P + \nabla \Phi_G -\nu\left[\nabla^2\mathbf{v} + \frac{1}{3}\left(\nabla \cdot \mathbf{v} \right) \right] = 0 \end{equation} where it is understood that the gravitational potential Φ_{G} and the coefficient of kinematic viscosity ν are time independent. Now use the identity $\left(\mathbf{v} \cdot \nabla \right)\mathbf{v} = \frac{1}{2} \nabla \left( \mathbf{v} \cdot \mathbf{v}\right) - \mathbf{v} \times \left( \nabla \times \mathbf{v}\right)$, neglect viscosity for now, and integrate the momentum equation along a streamline from a reference point to the point of evaluation \begin{equation} \int{\mathbf{ds}\cdot \left[\nabla \left( \frac{1}{2}v^2\right) - \mathbf{v} \times \left( \nabla \times \mathbf{v}\right) + \frac{1}{\rho}\nabla P + \nabla \Phi_G \right]} = 0. \end{equation} Since ds is the line element of a streamline, it is in the same direction as v,so you get \begin{equation} \frac{1}{2}v^2 - \Phi_G +\int{\frac{dP}{\rho}} = \rm{cst} \end{equation} Which is Bernoulli’s equation for any steady, non-viscous flow. To evaluate the last term on the RHS let’s assume we are dealing with a monatomic ideal gas. Then \begin{equation} P = \left(\gamma - 1\right)\epsilon \rho = RT \rho. \end{equation} where R is the ideal gas constant. The first law of thermodynamics says that the change in internal energy ϵ plus the work done by the system is equal to the heat added, \begin{equation} dQ = d\epsilon + PdV. \end{equation} For an ideal gas \begin{align} d\epsilon &= \frac{R}{\gamma -1}dT \\ PdV &= -\left(\gamma -1\right)\epsilon \frac{d \rho}{\rho} = -RT\frac{d \rho}{\rho} \end{align} Then \begin{equation} dQ = \frac{R}{\gamma -1}dT - RT \frac{d \rho}{\rho}. \end{equation} We can rewrite \begin{equation} \frac{d\rho}{\rho} = \frac{1}{\rho} \frac{dP}{RT} - \frac{1}{\rho}\frac{P}{RT^2} dT \end{equation} so that \begin{align} dQ &= R\left( 1 + \frac{1}{\gamma-1}\right)dT - \frac{d P}{\rho} \\ &= \frac{\gamma R}{\gamma-1}dT - \frac{d P}{\rho} \end{align}
Let’s also introduce the enthalpy h in the limit that the number of particles in the system is constant, \begin{equation} dh = TdS + VdP = TdS + \frac{dP}{\rho} \end{equation} and also the Gibbs free energy G in the same particle conserving limit \begin{equation} dG = SdT + \frac{dP}{\rho} \end{equation} Now we assume two special cases, adiabatic and isothermal flows. First assume an adiabatic flow, dQ = 0. Then \begin{equation} \int{\frac{dP}{\rho}} = \frac{\gamma }{\gamma -1} RT \end{equation} which we could have also seen from the expression for the enthalpy when dQ = TdS = 0. For the isothermal case use the ideal gas equation P = RTρ and that T is constant to write dP = RTdρ, then \begin{equation} \int^{\rho}_{\rho_0}{\frac{dP}{\rho}} = RT \ln{\frac{\rho}{\rho_0}}. \end{equation} which we could have also seen from the expression for the Gibbs free energy with dT = 0. We can also write out these expressions in terms of the isothermal or adiabatic sound speeds by noting that for the adiabatic case, dS = 0 implies that \begin{equation} \frac{P}{\rho^{\gamma}} = cst \end{equation} then the adiabatic sound speed is \begin{equation} c^{\rm{ad}}_{s} = \sqrt{\frac{dP}{d\rho}} = \sqrt{\gamma \frac{P}{\rho}} = \sqrt{\gamma RT} \end{equation} The isothermal equation of state $P=(c^{\rm{iso}}_{s})^2 \rho$ gives us that $c^{\rm{iso}}_{s} = \sqrt{RT}$. So we can write \begin{equation} %\label{dP_ad} \int{\frac{dP}{\rho}} = \frac{(c^{\rm{ad}}_{s})^2 }{\gamma -1} = \frac{\gamma (c^{\rm{iso}}_{s})^2 }{\gamma -1} \quad \rm{Adiabatic} \ \rm{Flow} \end{equation} \begin{equation} %\label{dP_iso} \int{\frac{dP}{\rho}} = (c^{\rm{iso}}_{s})^2 \ln{\frac{\rho}{\rho_0}} \quad \rm{Isothermal} \ \rm{Flow} \end{equation}
Hydrostatic Balance
In a thin accretion disk around a point mass of mass M, hydrostatic balance gives \begin{equation} \frac{\partial P}{\partial z} = \rho \frac{GMz}{\left( r^2 + z^2 \right)^{3/2}} \end{equation} or when the disk scale height is much smaller than the disk radius, H ≪ r, \begin{equation} \frac{P}{H} = \rho \frac{GMH}{r^{3}}. \end{equation} If we define the disk Mach number as the ratio of the isothermal sound speed to the keplerian orbital velocity $v_K=\sqrt{GM/r}$, then we have an expression for the Mach number in terms of disk sound speed for hydrostatic equilibrium in the vertical direction, \begin{equation} \mathcal{M} = \frac{H}{r} = \frac{v_K}{c^{\rm{iso}}_s} \end{equation} Now we can rewrite ([dP_ad]) and ([dP_iso]) in terms of the disk Mach number \begin{equation} \int{\frac{dP}{\rho}} = \frac{\gamma}{\gamma -1} \frac{v^2_K}{\mathcal{M}^2}\quad \rm{Adiabatic} \ \rm{Flow} \end{equation} \begin{equation} \int{\frac{dP}{\rho}} = \frac{v^2_K}{\mathcal{M}^2} \ln{\frac{\rho}{\rho_0}} \quad \rm{Isothermal} \ \rm{Flow} \end{equation}
Authorea & Sumit Proposal
and 2 collaborators
#Introduction
- Knowledge transfer is one of the key aspects of understanding the world, as we pass on learnings from one generation to the other.
- International development is one of the critical sectors that needs major improvement in the way that we create, share, and apply knowledge.
- This is because international development, encapsulates our efforts to improve the basic living conditions and opportunities of marginalized and underserved people around the world.