Research Blog
Welcome to my Research Blog.
This is mostly meant to document what I am working on for myself, and to communicate with my colleagues. It is likely filled with errors!
This project is maintained by ndrakos
I am generating SEDs for each galaxy in the mock catalog. I have gone through how to do this in numerous previous posts. Originally, I was going to fit the age and metallicity of the galaxies using UV properties generated from distributions. However, I decided it will be more straightforward to generate all of the free parameters from distributions, and then get the resulting UV properties.
This will give me a working method to get results for the conference; later I will check that the mass-\(M_{\rm UV}\) and \(M_{\rm UV}\)–\(\beta\) relations are consistent with observations. If not, I plan on first generating parameters from the distributions, and then accepting/rejecting them based on the probabilty given the UV relations.
Here is the current implementation. It has changed slightly from this post.
To begin, each galaxy has a mass, \(M\) and a redshift \(z\). Given the cosmology, we can calculate \(t_{\rm age}\) which is the cosmological time at redshift \(z\).
First, we choose the age of the galaxy, \(a\). I am closely following the age distribution suggested in W18. Unlike W18, I used this for both star-forming and quiescent galaxies
The age, \(a\) is sampled from a truncated gaussian in \(\log_{\rm 10}(a/{\rm yr})\) centered on 9.3 with a standard deviation of 0.7. It is truncated so that the minimum age is \(\log_{\rm 10}(a/{\rm yr})=7\) (i.e. 10 Myr), and the maximum age is the minimum of \(\log_{\rm 10}(a/{\rm yr})=10.5\) and \(log_{\rm 10}((t_{\rm age}-1e7)/{\rm yr})\); this ensures star formation couldn’t have started earlier than 10 Myr.
Then FSPS parameter sf_start is then \(t_{\rm age}-a\)
The SFR, \(\psi\) is described using a delayed tau model, in which
\[\psi(t) \propto t \exp{-t/\tau}\]FSPS normalizes this, such that the total mass created over the star formation history is \(1\, M_{\odot}\). This means that the current star formation rate of the galaxy is:
\[\psi_{\rm N} = \dfrac{a}{\tau^2 -(\tau^2+ a \tau)\exp^{-a/\tau} } \exp{-a/\tau}\]To scale this to the galaxy, we need to know (1) \(M\) and (2) the fraction of the mass we expect to survive at time \(t_{\rm age}\).
To get this, I am following Shreiber et al. 2017 (equations 10 and 12 for star-forming (SF) and quiescent (Q) galaxies, respectively).
\(\psi\) not explicitly set in FSPS, but it is related to the age, e-folding time and mass of the galaxy
As in W18, we set the stellar and ISM metallicity to be equal, \(Z\)
We get \(Z\) for SF galaxies from the fundamental metallicity relation (eq 15 in W18). I am also following their scatter model (eqs 16-17). I am using a truncated distribution though, with \(-2.2<Z<0.24\).
For Q galaxies, \(Z\) is sampled uniformly from the range \(-2.2<Z<0.24\).
The FSPS parameters are logzsol and gas_logz.
\(U_S\) is selected from \(Z\)–\(U_S\) relation (eq 18 in W18), with a scatter of 0.3 dex sampled from a student’s t-distribution. I am truncating the distribution such that \(-4<\log_{10}{U_S}<-1\).
This should really only be for SF galaxies; this parameter shouldn’t matter for Q galaxies, so for now I am calculating \(U_S\) for Q galaxies the same way. I need to check that that is reasonable.
The FSPS parameter is gas_logu.
I plan on following W18 for this; since this parameter actually depends on the size and inclination of the galaxy, which I haven’t assigned yet, I have a simplified version of this working (see this post.)
As in W18, I neglect dust for quiescent galaxies. I am not sure how justified this is.
The FSPS parameter is dust2 (with the dust model we are using, dust1 must be set to zero).
Finally, we get the e-folding time, \(\tau\). Since this is dependent on the surviving stellar mass fraction, \(x\) (stellar_mass in FSPS) this has to be calculated last.
To get this, I iterativly solved for \(\tau\) from \(\psi(\tau) = \psi_N(\tau) \times\dfrac{M}{x}\), updating \(x\) on every iteration. In practice, it only takes a couple of iterations for \(\tau\) to converge.
I impose a maximum \(\tau\) of 100 Gyr… larger values than this have little effect on the SFR. This means that there will be many galaxies with \(\tau=100\), but I think that is okay.
I will save the parameters needed to reproduce the SEDs; \(a\), \(\tau\), \(Z\), \(\hat{\tau}_V\) and \(U_S\). Additionally, I’ll save the SFR \(\log_{10} \psi\).
I will also save \(M_{\rm UV}\) and \(\beta\), as calculated in this post.
Finally, I’ll calculate the magnitude in each filter, as outlined in this post
It is looping through each galaxy to assign the properties. Each galaxy takes about 0.1-60 seconds; I’m not sure why some are longer (though it seems to be in the sps.stellar_mass calculation), the time did not correlate with the values of any of the free parameters. On average, it takes about 0.4 second per galaxy. For the \(512^3\) simulations, I have about half a million galaxies. This means I expect it to take about 2-3 days to generate SEDs for every galaxy using the current implementation.
Since it is this slow, I parallelized it using mpi4py. It can run on my laptop in about 6 hours. It is probably worth it to get this running on a supercomputer.
I want to check the imposed and recovered distributions against observations. W18 a good starting place.. Are all of the models/assumptions consistent with available data? Should I update anything?