This is best seen in the g-r vs r-i plot To first order, the colors of low redshift ellipticals are only sensitive to the g-band, and only to the red edge of the g-band. The colors change as the 4000 A break sweeps towards the red edge.
There is -no- combination of star formation history that can reproduce the colors of z < 0.15 ellipticals. The new curves of Doi work worse than the old curves of Gunn. Probably the photometry zeropoints are wrong by 5%.
Just re-zeroing the k-correction curves to the colors of low-z brightest cluster galaxies works. Here is the full set of maxBcg calibration plots before and after the changing of the z=0 k-correction colors.
Here is a plot of the colors of old galaxies out to z=2 in r-i, z-Ks. The bluer curve is an S0, the redder curve a BCG. The ticks at at 0.5 in z, the circles at z=1.0 and z=2.0.
Consider the plot above. The black dots are the models explored below. There is a nice 1-dimensional family, with two side branches. The main sequence are very long infall and long exponential models on the blue, through 0.5 Gyr gas mass proportional SFR, 3.0 Gyr galactic wind models models, through models with infall of hydrogen, then infall of non-primordial gas. The upper branch are non-standard star formation histories: instantaneous bursts or exponential SFR models. The effect is not that of metallicity, which is degenerate with age along the main sequence and on the branch; rather it relates to the star formation histories and hence probably to the relative populations of stars on the giant branch.
The orange diamonds are models of the Hubble sequence; the bluest one of which is a Sd galaxy.
THe blue circled cross is the brightest cluster galaxy data. The red dots are Kennicut spectra run through as designed SDSS filter curves by Fukugita et al.
That leaves the lower branch of black dots: these are a couple of models as on the main sequence (the ones with diamonds around them, in fact), but run through Gunn filter cirves.
Now, we -know- that the SDSS camera filters have the curves as mesured by Doi, with red edges bluer than as desired. How is it that models using Gunn curve filters work better? The answer is that the photometry has been carefully placed on the MT/USNO system which is measured through the filters in air, and hence much like the Gunn curves.
So, the right thing to do is to use MT/USNO filter curves for this work; the Gunn curves are quite close.
Now, one can look at the reddest Fukugita point, and see that it is redder than the BCG point. In reality, BCG's are almost certainly redder than the ellipticals used in Fukugita's point, as they are more luminous and hence have higher metallicity. So what is happening here? Fukugita's filter curves, calculated well in advance of the filter manufacturing, could be the cause. Perhaps; or perhaps the transformation of the colors from the 2.5m natural system to the MT/USNO system is inaccurate at the 5% level for the highly structured spectra of BCG in the restframe g-band.
I argue that it will be difficult to convince oneself that the latter effect is not a problem, and I consider this a good argument for placing the SDSS photometry on the 2.5m natural system.
I use Fioc and Rocca-Volmerange's Pegase.2 to perform the galaxy spectral syntheses.
| Spectral Type | Infall Timescale (Gyr) | Galactic Wind Onset (Gyr) | Extinction Geometry |
|---|---|---|---|
| BCG | 0.5 | 3.0 | spheroidal |
| E | 0.5 | 3.0 | spheroidal |
| S0 | 1.0 | none | spheroidal |
| Sa | 2.0 | none | disk, inclination-averaged |
| Sb | 3.0 | none | disk, inclination-averaged |
| Sbc | 5.0 | none | disk, inclination-averaged |
| Sc | 10.0 | none | disk, inclination-averaged |
| Sd | 14.0 | none | disk, inclination-averaged |
| Im | 20.0 | none | disk, inclination-averaged |
| Consistent evolution of the stellar metallicity | |
| Metallicity of the infalling gas: 0.00 | except for BCG, where metallicity of the infalling gas: 0.005 |
| Mass fraction of substellar objects: 0.00 | |
| Nebular emission | |
| Scalo 98 Initial Mass Function |
The Pegase header information, which gives the details about the scenarios.
These are the k-corrections in the file at the top of the page.
None of the models above work well for the observed BCG redshift diagram. The S0 model works well below z = 0.2, and the E works well above z = 0.2; the difference being the galactic wind, primarily.
I explored several models in an attempt to match the diagram, varying infall timescales and galacitic wind timescales:
| Spectral Type | Infall Timescale (Gyr) | Galactic Wind Onset (Gyr) | Extinction Geometry |
|---|---|---|---|
| Ew0 | 0.5 | 3.0 | spheroidal |
| Ew1 | 0.5 | 10.0 | spheroidal |
| Ew2 | 0.5 | 20.0 | spheroidal |
| Ew3 | 1.0 | 20.0 | spheroidal |
| E1 | Inst Burst | none | spheroidal |
| E2 | 0.1 | none | spheroidal |
| E3 | 0.5 | none | spheroidal |
| S0 | 1.0 | none | spheroidal |
| Consistent evolution of the stellar metallicity |
| Metallicity of the infalling gas: 0.00 (also initial metallicity of E1) |
| Mass fraction of substellar objects: 0.00 |
| Nebular emission |
| Scalo 98 Initial Mass Function |
The Pegase header information, which gives the details about the scenarios.
And tried a couple around metalicity, at 1/20 solar, solar, and twice solar:
| Spectral Type | Infall Timescale (Gyr) | Initial metallicity | Extinction Geometry |
|---|---|---|---|
| Em0 | Inst Burst | 0.001 | spheroidal |
| Em1 | Inst Burst | 0.02 | spheroidal |
| Em2 | Inst Burst | 0.04 | spheroidal |
| Consistent evolution of the stellar metallicity |
| No Infall (same as E1 above) |
| No Galactic Wind |
| Mass fraction of substellar objects: 0.00 |
| Nebular emission |
| Scalo 98 Initial Mass Function |
The Pegase header information, which gives the details about the scenarios.
The non-galactic wind models have too much star formation at z=0.5. The upturn in r-i color happens at g-r=1.3, not at the observed g-r=1.6.
The initial burst models are strange.
The galactic wind models work well at z > 0.3, but fail at later z. This seems to be because they have too small a luminosity averaged metallicity (0.025); the normal models have metallicity of about 0.035, and work well at z < 0.3; primarily they are bluer in g-r, and redder in r-i.
So I am trying two more models: a 1 Gyr burst model, and a standard E model with galactic winds at 3 Gyr, but with an initial metallicty of 1/4 solar, and with infalling gas metallicity of 1/4 solar.
| Spectral Type | Infall Timescale (Gyr) | Initial metallicity | Extinction Geometry |
|---|---|---|---|
| gyr | 1 Gyr Burst | 0.0 | spheroidal |
| nonpri | 0.5/3 Gyr winds | 0.005 | spheroidal |
| nonpri2 | 0.5/3 Gyr winds | 0.025 | spheroidal |
| Consistent evolution of the stellar metallicity |
| Metallicity of the infalling gas: same as initial |
| Consistent evolution of the stellar metallicity |
| Mass fraction of substellar objects: 0.00 |
| Nebular emission |
| Scalo 98 Initial Mass Function |
The Pegase header information, which gives the details about the scenarios.
What you find is that for a given age, which all of these models are for, metallicity shifts the low-z locus red,red in g-r,r-i for lower metallicity, almost exactly perpindicular to the track (i.e., along the high-z turnoff). (Actually, I am, acting later, unable to reproduce this logic...)
The straight 1 Gyr burst model I ran, starting from 0 metallicity, ends up with a luminosity weighted metallicy of 0.025, solar. This is much too low... but is the same as that of the 0.1Gyr/3Gyr Ew0 model, though the latter has a very different metallicity history. And the 1 Gyr k-corr curves are shifted red,red from the 0.1/3 model. So, I am wrong about the shift in the low-z locus being one in metallicity. Change from standard E model was 0.04.
I just did back to back models: compare E3 (0.5 Gyr, no winds, 0 initial/infall metallicity), Ew0 (0.5 Gyr, 3 Gyr winds, 0 initial/infall metallicity), nonpri (0.5 Gyr, 3 Gyr winds, 0.005 initial/infall metallicity), nonpri (0.5 Gyr, 3 Gyr winds, 0.025 initial/infall metallicity),
| model | z=0 metallicity | comment |
|---|---|---|
| E3 | 0.42 | bluer in g-r by 0.12 |
| Ew0 | 0.24 | same as next two |
| nonpri | 0.28 | all 3 show del 0.1 red shift in g-r/r-i turnoff with increaseing metallicity |
| nonpri2 | 0.44 | all 3 show del 0.04 red shift in g-r/r-i z=0 endpoint with increaseing metallicity |
| gyr | 0.25 | same g-r/r-i turnoff as Ew0, but 0.1,0.1 redder in g-r/r-i endpoint than Ew0 |
The endpoint, though, seems to have to do with the star formation history.
If you look at the E1, Em0, Em1, Em2 initial burst scenarios, you see that E1 (at zero metallicity) has an endpoint at g-r=0.7, Em0 (at 1/20 solar metallicity) has an endpoint at g-r=0.8 (near E3), but that both Em1 (at solar metallicity) and Em2 (at twice solar) have very red endpoints, at g-r=1.15-1.2. As if it takes low-metallicity dwarf K stars to make the blue endpoint.
Now the standard gas infall rate matching star formation rate scenarios S0 (timescale = 1 Gyr), E3 (0.5 Gyr), and E2 (0.1 Gyr). The latter two are essentially indisinguishable from each other, and have a turnoff about 0.1 mag bluer than S0 but otherwise close. These models fundamentally have a problem with the z > 0.3 objects.
The shocking thing about the S0, Ew2, Ew1, Ew0 scenarios (which have galactic winds kicking in at various ages) is that Ew1, which has the onset of winds at 10 Gyrs, about z=0.4, shows an abrupt transition from the standard infall rate/star formation rate match models above, to the very red g-r turnoff models and too blue in r-i along the locus of the early onset galacitc wind models. The model shows the transition essentally right at the peak of the kcorr curve. The endpoint is also affected. So the difference in the locus and the endpoint is due to the small amounts of ongoing star formation that the galactic winds stops.
Try a couple without infall (these should be doomed to failure).
| Spectral Type | Star Formation Timescale (Gyr) | Galactic Wind Onset (Gyr) | Extinction Geometry |
|---|---|---|---|
| E4 | 0.5 | none | spheroidal |
| E5 | 0.5 | 3 | spheroidal |
| Consistent evolution of the stellar metallicity |
| No infalling gas |
| Mass fraction of substellar objects: 0.00 |
| Nebular emission |
| Scalo 98 Initial Mass Function |
The Pegase header information, which gives the details about the scenarios.
E4 differs only marginally from E3: it has a final metallicity of 0.042, and has a slightly bluer turnoff than E3. E5 looks like Ew0, though with a bluer turnoff, probably due to high metallicity.
E5 has a final metallicity of 0.025; solar. The galactic wind coming in at 3 Gyr eliminates star formation before the very high metallicity stars form.
Now try a couple with very slow infall, but normally quick E star formation.
| Spectral Type | Star Formation Timescale (Gyr) | Infall Timescale (Gyr) | Infall Metallicity | Extinction Geometry |
|---|---|---|---|---|
| E6 | 0.5 | 14 | 0.00 | spheroidal |
| E7 | 0.5 | 14 | 0.01 | spheroidal |
| Consistent evolution of the stellar metallicity |
| Mass fraction of substellar objects: 0.00 |
| Nebular emission |
| Scalo 98 Initial Mass Function |
The Pegase header information, which gives the details about the scenarios.
Very bad, that pair: they look like spirals...
So, for our final 2 tries, we do an no-infall model where the metallicity is allowe dot get high before galacitc winds truncate them.
| Spectral Type | Star Formation Timescale (Gyr) | Galactic Wind Onset (Gyr) | Extinction Geometry |
|---|---|---|---|
| E8 | 0.5 | 6 | spheroidal |
| Consistent evolution of the stellar metallicity |
| No infalling gas |
| Mass fraction of substellar objects: 0.00 |
| Nebular emission |
| Scalo 98 Initial Mass Function |
E8 differs in no important way from E5, despite having the metallicity change from 0.026 to 0.031.
and a exponentially decaying star formation rate:
| Spectral Type | Exp. Star Formation Timescale (Gyr) | Extinction Geometry |
|---|---|---|
| E9 | 0.5 | spheroidal |
| E10 | 1.0 | spheroidal |
| E11 | 2.0 | spheroidal |
| E12 | 50 | spheroidal |
| Consistent evolution of the stellar metallicity |
| No infalling gas |
| No Galactic Wind |
| Mass fraction of substellar objects: 0.00 |
| Nebular emission |
| Scalo 98 Initial Mass Function |
And a set with the old, Gunn filter curves.
| Spectral Type | Star Formation Timescale (Gyr) | Initial/Infall metallicity | Extinction Geometry | Final metallicity |
|---|---|---|---|---|
| E20 | 0.5 infall 3.0 GW | 0.01 | spheroidal | 0.032 |
| E24 | 0.5 infall 3.0 GW | 0.00 | spheroidal | 0.024 |
| Consistent evolution of the stellar metallicity |
| Mass fraction of substellar objects: 0.00 |
| Nebular emission |
| Scalo 98 Initial Mass Function |
This -might- be due to the extinction, so I'm trying one without extinction.
Having said that, the two curves that work the best are E3, the 0.5 Gyr infall, no galactic wind model, and nonpri, which is the 0.5 Gyr infall, 3 Gyr galactic winds, and with inital and infall metallicity of 0.005. The latter works slightly better. The former fails completely in u-g; but then the latter does not work at z=0 in g-r. The u-g failure is complete, however, and that -must- rule out extinction as a problem.
Perhaps the filters were as designed in Fall 1998 and Spring of 1999, when 94/125 and 752/756 were taken.
Now, lets go back and prune the huge number of scenarios down to a useable number. Among the near misses: E3 works for g-r/r-i but fails in u-g; nonpri2 isn't as good as nonpri; gyr has a redder z=0 point than nonpri, which is a problem. Among the disasters: all infall models without galactic wind onsets fail in u-g; initial burst models are disasters, far too red; exponential star formation models are too red, but not as bad (the key time for flipover of the turnoff is about 1.5 Gyr, definately between 1.0 and 2.0).
Instructive is Ew1, which as galactic wind onset at z=0.4. The turnoff is too blue until the winds kick in, whereupon the curve transitions immediately to the old population that matches the data. But even this extended star formation model cannot reproduce the z=0 endpoint of the data.
The decent models are the following:
| Spectral Type | Star Formation Timescale (Gyr) | Initial/Infall metallicity | Extinction Geometry | z=0 metallicity | Filter Curves |
|---|---|---|---|---|---|
| Ew0 | 0.5 infall 3.0 GW | 0.00 | spheroidal | 0.024 | Doi |
| nonpri | 0.5 infall 3.0 GW | 0.005 | spheroidal | 0.028 | Doi |
| E24 | 0.5 infall 3.0 GW | 0.00 | spheroidal | 0.024 | Gunn |
| E20 | 0.5 infall 3.0 GW | 0.01 | spheroidal | 0.032 | Gunn |
| Consistent evolution of the stellar metallicity |
| Mass fraction of substellar objects: 0.00 |
| Nebular emission |
| Scalo 98 Initial Mass Function |
James Annis
16 June 2000
Chicago