Extragalactic – Page 3 – A blog about galaxies and probabilistic inference

2022-04-26

Adding emission lines to non-parametric kinematic models

This is still experimental and I’m not sure how much farther I’ll pursue it, but I tried a straightforward way to add emission lines to non-parametric line of sight velocity distribution (LOSVD) models. The idea is simple enough: model the line profiles directly using Stan’s simplex data type with each modeled line represented by a vector of mostly zeroes and with the simplex centered on the line’s rest wavelength. Although not essential I’m assuming I will have estimates of redshift offsets for each fiber or spaxel in a MaNGA data file (RSS or cube), so any additional offsets should be small. I’ve chosen to ignore the fact that the discretized line profiles will differ between lines because their central wavelengths will fall at different points within their assigned wavelength bins. Also, different lines could arise from kinematically distinct regions, which is not uncommon in galaxies with broad line AGNs. The obvious solution to this is to allow multiple line profiles. For these initial exercises I’m using a single line profile for all modeled lines (I fit 18 at present). As I’ve done since I started these modeling exercises I am fitting emission lines and stellar contributions simultaneously, with the stellar part represented by a small set of eigenspectra derived from my usual EMILES based library.

Below the “fold” I’ve included the Stan code in it’s current (but certainly not final) form. About half of the code for modeling the stellar LOSVD, is adopted from the original version that I wrote about last year. The emission line model portion takes advantage of an odd feature of Stan, namely the ability to store a matrix in sparse form and perform one specific operation — matrix multiplication with a vector. I still haven’t figured out the particular matrix representation used, so I just create a dummy matrix for the emission lines in the transformed data section and extract the two vectors describing the positions of the non-zero elements of the matrix. In the model section the simplex vector representing the line profiles is repeated as many times as there are lines to fill in the non-zeros.

Another thing to note is that Stan doesn’t know how to work with missing data. In general there will be gaps in spectra that were masked for some reason, while the input templates must be complete over the covered spectrum (plus a few extra at each end for the convolution). This requires a bit of housekeeping that’s mostly done in the R code that sets up the input data.

In the models I ran last year I ignored dust reddening since I didn’t expect it to be significant in the passively evolving Coma cluster galaxies I tested them on. In general reddening isn’t ignorable though and there’s the potential for template mismatch without some allowance for it. For now I inserted the function I use for “modified Calzetti” attenuation but it’s not actually used. In the one test I tried including attenuation in the model significantly increased execution time. I will probably look at using a multiplicative polynomial for the same purpose. A final thing to note is there are no explicit priors for the two simplex vectors that represent the stellar velocity convolution kernel and emission line profile, which means that the priors default to a maximally diffuse dirichlet distribution. This turns out to be an important issue that I will discuss further below.

I’ve run sets of models for a small sample of galaxies so far. so lets look at some results. For these runs I used 500 warmup and 500 post-warmup iterations per chain with 4 parallel chains for a total post-warmup sample size of 2000. The stellar templates are represented by 6 eigenspectra created from singular value decompositions of my standard EMILES based SSP library. I currently fit 18 emission lines — Balmer lines from Hα through Hζ and a selection of the stronger forbidden lines. Model runs typically take 2-3 minutes for sampling on my old 4th generation Intel core I7 based PC. This can undoubtedly be reduced by factors of at least several with multithreading.

In this post I’m going to look in some detail at results for Markarian 888, which was the main topic of my last post. Recall this is one of Schawinski’s “blue early type galaxies” that turns out to have obvious spiral-like structure in its inner region and clear evidence for a relatively recent merger.

First, the graph below shows the central fiber spectrum, and below that the results of a model run for the stellar velocity convolution kernel. From those I can calculate velocity offsets¹

\( \delta v = 69 \times \sum\limits_{k = -\lfloor K/2 \rfloor}^{\lfloor K/2 \rfloor} k p_i \)

and velocity dispersions

\(
v_{disp} = 69 \times \sqrt{\sum\limits_{k = -\lfloor K/2 \rfloor}^{\lfloor K/2 \rfloor} k^2 p_i – \delta v^2}
\)

for each draw from the posteriors, and these are shown as histograms in the middle and right graphs. This was a high signal to noise spectrum with prominent emission and absorption lines, a favorable situation for this modeling exercise and in fact the results look very promising with an especially well determined distribution for the emission lines. In summary, the posterior mean stellar velocity offset was 25 km/sec. with a 95% credible interval of (19.8, 31.3), while the corresponding values for emission lines were 24.3 and (22.8, 25.9), so the credible interval for emission lines lies entirely within that for stars.

The corresponding values for velocity dispersions on the other hand differ quite a lot: 141 km/sec. for stars with a 95% credible interval of (133.6, 150.3) versus 109 km/sec and (106, 111) for gas. I’ll say some more about this below, but I think this is already a sign that the second moments (at least) of these velocity distributions need to be treated with caution.

mrk888_centralspec_losv — Markarian 888 – mangaid 9894-3703 Central fiber spectrum, modeled stellar and ionized gas losvd

After running the code for every binned spectrum in the IFU I get stellar and gas velocity maps as shown below. These look similar to each other and to the map in the last post based on my hybrid red shift offset fitting routine, although a closer look will show a systematic decoupling of gas and stellar velocities.

mrk888_st_em_losvd — Stellar and ionized gas velocity maps for Mrk 888 (MaNGA plateifu 9894-3703)

I often take a look at the official MaNGA data analysis pipeline results, usually through the “Marvin” interface. Generally my results look similar for any given quantity, but it’s hard to tell how closely since we’re looking at different things (binned RSS spectra vs. cubes, for one) and I’m really just doing a visual comparison. As more or less a one off exercise I decided to compare velocity fields from the cubes. First, here are stellar and Hα maps from the DAP. These are from the “HYB10-MILESHC-MASTARSSP” sequence, which refers to the binning strategy and template inputs.

mrk888_vel_maps_per_dap — Mrk 888 – stellar and gas velocity fields derived from non-parametric LOSVD models

Next are my stellar and ionized gas velocity maps. Evidently these are considerably “noisier” in appearance, but similar overall. The noisiness may be due to different binning strategies: I modeled velocity distributions for every spaxel that met a minimal signal to noise requirement.

mrk888_vel_maps_per_moi — Mrk 888 – stellar and gas velocity fields derived from non-parametric LOSVD models

For a more quantitative comparison here are scatterplots of the mean stellar and gas velocity offsets from my runs against the MaNGA DAP. Both of these show slight tilts, that is the slopes are less than one, and small offsets. I’m tempted to suspect systematic errors somewhere, but I haven’t found any yet. And I have no hypothesis about the decidedly non-random behavior of the gas velocity plots. So there are still questions to be answered, but the magnitude of differences is no more than about ±1 wavelength bin (69 km/sec). For my main purposes this is good enough.

mrk888_vel_comp — Mrk 888 – scatter plot of mean stellar and gas velocities – my models vs. DAP

One more pair of graphs for this galaxy. In the initial maximum likelihood fit to a spectrum I estimate stellar and gas velocity dispersions with a single component gaussian. The graphs below plot the velocity dispersions from the Bayesian models calculated by the formula above against the ML fit values. The stellar velocity dispersions behave pretty much the same as I noted before: there’s a weak positive correlation between the non-parametric models and the maximum likelihood estimates with the former generally offset to higher values. The gas velocity dispersion estimates show an even larger discrepancy along with an apparently nonlinear trend.

mrk_888_vdisp — Mrk 888 – velocity dispersions from Bayesian nonparametric losvd models vs. estimates from maximum likelihood fitting

More briefly now, since this got longer than I wanted. I also ran models for the “Zoogems” target NGC 810, which I noted two posts ago has interesting kinematics, in particular a rapidly rotating disk that isn’t evident in the stellar velocity map from the DAP. From the maps below we see that the rapidly rotating component is the ionized gas, which has a mean rotation velocity as much as 150 km/sec larger than the stellar component.

ngc_810_st_em — NGC 810 – mean stellar and gas velocity maps

ngc_810_em-st — NGC 810 – difference between mean gas and stellar velocities

Finally, here are two more graphs of the kinematic models for the spectra with the largest positive and negative differences between stellar and gas velocity (these are the reddest and bluest patches in the map above. These show the spectra in the top row, followed by the posterior distribution of the stellar LOSVD and distributions of the first two moments, then the same for the emission line profiles.

ngc810_175_spec_los — NGC 810 – sample MaNGA spectrum, non-parametric stellar LOSVD and emission line profile

ngc810_90_spec_los — NGC 810 – sample MaNGA spectrum, non-parametric stellar LOSVD and emission line profile

The second set of graphs illustrates a significant problem: when there’s poor data — in this case no detectable emission lines — the models tend to return the prior, which for now is a maximally diffuse dirichlet. This will bias second moment estimates to the high side and can lead to spurious correlations, for example the increase of velocity dispersion with radius that I noted in the last post on this topic.

At the same time this spectrum is in the region of overlap between the main galaxy and its companion, and two peaks in the stellar velocity distribution are clearly seen at about the right velocity offset (~340 km/sec).

A short to do list:

Investigate informative priors.
Allow for dust reddening. I tried using a modified Calzetti attenuation relation in the code (note its presence in the code below, although it’s not used in the model), but it adds too much to execution time. A low order multiplicative polynomial might suffice.
Investigate systematics between my estimates and those in the DAP.

2022-01-282022-04-02

What fraction of Schawinski’s “Blue early type galaxies” are ellipticals?

The first iteration of Galaxy Zoo led to several collections of distinct objects, including a sample of 215 “blue early type galaxies” published in Schawinski et al. (2009)¹I found this an interesting group of galaxies, partly because of a possible link to post-starburst (K+A) galaxies that was discussed in the original paper. The authors discuss at some length the likelihood that these are results of mergers in the cosmologically recent past, with at least one of the progenitors being gas rich. Many (at least 25% and possibly more than half) were found to be currently starforming and the rest likely to have only recently ceased forming stars as inferred from their blue colors.

The ongoing Zoogems program has 12 of Schawinski’s blue ETGs on its target list, of which 6 have been observed so far as of mid-January 2022. Somewhat surprisingly there are 24 in the final MaNGA release, over 11% of the sample!

Taking a look at the 6 with HST observations I would say none of these are typical ellipticals. Five show some degree of spiral structure although in 4 it’s embedded in a more diffuse body. One appears to me to be an S0 with both inner and outer rings — this is in agreement with the one published morphological classification I’ve found. All of the others appear more disky than ellipsoidal to me, although this is just my possibly flawed qualitative judgment. At least two are visibly disturbed. One (CGCG 315-014) is connected to a nearby galaxy with a long tidal tail as seen in the Legacy Survey thumbnail below. Markarian 888, which will be the subject of the rest of this post, has shells that extend well past the main body of the galaxy and prominent, centrally concentrated dust lanes.

So far it’s the only Zoogems blue etg target with a MaNGA observation (two others on the target list are in MaNGA but of course there’s no guarantee they will ever be observed). As is often the case the IFU could have been larger — this was observed with a 37 fiber bundle giving 111 dithered spectra in the RSS file.

MRK 888 SDSS thumbnail with MaNGA IFU footprint

As always the first step in analyzing these data is to estimate redshift offsets for each spectrum, and from there we get a velocity field, which in this case shows a rapid rotator with a fairly symmetrical radial velocity pattern.

Mrk 888 (MaNGA plateifu 9894-3703) velocity field

Visual inspection suggests the line of sight velocity distribution is consistent with a rotating thin disk, so I fed the data to my Gaussian process based rotation modeling code, with results summarized below. In fact the model does an excellent job of accounting for the data, with residuals (not shown) from the model fit (top right) in a range of ±15 km/sec. One unusual feature of the velocity field is the rotation velocity turns over at somewhat less than one effective radius. Whether the rotation curve declines smoothly outside the IFU footprint or is kinematically disconnected from the outer parts of the galaxy is of course unknowable at this time.

I also ran my usual star formation history modeling code on the data binned to 97 spectra. First, here are some summary results. The stellar mass density declines roughly exponentially, which is consistent with a disky morphology:

Model estimate of stellar mass density vs. radius

Next are maps of the estimated Hα luminosity density and, on the right, the BPT classification from the [O III]/Hβ vs. [N II]/Hα diagnostic. The contours are elliptical with major axes closely aligned to the rotation axis (the posterior mean for the angle is the dashed line in the velocity field plot above). Again, the emission appears to arise in a disk.

The proper interpretation of the “composite” BPT classification is something I think I’ve written about in the past. It was originally suggested to indicate a mix of AGN and stellar ionization, but here it arises in a thin ring of weak but detectable emission just outside the star forming region. If it’s truly composite it’s likely to arise from a mix of weak star formation and ionization by hot evolved stars. In any case there’s no evidence for an AGN in the optical data.

(L) Hα luminosity density (R) BPT classification from [O III]/Hβ vs {N II]/Hα diagnostic

Next are maps of the modeled (100 Myr average) star formation rate density and specific star formation rate, and in the second row scatter plots of the same estimates against radius in kpc. The trends with radius are somewhat unusual, especially for SSFR which in a normal disk galaxy typically increases with radius even if the highest total star formation rates are centrally concentrated. Highly centrally concentrated star formation in the aftermath of mergers is predicted by some simulations.

(TL) star formation rate density; (TR) specific star formation rate; (bottom row) scatter plots vs. radius

A couple more graphs will round out my discussion of summary model estimates. As I’ve shown several times before there’s a pretty tight linear relationship between modeled SFR density and estimated Hα luminosity density. In this plot Hα is corrected for modeled stellar attenuation, which is expected always to underestimate the attenuation in emission line emitting regions. That, and the fact that Hα emission and the model star formation rate estimates probe order of magnitude different time scales probably account for the systematic offset from the standard calibration given by the straight line.

Model star formation rate density vs. Hα luminosity density corrected for *stellar attenuation*. Straight line is calibration from Calzetti (2012).

And, once again I show a map of the modeled optical depth of stellar attenuation. The region of highest optical depth nicely tracks the visible dust (the HST image at the top is rotated about 90º from the SDSS image). Outside the dusty region there appears to be a shallow gradient, which might indicate that the nearer side is to the northeast.

Map of modeled optical depth of stellar attenuation

Finally here are plots of the model star formation history for all spectra ordered by distance from the IFU center. In the inner 1.5 kpc or so there’s some recent burstiness with possibly a very recent acceleration of star formation. For reasons I’ve discussed recently I don’t take either the timing or magnitude of bursts of star formation too seriously, but the behavior of the models is consistent with a recent revival of star formation due presumably to a merger, for which there are multiple lines of evidence.

model star fomation histories for all spectra

With 24 of these galaxies and another 31 from the compilation of Melnick and dePropris and the post-starburst ancillary program in the final release of MaNGA these samples satisfy my criteria of being manageably sized for my computing resources while large enough to say something about the groups. So, when time permits I plan to take a look. I already have the data in hand.

2022-01-152022-01-17

NGC 810 – interesting kinematics in a Zoogems and MaNGA target

The final release of SDSS MaNGA went public back in early December as promised, and I’ve spent the last month or so of my hobby time looking for manageable sized samples of interesting galaxies. One sample I looked at out of curiosity was the Zoogems target list, which is an HST gap filler imaging program with about 300 galaxies selected (mostly) by Galaxy Zoo volunteers. It turns out there are 11 targets with MaNGA data, of which 5 have been observed by HST so far.

As can be seen from the thumbnails above this is a pretty diverse lot, with several in progress mergers and merger remnants, some normal looking spirals at least two of which were from Masters’ red spirals sample, and 3 of Schawinski’s blue early type galaxies. Only one of those 3 has HST imaging so far (number 8 in the thumbnails above), although there are a surprising 24 blue ellipticals in the final MaNGA release out of 215 in Schawinski’s original sample.

Of the 5 Zoogems galaxies that have been observed so far the one that caught my eye as deserving an early look was number 3 in the top row, NGC 810, an apparent elliptical with an unusual dust lane that’s almost perfectly aligned with the minor axis. There are also hints of shells indicating a likely merger sometime in the past.

NGC 810 HST ACS, proposal id 15445, PI Keel

The MaNGA data, which is new in DR17, only covers the central part of the galaxy with the companion just photobombing the edge. A larger IFU would have been nice for this observation, but the data quality is better than average in terms of nominal signal to noise. I was able to use all 183 fiber/position combinations in the RSS file without binning.

NGC 810 – plateifu 9514-6101 – MaNGA IFU footprint

The first step in the analysis process after loading the data is to estimate redshift offsets from the system redshift for each spectrum, and from that it’s straightforward to calculate a velocity field, which in this galaxy looks like¹:

NGC 810 (plateifu 9514-6101) – losvd estimated from cube

It turns out the redshift assigned to this system was that of the companion galaxy, which was the only SDSS spectroscopic target in the immediate vicinity and is evidently blueshifted by ~350 km/sec from the target. What’s more interesting though² is the apparent rapidly rotating disk that’s aligned with and somewhat thicker than the dust lane. There may also be overall prolate rotation outside the disk although the presence of the companion makes it hard to tell based solely on visual inspection. In hopes of separating out multiple velocity components I returned to the non-parametric line of sight velocity distribution models that I wrote some posts about last year. Unlike the ones I practiced on previously this galaxy has non-negligible amounts of emission, at least in the central region, so I just temporarily masked the regions around the emission lines that I fit. That results in a pure stellar velocity distribution. The results were a bit surprising:

NGC 810 (plateifu 9514-6101) (L) velocity field estimated from RSS file (M) stellar velocity offsets (R) net stellar velocity

In the left pane above is the velocity field from the RSS data, with the system redshift adjusted to the IFU center. For the LOSVD models I set the adopted redshift of each spectrum to the system redshift plus the offset calculated previously. Now I had hoped to be able to cleanly separate the contribution of the companion from that of the main galaxy, which so far I haven’t been able to do. But what I did find that was unexpected is that the average stellar velocities in the disk partially offset the original measurements (middle pane), so the net stellar velocity field shows a much more slowly rotating stellar disk.

As I’ve written before I use a set of 15 eigenspectra from a principal components analysis of some tens of thousands of SDSS spectra that I performed some years ago for redshift offset estimation. Those galaxies were of all types and include systems both with and without significant emission. The redshift estimation routine just does straightforward template matching and returns a single value for the best fitting offset. Since the templates encode information about both emission and absorption lines that estimate could be most applicable to the ionized gas, stars, or some combination. In this case it’s possible emission lines were driving the original fits, implying the gas and stars in the disk are kinematically decoupled. I have not verified that though.

Another issue I noticed is that the stellar velocity field from the official MaNGA Data Analysis Pipeline looks rather different from mine, with barely a hint of a kinematically distinct disk. This wasn’t really evident in the Marvin webpage, which makes some really unfortunate choices for color palettes. So here is the same data rendered with a more nearly perceptually uniform rainbow palette³:

NGC 810 (plateifu 9514-6101) Stellar velocity field per MaNGA DAP

I decided to re-run my LOSVD modeling code on the RSS data, this time setting the redshift offset to 0 for each fiber, so this is now measuring velocities relative to the overall system velocity. I also used a larger convolution kernel (25 vs. 21 in the first set of runs). The map of the average velocity offsets is:

NGC 810 (plateifu 9514-6101) Stellar losvd from nonparametric model

Although not a perfect match this is somewhat closer to the DAP map. I suspect what’s happening here is that there really are at least two, and more likely 3 distinct kinematic components. I haven’t read the DAP release paper in a while and don’t know exactly how they estimate stellar velocities, but in any case their model just returns a single value for visualization purposes. To see the (possible) complexity of the actual data here are the results for a single fiber with the largest positive velocity offset in the map above. Again, I don’t know how much of the structure in the posterior distribution of the convolution kernel is real, but it’s evident there’s more complexity than is captured in the first two moments shown in the middle and right panes.

Besides the kinematic modeling I did run star formation history models on the full RSS data set using the same tools as in recent posts. I’m not going to discuss them in detail, but some summary maps are worth showing. In the graphic below these are, from top left, stellar mass density, Hα luminosity density uncorrected for attenuation, SFR density (as usual 100Myr average), and stellar dust attenuation.

There’s no sign of a disk in the stellar mass map, which faithfully follows the distribution of light. A disk is visible in Hα and the small amount of recent starformation is also confined to a disk and nuclear region. In the fourth pane I show the modeled stellar dust attenuation, mostly just to demonstrate that this component of the model does capture something of reality.

ngc810_model_summaries — NGC 810 – a sampling of quantities derived from star formation history models

Getting back briefly to the first paragraph, there are 8 post-starburst galaxies from the catalog of Melnick and de Propris and 24 from an ancillary program to observe post-starburst galaxies from various sources that was added for DR17. There’s just one galaxy from the former catalog in the latter set, so that makes 31 total, an easily manageable number. There are also 24 of Schawinski’s blue ellipticals. Of course there are many disk galaxies, far too many for me to look at.

2021-11-242021-12-01

Another look at the PYPOPSTAR SSP model library

After a month off I returned to have another look at Millan-Irigoyen et al.’s high resolution “pypopstar” SSP model spectral libraries. First, I couldn’t find a more suitable subset of the full library than I used last time, so I decided just to try augmenting the existing Emiles based library with some younger spectra from pypopstar. Of course I had already done this with models from the 2013 update of BC03, so the plan was to replace those with a slightly finer grained selection at the young end. That raises the question of which ages to select. The youngest age model in the BaSTI isochrone based library is 30Myr (log T = 7.48), and we’re spoiled for choice of models at younger ages than that: there are 53 between log T = 5 and log T = 7.45, far more than necessary. Looking at the graph below, which just plots model spectra for the solar metallicity bin at decadal time invervals there’s very little spectral evolution between 10⁵ and 10⁶ years with the latter being slightly brighter at all relevant wavelengths. This is no surprise since even the most massive stars have main sequence lifetimes ∼10⁶ years. The model spectra continue to get brighter up to around 10^6.6 years (4 Myr) and then turn around, becoming noticeably fainter and redder by 10⁷ years.

pyspecz02 — pypopstar solar metallicity model spectra in decadal age increments

I decided to take the log T = 6 models as youngest, discarding the sub Myr ones altogether. This is mostly due to the inability to distinguish them and also just for purposes of visualization. I usually use logarithmically scaled lookback time axes in SFH history plots, and selecting a minimum value of 5 results in too much real estate given to very recent times where usually nothing much is happening.

Without giving this a lot of thought I selected just 3 ages to add: log T = 6, 6.51, and 7. The youngest Emiles model is log T = 7.48, so this gives nearly constant increments around 0.5 dex. This choice gives a reasonably smooth transition from the theoretical spectra to empirical ones, except for maybe the lowest metallicity bin. I also chose the “total” spectra including both stellar and emission continuum light in hopes of better modeling the continuum in star forming galaxies. To merge the high resolution pypopstar models into the library I just used a spline fit to interpolate the model spectra onto the same wavelength grid as Miles. This should (I hope) preserve total flux nearly enough. A more refined treatment would also consider that these still have higher resolution than Miles spectra, which are around 2.5 Å. I didn’t take the time. The merged library therefore has 56 time bins times 4 metallicity bins for a total of 224 model spectra. I retained the same rest frame wavelength range (3464.9 – 8864 Å) as the Emiles subset I’ve been using for several years

youngspec_combo — The youngest SSP model spectra for the EMILES library augmented with young pypopstar spectra

The obvious next step is to use this library in some models and see how they compare to Emiles. Paging through my samples of spirals with MaNGA observations I picked, for no really good reason, this one:

MaNGA plateifu 8452-12703 (mangaid 1-148068)

Clearly it has star forming regions in its arms as well as a prominent bar and rather red, possibly passively evolving nucleus. After binning to my usual threshold S/N of 5 there were 122 spectra, which were analyzed in the usual way using both Emiles and Emiles + popstar. And here’s the main result of interest, the model star formation histories for all 122 spectra, ordered by distance from the nucleus.

Model star formation histories for MaNGA plateifu 8452-12703 compared. Red: Emiles + pypopstar Blue: Emiles + BC03

There’s little or no difference in the model star formation histories for the common components of the libraries. The pypopstar components indicate that the star formation rate continues at relatively constant rates up to recent times. The modest differences at the young end don’t necessarily mean anything. I more or less arbitrarily assigned an age of 10Myr to the BC03 model spectra, which were actually taken from 1Myr models. There’s no real way to tell what the actual effective age of those contributors is — if it’s typically younger than 10Myr the SFR in the youngest bin would be correspondingly higher and a little lower in the next age bin.

Given the similarities in the detailed star formation histories it shouldn’t be much of a surprise that summary quantities are quite similar too. To illustrate a few, here are mean values of the stellar mass surface density:

Model mean values of stellar mass density for MaNGA plateifu 8452-12703 compared — Emiles + pypopstar vs Emiles + BC03

the star formation rate surface density (100 Myr average):

Model mean values of SFR density for MaNGA plateifu 8452-12703 compared — Emiles + pypopstar vs Emiles + BC03

The specific SFR:

ssfr_comp — Model mean values of SSFR for MaNGA plateifu 8452-12703 compared — Emiles + pypopstar vs Emiles + BC03

The lines with confidence intervals in these plots are from OLS fits taking no account of nominal uncertainties in either sets of variables, and shouldn’t be used to infer any trends. In any case all differences are very small. Finally, here are histograms of all sample values of SFR density for all spectra. Again, these are nearly identical:

sigma_sfr_dist_comp — Sample distributions of SFR density over all spectra compared — Emiles + pypopstar vs Emiles + BC03

After running multiple sets of models it became apparent that this wasn’t a very stringent test of the usefulness of the proposed library additions because this galaxy has very anemic star formation. In fact it’s one of Masters et al.‘s “passive” red spirals, which I should have recognized. It was also one of the first several dozen galaxies with AGN found in MaNGA, which doesn’t necessarily (but might, along with perhaps the prominent bar) account for the weak star formation. My model runs show “LINER” like emission line ratios in the center, which does point to the presence of a weak AGN.

Briefly now, I picked two more disk galaxies with obvious regions of vigorous star formation and repeated this exercise. To make this short I’m just going to post the star formation histories for all binned spectra.

MaNGA plateifu 8449-3703 (RA 169.299, DEC 23.586)

MaNGA 1-488712, plateifu 8449-3703 — SDSS cutout

Model star formation histories for MaNGA plateifu 8449-3703 compared. Blue: Emiles + pypopstar Red: Emiles + BC03

MaNGA plateifu 8318-9101 (RA 196.086 DEC 45.057)

MaNGA 1-259618, plateifu 8318-9101 — SDSS cutout

Model star formation histories for MaNGA plateifu 8318-9101 compared. Blue: Emiles + pypopstar Red: Emiles + BC03

Spectra in nearby age and metallicity bins are highly corrrelated, which among other things means that adding or subtracting some from the set of “predictors” potentially changes the values inferred for others as well. In these two sets of model runs we do see some differences in the common Emiles portion of the libraries, but they’re quite small and change no qualitative inferences. So my conclusion for now is that adding these theoretical spectra is a reasonable strategy, but one that doesn’t have much apparent impact on model results.

Well that’s probably all for a while. The final MaNGA data release is now promised for December 2021, which should approximately double the number of galaxies and I hope offer some data reduction improvements. There will also be a very large release of stellar spectra that should form the basis for new SSP libraries in the (hopefully) near future.

2021-08-23

One final look at KUG0859+406 and a new SSP model library

Back in July a paper by Millan-Irigoyen et al. titled “HY-PYPOPSTAR: high wavelength-resolution stellar populations evolutionary synthesis model” was posted to arxiv, and shortly thereafter data in the form of the promised high resolution spectra were made available at https://www.fractal-es.com/PopStar/#ingredients. Unlike MILES and its variations or BC03 this is a purely theoretical library, with the spectra calculated from model atmospheres instead of using empirical spectra of actual stars.

I looked briefly at one other theoretical library some time ago and concluded (IIRC) that the model spectra had much too blue continua at all ages, making it unsuitable for full spectrum fitting. A brief visual inspection of this library (as well as Figure 8 in the paper) indicates that’s not the case here. One thing that may compromise its usefulness is that although there are 106 age bins in the models they are very irregularly spaced and heavily weighted towards younger ages as shown below.

Age range	Number of spectra
5 ≤ log T < 6	4
6 ≤ log T < 7	34
7 ≤ log T < 8	35
8 ≤ log T < 9	9
9 ≤ log T < 10	15
log T ≥ 10	9

Number of SSP model spectra by age range in HR-pypopstar

At least in the wavelength range of SDSS/MaNGA spectra there is little evolution in spectroscopic properties between 10⁵ and 10⁶ years and even though it speeds up afterwards the effective time resolution of SFH models is still lower than the supplied number of time bins for the next two decades.

pypop_young_spec — Sample young population spectra from hrPypopstar

For a preliminary look at the library’s suitability for full spectrum modeling I selected a 42 time bin subset with all 4 available metallicity bins and Kroupa IMF, truncating the wavelength range to 3400-9000 Å, which is just a little larger than the Emiles subset I use. The time bins were chosen by hand — I was trying to get evenly spaced bins in log time but this proved not to be feasible. The authors produced two sets of libraries for each of 4 IMFs: they did an apparently careful job of counting the number of ionizing photons for several species and calculated sets of SSP models with and without emission continuum. For these trial runs I used both sets of libraries, which I’ll compare below. No code modifications were required because they use the same peculiar but computationally convenient flux units for spectra.

I just ran a few models for the central fiber spectrum of KUG 0859+406 (MaNGA plateifu 8440-6104). First, here is the star formation rate history compared to the most recent Emiles run:

sfh_emiles_popstar — Model star formation histories for central fiber of MaNGA plateifu 8440-6104
(T) Emiles
(M) hrPypopstar with emission continuum (
B) hrPypopstar stellar light only

Or, looking at the model mass growth histories:

mgh_emiles_popstar — Model mass growth histories for central fiber of MaNGA plateifu 8440-6104 Red: Emiles Blue: hrpypopstar including emission continuum Green: hrpypostar stellar light only

The starburst occurs later and is somewhat weaker in the pypopstar models. Interestingly all models have a late time revival of star formation after a period of quiescence. To get all the graphs to line up I truncated the pypopstar model star formation histories at 10 Myr. Here are the full histories:

sfh_popstar_popstarst — Model star formation histories for central fiber of MaNGA plateifu 8440-6104 (T) hrPypopstar with emission continuum (B) hrPypopstar stellar light only

Emission continuum is significant mostly at ages < 10Myr and this is reflected in some difference in late time model star formation histories. This has little effect on other modeled quantities.

At a glance fits to the galaxy flux data look very similar. Both sets of models have problems in some wavelength ranges and both have some issues with the [N II]+Hα emission complex, probably because the lines don’t quite have gaussian profiles. In terms of summed log-likelihood the Emiles fit is actually almost a factor of 2 better than pypopstar.

ppfits_compared — Comparison of model fits to data (L) Emiles (R) Hrpypopstar

The pypopstar models have larger optical depths of attenuation and steeper attenuation curves than the Emiles models, demonstrating once again the interplay among attenuation, attenuation relationship, and stellar ages:

tauv_delta_emiles_pypostar — Model distributions of attenuation parameters τ_V and δ for runs with Emiles library and hrPypopstar on the central fiber of MaNGA plateifu 8440-6104

Some other modeled quantities are very similar, for example the stellar mass density:

sigma_mstar_comp — Comparison of model stellar mass density red: Emiles blue: hrpypopstar with emission continuum

While the modeled specific star formation rate differs by ~0.4 dex thanks to the more recent starburst in the pypopstar models:

I still haven’t decided exactly what to do with these interesting SSP model libraries. I will probably take a more systematic look at extracting a subset of time bins that evolve at a consistent rate by some measure. This will certainly require many fewer than the published 106 bins. What may be more promising is to graft some young age SSPs onto my existing Emiles library. The 4 published metallicity bins are pretty closely matched to the Emiles subset I use, and 4 or 5 SSP’s would fill out the ages up to the youngest (30 Myr) in the BaSTI isochrones. I already use unevolved BC03 models for this purpose. Using the models that include continuum emission would also solve the problem of how to model that in starforming galaxies (but not galaxies with strong AGN emission unfortunately).

2021-08-102021-08-10

KUG 0859+406 – unravelling the differences between 2018 and 2021 model runs

I did have my old data and model runs of course, in fact they were spread over several directories on two machines. I’m going to refer to it by this catalog designation, KUG standing for the “Kiso survey of Ultraviolet-excess Galaxies.” It’s also a low power radio source with catalog entries in both FIRST and NVSS, and of course it’s in MaNGA with plateifu ID 8440-6104 (mangaid 01-216976).

In my 2018 model runs, which were interesting enough to write 3 posts about, I found this galaxy had undergone an extraordinarily large burst of star formation that began ~1 Gyr ago with locally as much as 60% of the present day stellar mass born in the burst and something like 40% of the mass over the footprint of the IFU. In this years model runs the peak burst fraction was a considerably more modest ~25% and globally barely amounted to a slight enhancement of star formation. The starburst was also much more localized than in the earlier runs:

burst_strengths_compared — Fractional stellar mass in stars between 0.1 and 1.75 Gyr old in 2018 and 2021 model runs

So what happened? First, here is a comparison of modeled star formation histories for the innermost fiber, which got the largest injection of mass in the starburst.

central_sfh_compared — Model star formation histories for central fiber of MaNGA plateifu 8440-6104, 2018 and 2021 model runs

The obvious remark is the double peaked starburst noted back in 2018 (and discussed at some length) has been replaced with a single narrow peak with a slow ramp up and fast decay. The peak SFR is a little larger than before but the total mass in the burst is lower.

I’ve made several changes in model formulation since 2018, of which the most important in the current context is adopting the more flexible “modified Calzetti” attenuation relation that adds an additional slope parameter to the prescription. In the current year model runs a steeper than Calzetti relation is favored throughout the IFU footprint, particularly in the central region where the starburst was strongest:

map_delta — Map of modified Cal;zetti slope parameter δ — MaNGA plateifu 8440-6104

A smaller optical depth of attenuation is also favored throughout:

tauv_compared — Modeled optical depth of attenuation – 2021 runs vs. 2018 MaNGA plateifu 8440-6104

This has a couple predictable consequences. Steeper attenuation will favor an intrinsically bluer, hence younger population while a lower optical depth requires less light, and hence mass in the stellar population. I can test this directly by returning to a model with Calzetti attenuation, and here is the result for the central fiber (this model run is labeled 2021 (c) in the legend below):

mgh_compared — Mass growth histories – 2021 run 2021 run with Calzetti attenuation 2018 run Central fiber of MaNGA plateifu 8440-6104

So, an eyeball analysis suggests about 3/4 of the difference between the 2018 and 2021 runs is due to the modification to the attenuation relation. The other changes I’ve made to the models are to change the stellar contribution parameters from a non-negative vector to a simplex, and at the same time changing the way I rescale the data. In early runs the SSP model fluxes were scaled to make the maximum stellar contribution ≈ 1, while the current models scale both the galaxy and SSP fluxes to ≈ 1 in the neighborhood of V, making the individual stellar contributions approximately the fraction of light contributed. An additional scale factor parameter in the model is used to adjust the overall fit. Assuming I did this right this should have no effect on a deterministic maximum likelihood solution, but with MCMC who knows?

Although the fit to the data looks about the same between the model with and without the attenuation modification the summed log-likelihood is consistently about 1% higher for the modified Calzetti model with no overlap at all in the distribution of likelihood. This suggests the case for a steeper than Calzetti attenuation is a fairly robust result.

ppfits — “Posterior predictive” fits to galaxy flux data – modified Calzetti attenuation vs. Calzetti – central fiber of MaNGA plateifu 8440-6104

The galaxy flux data also changed a little bit. The early runs were on the DR14 release (version 2_1_2 of the MaNGA DRP) while the recent ones used the DR15 release (ver 2_4_3). Most of the calibration differences resemble random noise, but there is some curvature that systematically affects both the red and blue ends of the spectrum and could cause some change in the temperature distribution of the models:

measured_flux_compared — Difference in measured flux from DR14 to DR15 – central fiber of MaNGA plateifu 8440-6104

While the detailed star formation histories changed, quantities that aren’t too model dependent didn’t very much. One example is shown below. Also, the kinematic maps agree with the earlier ones in detail.

halpha_luminosity_compared — Hα luminosity density – 2021 runs vs. 2018 MaNGA plateifu 8440-6104

velocity_field_8440_6104 — Velocity field of MaNGA plateifu 8440-6104 from 2021 model runs. Map interpolated from RSS file spectra.

One input that hasn’t changed are the emiles SSP model spectra, although there have been some procedural changes in how I handle the modeling. Early on I often used a much smaller subset of SSP models with just 27 time bins and 3 metallicities for preliminary modeling, including my first models on the same binning of these data. I also routinely ran 250 warmup iterations with just 250 more per chain. My current standard practice is always to use the largest emiles subset with 216 SSP models in 54 time bins and 4 metallicities, and I generally run 750 post-warmup iterations per chain but still with only 250 warmup iterations. This is generally enough and if adaptation fails it is usually fairly obvious. The small sample size of the earlier runs mostly effects the precision of inferences rather than means.

To conclude for now, my speculation about whether it might be possible to say something about the timing of critical events in a merger from the model star formation history was too optimistic. On a positive note though both sets of model runs retrodict that coalescence occurred at a lookback time around 500Myr ago, which is consistent with the fact that tidal tails and other merger signatures are clearly visible even in SDSS imaging. Both sets of model runs also have that odd uptick in star formation at 30Myr in the central fiber. And while the difference in burst mass contributions is a little disconcerting the current runs are more consistent with the likely gas content of ordinary spiral galaxies.

This example illustrates another well known “degeneracy” among attenuation (and adopted attenuation relation), mass, and stellar age. Whether I’ve broken the degeneracy by adopting the more flexible attenuation prescription described some time ago remains to be validated.

2021-07-31

Arxiv notes: Wu (2021), “Searching for local counterparts of high-redshift post-starburst galaxies…”

This paper (arxiv ID 2103.16070) is pretty old by now, having been posted on arxiv back in early April. The basic premise of the work is mildly interesting: the author searched MaNGA for galaxies that would meet conventional criteria for post-starburst (aka K+A etc.) spectra if observed at a redshift high enough that the entire galaxy would be covered by a single fiber like the original SDSS spectroscopes. Somewhat surprisingly, he found just 9 that met his selection criteria in the DR15 sample of ~4500 galaxies.

I have to say the paper itself is forgettable, but a manageably sized sample of MaNGA data that’s complete by some criterion is worth a look, and I have a long-standing interest in post-starburst galaxies in particular. So, I ran my current SFH modeling code on all 9 — by the way this was completed some time ago. It’s just taken me a while to get around to generating some graphics and sitting down to write.

The author only measured a few observable quantities: Hδ equivalent width and the 4000Å break index D_n(4000), along with Hα emission equivalent width and (normalized) fluxes. I long ago validated my own absorption line measurements of SDSS single fiber spectra against the MPA-JHU measurement pipeline, which was the gold standard for several years (but last run on DR8). My measurements and uncertainty estimates are in excellent agreement with theirs, so I have a fair amount of confidence in them. Emission line fluxes also agree with published measurements with considerably more scatter. My emission line equivalent widths on the other hand are completely unchecked. So, one of my tasks was to compare my equivalent width measurements with Wu’s. I did not attempt to exactly reproduce his work – I binned spatially using my usual Voronoi partitioning approach whereas Wu binned in elliptical annuli. With that difference in mind the next two plots should be compared to his Figures 4 and 5.

The first two graphs show the radial trends (relative to the effective radii per the NASA/SLOAN catalog) in the Lick Hδ_A and D_n(4000) indexes. These both show very similar trends to Wu’s measurements although with more scatter. This is expected because fewer spectra go into each point in general — from the text it appears Wu binned several separate measurements for each displayed point. Also, I made no attempt to deproject distances. One feature of the Hδ versus radius plot that’s a little different is the trend generally flattens out beyond ∼1 effective radius, while Wu shows a roughly linear trend out to 1.5 R_e. This might just be a visible effect of me displaying the trends out to larger radii.

d4000_hdelta_re — Radial trends of Lick Hδ_A and D_n4000 for 9 MaNGA “post-starburst” galaxies from Wu (2021) – arxiv 2103.16070

The Hα emission line measurements are similarly in broad agreement. Like Wu, I find that there are two distinct trends in emission: either moderately strong centrally with a rapid decline or weak throughout with a relatively flat trend. One galaxy (with MaNGA plateifu 9876-12701) has no detectable emission. I haven’t looked in detail at emission line ratios to compare to Wu’s Figure 7, but there’s general agreement that some residual star formation is present in some of the sample and weak AGN or ionization by hot evolved stars in others.

Radial trends of Lick Hα equivalent width and luminosity density for 9 MaNGA “post-starburst” galaxies from Wu (2021) – arxiv 2103.16070

A fairly common failing of this literature (IMO) is the use of proxies for recent star formation but not attempting actually to model star formation histories. There are plenty of publicly available tools for that available now, so there’s really no reason not to perform such modeling exercises. Wu did do some toy evolutionary modeling and posted a graph of trajectories through the Hα emission – Hδ absorption plane, which can scarcely unambiguously constrain star formation histories. Of course much of my hobby time is spent generating fine grained model star formation histories, so let’s take a look at a few selected results.

First, here are maps of the modeled fraction of the current stellar mass in stars of ages between 0.1 and 1 Gyr, very roughly the age range that produces a post-starbursty spectrum. Six of the galaxies have more or less strongly centrally concentrated intermediate age populations, which is generally what’s expected especially in the major merger pathway to a post-starburst interval. I’ll discuss this a little further below.

burst_fraction_maps — Maps of fractional stellar mass in intermediate age populations for 9 MaNGA “post-starburst” galaxies from Wu (2021) – arxiv 2103.16070

In more detail here are summed mass growth histories for the sample, that is all modeled star formation histories for a given observation are summed to produce a single global estimate. I’ve shown total masses here. Because of the pointing strategy MaNGA uses the fiber positions overlap to produce a 100% filling factor, so simply summing overestimates masses by about 0.2dex according to a calculation I performed some time ago. The present day masses in the plot below actually agree pretty well with the values listed in Table 1 of the paper, with an average difference of ~0.1 dex (this is probably because at least some of the light falls outside the IFU footprint in most of these galaxies, offsetting some of the overcounted mass).

total_mgh — Integrated mass growth histories for 9 MaNGA “post-starburst” galaxies from Wu (2021) – arxiv 2103.16070

Somewhat surprisingly several of these galaxies show little evidence of an actual burst of star formation in the recent past, at least at the global level. Some of these could simply have had star formation truncated recently, which can produce a poststarburst spectral signature for a time. Overall intermediate age stars contribute ~ 6-20% of the present day stellar mass, with the two largest contributions in the low mass galaxies in the bottom row of the plot.

There are some other oddities in this small sample. At least 3 galaxies are dwarf ellipticals or perhaps dwarf irregulars (in the case of plateifu 9876-12701), and two others have stellar masses under ~5 x 10⁹ M_⊙. Two of the low mass galaxies are in or near the Coma cluster, which suggests environmental effects as the probable cause of quenching. Another possible issue with the low mass galaxies is the infamous “age-metallicity degeneracy,” which refers to the fact that old, low metallicity populations “look like” younger, more metal rich ones by many measures. The Balmer lines in particular fade more slowly with age in lower metallicity populations, and the 4000Å break also becomes metallicity sensitive (smaller at low metallicities) at older ages.

There is only one clear merger remnant in the sample (with plateifu 8440-6104, which I will get to in a moment). One other galaxy (plateifu 8458-6102) is located in a compact group that appears (in Legacy survey imaging) to be embedded in a cloud of extragalactic light. Finally, two galaxies in this sample have been cataloged as K+A based on SDSS spectra — 8080-3702 and 9494-3701, while two others in the catalog of Melnick and dePropris (2013) are not.

The one clear merger remnant in the sample is an old friend of mine, and in fact I wrote three lengthy posts about this one back in 2018. In perusing those posts I noticed that the current set of model runs have a slightly weaker and more recent burst than the earlier runs. Also a double peak in the earlier runs has gone away in these, which means my early speculation that it might be possible to time crucial events in a merger from the detailed SFH model was too optimistic. On the other hand the model burst strength in the earlier runs was uncomfortably large, indicating an exceptionally gas rich merger and efficient processing of gas into stars. The current runs have a more reasonable ~10% of mass in the burst. So, I will look into those earlier runs and try to figure out what changed. Fortunately I’m a data hoarder and R is self-archiving to some extent.

kug0839+406 — KUG 0839+406, one of 9 “post-starburst” galaxies in Wu (2021)

The idea of looking at the integrated properties of IFU data to pick a post-starburst sample seems reasonable, but this sample appears to me to be both incomplete and possibly with some false positives. When DR17 is finally released I plan to try to develop my own criteria. As I’ve already shown using SDSS spectra alone to select a sample is doomed to produce lots of false positives.

I should finally mention one other paper pursuing a similar idea by Greene et al. (2021) showed up on arxiv recently. The authors lost me when they used the phrase “carefully curated” in their introduction, which was otherwise pretty well written up to that point. Maybe I’ll take another look anyway.

2021-07-142021-07-14

Do the details of the line of sight velocity distribution matter for star formation history modeling? Probably not much.

I decided to try a set of models for one galaxy – NGC 4889 (with MaNGA plateifu 8479-12701), which had the highest overall velocity dispersion of the Coma sample I’ve been discussing in the last several posts. It also has some evidence for multiple kinematic components which isn’t too much of a surprise since it’s one of the central cD galaxies in Coma. The SSP model spectra fed to the SFH models were preconvolved with the element wise means of the LOSVD convolution kernels from the velocity distribution modeling exercise. Again, this is an expedient to avoid what could otherwise be prohibitively computationally expensive. The models I ran were the same as described back in this post — these ignore emission but do model dust attenuation with the usual modified Calzetti attenuation relation.

To get quickly to the results, here are model star formation histories compared to the previous runs that used the full model in its current form. Usually I like these plots of results from all spectra in an IFU, but in this one all 381 spectra met my S/N criterion, so the plot is pretty crowded. You really need to see it live on a 4K monitor to see the details.

NGC 4889 (MaNGA plateifu 8479-12701) Model star formation histories for all spectra, runs with non-parametric LOSVD vs. single gaussian stellar velocity dispersions

Well it’s pretty hard to see but differences in model SFH’s are mostly in the youngest age bins, which are very poorly constrained anyway in these presumably passively evolving galaxies. Here’s a closer look at a single model run that had the largest difference in estimated stellar mass density (more on this right below) of about 0.19 dex:

mgh_comparison_8479-12701 — NGC 4889 (MaNGA plateifu 8479-12701) Model mass growth histories for a single spectrum – runs with non-parametric LOSVD vs. single Gaussian stellar velocity dispersion

So, the difference in star formation histories was slower mass build up between about 12-5 Gyr look back times in the second run, which was responsible for the lower current day stellar mass density. How this resulted from the choice of LOSVD is not at all obvious.

Let’s look at a few summary results. First, the model stellar mass surface densities:

sigma_mstar_comparison_8479-12701 — NGC 4889 (MaNGA plateifu 8479-12701) Model Σ_M* – runs with non-parametric LOSVD vs. single Gaussian stellar velocity dispersion

These fall on an almost exactly one to one relation with a few hands full of outliers. Oddly these are mostly in the higher signal to noise area of the IFU (i.e. near the center).

Results for star formation rate density and specific star formation rate are even more consistent between runs, with essentially no differences larger than the nominal 1 σ error bars.

sigma_sfr_comparison_8479-12701 — NGC 4889 (MaNGA plateifu 8479-12701) Model Σ_sfr – runs with non-parametric LOSVD vs. single Gaussian stellar velocity dispersion

ssfr_comparison_8479-12701 — NGC 4889 (MaNGA plateifu 8479-12701) Model SSFR – runs with non-parametric LOSVD vs. single Gaussian stellar velocity dispersion

One problem I encountered was that I had to re-run some models either for technical reasons or because of obvious convergence failures. I suspect there could have been some convergence issues in both sets of runs and am slightly worried that could be the source of the few differences in summary measures seen. Oddly, there were almost no suspicious convergence diagnostics in either set of runs (once the latter were run to satisfactory conclusion), and Stan is quite aggressive about reporting possible convergence issues.

Anyway, modeling kinematics remains an interesting topic to me, but it seems somewhat decoupled from modeling star formation histories. Right now I’m waiting for the final SDSS data release to decide what projects I want to tackle.

I’m going to end with a couple of asides. First, I recognize that all of these error bars are overoptimistic, maybe by a lot. The main reason, I think, is that I treat the flux values as independent which they clearly are not¹, which effectively results in overestimating the sample size. One possible partial solution is to allow the flux uncertainties to vary from their nominal values by, for example, a factor > 1. This would involve adding as few as one parameter to the models, which is something I’ve actually tried in the past. I may relook at that.

One interesting feature of the previous two graphs is the rather obvious systematic trend with radius of both SFR density and specific star formation rate, as shown more directly below taken from the first set of model runs:

sfr_ssfr_d_8479-12701 — NGC 4889 (MaNGA plateifu 8479-12701) Σ_SFR and SSFR vs. distance from IFU center

Are these real trends? I don’t know, but I don’t see an obvious reason why they might be spurious features of the models. In normal star forming galaxies I encounter trends with radius in both directions and sometimes no trend at all.

As a final and related aside there was a paper by Sedgwick et al. that showed up on arxiv not long ago that presented estimates of star formation rates of early type galaxies from observations of core collapse supernovae carefully matched to host galaxies with high confidence morphological classifications. To oversimplify their conclusions they found that typically massive ellipticals might have specific star formation rates ∼ 10^-11 / yr, which is somewhat higher than usually supposed. As I mentioned in my last post my models will always have some contribution from young stars and I typically get central estimates of SSFR > ∼ 10^-11.5 even in galaxies with no hint of emission (as is the case with this Coma sample). This particular galaxy has a total stellar mass within the IFU of ∼ 10^11.5 M_⊙ , so it could be forming stars at a rate of ∼ 1 M_⊙ / yr.

Well, I think I have one more post to write before the SDSS DR17 release.

2021-05-27

A little more on nonparametric line of sight velocity distribution modeling – is regularization needed?

A while back I completed LOSVD models for 3348 spectra in the 33 Coma Cluster galaxies I chose for an initial sample. I want to look briefly at a couple summary statistics from the models. For each sample in the posterior I calculate first and second moments of the velocity distribution, and from those I calculate means and standard deviations of velocity offsets and velocity dispersions. Recall from the earlier posts that wavelengths are in the spectrum rest frame with peculiar velocities estimated by fitting a set of eigenspectra to the data. The first plot below is the mean velocity offset with errorbars ± 1 standard deviation versus the signal to noise in each spectrum. The horizontal line is the overall median of 5.25 km/sec. This is less than 1/10th the width of a wavelength bin and, I think, consistent with the absolute wavelength calibration accuracy claimed by the MaNGA team. From an eyeball analysis there doesn’t appear to be any trend in the mean with S/N, but the dispersion in estimates increases as the data quality gets worse. This seems unlikely to be a real problem. Two outliers cut off from the graph had mean velocity offsets of ≈ 200 km/sec, which is only 3 wavelength bins.

voff_v_snr — Mean velocity offset and standard deviation of mean vs. spectrum S/N for 33 passively evolving Coma Cluster galaxies. Solid horizontal line is median offset.

Possibly more concerning is that the mean velocity dispersion also shows a systematic trend with S/N:

vdisp_v_snr — Mean velocity dispersion and standard deviation of mean vs. spectrum S/N for 33 passively evolving Coma Cluster galaxies.

Of course there is a wide range of velocity dispersions since there’s a range of galaxy masses in this sample, but each galaxy shows a similar trend. This matters because, of course, S/N correlates strongly with distance from the nucleus which is usually the IFU center and this in turn leads to potentially spurious correlations with distance.

MaNGA spectrum S/N vs. distance from IFU center in kpc. — 33 passively evolving Coma Cluster galaxies

For example here are results for the cD galaxy NGC 4889 with MaNGA plateifu 8479-12701. This has the highest overall velocity dispersion in the sample by a fair margin as seen in the plots above. Plotting the estimated velocity dispersion against distance from the IFU center shows an apparent systematic increase¹:

NGC 4889 (MaNGA plateifu 8479-12701) – mean velocity dispersion vs. radius per nonparametric LOSVD fit.

Now this could be a real trend: my recollection is the outskirts of cD galaxies have essentially the velocity dispersion of the clusters they live in, which is taken as strong evidence that they grow by cannibalism. But the IFU only covers the inner part of this galaxy and in any case the confounding effect of the correlation between S/N and modeled velocity dispersion prevents any conclusion. Just for comparison here is the same relation using the single gaussian estimates from the preliminary maximum likelihood fits:

NGC 4889 (MaNGA plateifu 8479-12701) – velocity dispersion vs. radius per maximum likelihood fit.

So, if we’re interested in kinematics or dynamics some regularization with an informative prior seems advisable. What’s not so clear is whether this matters in SFH modeling, which as I’ve said many times is what most interests me. There’s one way to find out…

2021-04-20

Confronting SFH models with observables – some results for normal disk galaxies

I’ve posted versions of some of these graphs before for both individual galaxies and a few larger samples, but I think they’ve all been unusual ones. I recently managed to complete model runs on 40 of the spirals from the normal barred and non-barred sample I discussed back in this post. The 20 barred and 20 non-barred galaxies in the sample aren’t really enough to address the results in the paper by Fraser-McKelvie that was the starting point for my investigation and more importantly the initial sample was chosen entirely at my whim. Unfortunately I don’t have the computer resources to analyze more than a small fraction of MaNGA galaxies. The sampling part of the modeling process takes about 15 minutes per spectrum on my 16 core PC (which is a huge improvement) and there are typically ~120 binned spectra per galaxy, so it takes ~30 hours per galaxy with one PC running at full capacity. I should probably take up cryptocurrency mining instead.

This sample comprises 5086 model runs with 2967 spectra of non-barred and 2119 of barred spirals. For some of the plots I’ll add results for 3348 spectra of 33 passively evolving Coma cluster galaxies.

Anyway, first: the modeled star formation rate density versus the rate predicted from the Hα luminosity density, which is easily the most widely used star formation rate calibrator at optical wavelengths. The first plot below shows all spectra with estimates for both values. Red dots are (non-barred) spirals, blue are barred. Both sets of quantities have uncertainties calculated, but I’ve left off error bars for clarity. Units on both axes are log₁₀(M_☉/yr/kpc²). I adopted the relation log(SFR) = log(L_Hα) – 41.26 from a review by Calzetti (2012), which is the straight line in these graphs. That calibration is traceable back to Kennicutt (1983), which as far as I know has never been revisited except for small adjustments to account for changing fashions in assumed stellar initial mass functions. In the left panel of the plot below Hα is uncorrected for attenuation. In the right it’s corrected using the modeled stellar attenuation, which as I noted some time ago will systematically underestimate the attenuation in H II regions. Not too surprisingly almost all points lie above the calibration line — the SFH models include a treatment of attenuation that might be too simple but still does make a correction for starlight lost to dust. The more important observation though is there’s a pretty tight relationship between modeled SFR density and estimated Hα luminosity density that holds over a nearly 3 order of magnitude range in both. The scatter around a simple regression line in the graphs below is about 0.2 dex. It’s not really evident on visual inspection but the points do shift slightly to the right in the right hand plot and there’s also a very slight reduction in scatter. These galaxies are actually not especially dusty, with an average model optical depth of around 0.25 (which corresponds to E(B-V) ≈ 0.07).

sfr_ha_40spirals — SFR density vs. prediction from Hα luminosity for 40 normal spirals. (L) Hα luminosity uncorrected for attenuation. (R) Hα corrected using estimated attenuation of stellar component.

To take a more refined look at this I limited the sample to regions with star forming emission line ratios using the standard BPT diagnostic based on [O III]/Hβ vs. [N II]/Hα. I require at least a 3σ detection in each line to make a classification, so besides limiting the analysis to regions that are in fact (I hope) forming stars it allows correcting Hα attenuation for the observed Balmer decrement since Hβ is by construction at least nominally detected. Now we get the results shown in the plot below. Units and symbols are as before. Hα luminosity is corrected using the Balmer decrement assuming an intrinsic ratio of 2.86 and the same attenuation curve shape as returned by the model. The SFR-Hα calibration line is the thick red one. The blue lines with grey ribbons are from “robust” simple regressions using the function lmrob in the R package robustbase¹

Model estimates of star formation rate density vs. SFR predicted from Hα luminosity density.

So the model SFR density straddles the calibration line, but with a distinct tilt — regions with relatively low Hα luminosity have higher than expected star formation. To quantify this here is the output from the function lmrob:

Call:
lmrob(formula = sigma_sfr_m ~ sigma_sfr_ha, data = df.sfr)
 \--> method = "MM"
Residuals:
      Min        1Q    Median        3Q       Max 
-3.862996 -0.142375  0.004122  0.137030  1.305471 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -0.174336   0.019224  -9.069   <2e-16 ***
sigma_sfr_ha  0.785954   0.009948  79.008   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Robust residual standard error: 0.2097 
Multiple R-squared:  0.7402,	Adjusted R-squared:  0.7401 
Convergence in 10 IRWLS iterations

Robustness weights: 
 6 observations c(781,802,933,941,2121,2330) are outliers with |weight| = 0 ( < 3.8e-05); 
 223 weights are ~= 1. The remaining 2424 ones are summarized as
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0107  0.8692  0.9525  0.9020  0.9854  0.9990

I also ran my Bayesian measurement error model on this data set and got the following estimates for the intercept, slope, and residual standard deviation:


         mean      se_mean          sd       2.5%        25%        50%        75%      97.5%    n_eff      Rhat
b0 -0.1942387 1.943297e-04 0.018346806 -0.2312241 -0.2063781 -0.1943811 -0.1819499 -0.1589849 8913.379 0.9997482
b1  0.7767853 9.828814e-05 0.009436693  0.7579702  0.7706115  0.7768086  0.7830051  0.7949343 9218.014 0.9995628
s   0.2044701 3.837428e-05 0.003319280  0.1981119  0.2021872  0.2043949  0.2067169  0.2110549 7481.821 0.9997152

Almost the same! So, how to interpret that slight “tilt”? The obvious comment is that the model results probe a very different time scale — by construction 100 Myr — than Hα (5-10 Myr). As a really toy model consider an isolated, instantaneous burst of star formation. As the population ages its star formation rate will be calculated to be constant from its birth up until 100 Myr when it drops to 0, while its emission line luminosity declines steadily. So its trajectory in the plot above will be horizontally from right to left until it disappears. In fact in spiral galaxies in the local universe star formation is generally localized, usually along the leading edges of arms in grand design spirals. Slightly older populations will be more dispersed.

This can be seen pretty clearly in the SFR maps for two galaxies from this sample below. In both cases regions with high star formation rate track the spiral arms closely, but are more diffuse than regions with high Hα luminosity.

Second topic: the spectral region around the 4000Å “break” has long been known to be sensitive to stellar age. Its use as a quantitative specific star formation rate indicator apparently dates to Brinchmann et al. (2004)². More recently Bluck et al. (2020) used a similar technique at the sub-galactic level on MaNGA galaxies. Both studies use D4000 as a secondary star formation rate indicator, preferring Hα luminosity as the primary SFR calibrator with D4000 reserved for galaxies (or regions) with non-starforming emission line ratios or lacking emission. Oddly, I have been unable to find an actual calibration formula in a slightly better than cursory search of the literature — both of the cited papers present schematic graphs with overlaid curves giving the adopted relationships and approximate uncertainties. The Brinchmann version from the published paper is copied and pasted below.

In the two graphs below I’ve added data from the passively evolving Coma cluster sample comprising 3348 binned spectra in 33 galaxies. There are two versions of the same graphs. Individual points are displayed in the first, as before with error bars suppressed to aid (slightly) clarity. The second displays the density of points at arbitrarily spaced contour intervals. The straight line is the “robust” regression line calculated for the spiral sample only, which for the sake of completeness is

\( \log10(sSFR) = -7.11 (\pm 0.02) – 2.11 (\pm 0.015) D_n(4000)\)

d4000_ssfr_40spirals_asscatter — Model sSFR vs. measured value of D4000. 40 barred and non-barred spirals + 33 passively evolving Coma cluster galaxies.

Model sSFR vs. measured value of D4000. 40 barred and non-barred spirals + 33 passively evolving Coma cluster galaxies. — Model sSFR vs. measured value of D4000 (2D density version). 40 barred and non-barred spirals + 33 passively evolving Coma cluster galaxies.


Call:
lmrob(formula = ssfr_m ~ d4000_n, data = df.ssfr)
 \--> method = "MM"
Residuals:
       Min         1Q     Median         3Q        Max 
-0.9802409 -0.0916555 -0.0005187  0.0962981  7.1748499 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -7.10757    0.02009  -353.8   <2e-16 ***
d4000_n     -2.10894    0.01418  -148.7   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Robust residual standard error: 0.1384 
Multiple R-squared:  0.9043,	Adjusted R-squared:  0.9043 
Convergence in 13 IRWLS iterations

Robustness weights: 
 39 observations c(45,958,1003,1165,1200,1230,1249,1279,1280,1281,1282,1283,1294,1298,1299,1992,2040,2047,2713,2722,2723,2729,2735,2736,2974,3212,3226,3250,3667,3668,3671,3677,3685,3687,3688,3691,4056,4058,4083)
	 are outliers with |weight| <= 1.1e-05 ( < 2.1e-05); 
 418 weights are ~= 1. The remaining 4310 ones are summarized as
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
0.0001994 0.8684000 0.9514000 0.8911000 0.9850000 0.9990000

The relation between D4000 and sSFR as estimated by Brinchmann et al. 2004

All three groups follow the same relation but with some obvious differences in distribution. The non-barred spiral sample extends to higher star formation rates (either density or sSFR) than barred spirals, which in turn extend into the passively evolving range. The Coma cluster sample has a long tail of high D4000 values (or high specific star formation rates at given D4000) — this is likely because D4000 becomes sensitive to metallicity in older populations and this sample contains some of the most massive (and highest metallicity) galaxies in the local universe. Also, as I’ve noted before these models “want” to produce a smoothly varying mass growth history, which means that even the reddest and deadest elliptical will have some contribution from young populations. This seems to put a floor on modeled specific SFR of ∼10^-11.5 yr^-1.

Just to touch briefly on the paper by Fraser-McKelvie et al. barred spirals in this sample do have lower overall star formation than non-barred, with large areas in the green valley or even passively evolving. This sample is too incomplete to say much more. For the sake of having a visualization here is the spatially resolved Σ_SFR vs. Σ_M* relation. The dashed line is Bluck’s estimate of the star forming “main sequence,” which looks displaced downward compared to my estimates.

mstar_sfr_40spirals+33etg — Model SFR density vs. stellar mass density. 40 barred and non-barred spirals + 33 passively evolving Coma cluster galaxies.

Finally, here are a couple of grand design spirals, one barred and one (maybe) not to illustrate how model results track morphological features. In the barred galaxy note that the arms are clearly visible in the SFR maps but they aren’t visible at all in the stellar mass map, which does show the presence of the very prominent bar.

NGC 6001 – thumbnail with MaNGA IFU footprint

NGC 6001 (MaNGA plateifu 9041-12701) (L) Model SFR surface density (M) Hα luminosity density (R) sSFR

*NGC 5888- thumbnail with MaNGA IFU footprint*

NGC 5888 (MaNGA plateifu 9871-12702) (L) Model SFR surface density (M) Hα luminosity density (R) sSFR

9871-12702_stellar_mass_density — NGC 5888 (MaNGA plateifu 9871-12702) – Log model stellar mass density (M_sun/kpc²

I’m not sure how much more I’m going to do with normal spirals. As I’ve said repeatedly the full sample is much too large for my computing resources.

Next time (probably) I’m going to return to a very small sample of post-starburst galaxies, which I may also return to when the final SDSS public data is released.