meeting 2025 05 12 n410 - JacobPilawa/TriaxSchwarzschild_wiki

Context

Doing some more follow up work on the additive polynomial behavior we are seeing with N57/N315/N410. I'm trying to pin down what exactly is leading to inflated moment values when switching off the additive polynomial.
Major Takeaways:
- There seems to be a clear trend that the size of the additive polynomial (for N57, N315, and N410) correlates with the difference in sigma between the adeg=-1 and adeg=0 cases, with adeg=-1 having "inflated" values.
- When limiting the fits to only the Barth library, the templates that are preferred are quite different, with the adeg=-1 cases seeming to consistenly prefer three templates, with adeg=0 being slightly more "evenly distributed."
- The quality of the fits between the adeg=-1 and adeg=0 are virtually identicaly in terms of both RMS and when visually inspecting the spectra.
- I also ran quite large tests where I fit every spectra with adeg=-1,0,1,2...,20 since there are a few papers below which do this. It does seem like there's quite a bit of variation in particular for orders >=8 or so. There does appear to be, in general, "flat" parts with polynomial orders around 1/2/3 in a great deal of the spectra.
- I've also tried running N57 with both the Barth stars alone and with the trimmed library Emily had passed my way, and I do seem to be finding a difference in kinematics when using the Barth library vs. the trimmed library for both the adeg=0 and adeg=-1 cases, but I need to look at these a bit closer still.
Where to go from here:
- I'm struggling a bit with how we salvage everything from here. I've looked through the pPXF routines and feel like I've played around with the knobs quite a bit, but can't seem to get a fixed set of robust results which agree in all cases (changing adeg/libraries/etc). I'm happy to keep running more tests to converge on something, or try any other avenues that come to mind.
- I'm currently trying to see if I can bound the adeg in the adeg=0 case to be within a small range around 0 to see if maybe it's just getting caught in a local minimum or something, but I am not too hopeful that will fix things. I'm also checking N315 and N410 with the trimmed libraries, but again, not sure that will give us any new information.

A little bit of background/literature review: I was trying to see if the additive/multiplicative polynomials have been studied before and found a few interesting papers highlighting their importance:
- Mehrgan+23 seems to encounter a similar phenomenon that we are seeing (in their section 3.3 for example). They state that, at least in their tests, the additive and multiplicative polynomials seem to change the recovered LOSVD shape when the templates used do not contain the "true" spectrum (they have a mock test setup here which allows them to test this exactly). In particular, they argue that polynomials add freedom to the fit to homogenise template mismatches in different spectral regions. So even if the fit is technically getting better in terms of RMS, they say: "The additive/multiplicative polynomials modify the effective template such that template mismatch in Mgb and the Fe features is actually increased. However it is increased in such a way that at the same time the mismatch is homogenized over the wavelength region such that in combination with a respectively distorted LOSVD the fit to the spectrum becomes overall much better."
- One of Cappellari's recent pPXF papers in Section 6.2 states that "I run models with both multiplicative and additive polynomials degree from mdegree=degree=-1 (i.e. using only attenuation and no polynomials) to degree 4 and found that the solution changes slightly without polynomials but quickly stabilizes as soon as one allows for a non-zero degree" and that his "standard" setup is using adeg=-1, and mdeg=2. This is slightly different than what he says in this paper, which suggest that "I adopt the default degree=4 additive polynomials, but my results are totally insensitive to this choice."
- The paper Chung-Pei had found which claims sub-percent precision is also slightly different, saying that they find stable results for a range of additive (order 5-7) and multiplicative (1-3) are suitable for the MUSE/KCWI/SDSS data, but they advocate for additive of degree 1 and multiplicative of degree = 0 for JWST data.
- Throughout all these works (and I think as we have come to understand), folks are saying that the additive polynomials are mostly used in cases where there is imperfect sky subtraction or additional light from something like an AGN.
A few other works I've found which seem to test adegree for their fits also find quite a bit of movement in their results:
- Appendix A finds a ~10 km/s difference depending on the additive polynomial choice, and they ultimately choose adeg=20 due to it "flattening out" in this region.
- Appendix A here seems to find that velocity dispersion consistently rises with additive polynomial degree, but they say that the smallest change occurs between adeg=10 to 30, so they adopt a value in that range.
- Figure 14 of this paper seems to show a trend similar to what we find, where sigma seems to be inflated for p=0 (no additive polynomial). They attribute this to "template mismatch"

Diagnostics:

First, here are some plots showing the difference in moment values (adeg=0 minus adeg=-1 cases) plotted as a function of the additive constant used in the fits. There's a very strong trend here indicating the the inflation of moments in the adeg=-1 case (negative values) correlates with the additive polynomial used in the fit. I've highlighted the 10 highest and 10 lowest difference cases for each moment to look at more closely below.
- The trend is strongest in sigma and seems to get increasingly weaker for the higher order moments, but it's absolutely still present even in the h8 panels.

N57	N315	N410

One thing I was interested in checking out -- do the spectra which most strongly disagree have appreciably different template weights? What about the spectra between the adeg=0 and adeg=-1 cases as a whole?
- So first, here's a comparison of the total template weights for both N57 and N315, and I've included a second set of plots comparing the weights for each individual spectrum:

N57	N315

And here are the template weights for the 10 individual high and low set of spectra in both cases. These plot may take a minute to load. **One thing that stands out to meet looking at the "low difference" cases -- it seems like scan603.fits is preferred in a lot of the adeg=-1 cases, but doens't make as frequent of an appearance in the adeg=0 cases.**

	N57	N315
high difference
low difference

Associated Spectra

And here's the spectra associated with the 10 high and the 10 low differences:

N57: High Differences

Adeg=0	Adeg=-1

N57: Low Differences

Adeg=0	Adeg=-1

N315: High Differences

Adeg=0	Adeg=-1

N315: Low Differences

Adeg=0	Adeg=-1

Sigma as a function of adeg for each spectrum

One thing I wanted to try was, for each spectrum, fit the data with a range of additive polynomials like some of the papers at the top do. I've done this for N315/N57, and will put plots below. Still need to look at this a bit more carefully/cross check with the actual spectra and template diagnositcs above.
- Note that the leftmost point in each panel has adeg=-1 (aka no additive polynomial).
Takeaways:
- For both galaxies, it seems like polynomials order ~8 and above lead to some quite erratic behavior in the kinematics. There are often huge jumps for these higher polynomial orders, or very large disagremeents with the lower order polynomials. It also seems like, for the most part, very high polynomial orders result in very low sigma values.
- For N57: it does seem like low order polynomials are the most stable, and it seems like the "peak stability" is around an order of 1, 2, or 3. Even then, however, there is still a bit of movement in the sigma values when changing the polynomial order, though it would be good to have a sense of the error bars on these fits, too. I'll try to run one of those cases this afternoon.
- For N315: this is a very similar story to N57, where low polynomials seem to be more stable than high order polynomials, but there are a few bins in particular for N315 which are all over the place, and we've seen these bins giving us some trouble in the past. Specifically bins 0, 19, and 21 have always been extremely weird (these are the three bins that we modified the Barth library for, actually), and they seem to be extremely erratic.

Sigma as a function of adeg for the N315 spectra. This may take a second to load.

Plot	Zoomed

And the same for N57

Plot	Zoomed

And once more for N410 -- note that this is using the symmetric binning scheme that Irina also used

Plot	Zoomed

Some Trimmed Template Library Testing

N57

I've started reprocessing the N57/N315 with the trimmed CAT library Emily sent earlier this week and will put up some diagnostics here as they come in.
Using the trimmed library, it seems like the adeg=0 case (our current fiducial N57 case) agrees better when swapping out the libraries but there is still quite a bit of scatter in both instances (the adeg=-1 and adeg=0 cases). The RMS of the spectra are virtually identical, and I'm not seeing anything too bizarre in the individual spectra which makes this all that much more frustrating.

Adeg=0 Library Comparison	Adeg=-1 Library Comparison

And here are side-by-sides of the RMS vs spectra number of these cases:

	Adeg=0	Adeg=-1
Barth
Trimmed

And I've included the large spectra fit plots here for the trimmed library fits. It may take a minute to load these

Adeg=0	Adeg=-1

N410

I've reprocessed N410 (symmetric binned spectrum to match Irina, also using only nGH = 6, also to match Irina). I've fit the data with the adeg=0, medg=3, startingguess=[0,200], bias=0.2. The difference between the two fits are the templates. In one case, I'm using the 15 stars from Barth 20002, and in the other case, I'm using the trimmed set of templates Emily had passed my way.
Here's 1-to-1 plots for the resulting kinematics:

1-to-1 Comparison

And here are the spectral fits themselves using the Barth library vs. Trimmed Library. It might take a minute to load these large plots.

Barth	Trimmed

I've also plotted the differences between the spectral fits here, which actually look quite similar across all spectra, but there are some quite significant differences in the moments that are preffered. Currently the sigma difference is included in the title to give a sense of the discrepency, but I don't see the same trends in the center (at least not as obviously) as we saw with N57 below:
- There does look to be a systematic "wiggle" though between the two template libraries. At least to me there seem to be ~5 noticeable peaks in the resdiuals here. Potentially this is a sign that we need a higher order polynomial here?

N410 Spectral Differences (Barth vs. Trimmed)

We can also look at the template distribution for N410 which is a bit interesting to look at. At least for N410, the templates that are being picked look very, very strange (check the side-by-side plot of the template spectra):

First, here are the template distributions for all the N410 bins

Barth Library	Trimmed Library

And here are the 15 most common templates between the two cases. Note that the Barth library only has 15 stars in the first place:

Barth Library Sums	Trimmed Library Sums

And lastly, here's a side-by side of the 15 most common spectra

Most Common Templates

05/16/2025 Spectra Work

After meeting with Emily yesterday, we decided that it's probably best to look at the actual difference between the spectra between the adeg=0 and adeg=-1 fits, hoping to maybe see features in the residuals which correlate with the sigma difference. At least for N57, it sort of seems like the central portion of the wavelength range has quite a large misfit between the two cases, and this seems to be correlated with the difference in sigma. This part of the spectrum does have some very strange sky lines in many of the spectra, and so I suspect that potentially masking larger fractions of this region near ~8600 Angstroms could potentially improve the situation. I'm running some of those tests now.
- I'm also making equivalent diagnostics when varying the template library to see if there are additional correlated features there, including correlations with features in the template spectra themselves.
For now, here's a large plot comparing the difference in the best-fitting preliminary spectra for the adeg=0 and adeg=-1 cases. Specfically, I'm plotting the difference between adeg=0 and adeg=-1. I've ordered them from the smallest difference to largest difference (basically in order of how extreme the inflation is):

N57

Given this, I wanted to see if we can isolate any of the difference to the mask itself, or if there are still other issues driving these differences. So I've refit N57 two more times, one in which I mask a large chunk of the "middle" part of the spectral range, and another where I fit the spectra without a mask at all. The diagnostics for these tests are below.

Testing Masking a Large Range in the Middle vs. No Mask

Here are the spectral fits when using the original mask, a large mask over the central region, and no mask on the data for the 10 spectra I had highlighted above (which had the largest differences between the adeg=0 and adeg=-1 cases. Note I've got two sets here, one which uses adeg=0 (fiducial case) and one that uses adeg=-1.