meeting 2025 06 20 n57 - JacobPilawa/TriaxSchwarzschild_wiki_6 GitHub Wiki

We had been working on the N57 spectra for a bit before receiving the N315 report. The diagnostics at the time are spread over a few different bullets, so I wanted to gather the latest N57 diagnostics onto this page. It will likely be a bit all over the place, but should give proper context on where we left off.

The diagnostics below are largely coming from the first 6 bullets of the N410 page (here). They were posted here originally since we were doing some bulk testing of N410/N57/N315 all together, and I hadn't created an N57 on the newest TriaxSchwarzschild wiki #6. I tried to trim down the relevant bullets from those pages to contain only the N57 content below.

Note that the original N57 page is located here.

Summary of the bullets below:

• 05/08 Page: Not many new diagnositcs here, but contained some useful links to past N57 diagnostic pages.
• 05/09 Page: Comparisons of some adeg=0 vs. adeg=-1 fits to N57; seemed like the adeg=-1 case were consistently elevated compared to the adeg=0 case.
• 05/12 Page: Literature search for polynomial diagnostics; plotting value of the polynomial vs. moment "inflation" which seems to be a pretty clear relationship; plotting sigma as a function of the additive degree for each spectrum showing that there is a "sweet spot" for adeg=1/2/3 or so, with polynomial degrees >8 or so being quite erratic; also some attempts at fitting the spectra with the "trimmed" library from Emily
  • This page also contained some comparisons of the spectra after masking a large portion of the wavelength range -- at the time, Emily and I had noticed that the central portion of the spectra seemed to disagree the most between the adeg=-1 and adeg=0 cases. We had hoped that masking a large part of the central part of the wavelength range would ameliorate this issue, but we didn't seem to have much success. It also seemed like the "size" of this discrepency roughly tracked with the sigma inflation, but it wasn't extremely clear why that was the case.
• 05/22 Page: I left out the diagnostics from this bullet since it wasn't the most optimal test. On this page, I had tried to iteratively trim away the highest weight templates until I converged on the Barth results. However, I had been trimming away the "top" weights rather than removing based on physical reasons (such as spetral type). The next bullet explored this a bit more systematically.
• 05/28 Page: This was a more principled approach to trimming the template library. Specficially I tracked down the spectral type for all stars in our CAT library, and tried to select only GKM (or GKM Main Sequence stars), but it still was giving a decent amount of scatter vs. Barth only vs. the full library. We hadn't discussed these results that much since the N315 reviewer report was returned to us.

Note that this page doesn't actually have new diagnostics, but references some of the N57 work we had done, so I included the relevant bits from that page here.

Checking out the additive and multiplicative polynomials a bit more carefully here since they seem to be behaving a bit weird.

It seems like we did do a bit of testing on the additive and multiplicative polynomials for NGC57

• Irina seems to have consistently used adeg=0, mdeg=3 in all of her fits (at least that is what is listed on BOX in some of her diagnostics files), so we had been generally defaulting to these values for our fits.
• The N57 results didn't appear at the time to be as sensitive to the polynomials, but I think we were more motivated by preserving the settings that Irina/Melanie had used rather than doing extensive testing between ade=0 and adeg=-1 here.

Takeaways:

• It seems I can do a pretty decent job of reproducing Irina's results using the symmetrically-binned data using the settings she lists on BOX/in Massive XIII.
• One thing I noticed, though, is that the settings that she uses for the Mitchell data appear to use a multiplicative degree of 7 for the data, but still uses an additive polynomial of degree 0. I've never reprocessed the Mitchell spectra so unsure how this was deteremined, or if this should be in the back of our mind when we compare the GMOS and Mitchell data near the overlapping region.
  • We used adeg=0 for N2693/N57, but for N315 we switched it off due to the additive polynomial being quite negative, but I don't think we took a lot of time to understand this or properly test this after we fixed all the spectral fitting issues.
• When I change the settings on BOX to leave off the additive polynomial, I get some tension in the kinematics. Turning the additive polynomial off seems to raise our moments relative to having the additive polynomial in the mix.

Doing some follow up work from the meeting yesterday on the additive polynomials for our old galaxies. I've gone back and refit the spectra using adeg=0 and adeg=-1 for N57, and have some diagnostics below. At this level it does seem like the adeg=-1 cases have elevated moments for N57. With that said, I'm still trying to sort out why this is the case, and if there is any way to justify our current choice of adeg=0 for N57 as we have in the 'publication' so far.

So to that end, I've reprocessed the N57 spectra with the settings used in their minimizations, changing only the additive polynomial degree between the two fits.

For N57, our final pPXF fits (currently in the paper) used:

• (Barth stars) + (bias=0.2) + (starting guess=[0,200]) + (adeg=0). The bullet on the 3/17 page which features fits with adeg=-1 were from my attempts at reconciling the new code with the old code. This was prior to fixing the starting guess bug in the new code. The first results for N57 after fixing the starting guess issue are on the 3/19 page.
• The 3/18 page is very close to the diagnostics below, showing the fits with adeg=0 and adeg=-1, but using the incorrect starting guess (it doesn't seem like the starting guess was as much of an issue for N57 since the spectra all "looked" fine at the time). You're correct that this pages though does seem to show a difference between the adeg=0 and adeg=-1 case, which will be a bit clearer in the plots below.

• In both cases, the adeg=-1 case are ever-so-subtly worse fit than the adeg=0 case, but this is unsurprising since adeg=0 is effectively a new degree of freedom for the fit.

Doing some more follow up work on the additive polynomial behavior we are seeing with N57. 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 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.

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"

• 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.

• So first, here's a comparison of the total template weights for both N57, and I've included a second set of plots comparing the weights for each individual spectrum:

• Note that the leftmost point in each panel has adeg=-1 (aka no additive polynomial).

• 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.

• Note that there are two categories which appear in the plot which are not actually spectral types. There are 10 stars which are not matched on SIMBAD (I can check these out more carefully but wanted to move forward for now), which get labelled as "N" due to being "Not Found" in the database. Theres another star that is listed as a type "kA9hF2mF2(IV)" star, which is the lowercase "k" entry.