M82 Chandra → SQUDE Mock Spectrum Tutorial

The three figures are deliberately separated. Figure 1 contains only Chandra data, the Chandra-RMF-folded total model, and its response-folded model components; Figure 2 contains only SQUDE mock data and its SQUDE-RMF model; Figure 3 is the only common-axis comparison of SQUDE mock data, SQUDE model, and Chandra-RMF model. No empirical polynomial or image-level scaling is used.

Figure 1 · Chandra4′×4′ ACIS PHA, 50 counts/bin, 458 displayed bins; total and every model component are folded through the Chandra response.

Figure 2 · SQUDE mock50 ks seeded fake_pha from the same Chandra best-fit source model through the SQUDE ARF/RMF.

Figure 3 · RMF controlThe source and SQUDE ARF are fixed; only redistribution is replaced by the Chandra RMF.

1. Chandra ACIS data + total model + model components

This is the original combined 4′×4′ Chandra ACIS spectrum: it contains no SQUDE mock data or SQUDE response. Black points are Chandra data; orange is the total model forward-folded through the Chandra RMF and rate-conservingly rebinned onto the same 458 data bins. Dashed/dotted curves are the five model components; each is independently folded through the same Chandra response and rebinned to the data bins, rather than plotted as an unconvolved source spectrum.

tbabs_Gal × [tbabs_wind × (vapec_cool + vapec_hot + 2 Gaussian line proxies) + tbabs_PL × powerlaw]

CX semantics: the fixed 0.777/1.234-keV Gaussians are phenomenological soft-line diagnostics/proxies for this response tutorial. They are not a complete multi-line physical charge-exchange model like Zhang et al. (2014), and do not support an independent CX abundance or CX flux-fraction inference.

Chandra ACIS data, Chandra-RMF-folded total model and model components — Figure 1. Chandra only: 458 group=50 data bins; black data, orange total model, cool/hot VAPEC, two CX line proxies, and absorbed power law. Every model curve is folded through the Chandra response.

Download 1-column PNG Download 2-column PNG

Scientific scope: the current CIAO 4.18 source-only baseline gives χ²_Gehrels/dof = 1125.65/444 = 2.535. It is a reproducible response-propagation input, not a final publication-grade M82 physical fit; the component curves only expose model decomposition and do not improve or hide this limitation.

2. SQUDE mock data + SQUDE model

The fitted source from Figure 1 is passed through SQUDE ARF v1.1.1 and RMF v1.1.2 using a 50 ks fake_pha. The Sherpa UI-session Poisson RNG is fixed by set_rng(numpy.random.default_rng(20260719)); this reproducible realization has 58,298 raw counts. The original uses group_counts(50); the new min30 version reuses the identical raw PHA and changes only the display layer to group_counts(30). Both are linear–linear.

set_rng(numpy.random.default_rng(20260719))
set_source(2, chandra_bestfit_model)
fake_pha(2, arf="SQUDE_rsp_v1.1.1.arf", rmf="SQUDE_rsp_v1.1.2.rmf",
         exposure=50000.0, grouped=False, method=poisson_noise)

SQUDE mock data and SQUDE model — Figure 2. SQUDE only: black is the new mock data and orange is the same source model folded through the SQUDE RMF.

min50 1-column min50 2-column min30 1-column min30 2-column

3. SQUDE mock + SQUDE model + Chandra-RMF model

This is the full-aperture three-object comparison; each regional section below now has a separate analogue. Black points remain the Figure-2 SQUDE mock data; orange remains the SQUDE-RMF model; black dash-dot is the same best-fit source redistributed through the Chandra RMF. Both models retain the same SQUDE ARF, so the difference is RMF redistribution only.

r^control_i = Σ_j R^Chandra_ij F_j A^SQUDE_j; then overlap-rebin conservingly to the SQUDE data grid.

Full-aperture min50 RMF control — Figure 3 grouping-sensitivity slider. Both sides use the same raw PHA, source, responses, seed, and control operator; only display grouping changes. The slider pair has identical x/y limits. The Chandra-RMF control is not a Chandra-data spectrum.

Full-aperture min30 RMF control — Figure 3 grouping-sensitivity slider. Both sides use the same raw PHA, source, responses, seed, and control operator; only display grouping changes. The slider pair has identical x/y limits. The Chandra-RMF control is not a Chandra-data spectrum.

min50 1-column min50 2-column min30 1-column min30 2-column min50 CSV min30 CSV

Three-region extension: North / Center / South

Each region uses its own Chandra PHA/ARF/RMF and has three scientifically separate figures. Figure A is real Chandra data plus response-folded total/components. Figure B is an independently seeded 50 ks SQUDE fake_pha plus its SQUDE-folded model. Figure C mirrors the full-aperture Figure 3: the same SQUDE mock, the SQUDE-RMF model, and a Chandra-RMF redistribution control at fixed SQUDE ARF. Figure C is not a Chandra-data spectrum. North/South retain the five original model components; Center uses the eight-epoch joint diffuse/CX-line-proxy/Fe-K plus epoch-variable XRB/ULX model. Every SQUDE panel retains the original min50 asset and adds a min30 version that changes display grouping only.

Region	Chandra bins	baseline rstat	0.3–4 keV thermal fraction	SQUDE raw counts / seed
North wind 80″×80″	176	1.096	95.8%	3,636 / 2026071901
Center starburst 40″×80″	459	1.200 joint	58.5%	27,040 / 2026071902
South wind 80″×80″	154	1.199	87.8%	4,916 / 2026071903

Center method and scope: the eight center epochs differ in count rate by a factor of 2.40, invalidating the merged-spectrum static fit (rstat=8.61). The replacement jointly fits all eight PHAs: diffuse VAPEC/CX-line-proxy/Fe-K parameters are shared, while each ObsID has an independent absorbed XRB/ULX normalization and effective absorption; the XRB slope is tied. The result is χ²_Gehrels/dof=2576.83/2147=1.200, Q=3.27×10⁻¹⁰, kT=0.709 keV, Γ_XRB=1.18, and an exposure-weighted 0.3–4 keV thermal fraction of 58.5%. The low Q means the formal null is still rejected: this is a substantially improved tutorial forward model, not a final physical fit. Broad-aperture point-source pile-up is not modeled separately and the legacy PHAs have no BACKFILE; a point-source-excised re-extraction remains preferred for diffuse-only inference.

Numerical validation and reproduction

Check	Result
Explicit Chandra RMF operator vs Sherpa native fold	p95 relative error = 2.45×10⁻¹⁵
Chandra total vs sum of Chandra-response-folded model components	p95 relative error = 2.83×10⁻¹⁵
SQUDE total vs sum of model components	p95 relative error = 5.92×10⁻¹⁶
Three-region Chandra component closure	p95 ≤ 3.42×10⁻¹⁵ in every region
Regional/eight-epoch explicit RMF operator vs Sherpa	p95 ≤ 2.79×10⁻¹⁵
Three-region SQUDE component closure	p95 ≤ 6.28×10⁻¹⁶ in every region
min50 → min30 displayed bins (0.5–1.7 keV)	Full 662→971; North 61→101; Center 297→464; South 83→139; unchanged raw PHA
Three-region Chandra-RMF control rate-conserving rebin	relative rate error ≤ 1.90×10⁻¹⁶

cd ~/program/M82
export ASCDS_OVERRIDE=1
source ~/software/ciao-4.18/bin/ciao.sh -q
export PFILES="$PWD/pfiles;$ASCDS_INSTALL/param:"
python scripts/make_m82_mock_tutorial_figure_set.py
python scripts/make_m82_three_region_joint_center_tutorial_figures.py

Download complete executable script

SQUDE M82

1. Chandra ACIS data + total model + model components

2. SQUDE mock data + SQUDE model

3. SQUDE mock + SQUDE model + Chandra-RMF model

Three-region extension: North / Center / South

North wind · 80″×80″

Center starburst · 40″×80″

South wind · 80″×80″

Numerical validation and reproduction