Permitted lines

Extract O II and C II lines from MUSE
For the O II lines, we need to isolate the 4649 blend
For C II pure recomb lines
- We have 4620 supposedly ?!
  - Very weak and there may be another line at 4621
- Also 4803 but blended with N II and [Co II]
- 5342.40 - very weak
- 6151.43 - might be good
- 6461.96 - weak but should be clear
  - This is definitely the best bet for C II lines
  - Escalante:2012a have it being all recombination
  - Whereas 7231 and 7236 are 20 to 40% fluorescent in IC 418
N II lines
- These are generally weak and must be a mixture of recombination and fluorescence
Si II lines
- These are much stronger, also mixture
More O II lines from Manu/Adal
- 4609, 4610 - Escalante:2012a says is 100% recombination
  - Terms are in LK coupling scheme
    - 3d 2D5/2–4f F[4]o7/2
    - 3d 2D3/2–4f F[2]o5/2
  - Unfortunately, there is an [Fe III] line at 4607
  - Also N II 4607 but that is weaker
  - 4607 to 4610 are blended in Manu and MUSE
  - The O II lines are well separated from [Fe III] in Adal
  - Discussed further below
- 4596
[ ] Excitation of O II V1
- Multiplet (quartet) is 3s ^4P → 3p ^4D
  - Storey:2017a has more rigorous terminology
  - But backwards: UPPER → LOWER
  - 2s² 2p²(.³P) 3p .⁴D_o → 2s² 2p²(.³P) 3s .⁴P_e
  - 2s22p2(3P)3p 4Do - 2s22p2(3P)3s 4Pe
  - E.g., 4649.13 is index 8790
- Ground state is 2p3 ^4S
  - Resonant absorption 2p3 ^4S → 3d ^4P (429.650 → 429.716 Å)
    - so that is 2.12 Rydbergs
  - Followed by decay to 3p terms
  - Need to make a diagram and work out if it is feasible
- Velocity gradients in Big Arc will tend to make fluorescence more efficient
- Interestingly, the analogous N I multiplet is at 8680-8719
  - N I and O II are identical in electron configuration
  - We see all these lines nicely in the MUSE data
  - They are all at least 95% fluoresced
  - [ ] We could look at the equivalent of the 3d-4f lines in N I
Case of the 3d-4f lines
- These should not have a fluorescent component
  - except that maybe they might if intercombination lines are important
- But they give the same abundances as the other lines (in Eduardo HH 529 data)
- Strongest lines:
  - 4303.8: I ≈ 0.63e-4 Hb (Escalante:2013a)
    - Compare with 4649 ≈ 6.7e-4 Hb
      - ODell:2010a have 4959/Hb = 0.7 to 1.0 in slits 10 and 11, which cover area of Adal’s slit 6
      - Adal has 4649/4959 = 10 → 12 times 1e-4
      - Eduardo (cut 2) has I(4649.13) = 11.4 in nebula and 24 in shock !!
    - Eduardo 4959/Hb in cut 2
      - 1.15 in nebula
      - 1.67 in shock
    - Seen in Manu data - about 5 times weaker than 4317 and 4320 (3s ^4P - 3p ^4P)
      - Which are themselves about 4 times weaker than V1
      - E.g., Manu has 4649 = 1.13 x cont
      - I(4304) = 0.01 x cont, so 13 x weaker than 4649 => I(4304) = 0.77 1e-4 I(Hb)
      - Within the errors, this is consistent with Escalante predicted, especially if we add in the 4303.5 contribution: 0.09 + 0.63 = 0.72
    - Observed in Eduardo: I = 2.0 (cut 3) and 2.1 (cut 2 neb), and 4.6 (cut 2 shock) !!!
  - 4277 complex
    - Strongest component: 4275.5 with predicted I = 0.84
      - Blended with [Fe II] 4276.84 in Manu
      - Observed in Eduardo with observed I = 1.6
  - 4609.3: predicted I ≈ 0.66e-4 Hb (Escalante:2013a)
    - Also, weaker component at 4610.2
    - Seen in Manu, but blend with [Fe III] 4607
    - Very well isolated in Adal: I(4609) = 1e-4 I(4959)
    - So this has observed intensity that maybe is slightly higher than predicted (by about 30%)

What states can we have

3 outer electrons
Ground state is 2p^3 ^4S
- 2S+1 = 4 => S = 3/2 so all 3 spins are aligned
- L=0 so J = 3/2
Pumped state: one electron goes from 2p → 3d
- L = 0 → 1 for E1 transition so must be a ^4P state
- In fact only ^4P levels can be directly pumped from ground
  - At least I would have thought, although Escalante also mention ^4S → ^4D transition, which has Δ L = 2, so must be quadrupole
- So 2p^2 3d ^4P has L=1, S=3/2, J= 5/2, 3/2, 1/2

If we pump the 3d .⁴P level then we need the transition

3d .⁴P_e → 3p .⁴D_o in order to populate the upper level of V1

Storey has the following components:

IND	wav	2JI	2JF	Other	Manu
8494	3864.13	1	1	Si II 3863	Blend
8493	3872.44	1	3	[Ne III] 3869
8515	3874.09	3	1	He I 3878
8514	3882.45	3	3	H I 3889	?
8566	3893.52	5	3	H I 3889
8513	3896.30	3	5		faint
8565	3907.45	5	5		yes
8564	3926.58	5	7	He I 3927

Unfortunately, most will be blended with other lines

We should also get another route down via 3p .⁴S:

3d .⁴P_e → 3p .⁴S_o followed by 3p .⁴S_o → 3s .⁴P_e
- which ends at same lower level as V1

3d .⁴P_e → 3p .⁴S_o or 2s22p2(3P)3d 4Pe - 2s22p2(3P)3p 4So

IND	wav	2JI	2JF	Other	Manu	MUSE	Adal
8489	4890.86	1	3	[Fe II] 4890	Blend?	Blend?	weak but resolved
8507	4906.83	3	3	[Fe II] 4905	Blend?	Blend	Weak
8559	4924.53	5	3	He I 4922, [Fe III] 4925	Blend?	No	Possibly

3p .⁴S_o → 3s .⁴P_e or 2s22p2(3P)3p 4So - 2s22p2(3P)3s 4Pe

IND wav 2JI 2JF Other Manu

8730 3712.74 3 1 H I 3712 No

8729 3727.32 3 3 [O II] 3726 No

8728 3749.48 3 5 H I 3750 No
So this is the cursed multiplet - no chance of ever seeing it

The paper

Moved to its own repo
~/Dropbox/orion-oii-paper/

Summary of the types of O II lines and what they tell us

The singly-excited lines can be pumped by radiative recombination or fluorescence
- The low-L quartet transitions might have a fluorescent contribution
  - The s-pumped multiplets (descendants of 4s ^4P)
    - 4s ^4P → 3p ^4D
    - include V1: 3p ^4D → 3s ^4P
  - The d-pumped multiplets (descendants of 3d ^4P and 3d ^4D)
    - 3d ^4P,D → 3p ^4P
    - 3p ^4P → 3s ^4P
  - Note that the d-pumped lines have a small s-pumping contribution and vice-versa
- The high-L transitions should be pure recombination
  - They are described by LK coupling instead of LS coupling
  - mainly 4f D,F,G → 3d ^4P,D,F
- The low-L doublet transitions can also have fluorescence (maybe)
The core-excited lines are mainly dielectronic recombination
- But Escalante:2012a say that could also be other routes (including fluorescence)
- They are called with parentage other than ^3P in Fang:2013a
  - They all have parentage of ^1D
- Assuming that they are from DR, they can give T diagnostics

The four types of O++ temperature

T(CEL) : 4363 / 5007
- Strongly biased to high-T
- d R / d T > 0
T(ORL-CEL) : V1 Sum / 4959
- Mostly unbiased (slightly to high-T)
- d R / d T < 0
- R increases with fluorescence
- => T decreases with fluorescence
T(3d-4f) : V1 Sum / V48a Sum or 4649/4089
- Biased to low-T
- d R / d T > 0
- R increases with fluorescence
- => T increases with fluorescence
T(DR) : V1 Sum / V15 Sum or 4649/4591
- Mostly unbiased (slightly low-T)
- d R / d T < 0
- R increases with fluorescence
- => T decreases with fluorescence (?)
  - That is, assuming that V15 is not fluoresced

Expected T ordering from t^2 fluctuations

T(3d-4f) < T(DR) ~= T(ORL-CEL) < T(CEL)
Example: NGC 7009
- T(3d-4f) = 1000 K
- T(DR) = 3000 K
- T(ORL-CEL) = ?
- T(CEL) = 10,000 K

Expected T ordering from fluorescence

T(DR) < T(ORL-CEL) < T(CEL) < T(3d-4f)
- Example: Orion (Eduardo nebula)
  - T(DR) = 4500 K
  - T(ORL-CEL) = 8000 K
  - T(CEL) = 8500 K
  - T(3d-4f) = 10,000 K

Eduardo O II strengths

	4590.97	4595.96	4649	4649/4591	4275.55	4649/4276	4189.79	4649/4190	4276/4591	4089.29	4649/4089
Cut 1 shock			34.2	34.20 / 0		34.20 / 0		34.20 / 0	0/0		34.20 / 0
Cut 2 shock	4.2	2.0	25.8	6.14	2.8	9.21	4.7	5.49	0.67		25.80 / 0
Cut 3 shock	5.4		26.5	4.91		26.50 / 0	7.5	3.53	0.00		26.50 / 0
Cut 1 neb	2.7	2.2	11.2	4.15	1.4	8.00	2.3	4.87	0.52	2.5	4.48
Cut 2 neb	2.4	2.0	12.2	5.08	1.7	7.18	2.0	6.10	0.71	3.1	3.94
Cut 3 neb	2.4	1.5	12.9	5.38	1.6	8.06	2.1	6.14	0.67	2.6	4.96
Cut 4	2.5	2.0	12.6	5.04	1.9	6.63	2.3	5.48	0.76	2.5	5.04

Te, ne diagnostics from O II

Eduardo uses components of V1 as density indicator
- This is fine and is what everyone does
Then they use 3d-4f lines 4089.29, 4275.55 as Te indicators
- But 4089.29 is disfavored because it is affected by a ghost
- Why these? The T sensitivity is not very high
- Variation in ratio between 3000 → 10000 K (Case B @ 1e4 pcc)
  1. 4649/4276: 5.58 → 7.52 - factor of 1.35 increasing with T
    - 3s-3p / 3d-4f
  2. 4649/4089: 2.99 → 3.98 - factor of 1.33 increasing with T
    - 3s-3p / 3d-4f
  3. 4649/4190: 5.59 → 3.43 - factor of 1.63 decreasing with T
    - 3s-3p / DR
  4. 4649/4591: 6.00 → 3.70 - factor of 1.62 decreasing with T
    - 3s-3p / DR
  5. 4276/4591: 1.08 → 0.49 - factor of 2.20 decreasing with T
    - 3d-4f / DR
- So, T-diagnostics 1 and 2 are what Eduardo uses
  - He gets values of 6.6 to 9.2 for 4649/4276, which would actually suggest T > 16,000 K for HH 529-II shock
  - Average nebula is 7.47 +/- 0.34, which gives 9800 +/- 1500 K, which is a bit high
  - Uncertainties are quite high however, so this is probably consistent with what is shown in Fig 8 of HH 529 paper
  - If there were a 20% fluorescence contribution to V1 as suggested by MUSE analysis, then this would bring the nebula ratio down to 6.23 +/- 0.28, which implies T = 5300 +/- 600 K, which is now a bit on the low side
  - For 4649/4089, average nebula is 4.60 +/- 0.25, which implies T = 15,200 +/- 2000 K
  - Again, with a 20% fluorescence contribution to 4649, this is reduced to 3.83 +/- 0.21 = T = 8900 +/- 1700 K
  - So averaging the 4649/4276 and 4649/4089 gives 12,500 +/- 2700 K, or 7100 +/- 2000 K after correcting for 20% fluorescence
- T-diagnostics 3 and 4 are what Fang:2013a use for NGC 7009
  - Nebula has 4649/4591 = 4.15 → 5.38 = 4.9 +/- 0.3 => T = 4500 +/- 500 K
  - Nebula has 4649/4190 = 4.87 → 6.14 = 5.65 +/- 0.30 => T = 3100 +/- 200 K
  - With the 20% fluorescence correction, these become:
    - 4649/4591 = 4.1 +/- 0.2 => T = 7000 +/- 1000 K
    - 4649/4190 = 4.71 +/- 0.25 => T = 3900 +/- 500 K
  - This is better, but still too low, so maybe the fluorescence correction should be higher
- Finally, T-diagnostic 5 should eliminate dependence on fluorescence (unless the DR lines are fluoresced)
  - Nebula 4276/4591 = 0.67 +/- 0.05 => T = 6000 +/- 700 K
  - So this is still a bit on the low side, especially since it is a lower limit if there is fluorescent contribution to V15 4591
Manu results
- 4649/4591 is noisy but varies from 9.0 +/- 2.0 in inner nebula to 6.0 +/- 3.0 in outer nebula
  - V1-sum fractional excess is about 1.0 close to Trapezium and is about 0.5 in Big Arc
  - So this could mean that corrected 4649/4591 = 4.0 in both cases => T = 7500 +/- 4000 K
  - Yes, that makes sense
Adal results

Theoretical recombination line ratios from Storey for Case B @ 1e4 pcc

The 3d-4f lines have a steeper fall of emissivity with T than the V1 lines
- This gives one type of T diagnostic, such as 4649/4089 (V1/V48a) or 4649/4276 (V1/V67)
- E.g., Fig 17 of Fang:2013a, where the theoretical curve agrees reasonably well with what I have calculated from Storey (presumably because they use the same source)
  - Note that they measure 4649/4089 = 2.5 for Saturn Nebula, which is much lower than in Orion, and which implies a low T ≈ 1000 - 1500 K
The ^1D parentage lines (core-excited) have an emissivity that rises with T (dielectronic recombination)
- This gives the second type of T diagnostic, such as 4649/4591 (V1/V15) or 4649/4190 (V1/V36)
- There are also M101 and M105 lines, but these are either weak or masked by other lines in Manu spectra
- Also 4347 line (V16), but it is stuck among stronger lines of V2 (3s-3p ^4P) at 4345 and 4349

log10(T)	4089.29	4275.55	4649.13	4649/4276	4649/4089	4189.79	4189.58	4649/4190	4590.97	4649/4591	4276/4591
2.000	1.229E-23	7.288E-24	2.827E-23	3.88	2.30	1.680E-26	6.926E-28	1616.11	7.061E-26	400.37	103.21
2.100	9.925E-24	5.993E-24	2.270E-23	3.79	2.29	1.362E-26	5.075E-28	1606.80	5.696E-26	398.53	105.21
2.200	8.023E-24	4.872E-24	1.824E-23	3.74	2.27	1.105E-26	3.777E-28	1596.12	4.627E-26	394.21	105.30
2.300	6.351E-24	3.870E-24	1.443E-23	3.73	2.27	8.854E-27	2.810E-28	1579.64	3.731E-26	386.76	103.73
2.400	5.110E-24	3.080E-24	1.160E-23	3.77	2.27	7.259E-27	2.183E-28	1551.36	3.091E-26	375.28	99.64
2.500	4.097E-24	2.435E-24	9.339E-24	3.84	2.28	6.212E-27	1.909E-28	1458.56	2.626E-26	355.64	92.73
2.600	3.286E-24	1.923E-24	7.555E-24	3.93	2.30	6.740E-27	2.900E-28	1074.68	2.444E-26	309.12	78.68
2.700	2.639E-24	1.521E-24	6.150E-24	4.04	2.33	1.204E-26	8.153E-28	478.40	2.859E-26	215.11	53.20
2.800	2.120E-24	1.205E-24	5.031E-24	4.18	2.37	2.754E-26	2.295E-27	168.63	4.359E-26	115.42	27.64
2.900	1.701E-24	9.577E-25	4.130E-24	4.31	2.43	5.714E-26	5.130E-27	66.32	7.246E-26	57.00	13.22
3.000	1.368E-24	7.610E-25	3.406E-24	4.48	2.49	9.909E-26	9.173E-27	31.46	1.129E-25	30.17	6.74
3.100	1.098E-24	6.051E-25	2.817E-24	4.66	2.57	1.446E-25	1.357E-26	17.81	1.562E-25	18.03	3.87
3.200	8.801E-25	4.809E-25	2.334E-24	4.85	2.65	1.834E-25	1.727E-26	11.63	1.926E-25	12.12	2.50
3.300	7.032E-25	3.816E-25	1.934E-24	5.07	2.75	2.087E-25	1.952E-26	8.47	2.157E-25	8.97	1.77
3.400	5.595E-25	3.019E-25	1.603E-24	5.31	2.87	2.193E-25	2.012E-26	6.70	2.244E-25	7.14	1.35
3.500	4.435E-25	2.381E-25	1.328E-24	5.58	2.99	2.182E-25	1.934E-26	5.59	2.214E-25	6.00	1.08
3.600	3.495E-25	1.871E-25	1.099E-24	5.87	3.14	2.092E-25	1.764E-26	4.84	2.107E-25	5.22	0.89
3.700	2.743E-25	1.463E-25	9.083E-25	6.21	3.31	1.953E-25	1.547E-26	4.31	1.954E-25	4.65	0.75
3.800	2.142E-25	1.139E-25	7.502E-25	6.59	3.50	1.786E-25	1.318E-26	3.91	1.776E-25	4.22	0.64
3.900	1.665E-25	8.827E-26	6.197E-25	7.02	3.72	1.600E-25	1.098E-26	3.62	1.584E-25	3.91	0.56
4.000	1.289E-25	6.812E-26	5.124E-25	7.52	3.98	1.402E-25	8.974E-27	3.43	1.385E-25	3.70	0.49
4.100	9.936E-26	5.236E-26	4.255E-25	8.13	4.28	1.201E-25	7.217E-27	3.34	1.184E-25	3.59	0.44
4.200	7.644E-26	4.015E-26	3.568E-25	8.89	4.67	1.004E-25	5.714E-27	3.36	9.901E-26	3.60	0.41
4.300	5.915E-26	3.094E-26	3.059E-25	9.89	5.17	8.202E-26	4.456E-27	3.54	8.115E-26	3.77	0.38
4.400	4.707E-26	2.448E-26	2.740E-25	11.19	5.82	6.552E-26	3.424E-27	3.97	6.575E-26	4.17	0.37

Potential diagnostics of fluorescence

Other 3d-4f lines that Eduardo uses in his Table 13

Values given as (Storey XXX) are effective recomb rates for Case B at 1e4 K and 1e4 pcc
4087.15
- Manu sees blend at 4085
  - 4085.11 3p ^4D - 3d ^4F (feeds into V1) (Storey 6.2e-26)
  - 4086.59 3d ^4F - 4f D 2[2] (Storey 8.5e-28)
  - 4086.71 3d ^4F - 4f D 2[2] (Storey 3.6e-29)
  - 4087.15 3d ^4F - 4f G 2[3] (Storey 4.4e-26)
  - 4087.56 3p ^2P - 4s ^4P (Storey 1.4e-31) intercombination
- Eduardo sees 4085.11 and 4087.15 with same strength in nebula: 1.8e-4 Hb
4089.29
- Manu sees blend
  - 4088.27 3d ^4F - 4f G 2[5] (Storey 2.4e-27)
  - 4089.29 3d ^4F - 4f G 2[5] (Storey 1.29e-25)
  - 4090.27 3p ^2D - 4d ^4F (Storey 2.5e-30)
  - 4092.93 3p ^4D - 3d ^4F (Storey 4.2e-26)
4095.64
4097.26
4275.55

Diagnostics from Bastin thesis

These have overlap with other lines, but he has particular combinations, which he chooses because:
1. Limited case sensitivity - I need to check up on this for other ratios
2. Unaffected by blending
3. Stronger lines
Ones he chooses are:
4661/4089
- This is V1/3d-4f, so should be diagnostic of T and fluorescence, but also weakly of density
4414/4089
- 4414.9 is a doublet line in 3s-3p, so will be rad recomb plus maybe fluorescence
- In Orion it is in blend with [Fe II] 4413.78, which is slightly brighter

O II V1 / 4610

This can be measured in Adal slits easily
Trickier in Manu because of blend with [Fe III] 4607
Take 4649 / 4609 to be definite
4610 is a blend:
- 4609.44 3d.²D_e - 4f F 2[4]
- 4610.20 3d.²D_e - 4f F 2[2]
4649 is
- 4649.13 V1 3s.⁴P - 3p.⁴D_o
Adal measurements - units of 1e-4 I(4959)

Zone 4649 4610 4649/4610

A 11.4 1.2 9.50

B 12.8 1.0 12.80

C 12.8 1.0 12.80

D 10.6 1.0 10.60

E 10.7 1.1 9.73

F 10.4 1.2 8.67
UVES observations (Adal HH202 and Eduardo HH529 are missing the 4610 lines)

Storey recomb ratios

Case B, 3000-1e4 K, 1e4 pcc:

T	4649.13	4609.44	4610.20	4649/4610
3.5	1.328E-24	1.989E-25	5.794E-26	5.17
3.6	1.099E-24	1.555E-25	4.562E-26	5.46
3.7	9.083E-25	1.210E-25	3.578E-26	5.79
3.8	7.502E-25	9.373E-26	2.793E-26	6.17
3.9	6.197E-25	7.231E-26	2.170E-26	6.59
4.0	5.124E-25	5.553E-26	1.678E-26	7.09

Case B, 3000-1e4 K, 1e3 pcc:

T	4649.13	4609.44	4610.20	4649/4610
3.5	9.742E-25	1.844E-25	5.151E-26	4.13
3.6	7.725E-25	1.396E-25	3.960E-26	4.31
3.7	6.114E-25	1.053E-25	3.030E-26	4.51
3.8	4.832E-25	7.947E-26	2.303E-26	4.71
3.9	3.823E-25	5.946E-26	1.746E-26	4.97
4.0	3.031E-25	4.432E-26	1.318E-26	5.27

Case B, 3000-1e4 K, 1e5 pcc:

T	4649.13	4609.44	4610.20	4649/4610
3.5	1.407E-24	2.046E-25	5.929E-26	5.33
3.6	1.172E-24	1.610E-25	4.683E-26	5.64
3.7	9.757E-25	1.262E-25	3.684E-26	5.98
3.8	8.122E-25	9.859E-26	2.885E-26	6.37
3.9	6.758E-25	7.661E-26	2.248E-26	6.82
4.0	5.627E-25	5.922E-26	1.743E-26	7.34

O II 4317 / 4304

Ratio
- 4317.0: 3s.⁴P_1/2 - 3p.⁴P_3/2^o
  - Minor contribution from 4317.7 3d-4f
  - Also 4319.6 of same multiplet
- 4303.8: 3d.⁴P_5/2 - 4f.D[3]^o_5/2
Ratio from Escalante:2013a
- With fluorescence: 1.58/0.63 = 2.51
- Just recombination: 0.605 1.58/0.63 = 1.52

[X] Should check theoretical ratio from Storey

Full range is 0.56 to 1.2

Case B, 3000-1e4 K, 1e4 pcc:

T	4303.82	4317.14	4317/4303
3.5	2.236E-25	1.864E-25	0.83
3.6	1.768E-25	1.534E-25	0.87
3.7	1.397E-25	1.264E-25	0.90
3.8	1.100E-25	1.042E-25	0.95
3.9	8.619E-26	8.586E-26	1.00
4.0	6.700E-26	7.073E-26	1.06

Case B, 3000-1e4 K, 1e3 pcc:

T	4303.82	4317.14	4317/4303
3.5	4.019E-25	2.261E-25	0.56
3.6	3.309E-25	1.876E-25	0.57
3.7	2.718E-25	1.557E-25	0.57
3.8	2.222E-25	1.292E-25	0.58
3.9	1.804E-25	1.071E-25	0.59
4.0	1.453E-25	8.883E-26	0.61

Case B, 3000-1e4 K, 1e5 pcc:

T	4303.82	4317.14	4317/4303
3.5	2.051E-25	1.827E-25	0.89
3.6	1.603E-25	1.501E-25	0.94
3.7	1.251E-25	1.234E-25	0.99
3.8	9.731E-26	1.013E-25	1.04
3.9	7.529E-26	8.326E-26	1.11
4.0	5.779E-26	6.836E-26	1.18

Ratio from Manu
- As high as 3
- As low as 1
Ratio from Eduardo
- cut 2 nebula: 0.028/0.021 = 1.33
- cut 2 shock: 0.071/0.046 = 1.54
- cut 3 nebula: 0.026/0.020 = 1.30
- cut 1 nebula: 0.019/0.018 = 1.06
- cut 4 nebula: 0.027/0.026 = 1.04
Ratio from Adal HH202
- Nebula: 0.021/0.027 = 0.78 +/- 0.3
- Shocks: 0.045/0.016 = 2.8 +/- 1
So in summary, the ratios are generally higher than the recombination predictions

Analyze the pumping line

This is now in a separate file:
- oii-fluorescence.org

Revisiting the Adal and Manu analysis

The Adal spectra are plotted for 6 different sections of Slit 6

x range

0:40 Red bay

40:50

50:62

67:80

80:95

95:154
- Numbers x correspond to pixels of length 1.2 arcsec along slit
- Note that 62:67 is omitted - corresponds to 159-350
  - x=65 → 78 arcsec from left edge
- Total length = 154 1.2 = 185 arcsec

Adal’s V1 line strengths

In units of 1e-4 I(4959) ≈ 1e-4 I(Hb) in the bright zones
4649: 10 → 12
4642: 7 → 8
These are about 50% higher than predictions of Escalante:2012a for IC 418
More details are given down here in Ratios within the V1 multiplet
- Sum V1 = 32 → 36 in these units
- If interpreted in terms of recombination, this implies T = 7500 → 7750 K

Extract maps from MUSE cubes

This is copied from Raman project
- Remove continuum from cube
But we change the wavelengths because we are working with wavsec0
- Total range is 4595 → 5191 Å

import sys
import numpy as np
from astropy.io import fits
from astropy.wcs import WCS
from numpy.polynomial import Chebyshev as T
import itertools

try:
    DATADIR = sys.argv[1]
    SUFFIX = sys.argv[2]
    OUTDIR = sys.argv[3]
except IndexError:
    sys.exit(f"Usage: {sys.argv[0]} DATADIR SUFFIX OUTDIR")

infile = f"muse-hr-data-wavsec0{SUFFIX}.fits"
hdu = fits.open(f"{DATADIR}/{infile}")["DATA"]
w = WCS(hdu)
nwav, ny, nx = hdu.data.shape
wavpix = np.arange(nwav)

# Two pairs of adjacent sections for the true continuum

# Wavelength sections of clean continuum (lots of small sections)
clean_sections = [
    [4610.0, 4616.0], [4624.0, 4627.0], # between C II, N II, O II
    [4690.0, 4697.0], [4720.0, 4730.0], # between He I and Ar IV
    [4746.0, 4750.0], [4760.0, 4765.0], # between Fe III lines
    [4782.0, 4786.0], [4820.0, 4830.0], # next to Hb
    [4910.0, 4916.0], [5060.0, 5080.0], # to the red
    [5090.0, 5100.0], [5170.0, 5185.0], # to the red
]

cont_slices = []
for wavs in clean_sections:
    wavs = 1e-10*np.array(wavs)
    _, _, wpix = w.world_to_pixel_values([0, 0], [0, 0], wavs)
    cont_slices.append(slice(*wpix.astype(int)))


# Use median over each section to avoid weak lines
cont_maps = np.array([np.median(hdu.data[_, :, :], axis=0) for _ in cont_slices])
cont_wavpix = np.array([np.median(wavpix[_], axis=0) for _ in cont_slices])
# Inefficient but simple algorithm - loop over spaxels
bgdata = np.empty_like(hdu.data)
for j, i in itertools.product(range(ny), range(nx)):
    # Fit polynomial to BG
    try:
        p = T.fit(cont_wavpix, cont_maps[:, j, i], deg=2)
        # and fill in the BG spectrum of this spaxel
        bgdata[:, j, i] = p(wavpix)
    except:
        bgdata[:, j, i] = np.nan



for suffix, cube in [
        ["cont", bgdata],
        ["cont-sub", hdu.data - bgdata],
        # ["cont-div", hdu.data/bgdata],
]:
    outfile = infile.replace(".fits", f"-{suffix}.fits")
    fits.PrimaryHDU(header=hdu.header, data=cube).writeto(
        f"{OUTDIR}/{outfile}", overwrite=True)
    print(f"Written {outfile}")

python muse/subtract-continuum-wavsec0.py $DATADIR $SUFFIX $OUTDIR

Now we do a simple extraction of the whole V1 multiplet

import sys
import numpy as np
from astropy.io import fits
from astropy.wcs import WCS

try:
    DATADIR = sys.argv[1]
    SUFFIX = sys.argv[2]
    OUTDIR = sys.argv[3]
except IndexError:
    sys.exit(f"Usage: {sys.argv[0]} DATADIR SUFFIX OUTDIR")

infile = f"muse-hr-data-wavsec0{SUFFIX}-cont-sub.fits"
outfile = f"o_ii-v1-sum{SUFFIX}.fits"
hdu = fits.open(f"{DATADIR}/{infile}")["DATA"]
w = WCS(hdu)
nwav, ny, nx = hdu.data.shape


# Wavelength sections of O II V1 multiplet
v1_sections = [
    [49, 71], [79, 83], [90, 102]
]

im = np.zeros((ny, nx))
for i1, i2 in v1_sections:
    im += np.sum(hdu.data[i1:i2, :, :], axis=0)

fits.PrimaryHDU(header=w.celestial.to_header(), data=im).writeto(
        f"{OUTDIR}/{outfile}", overwrite=True)
print(f"Written {outfile}")

python muse/extract-o_ii-v1-sum.py $DATADIR $SUFFIX $OUTDIR

Extraction of multiplet in 4 sections

pix1	pix2	wav1	wav2	O II V1 lines	Others	Label
38	44	4627.3	4632.4		N II 4631, [Ni II] 4628	N_II-4631
44	49	4632.4	4636.65		N III 4634	N_III-4634
49	62	4636.65	4646.0	4639, 4642	N III 4641, N II 4643	O_II-V1-4639-42
62	71	4646.0	4654.5	4649, 4651		O_II-V1-4649-51
79	83	4662.15	4664.7	4662	(Red wing of 4658)	O_II-V1-4662
90	102	4671.5	4680.85	4674, 4676		O_II-V1-4674-76
101	119	4679.15	4694.45		He II 4686 abs	He_II-4686

import sys
import numpy as np
from astropy.io import fits
from astropy.wcs import WCS

try:
    DATADIR = sys.argv[1]
    SUFFIX = sys.argv[2]
    OUTDIR = sys.argv[3]
except IndexError:
    sys.exit(f"Usage: {sys.argv[0]} DATADIR SUFFIX OUTDIR")

infile = f"muse-hr-data-wavsec0{SUFFIX}-cont-sub.fits"
infile_bg = f"muse-hr-data-wavsec0{SUFFIX}-cont.fits"
hdu = fits.open(f"{DATADIR}/{infile}")["DATA"]
hdubg = fits.open(f"{DATADIR}/{infile_bg}")["DATA"]
w = WCS(hdu)
nwav, ny, nx = hdu.data.shape
wavpix = np.arange(nwav)
_, _, wavs = w.pixel_to_world_values([0]*nwav, [0]*nwav, wavpix)
wavs *= 1.e10
for i1, i2, _, _, _, _, label in TAB:
    outfile = f"{label}-sum{SUFFIX}.fits"
    imsum = np.sum(hdu.data[i1:i2, :, :], axis=0)
    fits.PrimaryHDU(
        header=w.celestial.to_header(),
        data=imsum
    ).writeto(f"{OUTDIR}/{outfile}", overwrite=True)
    print(f"Written {outfile}")

    outfile = f"{label}-wav{SUFFIX}.fits"
    imwav = np.sum(hdu.data[i1:i2, :, :]*wavs[i1:i2, None, None], axis=0)/imsum
    fits.PrimaryHDU(
        header=w.celestial.to_header(),
        data=imwav
    ).writeto(f"{OUTDIR}/{outfile}", overwrite=True)
    print(f"Written {outfile}")

    outfile = f"{label}-bg{SUFFIX}.fits"
    imsum = np.sum(hdubg.data[i1:i2, :, :], axis=0)
    fits.PrimaryHDU(
        header=w.celestial.to_header(),
        data=imsum
    ).writeto(f"{OUTDIR}/{outfile}", overwrite=True)
    print(f"Written {outfile}")

python muse/extract-o_ii-v1-sections.py $DATADIR $SUFFIX $OUTDIR

Do multibinning of V1 images

import sys
from pathlib import Path
from distutils.dep_util import newer, newer_group
import numpy as np
sys.path.append("/Users/will/Dropbox/multibin-maps")
from rebin_utils import downsample, oversample, pad_array
from astropy.io import fits

nlist = [1, 2, 4, 8, 16, 32, 64, 128, 256]
mingoods = [2, 2, 2, 2, 2, 2, 2, 2, 2]


try:
    datadir = Path(sys.argv[1])
    infile = sys.argv[2]
    contfile = sys.argv[3]
    cont_threshold = float(sys.argv[4])
except:
    sys.exit('Usage: {} DATADIR INFILE CONTFILE CONT_THRESHOLD'.format(sys.argv[0]))


hdu = fits.open(datadir / infile)[0]
if hdu.data is None:
    hdu = fits.open(datadir / infile)[1]
hdr = hdu.header
# Maximum binning
nmax = nlist[-1]

# continuum image
chdu = fits.open(datadir / contfile)[0]
if chdu.data is None:
    chdu = fits.open(datadir / contfile)[1]

# Pad arrays to nearest multiple of nmax
im = pad_array(hdu.data, nmax)
cim = pad_array(chdu.data, nmax)

w = np.ones_like(im)
starmask = cim > cont_threshold

# If we pad the starmask and combine it with the padded image, then we
# automatically deal with the case where the input files have already
# been padded
m =  np.isfinite(im) & (~pad_array(starmask, nmax))

for n, mingood in zip(nlist, mingoods):
    im[~m] = 0.0
    outfile = infile.replace('.fits', '-bin{:03d}.fits'.format(n))
    print('Saving', outfile)
    # Save both the scaled image and the weights, but at the full resolution
    fits.HDUList([
        fits.PrimaryHDU(),
        fits.ImageHDU(data=oversample(im, n), header=hdr, name='scaled'),
        fits.ImageHDU(data=oversample(w, n), header=hdr, name='weight'),
    ]).writeto(datadir / outfile, clobber=True)
    # Now do the rebinning by a factor of two
    [im,], m, w = downsample([im,], m, weights=w, mingood=mingood)

python muse/multibin-map-orl.py ../Orion-HH-data/MUSE O_II-V1-4649-51-sum.fits O_II-V1-4649-51-bg.fits 1.0e7

python muse/multibin-map-orl.py ../Orion-HH-data/MUSE O_II-V1-4639-42-sum.fits O_II-V1-4649-51-bg.fits 1.0e7

python muse/multibin-map-orl.py ../Orion-HH-data/MUSE N_III-4634-sum.fits O_II-V1-4649-51-bg.fits 1.0e7

python muse/multibin-map-orl.py ../Orion-HH-data/MUSE N_II-4631-sum.fits O_II-V1-4649-51-bg.fits 1.0e7

python muse/multibin-map-orl.py ../Orion-HH-data/MUSE He_II-4686-sum.fits O_II-V1-4649-51-bg.fits 1.0e7

python muse/multibin-map-orl.py ../Orion-HH-data/MUSE linesum-O_III-5007.fits O_II-V1-4649-51-bg.fits 1.0e7

Redo multibinning for extinction-corrected maps

Have a more generous continuum mask, since otherwise we get bad extinction around th2A

LINES="O_II-V1-4649-51-sum O_II-V1-4639-42-sum N_III-4634-sum N_II-4631-sum He_II-4686-sum linesum-O_III-5007"
for line in $LINES; do
    python muse/multibin-map-orl.py ../Orion-HH-data/MUSE ${line}-excorr.fits O_II-V1-4649-51-bg.fits 2.0e6
done

Combine multibinned images

Try a different strategy this time
- Use a high s/n image, such as O_III-5007, as a template
- Make a series of masks at different levels on this image
- Use those to select the multigrid levels to combine

import sys
from pathlib import Path
import numpy as np
from astropy.io import fits

datadir = Path("~/Dropbox/Orion-HH-data/MUSE").expanduser()

try:
    fileroot = sys.argv[1]
    threshold = float(sys.argv[2])
    STEEPNESS = float(sys.argv[3])
    SUFFIX = sys.argv[4]
except IndexError:
    sys.exit(f'Usage: {sys.argv[0]} FILEROOT THRESHOLD STEEPNESS SUFFIX')


refhdu = fits.open(datadir / "linesum-O_III-5007-bin001.fits")["SCALED"]
outim = np.empty_like(refhdu.data)
nlist = [1, 2, 4, 8, 16, 32, 64, 128, 256]
for n in reversed(nlist):
    hdu = fits.open(datadir / f"{fileroot}-bin{n:03d}.fits")["SCALED"]
    mask = refhdu.data >= threshold/n**STEEPNESS
    outim[mask] = hdu.data[mask]

fits.PrimaryHDU(
    header=hdu.header,
    data=outim,
).writeto(
    datadir / f"{fileroot}-multibin{SUFFIX}.fits",
    overwrite=True,
)

LINES="O_II-V1-4649-51-sum O_II-V1-4639-42-sum N_III-4634-sum N_II-4631-sum linesum-O_III-5007"
for line in $LINES; do
    python muse/multibin-combine.py ${line}-excorr 2e9 1.5 -coarse-2e9-1p5
done

LINES="O_II-V1-4649-51-sum O_II-V1-4639-42-sum N_III-4634-sum N_II-4631-sum linesum-O_III-5007"
for line in $LINES; do
    python muse/multibin-combine.py ${line}-excorr 1e9 1.5 -medium-1e9-1p5
done

LINES="O_II-V1-4649-51-sum O_II-V1-4639-42-sum N_III-4634-sum N_II-4631-sum linesum-O_III-5007"
for line in $LINES; do
    python muse/multibin-combine.py ${line}-excorr 3e8 1.5 -fine-3e8-1p5
done

LINES="O_II-V1-4649-51-sum O_II-V1-4639-42-sum N_III-4634-sum N_II-4631-sum linesum-O_III-5007"
for line in $LINES; do
    python muse/multibin-combine.py ${line}-excorr 1e8 1.5 -vfine-1e8-1p5
done

This makes maps of the [S III] temperature on the same grids as used

line=muse-derived-Te-iii
python muse/multibin-combine.py ${line} 2e9 1.5 -coarse-2e9-1p5
python muse/multibin-combine.py ${line} 1e9 1.5 -medium-1e9-1p5
python muse/multibin-combine.py ${line} 3e8 1.5 -fine-3e8-1p5
python muse/multibin-combine.py ${line} 1e8 1.5 -vfine-1e8-1p5

Do extinction correction

De-reddening must be done at the highest resolution, so before the multibinning
- There is very little noise in the Balmer decrement map, so this is OK
In the Orion MUSE project I de-reddened [S III] 6313/9069 using Ha to Pa a
But then I did another version
- Do extinction correction for all lines
- This used the Hb/Ha map and the Blagrave extinction law from pyneb

import sys
from pathlib import Path
import numpy as np
import pyneb
from astropy.io import fits

# Set up Blagrave 2007 extinction law
REDCORR = pyneb.extinction.red_corr.RedCorr(
    law='CCM89 Bal07', R_V=5.5, cHbeta=1.0)

def flambda(wav):
    """Find [(A_lam / A_Hb) - 1] as function of wavelength `wav`

    This is the same as given in Table 2 of Blagrave et al (2007)

    """
    return np.log10(REDCORR.getCorrHb(wav))


def CHb_from_RHbHa(RHbHa, balmer0=2.874):
    """Find base-10 extinction at H beta from balmer decrement `RHbHa`

    Assumes that the intrinsic Balmer decrement is `balmer0`

    """
    return np.log10(balmer0*RHbHa) / flambda(6563)


def CHb_from_R6563_9229(RBaPa, RBaPa0=112.0):
    """Find base-10 extinction at H beta from 6563/9229 decrement `RBaPa`

    Assumes that the intrinsic decrement is `RBaPa0`

    """
    return np.log10(RBaPa/RBaPa0) / (flambda(9229) - flambda(6563))



DATADIR = Path("../Orion-HH-data/MUSE")

if __name__ == '__main__':

    try:
        prefix = sys.argv[1]
        wav = int(sys.argv[2])
    except IndexError:
        print(f'Usage: {sys.argv[0]} LINEID WAV')

    hb_ha = fits.open(DATADIR / 'ratio-4861-6563.fits')[0].data
    chb = CHb_from_RHbHa(hb_ha)
    clam = (1.0 + flambda(wav))*chb
    fn = f"{prefix}.fits"
    hdu = fits.open(DATADIR / fn)[0]
    fn_new = f"{prefix}-excorr.fits"
    fits.PrimaryHDU(
        data=hdu.data*10**clam,
        header=hdu.header
    ).writeto(DATADIR / fn_new, overwrite=True)
    print(fn_new)

python muse/correct-for-extinction.py linesum-O_III-5007 5007

python muse/correct-for-extinction.py O_II-V1-4649-51-sum 4650
python muse/correct-for-extinction.py O_II-V1-4639-42-sum 4640
python muse/correct-for-extinction.py N_II-4631-sum 4631
python muse/correct-for-extinction.py N_III-4634-sum 4634

Subtract the N II and N III contamination from 4639-42 image

Find scale factor from Adal spectra
- N_II-4643 = 0.5 N_II-4631
- N_III-4641 = 1.5 N_III-4634

Take ratio of V1 to 5007 for the two main sections

import sys
import numpy as np
from astropy.io import fits
from astropy.wcs import WCS
from pathlib import Path 

datadir = Path("../Orion-HH-data/MUSE")
hdu5007, = fits.open(datadir /  f"linesum-O_III-5007-{SUFFIX}.fits")
hdu4650, = fits.open(datadir / f"O_II-V1-4649-51-sum-{SUFFIX}.fits")
hdu4640, = fits.open(datadir / f"O_II-V1-4639-42-sum-{SUFFIX}.fits")
hdu4631, = fits.open(datadir / f"N_II-4631-sum-{SUFFIX}.fits")
hdu4634, = fits.open(datadir / f"N_III-4634-sum-{SUFFIX}.fits")

fits.PrimaryHDU(
    header=hdu4650.header,
    data=hdu4650.data/hdu5007.data
).writeto(datadir / f"O_II-V1-4649-51-over-5007-{SUFFIX}.fits", overwrite=True)
fits.PrimaryHDU(
    header=hdu4640.header,
    data=hdu4640.data/hdu5007.data
).writeto(datadir / f"O_II-V1-4639-42-over-5007-{SUFFIX}.fits", overwrite=True)
fits.PrimaryHDU(
    header=hdu4650.header,
    data=hdu4650.data/hdu4640.data
).writeto(datadir / f"O_II-V1-4649-51-over-4639-42-{SUFFIX}.fits", overwrite=True)

# Correct the 4639-42 for the N_II and N_III
hdu4640.data -= 0.5*hdu4631.data + 1.5*hdu4634.data

fits.PrimaryHDU(
    header=hdu4640.header,
    data=hdu4640.data/hdu5007.data
).writeto(datadir / f"O_II-V1-4639-42-minus-N_II_III-over-5007-{SUFFIX}.fits", overwrite=True)
fits.PrimaryHDU(
    header=hdu4650.header,
    data=hdu4650.data/hdu4640.data
).writeto(datadir / f"O_II-V1-4649-51-over-4639-42-minus-N_II_III-{SUFFIX}.fits", overwrite=True)

Ratios within the V1 multiplet

In the Manu spectra I calculated various ratios

Dominant feature is a radial gradient from inside to outside
Ratios are with respect to sum 4639+4649+4651+4662+4676
- I think 4642 is not included because of contamination
- And 4676 must include 4674

From the table below, the ratio of the blends 4650/4640 is only predicted to vary by 15%

Ratio	Inner	Outer
4639	0.14	0.17
4642	0.38	0.34
4649	0.42	0.30
4651	0.15	0.18
4662	0.15	0.2
4676	0.10	0.10
4640	0.52	0.51
4650	0.57	0.48
4650/4640	1.10	0.94

This is broadly consistent with what we get from MUSE

In the Adal spectra we have all the lines and 6 regions

Best to have the table transposed

Line strengths in units of 0.0001 with respect to 4959

Zone	4639	4642	4649	4651	4662	4674	4676	Sum	40+50/Sum	50/40	50/5007	40/5007
A	4.0	8.3	11.4	4.0	4.9	0.9	2.9	36.4	0.76	1.25	5.3	4.2
B	4.6	8.1	12.8	4.2	4.9	0.9	2.9	38.4	0.77	1.34	5.8	4.4
C	4.5	8.3	12.8	4.5	5.0	0.9	2.8	38.8	0.78	1.35	5.9	4.4
D	3.8	7.2	10.6	3.5	4.0	0.8	2.4	32.3	0.78	1.28	4.8	3.8
E	3.9	7.2	10.7	3.7	4.0	0.7	2.3	32.5	0.78	1.30	4.9	3.8
F	5.0	8.5	10.4	5.1	5.4	1.1	3.3	38.8	0.75	1.15	5.3	4.6

So the absolute values of 50/40 are a bit larger than Manu’s, but the trend is the same
- Increases towards center
The sum of the 4640 blend and 4650 blend are about 0.77 of the total sum
- There is a slight dependence on density, but the variation is only 4%

Calculate a T from V1/5007 as in Peimbert-squared

Supposedly we have

Sum_V1/4959 = 6.56e-5*((T/1.e4)**-0.415)*np.exp(29160.0/T)

Theoretically: 5007/4959 = 2.91817
And we can estimate Sum_V1 = (4640 + 4650)/0.77

Make a table

T	1e4 Sum_V1/4959
6000	104.6
6500	69.6
7000	49.0
7250	41.8
7500	36.1
7750	31.4
8000	27.6
8500	21.7
9000	17.5
10000	12.1
11000	8.9
12000	6.9

So the Adal measurements suggest T = 7500 +/- 200 K
- [S III] measurements give T = 8500 +/- 300 K
- This is consistent with the factor of 0.9 I found for T(4363/5007) vs T(V1/4959)
Convert our measurements into a T map
Also calculate difference and ratio with [S III] temperature
And finally, calculate “excess” V1 emission
- That is calculate expected ratio V1/4959 from [S III] temperature
- Then multiply this by S(4959) and subtract from S(V1)

import sys
import numpy as np
from astropy.io import fits
from astropy.wcs import WCS
from pathlib import Path 

datadir = Path("../Orion-HH-data/MUSE")
hdu4650, = fits.open(datadir / f"O_II-V1-4649-51-over-5007-excorr-{SUFFIX}.fits")
hdu4640, = fits.open(datadir / f"O_II-V1-4639-42-minus-N_II_III-over-5007-excorr-{SUFFIX}.fits")
hduTiii, = fits.open(datadir / f"muse-derived-Te-iii-{SUFFIX}.fits")
hdu5007, = fits.open(datadir / f"linesum-O_III-5007-excorr-{SUFFIX}.fits")

def func_ratio_v1_4959(T):
    return 6.56e-5*((T/1.e4)**-0.415)*np.exp(29160.0/T)

# Grid of 10 K increments
Tgrid = np.linspace(5000.0, 15000.0, 1001)
Rgrid = func_ratio_v1_4959(Tgrid)
# Reverse arrays since we need ratio in ascending order for np.interp
Rgrid = Rgrid[::-1]
Tgrid = Tgrid[::-1]

RATIO_4640_50_OVER_SUM = 0.77
RATIO_5007_4959 = 2.91817
ratio_v1_4959 = RATIO_5007_4959*(hdu4640.data + hdu4650.data)/RATIO_4640_50_OVER_SUM

T = np.interp(ratio_v1_4959, Rgrid, Tgrid)
T[hdu4650.data < 0.0] = np.nan
T[T == Tgrid.max()] = np.nan
T[T == Tgrid.min()] = np.nan

fits.PrimaryHDU(
    header=hdu4650.header,
    data=ratio_v1_4959
).writeto(datadir / f"O_II-V1-sum-over-4959-{SUFFIX}.fits", overwrite=True)
fits.PrimaryHDU(
    header=hdu4650.header,
    data=T,
).writeto(datadir / f"T_Op2_ORL_CEL-{SUFFIX}.fits", overwrite=True)
fits.PrimaryHDU(
    header=hdu4650.header,
    data=hduTiii.data - T,
).writeto(datadir / f"Delta_T-{SUFFIX}.fits", overwrite=True)
fits.PrimaryHDU(
    header=hdu4650.header,
    data=T/hduTiii.data,
).writeto(datadir / f"T_ratio-{SUFFIX}.fits", overwrite=True)

ratio_from_T_SIII = func_ratio_v1_4959(hduTiii.data)
V1_from_T_S_III = ratio_from_T_SIII*hdu5007.data/RATIO_5007_4959
V1_total = (hdu4640.data + hdu4650.data)*hdu5007.data/RATIO_4640_50_OVER_SUM
V1_excess = V1_total - V1_from_T_S_III
fits.PrimaryHDU(
    header=hdu4650.header,
    data=V1_excess,
).writeto(datadir / f"O_II-V1-sum-excess-{SUFFIX}.fits", overwrite=True)
fits.PrimaryHDU(
    header=hdu4650.header,
    data=V1_excess/V1_from_T_S_III,
).writeto(datadir / f"O_II-V1-sum-frac-excess-{SUFFIX}.fits", overwrite=True)

Relation between Δ T and t^2

This is for T([O III]) instead of T([S III]) but we will assume that is close enough
Peimbert & Peimbert (2013) equations 10, 11
- give T(4363/4959) and T(V1/4959)
- in terms of T_0(O++) and t^2(O++)
For convenience, put t0 = T_0/1e4 Koii
Then we have
- T(4363/4959) / T_0 = 1 + 0.5 (9.13/t0 - 2.68) t^2 = 1 + a t^2
- T(V1/4959) / T_0 = 1 + 0.5 (2.916/t0 - 3.095 + 0.415/(2.916/t0 + 0.415)) t^2 = 1 + b t^2
- Δ T / T_0 = (a - b) t^2
Variation of the t^2 coefficients with t0

t0 a b a - b

0.7 5.18 0.58 4.6

0.75 4.75 0.44 4.31

0.8 4.37 0.33 4.04

0.85 4.03 0.22 3.81

0.9 3.73 0.13 3.6

0.95 3.47 0.05 3.42

1.00 3.23 -0.03 3.26
So both T are positively biased wrt mean T_0, especially T(4363/4959)
We expect T_0 to be similar to, but slightly lower than T(V1/4959)
- Taking T_0 = 7500 +/- 200 K gives (a - b) = 4.31 +/- 0.12
- This implies Δ T = 7500 (4.31 +/- 0.12) t^2 = (32325 +/- 900) t^2
- Or t^2 = (0.031 +/- 0.001) (Δ T / 1000 K)

Plane-of sky t^2

This can be crudely estimated from the standard deviation of T([S III])

Measured in a few representative boxes

T mean	stddev	t^2
8284	228.662	0.0008
8222.34	267.187	0.0011
8262.28	148.677	0.0003
8165.87	314.53	0.0015
7756.21	347.089	0.0020
7690.31	183.44	0.0006
7665.54	202.199	0.0007
7658.65	218.946	0.0008

Below the line are from T(V1/4959), although only for medium and coarse gridding since otherwise noise dominates
Anyway, it looks like plane-of-sky t^2 is about 0.001 for either diagnostic

Combine the excess maps

Only allow positive values

import sys
import numpy as np
from astropy.io import fits
from astropy.wcs import WCS
from pathlib import Path 


datadir = Path("../Orion-HH-data/MUSE")

im = None
for suffix in [
        "coarse-2e9-1p5",
        "medium-1e9-1p5",
        "fine-3e8-1p5",
#        "vfine-1e8-1p5",
]:
    hdu, = fits.open(datadir / f"O_II-V1-sum-excess-multibin-{suffix}.fits")
    if im is None:
        im = np.empty_like(hdu.data)
    m = hdu.data > 0.0
    im[m] = hdu.data[m]

fits.PrimaryHDU(
    header=hdu.header,
    data=im,
).writeto(datadir / f"O_II-V1-sum-excess-combo.fits", overwrite=True)

Compare with C II fluorescent

Use the 6463 line to remove the recombination contribution from 7231
With O II, try to subtract a fraction of [O III] 5007 from 4651, assuming a T
The excess O II certainly looks very much like fluorescence
- Many of the detailed morphologies are the same between O II and C II
The fractional excess is about 0.8 times the T(S_III) prediction in the Big Arc
- But much higher around Trapezium
A more realistic approach would be to combine T(S_III) with a t^2 value derived from plane-of-sky variations
- This might give a slightly larger predicted S(V1), so slightly less excess

Look at the O I and [O II] lines

This gives another T estimate for the singly-ionized metals zone

Fit Gaussians to O II multiple

4649, 4651 are blended
4642, 4639 are blended with N II and N III too
4674 and 4676 are blended
4631 is pure N II
4607 is pure N II

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muse-oii-permitted.org

muse-oii-permitted.org

Permitted lines

The paper

Summary of the types of O II lines and what they tell us

The four types of O++ temperature

Expected T ordering from t^2 fluctuations

Expected T ordering from fluorescence

Eduardo O II strengths

Te, ne diagnostics from O II

Theoretical recombination line ratios from Storey for Case B @ 1e4 pcc

Potential diagnostics of fluorescence

Other 3d-4f lines that Eduardo uses in his Table 13

Diagnostics from Bastin thesis

O II V1 / 4610

O II 4317 / 4304

Analyze the pumping line

Revisiting the Adal and Manu analysis

Adal’s V1 line strengths

Extract maps from MUSE cubes

Now we do a simple extraction of the whole V1 multiplet

Extraction of multiplet in 4 sections

Do multibinning of V1 images

Redo multibinning for extinction-corrected maps

Combine multibinned images

Do extinction correction

Subtract the N II and N III contamination from 4639-42 image

Take ratio of V1 to 5007 for the two main sections

Ratios within the V1 multiplet

Calculate a T from V1/5007 as in Peimbert-squared

Relation between Δ T and t^2

Plane-of sky t^2

Combine the excess maps

Compare with C II fluorescent

Look at the O I and [O II] lines

Fit Gaussians to O II multiple

Make a template for the O II V1 multiplet

IND	wav	2JI	2JF	Other	Manu
8730	3712.74	3	1	H I 3712	No
8729	3727.32	3	3	[O II] 3726	No
8728	3749.48	3	5	H I 3750	No

Zone	4649	4610	4649/4610
A	11.4	1.2	9.50
B	12.8	1.0	12.80
C	12.8	1.0	12.80
D	10.6	1.0	10.60
E	10.7	1.1	9.73
F	10.4	1.2	8.67

t0	a	b	a - b
0.7	5.18	0.58	4.6
0.75	4.75	0.44	4.31
0.8	4.37	0.33	4.04
0.85	4.03	0.22	3.81
0.9	3.73	0.13	3.6
0.95	3.47	0.05	3.42
1.00	3.23	-0.03	3.26

x range
0:40	Red bay
40:50
50:62
67:80
80:95
95:154

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Permitted lines

The paper

Summary of the types of O II lines and what they tell us

The four types of O++ temperature

Expected T ordering from t^2 fluctuations

Expected T ordering from fluorescence

Eduardo O II strengths

Te, ne diagnostics from O II

Theoretical recombination line ratios from Storey for Case B @ 1e4 pcc

Potential diagnostics of fluorescence

Other 3d-4f lines that Eduardo uses in his Table 13

Diagnostics from Bastin thesis

O II V1 / 4610

O II 4317 / 4304

Analyze the pumping line

Revisiting the Adal and Manu analysis

Adal’s V1 line strengths

Extract maps from MUSE cubes

Now we do a simple extraction of the whole V1 multiplet

Extraction of multiplet in 4 sections

Do multibinning of V1 images

Redo multibinning for extinction-corrected maps

Combine multibinned images

Do extinction correction

Subtract the N II and N III contamination from 4639-42 image

Take ratio of V1 to 5007 for the two main sections

Ratios within the V1 multiplet

Calculate a T from V1/5007 as in Peimbert-squared

Relation between Δ T and t^2

Plane-of sky t^2

Combine the excess maps

Compare with C II fluorescent

Look at the O I and [O II] lines

Fit Gaussians to O II multiple

Make a template for the O II V1 multiplet