NLTE inversions of Mg II h & k lines including PRD effects

Jaime de la Cruz Rodríguez

non-LTE inversions: Nicole

• One atom can be treated in non-LTE (statistical equilibrium). • 1.5D, each pixel is treated as a plane-parallel atmosphere. • Hydrostatic equilibrium to derive pressure scales given a tau

scale and a temperature profile. • Complete redistribution of scattered photons (CRD). • Fortran/MPI.

22

Fig. 8 Raster-scan observation of AR12394 (top) and AR12390 (bottom) on 2014-08-01 at 1083 nm with theTRIPPEL spectrograph at the Swedish 1-m Solar Telescope. From left to right the panels show images in thecontinuum, in Si I l10827 line center and in He I l10830 line absortion. Courtesy of J. Joshi, T. Libbrecht, G.Sliepen and D. Kiselman (Institute for Solar Physics, Stockholm University).

Line(s) Scattered photons Zeeman/Hanle Geometry IonizationCa II H & K PRD Zeeman (AR), Hanle (QS) 1.5D stat. equilibriumHa CRD Zeeman (AR), Hanle (QS) 3D non-equilibriumCa II IR triplet CRD Zeeman (AR), Hanle (QS) 1.5D stat. equilibriumMg II h & k PRD Zeeman, Hanle (k line) 1.5D stat. equilibriumHe I D3 & l10830 CRD (?) Zeeman + Hanle 3D (?) non-equilibrium

5 Inversions in the chromosphere: a selection of results

This volume includes dedicated chapters about sunspots (Rempel & Scharmer, same issue)and about photospheric magnetic fields in the quiet-Sun (Schussler et al., same issue). There-fore, we have chosen to focus on a small selection of results obtained from chromosphericstudies, and more specifically on those concerning inference of magnetic fields.

The first attempts to invert chromospheric data can be tracked back to the VAL andFAL atmospheres (see Vernazza et al. 1981 and Fontenla et al. 1993). Those studies usedspatially-averaged spectra, including many chromospheric lines from different species (atomsand ions), to derive models that could reproduce the observations. Nowadays, the VAL andFAL atmospheres are still used to derive radiative fluxes in the chromosphere or as referencechromospheric models. However, the chromosphere is highly dynamic and finely structured.These 1D models cannot catch those two inherent properties of the chromosphere, and it isnow widely accepted that spatio-temporal models must be used to characterize this regionof the Sun.

The following techniques have been particularly successful to derive magnetic fields inthe chromosphere:

Socas-Navarro et al. (2000, 2015)

FTS atlas: spatial average in quiet-Sun

Photosphere Chromosphere

non-LTE inversions in the Ca II 8542 line

Reversed C-shape bisector from Ca II isotopic splitting (Leenaarts et al. 2014)

Model: Depth-stratified atmosphere (working in optical-depth at 500 nm).

Parameters: temperature, vlos, Bz, Bx, By, vturbulent, Pgas, Pel.

Inversion : temperature, vlos, Bz, Bx, By, vturbulent. (hydrostatic eq. for Pgas).

HSRA

Nodes in depth-stratified atmosphere

Nodes define the locations where the model is perturbed and modified.

The number of nodes can be different for each parameter.

We need the entire atmosphere to integrate the RT equation.

HSRA

Nodes in depth-stratified atmosphere

Nodes define the locations where the model is perturbed and modified.

The number of nodes can be different for each parameter.

We need the entire atmosphere to integrate the RT equation.

HSRA

Nodes in depth-stratified atmosphere

Nodes define the locations where the model is perturbed and modified.

The number of nodes can be different for each parameter.

We need the entire atmosphere to integrate the RT equation.

The nodes are connected with a non-overshooting cubic Bezier splines.

HSRA

Nodes in depth-stratified atmosphere

non-LTE inversions: Nicole

Temperature maps over an active region

279.4 279.6 279.8 280.0 280.2 280.4

Wavelength [nm]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Inte

nsity

FALC (modified)

CRDPRD

The Mg II h & k lines (PRD vs CRD)

1.5D vs 3D radiative transfer

disk center in mg ii k2v

µ =

Mg II k2v courtesy of Sukhorukov & Leenaarts (in prep.)

1.5D vs 3D radiative transfer

Synthetic slitjaw in Mg II k at disk center courtesy of Sukhorukov & Leenaarts (in prep.)disc center in mg ii k slit-jaw

µ = .

Iris observation

non-LTE inversions: the Stockholm Inversion Code (SIC?)

• In-house Milne-Eddington and LTE implementations. • NLTE forward module based on RH (Uitenbroek 2001). • Multiple atoms can be treated in non-LTE (statistical equilibrium). • 1.5D, each pixel is treated as a plane-parallel atmosphere. • Hydrostatic equilibrium to derive pressure scales. • Complete and partial redistribution of scattered photons (CRD, PRD). • New possibilities with Ca II H & K and Mg II h & k along with Ca II IR lines. • Written in C/C++ / MPI / netCDF4.

22

Fig. 8 Raster-scan observation of AR12394 (top) and AR12390 (bottom) on 2014-08-01 at 1083 nm with theTRIPPEL spectrograph at the Swedish 1-m Solar Telescope. From left to right the panels show images in thecontinuum, in Si I l10827 line center and in He I l10830 line absortion. Courtesy of J. Joshi, T. Libbrecht, G.Sliepen and D. Kiselman (Institute for Solar Physics, Stockholm University).

Line(s) Scattered photons Zeeman/Hanle Geometry IonizationCa II H & K PRD Zeeman (AR), Hanle (QS) 1.5D stat. equilibriumHa CRD Zeeman (AR), Hanle (QS) 3D non-equilibriumCa II IR triplet CRD Zeeman (AR), Hanle (QS) 1.5D stat. equilibriumMg II h & k PRD Zeeman, Hanle (k line) 1.5D stat. equilibriumHe I D3 & l10830 CRD (?) Zeeman + Hanle 3D (?) non-equilibrium

5 Inversions in the chromosphere: a selection of results

This volume includes dedicated chapters about sunspots (Rempel & Scharmer, same issue)and about photospheric magnetic fields in the quiet-Sun (Schussler et al., same issue). There-fore, we have chosen to focus on a small selection of results obtained from chromosphericstudies, and more specifically on those concerning inference of magnetic fields.

The first attempts to invert chromospheric data can be tracked back to the VAL andFAL atmospheres (see Vernazza et al. 1981 and Fontenla et al. 1993). Those studies usedspatially-averaged spectra, including many chromospheric lines from different species (atomsand ions), to derive models that could reproduce the observations. Nowadays, the VAL andFAL atmospheres are still used to derive radiative fluxes in the chromosphere or as referencechromospheric models. However, the chromosphere is highly dynamic and finely structured.These 1D models cannot catch those two inherent properties of the chromosphere, and it isnow widely accepted that spatio-temporal models must be used to characterize this regionof the Sun.

The following techniques have been particularly successful to derive magnetic fields inthe chromosphere:

Spatially coupled inversions: PSF or sparsity

de la Cruz Rodríguez & van Noort (in prep.)

The parameters of the model atmosphere can be coupled using a spatial PSF or by imposing sparsity in a transformed basis (wavelet):

• van Noort (2012) • Asensio-Ramos & de la Cruz Rodríguez (2015)

First results with a modified FAL model

279.45 279.50 279.55 279.60 279.65 279.70 279.75 279.80

Wavelength [nm]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Nor

mal

ized

inte

nsity

Mg II h & k

Mg II onlyMg II + Ca II 8542 + Fe I 6302Mg II + Ca II 8542Obs

630.22 630.23 630.24 630.25 630.26 630.27

Wavelength [nm]

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1Fe I 6302

854.16 854.18 854.20 854.22 854.24 854.26

Wavelength [nm]

0.20

0.25

0.30

0.35

0.40

0.45

0.50

Ca II 8542

4

5

6

7

8

9

10

11

12

Tem

pera

ture

[kK

]

Temperature

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

v l.o

.s[k

ms�

1 ]

line-of-sight velocity

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

v tur

b[k

ms�

1 ]

Turbulent velocity

�8 �7 �6 �5 �4 �3 �2 �1 0log ⌧500 [dex]

0.0

0.2

0.4

0.6

0.8

1.0

|B|[

kG]

B strength

�8 �7 �6 �5 �4 �3 �2 �1 0log ⌧500 [dex]

20

30

40

50

60

70

80

Incl

inat

ion

[deg

]

B Inclination

�8 �7 �6 �5 �4 �3 �2 �1 0log ⌧500 [dex]

0

5

10

15

20

25

30

35

40

Azi

mut

h[d

eg]

B Azimuth

Carlsson et al. (2015) needed a significantly higher density than FAL to reproduce plage profiles.

First results with a Bifrost slice

�10

�8

�6

�4

�2

0

log

⌧ 500

log ⌧500 scale + cutoff at 50000 K

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

z[M

m]

Original z-scale

0 2 4 6 8 10 12 14 16x [Mm]

�10

�8

�6

�4

�2

0

log

⌧ 500

log ⌧500 scale + cutoff at 50000 K, 6 nodes

0 2 4 6 8 10 12 14 16x [Mm]

�10

�8

�6

�4

�2

0

log

⌧ 500

log ⌧500 scale, inverted with 6 nodes

A slice from the enhanced network model, Carlsson et al. (2015)

First results with a Bifrost slice

A slice from the enhanced network model, Carlsson et al. (2015)

3.5 3.6 3.7 3.8 3.9 4.0Original temperature [log K]

3.5

3.6

3.7

3.8

3.9

4.0

Inve

rted

tem

pera

ture

[log

K]

Inversion of IRIS data

2794 2796 2798 2800 2802 2804

Wavelength [A]

0.00

0.05

0.10

0.15

0.20

0.25

Nor

mal

ized

inte

nsity

�7 �6 �5 �4 �3 �2 �1 0log ⌧500

4

5

6

7

8

9

10

11

12

13Temperature [Kk]

�7 �6 �5 �4 �3 �2 �1 0log ⌧500

0

1

2

3

4

5

6

7

8Line-of-sight velocity [km s�1]

�7 �6 �5 �4 �3 �2 �1 0log ⌧500

0

2

4

6

8

10Turbulent velocity [km s�1]

Conclusions

• 1.5D (coupled) inversions including PRD effects are now possible: Ca II H & K, Mg II h & k.

• IRIS, CHROMIS (@Swedish 1-m Solar Telescope). • Hopefully soon we will have the first spatially-coupled

inversions of IRIS data!