energy solar phenomena: MSFC: B. Ramsey, S. Bongiorno GSFC: D. - PowerPoint PPT Presentation

Collaborators: Lindsay Glesener (University of Minnesota) Plasma Astrophysics Seminar Nicole Vilmer (LESIA, Observatoire de Paris) KU Leuven Eduard Kontar (University of Glasgow) 10 May 2019 FOXSI-3 Team UMN: Lindsay Glesener (PI), P .S. Athiray, S. Musset, J. Vievering X-ray diagnostics of high UCB: S. Courtade, J.-C. Buitrago Casas, S. Krucker, G. Dalton, P . Turin energy solar phenomena: MSFC: B. Ramsey, S. Bongiorno GSFC: D. Ryan, S. Christe from the RHESSI spacecraft Kavli IPMU: T . Takahashi, K. Furukawa ISAS: S. Watanabe NAOJ: N. Narukage to the FOXSI sounding rocket Nagoya Univ.: S. Ishikawa, I. Mitsuishi Tokyo Univ. of Science: K. Hagino Sophie Musset University of Minnesota

Solar flare: Sudden release of magnetic energy Heating X-rays Particle acceleration 6-8 keV 25-80 keV 195 Å 304 Å 21 aug 2002 335 Å (extreme ultraviolet) 1 15 fev 2011

X-ray diagnostic of solar flares Magnetic field lines Magnetic reconnection & Acceleration site Magnetic energy dissipation in e- e- the corona Plasma heating Particle acceleration Photosphere 2

X-ray diagnostic of solar flares Magnetic field lines Magnetic reconnection & Acceleration site Magnetic energy dissipation in the corona Plasma heating Particle acceleration Krucker et al. 2008 X-ray emission (bremsstrahlung) 2

X-ray diagnostic of solar flares Magnetic field lines Magnetic reconnection & Acceleration site Magnetic energy dissipation in Thermal emission the corona (hot plasma) Non-thermal emission (accelerated electrons) Plasma heating Particle acceleration Krucker et al. 2008 X-ray emission (bremsstrahlung) 2

X-ray diagnostic of solar flares Magnetic field lines Magnetic reconnection & Acceleration site Magnetic energy dissipation in Thermal emission the corona (hot plasma) Non-thermal emission (accelerated electrons) Plasma heating Particle acceleration Krucker et al. 2008 X-ray emission (bremsstrahlung) Coronal HXR source (non-thermal emission): fainter 2

Outline • Using X-ray imaging spectroscopy with RHESSI to constrain particle transport in the solar corona ▪ Diffusive transport of energetic electrons in coronal loops • Going further with focusing optics for solar X-ray diagnostics (FOXSI) ▪ Why do we need focusing optics for solar X-ray telescopes? ▪ The FOXSI sounding rocket • Recent results from the FOXSI sounding rocket ▪ Micro-flare observations with FOXSI-2 ▪ FOXSI-3 flight on Sept 7 2018 3

Coronal HXR sources Magnetic field lines From a photon spectrum to an electron spectrum 𝒒𝒊𝒑𝒖𝒑𝒐 𝒕𝒒𝒇𝒅𝒖𝒔𝒗𝒏 Acceleration site 𝜹 Krucker et al. 2008 4

Coronal HXR sources Magnetic field lines From a photon spectrum to an electron spectrum 𝒒𝒊𝒑𝒖𝒑𝒐 𝒕𝒒𝒇𝒅𝒖𝒔𝒗𝒏 Acceleration site Thin target approximation 𝜹 = 𝜺 + 𝟐 𝜹 Krucker et al. 2008 4

Coronal HXR sources Magnetic field lines From a photon spectrum to an electron spectrum 𝒒𝒊𝒑𝒖𝒑𝒐 𝒕𝒒𝒇𝒅𝒖𝒔𝒗𝒏 Acceleration site Thin target approximation 𝜹 = 𝜺 + 𝟐 Thick target approximation 𝜹 𝜹 = 𝜺 − 𝟐 Krucker et al. 2008 4

ሶ Coronal HXR sources Magnetic field lines From a photon spectrum to an electron spectrum 𝒒𝒊𝒑𝒖𝒑𝒐 𝒕𝒒𝒇𝒅𝒖𝒔𝒗𝒏 Acceleration site Thin target approximation 𝜹 = 𝜺 + 𝟐 Thick target approximation 𝜹 𝜹 = 𝜺 − 𝟐 « Standard » collisional propagation model Krucker et al. 2008 𝜹 𝒅𝒕 − 𝜹 𝒈𝒒 = 𝟑 𝑶 𝒅𝒕 = ሶ 𝑶 𝒈𝒒 4

X-ray imaging spectroscopy with RHESSI Battaglia & Benz (2006) 5

X-ray imaging spectroscopy with RHESSI Photon spectral index 𝛿 𝑀𝑈 − 𝛿 𝐺𝑄 ≠ 2 Need additional mechanism to collisional transport Battaglia & Benz (2006) 5

ሶ ሶ X-ray imaging spectroscopy with RHESSI Photon spectral index 𝛿 𝑀𝑈 − 𝛿 𝐺𝑄 ≠ 2 Need additional mechanism to collisional transport Battaglia & Benz (2006) Electron spectral index 𝜀 𝑀𝑈 − 𝜀 𝐺𝑄 < 0 Ratio of electron rate 𝑂 𝑀𝑈 > 1 𝑂 𝐺𝑄 Need additional mechanism to collisional transport Simoes & Kontar (2013) 5

Combination of radio and X-ray diagnostics X-rays: e- Bremsstrahlung emission emitted by electrons of a p+ few tens of keV Radio: Gyrosynchrotron emission emitted by electrons of a e- few hundred of keV X-ray and radio diagnostics offer the possibility to study energetic electron transport in two different energy ranges 6

Combination of radio and X-ray diagnostics Kuznetsov & Kontar (2015) X-rays: e- Bremsstrahlung emission emitted by electrons of a X-ray emission p+ few tens of keV (electrons < 100 keV) Radio: Gyrosynchrotron emission emitted by electrons of a e- few hundred of keV X-ray and radio diagnostics offer the possibility to study energetic electron Gyrosynchrotron emission transport in two different energy ranges (electrons with a few hundred of keV) 6

Radio diagnostics of May 21 2004 flare Kuznetsov & Kontar (2015) Spatial distribution of the density of energetic electrons with E > 60 keV X-ray emission (electrons < 100 keV) Gyrosynchrotron emission Energetic electrons are trapped in (electrons with a few hundred of keV) the corona, near the looptop 6

X-ray imaging spectroscopy Musset et al. (2018) 12-25 keV 25-50 keV Count flux [counts/s/cm 2 /keV] 50-100 keV 10 2 10 0 10 -2 10 100 Energy [keV] X-ray imaging spectroscopy 7 Musset et al. (2018)

ሶ ሶ ሶ ሶ ሶ X-ray imaging spectroscopy Musset et al. (2018) 12-25 keV 25-50 keV Count flux [counts/s/cm 2 /keV] 50-100 keV 10 2 10 0 10 -2 𝜀 = 4.4 ± 0.2 𝑂 = 0.12 ± 0.03 × 10 35 s −1 𝜀 = 4.2 ± 0.2 10 100 Energy [keV] 𝑂 = 0.06 ± 0.02 × 10 35 s −1 𝜀 = 5.2 ± 0.4 𝑶 𝑴𝑼 = 0.4 ± 0.2 × 10 35 s −1 X-ray imaging spectroscopy 𝑶 𝑴𝑼 𝑶 𝑮𝑸 = 2.2 → Electrons are trapped in the coronal part of the loop Coronal ambiant density 𝑜 = 1.2 ± 0.2 × 10 11 𝑑𝑛 −3 7 Musset et al. (2018)

Trapping of energetic electrons in the corona Energetic electron density above 25 keV (from X-rays) Energetic electron density above 60 keV From radio (Kuznetsov Distribution deduced & Kontar 2015) from gyrosynchrotron From emission is more peaked X-rays than the distribution deduced from X-rays Is trapping energy-dependent? 25 𝑜 𝑐,𝑀𝑈 ~1.6 𝑏𝑜𝑒 3.8 60 25 𝑜 𝑐,𝑀𝑈 𝑜 𝑐,𝐺𝑄 ~7.7 𝑏𝑜𝑒 9 60 𝑜 𝑐,𝐺𝑄 8 Musset et al. (2018)

Diffusive transport of energetic electrons Strong pitch angle scattering due to small scale 1 𝜖 (𝑈) 𝜖𝐺 = 𝜖 𝑒𝐹 (𝑈) = λ𝑤 𝐸 𝑨𝑨 𝜖𝑨 𝐸 𝑨𝑨 𝑒𝑦 𝐺 + 𝐺 0 𝑇(𝑨) magnetic fluctuations 3 𝑤 𝜖𝑨 𝜖𝐹 Collisions Source ➔ diffusive transport of energetic electrons Diffusion λ : sca cattering mean free path Kontar et al. (2014) 9

Diffusive transport of energetic electrons Strong pitch angle scattering due to small scale 1 𝜖 (𝑈) 𝜖𝐺 = 𝜖 𝑒𝐹 (𝑈) = λ𝑤 𝐸 𝑨𝑨 𝜖𝑨 𝐸 𝑨𝑨 𝑒𝑦 𝐺 + 𝐺 0 𝑇(𝑨) magnetic fluctuations 3 𝑤 𝜖𝑨 𝜖𝐹 Collisions Source ➔ diffusive transport of energetic electrons Diffusion λ : sca cattering mean free path Kontar et al. (2014) Suppose λ constant ∞ 𝑮 𝟏 𝐹 ′ 𝑨 2 𝐹 𝐺 𝐸 𝐹, 𝑨 = න 𝑒𝐹′ exp − 4𝒃 𝐹 ′2 − 𝐹 2 + 2𝒆 2 𝐿𝒐 𝟏 4𝜌𝒃 𝐹 ′2 − 𝐹 2 + 2𝒆 2 𝐹 𝒐 𝟏 density of the medium Free parameters are 𝒐 𝟏 , 𝒆 and 𝝁 𝒆 size of the acceleration region 𝒃 α λ/𝑜 0 𝑮 𝟏 injected electron spectrum Deduced from X-rays 9 Musset et al. (2018)

Model fit to spectral and spatial distributions Spectral distribution of Spatial distribution of energetic electrons energetic electrons at 25 keV Data Data Model Model Corona Bes est fit it to o bo both di distributions: 𝒐 = 𝟘. 𝟔 × 𝟐𝟏 𝟐𝟏 𝒅𝒏 −𝟒 𝒆 = 𝟔. 𝟔 × 𝟐𝟏 𝟗 𝒅𝒏 Footpoints 𝝁 = 𝟐. 𝟓 × 𝟐𝟏 𝟗 𝒅𝒏 The X-ray observations can be globally explained by the diffusive transport model. 10 Musset et al. (2018)

Can we also explain radio emissions? Energetic electron density above 25 keV Energetic electron density (from X-rays) above 60 keV Data Data Model Model Val alues of of th the model par arameters: 𝒐 = 𝟘. 𝟔 × 𝟐𝟏 𝟐𝟏 𝒅𝒏 −𝟒 𝒆 = 𝟔. 𝟔 × 𝟐𝟏 𝟗 𝒅𝒏 𝝁 = 𝟐. 𝟓 × 𝟐𝟏 𝟗 𝒅𝒏 𝝁 = 𝟐 × 𝟐𝟏 𝟖 𝒅𝒏 To explain both X-ray and radio emissions, need energy-dependent scattering mean free path 11 Musset et al. (2018)

Scattering mean free path dependence on energy Probing 2 energy domains (with X-ray and radio) ➔ Energy dependence of electron scattering mean free path, decreasing with increasing energy 12 Musset et al. (2018)