where do the spirals come from? · spirals come from? a multi-wavelength, high-resolution study of...

22
WHERE DO THE SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B COLLABORATORS : S. FACCHINI (MPE), M. TAZZARI (IOA CAMBRIDGE), P. PINILLA (U. OF ARIZONA), M. BENISTY (U. DE CHILE, CNRS), N. VAN DER MAREL (HERZBERG INSTITUTE), A. GARUFI (U. MADRID), L. PEREZ (U. DE CHILE, MPIR), E. VAN DISHOECK (STRW LEIDEN, MPE)

Upload: others

Post on 01-Oct-2020

1 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

WHERE DO THE SPIRALS COME FROM? Amulti-wavelength,high-resolutionstudyofHD135344B

COLLABORATORS : S. FACCHINI (MPE), M. TAZZARI (IOA CAMBRIDGE), P. PINILLA (U. OF ARIZONA), M. BENISTY (U. DE CHILE, CNRS), N. VAN

DER MAREL (HERZBERG INSTITUTE), A. GARUFI (U. MADRID), L. PEREZ (U. DE CHILE, MPIR), E. VAN DISHOECK (STRW LEIDEN, MPE)

Page 2: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Protoplanetary “disks”…

2

V12457Ori

Kraus+2017

HD135344B

vanderMarel+2016

Dusttraps:wheredustgrowsandplanetsform

SPF2 14 MARCH 2017 P. CAZZOLETTI

MWC758

Boehler+2018

Page 3: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

…or planet-forming disks?

3

Planetsareinvokedastheoriginofstructures:•  Planetscancarvetheinnergap•  Planetscangeneratepressurebumps(therings)(e.g.Pinilla+2012,Cazzoletti+2016)•  Planetscantriggervortices(theasymmetries)•  Planetscanlaunchspiralarms

•  1planet?(Fung&Dong2015)•  2planets?(Stolker+2016,2017)

Stolker+2017

HD135344B

SPF2 14 MARCH 2017 P. CAZZOLETTI

Page 4: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Vortex launching spirals?

4

Thevortexistriggeringdensitywaves(e.g.Zhu&Baruteau2015)

VLT/SPHERE

ALMA0.88mm

SPF2 14 MARCH 2017 P. CAZZOLETTI

(vanderMarel,Cazzolettetal.2016)

Page 5: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

More evidence

5

Benisty+15

V12457Ori

Kraus+2017

HD135344B

vanderMarel+2016

MWC758

Boehler+2018

Stolker+2017

SPF2 14 MARCH 2017 P. CAZZOLETTI

mm

NIR

Notanisolatedcase

Page 6: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Questions to answer

• 

6

SPF2 14 MARCH 2017 P. CAZZOLETTI

Page 7: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

New long wavelength ALMA data

7

•  Higherresolution:0.06”•  Band3andBand4data:expectedtobeopticallythin•  TobecombinedwithourBand7(0.88mm)andBand9(0.4mm)data

SPF2 14 MARCH 2017 P. CAZZOLETTI

: 2.75 mm : 1.9 mm

Cazzolettietal.inprep.

Page 8: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Fit of the brightness profile

8

SPF2 14 MARCH 2017 P. CAZZOLETTI

: 1.9 mm

OUTERASYMMETRICGAUSSIAN

•  FitforbothrealandimaginarypartineachUVpoint•  GALARIO(Tazzari+2018)

Aftercenteringanddeprojecting

Page 9: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Differences between the 4 bands

9

SPF2 14 MARCH 2017 P. CAZZOLETTI

Cazzolettietal.inprep.

Page 10: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Peak azimuthal shift

10

SPF2 14 MARCH 2017 P. CAZZOLETTI

Thecenterofthevortexshiftswithgrainsize

(Baruteau&Zhu2016)

Page 11: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Questions to answer

• 

11

SPF2 14 MARCH 2017 P. CAZZOLETTI

Page 12: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Is the vortex massive enough?

12

Mdust =F⌫d2

k⌫B⌫(Tdust)<latexit sha1_base64="WotHXgkrZEAnnEQql+iVEe4wu0A=">AAACIHicbVBPS8MwHE3nvzn/TT16CQ5hXkY3BOdBGBPEizBhdYN1ljRNt7A0LUkqjNKv4sWv4sWDit7005huO8zNBwmP996P5PfciFGpTPPbyK2srq1v5DcLW9s7u3vF/YN7GcYCEwuHLBRdF0nCKCeWooqRbiQIClxGOu7oKvM7j0RIGvK2GkekH6ABpz7FSGnJKdZvncQWAfRiqdJL2xcIJ9eOzWPoPdTSZDShzewut+eSp6lTLJkVcwK4TKozUgIztJzil+2FOA4IV5ghKXtVM1L9BAlFMSNpwY4liRAeoQHpacpRQGQ/mWyYwhOteNAPhT5cwYk6P5GgQMpx4OpkgNRQLnqZ+J/Xi5Vf7yeUR7EiHE8f8mMGVQizuqBHBcGKjTVBWFD9V4iHSLekdKkFXUJ1ceVlYtUqFxXz7qzUaM7ayIMjcAzKoArOQQPcgBawAAZP4AW8gXfj2Xg1PozPaTRnzGYOwR8YP78SbaOq</latexit><latexit sha1_base64="WotHXgkrZEAnnEQql+iVEe4wu0A=">AAACIHicbVBPS8MwHE3nvzn/TT16CQ5hXkY3BOdBGBPEizBhdYN1ljRNt7A0LUkqjNKv4sWv4sWDit7005huO8zNBwmP996P5PfciFGpTPPbyK2srq1v5DcLW9s7u3vF/YN7GcYCEwuHLBRdF0nCKCeWooqRbiQIClxGOu7oKvM7j0RIGvK2GkekH6ABpz7FSGnJKdZvncQWAfRiqdJL2xcIJ9eOzWPoPdTSZDShzewut+eSp6lTLJkVcwK4TKozUgIztJzil+2FOA4IV5ghKXtVM1L9BAlFMSNpwY4liRAeoQHpacpRQGQ/mWyYwhOteNAPhT5cwYk6P5GgQMpx4OpkgNRQLnqZ+J/Xi5Vf7yeUR7EiHE8f8mMGVQizuqBHBcGKjTVBWFD9V4iHSLekdKkFXUJ1ceVlYtUqFxXz7qzUaM7ayIMjcAzKoArOQQPcgBawAAZP4AW8gXfj2Xg1PozPaTRnzGYOwR8YP78SbaOq</latexit><latexit sha1_base64="WotHXgkrZEAnnEQql+iVEe4wu0A=">AAACIHicbVBPS8MwHE3nvzn/TT16CQ5hXkY3BOdBGBPEizBhdYN1ljRNt7A0LUkqjNKv4sWv4sWDit7005huO8zNBwmP996P5PfciFGpTPPbyK2srq1v5DcLW9s7u3vF/YN7GcYCEwuHLBRdF0nCKCeWooqRbiQIClxGOu7oKvM7j0RIGvK2GkekH6ABpz7FSGnJKdZvncQWAfRiqdJL2xcIJ9eOzWPoPdTSZDShzewut+eSp6lTLJkVcwK4TKozUgIztJzil+2FOA4IV5ghKXtVM1L9BAlFMSNpwY4liRAeoQHpacpRQGQ/mWyYwhOteNAPhT5cwYk6P5GgQMpx4OpkgNRQLnqZ+J/Xi5Vf7yeUR7EiHE8f8mMGVQizuqBHBcGKjTVBWFD9V4iHSLekdKkFXUJ1ceVlYtUqFxXz7qzUaM7ayIMjcAzKoArOQQPcgBawAAZP4AW8gXfj2Xg1PozPaTRnzGYOwR8YP78SbaOq</latexit>

Assumingopticallythinemission

Measured 140pc

10cm2/g@1000GHz 15K(vanderMarel+2015)

Mdust~30MEarth

SPF2 14 MARCH 2017 P. CAZZOLETTI

gas/dust=100

gas/dust=1-10

Mtot~10MJ

Mtot~0.2-1MJ

Probablynotenough

Page 13: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Optical thickness

13

Tbright = Tbb(1� e�⌧⌫ )<latexit sha1_base64="GX7UlLcYiDGDf9Yf4B4XSg2asq0=">AAACEnicbVDLSgMxFM3UV62vqks3wSJUoWVGBHUhFN24rNDaQqcOmTRtQzOZIbkjlGH+wY2/4saFiltX7vwb04egrQcunJxzL7n3+JHgGmz7y8osLC4tr2RXc2vrG5tb+e2dWx3GirI6DUWomj7RTHDJ6sBBsGakGAl8wRr+4GrkN+6Z0jyUNRhGrB2QnuRdTgkYycsf1bzEVQH2Fe/1Ib34efpp0Smxu6TkAok9V8bpoZcv2GV7DDxPnCkpoCmqXv7T7YQ0DpgEKojWLceOoJ0QBZwKlubcWLOI0AHpsZahkgRMt5PxTSk+MEoHd0NlSgIeq78nEhJoPQx80xkQ6OtZbyT+57Vi6J61Ey6jGJikk4+6scAQ4lFAuMMVoyCGhhCquNkV0z5RhIKJMWdCcGZPnif14/J52b45KVQup2lk0R7aR0XkoFNUQdeoiuqIogf0hF7Qq/VoPVtv1vukNWNNZ3bRH1gf35QPnYo=</latexit><latexit sha1_base64="GX7UlLcYiDGDf9Yf4B4XSg2asq0=">AAACEnicbVDLSgMxFM3UV62vqks3wSJUoWVGBHUhFN24rNDaQqcOmTRtQzOZIbkjlGH+wY2/4saFiltX7vwb04egrQcunJxzL7n3+JHgGmz7y8osLC4tr2RXc2vrG5tb+e2dWx3GirI6DUWomj7RTHDJ6sBBsGakGAl8wRr+4GrkN+6Z0jyUNRhGrB2QnuRdTgkYycsf1bzEVQH2Fe/1Ib34efpp0Smxu6TkAok9V8bpoZcv2GV7DDxPnCkpoCmqXv7T7YQ0DpgEKojWLceOoJ0QBZwKlubcWLOI0AHpsZahkgRMt5PxTSk+MEoHd0NlSgIeq78nEhJoPQx80xkQ6OtZbyT+57Vi6J61Ey6jGJikk4+6scAQ4lFAuMMVoyCGhhCquNkV0z5RhIKJMWdCcGZPnif14/J52b45KVQup2lk0R7aR0XkoFNUQdeoiuqIogf0hF7Qq/VoPVtv1vukNWNNZ3bRH1gf35QPnYo=</latexit><latexit sha1_base64="GX7UlLcYiDGDf9Yf4B4XSg2asq0=">AAACEnicbVDLSgMxFM3UV62vqks3wSJUoWVGBHUhFN24rNDaQqcOmTRtQzOZIbkjlGH+wY2/4saFiltX7vwb04egrQcunJxzL7n3+JHgGmz7y8osLC4tr2RXc2vrG5tb+e2dWx3GirI6DUWomj7RTHDJ6sBBsGakGAl8wRr+4GrkN+6Z0jyUNRhGrB2QnuRdTgkYycsf1bzEVQH2Fe/1Ib34efpp0Smxu6TkAok9V8bpoZcv2GV7DDxPnCkpoCmqXv7T7YQ0DpgEKojWLceOoJ0QBZwKlubcWLOI0AHpsZahkgRMt5PxTSk+MEoHd0NlSgIeq78nEhJoPQx80xkQ6OtZbyT+57Vi6J61Ey6jGJikk4+6scAQ4lFAuMMVoyCGhhCquNkV0z5RhIKJMWdCcGZPnif14/J52b45KVQup2lk0R7aR0XkoFNUQdeoiuqIogf0hF7Qq/VoPVtv1vukNWNNZ3bRH1gf35QPnYo=</latexit><latexit sha1_base64="C39OhB+IczRcjLNINXH29e9lt8M=">AAAB2HicbZDNSgMxFIXv1L86Vq1rN8EiuCpTN+pOcOOygmML7VAymTttaCYzJHeEMvQFXLhRfDB3vo3pz0KtBwIf5yTk3hMXSloKgi+vtrW9s7tX3/cPGv7h0XGz8WTz0ggMRa5y04+5RSU1hiRJYb8wyLNYYS+e3i3y3jMaK3P9SLMCo4yPtUyl4OSs7qjZCtrBUmwTOmtowVqj5ucwyUWZoSahuLWDTlBQVHFDUiic+8PSYsHFlI9x4FDzDG1ULcecs3PnJCzNjTua2NL9+aLimbWzLHY3M04T+zdbmP9lg5LS66iSuigJtVh9lJaKUc4WO7NEGhSkZg64MNLNysSEGy7INeO7Djp/N96E8LJ90w4eAqjDKZzBBXTgCm7hHroQgoAEXuDNm3iv3vuqqpq37uwEfsn7+Aap5IoM</latexit><latexit sha1_base64="gWB5KUM6BR3qSwsw69ZWFLLnnrs=">AAACB3icbZDLSgMxGIX/qbdab9Wtm2ARVLDMuFEXguDGZYVWhc44ZNJMG8xkhuQfoQzzDm58FTcuVHwDd76N6UXwdiBwck5C8n9RJoVB1/1wKjOzc/ML1cXa0vLK6lp9ffnSpLlmvMNSmerriBouheIdFCj5daY5TSLJr6Lbs1F/dce1Ealq4zDjQUL7SsSCUbRRWN9rh4WvExJp0R9gefK1jcodb5/fFPs+0jz0VV7uhvWG23THIn+NNzUNmKoV1t/9XsryhCtkkhrT9dwMg4JqFEzysubnhmeU3dI+71qraMJNUIxnKsm2TXokTrVdCsk4/X6joIkxwySyJxOKA/O7G4X/dd0c46OgECrLkSs2eSjOJcGUjACRntCcoRxaQ5kW9q+EDaimDC3GmoXg/R75r+kcNI+b7oULVdiELdgBDw7hFM6hBR1gcA+P8AwvzoPz5LxOaFWcKbYN+CHn7RPRApwN</latexit><latexit sha1_base64="gWB5KUM6BR3qSwsw69ZWFLLnnrs=">AAACB3icbZDLSgMxGIX/qbdab9Wtm2ARVLDMuFEXguDGZYVWhc44ZNJMG8xkhuQfoQzzDm58FTcuVHwDd76N6UXwdiBwck5C8n9RJoVB1/1wKjOzc/ML1cXa0vLK6lp9ffnSpLlmvMNSmerriBouheIdFCj5daY5TSLJr6Lbs1F/dce1Ealq4zDjQUL7SsSCUbRRWN9rh4WvExJp0R9gefK1jcodb5/fFPs+0jz0VV7uhvWG23THIn+NNzUNmKoV1t/9XsryhCtkkhrT9dwMg4JqFEzysubnhmeU3dI+71qraMJNUIxnKsm2TXokTrVdCsk4/X6joIkxwySyJxOKA/O7G4X/dd0c46OgECrLkSs2eSjOJcGUjACRntCcoRxaQ5kW9q+EDaimDC3GmoXg/R75r+kcNI+b7oULVdiELdgBDw7hFM6hBR1gcA+P8AwvzoPz5LxOaFWcKbYN+CHn7RPRApwN</latexit><latexit sha1_base64="sgMdgOpielhbMuUoml8LA1v8ros=">AAACEnicbVDLSgMxFM34rPVVdekmWIQqtMy4URdC0Y3LCh1b6NQhk6ZtaCYzJHeEMsw/uPFX3LhQcevKnX9j+hC09cCFk3PuJfeeIBZcg21/WQuLS8srq7m1/PrG5tZ2YWf3VkeJosylkYhUMyCaCS6ZCxwEa8aKkTAQrBEMrkZ+454pzSNZh2HM2iHpSd7llICR/MJx3U89FeJA8V4fsoufZ5CVnDK7S8sekMT3ZJId+YWiXbHHwPPEmZIimqLmFz69TkSTkEmggmjdcuwY2ilRwKlgWd5LNIsJHZAeaxkqSch0Ox3flOFDo3RwN1KmJOCx+nsiJaHWwzAwnSGBvp71RuJ/XiuB7lk75TJOgEk6+aibCAwRHgWEO1wxCmJoCKGKm10x7RNFKJgY8yYEZ/bkeeKeVM4r9o1drF5O08ihfXSASshBp6iKrlENuYiiB/SEXtCr9Wg9W2/W+6R1wZrO7KE/sD6+AZLPnYY=</latexit><latexit sha1_base64="GX7UlLcYiDGDf9Yf4B4XSg2asq0=">AAACEnicbVDLSgMxFM3UV62vqks3wSJUoWVGBHUhFN24rNDaQqcOmTRtQzOZIbkjlGH+wY2/4saFiltX7vwb04egrQcunJxzL7n3+JHgGmz7y8osLC4tr2RXc2vrG5tb+e2dWx3GirI6DUWomj7RTHDJ6sBBsGakGAl8wRr+4GrkN+6Z0jyUNRhGrB2QnuRdTgkYycsf1bzEVQH2Fe/1Ib34efpp0Smxu6TkAok9V8bpoZcv2GV7DDxPnCkpoCmqXv7T7YQ0DpgEKojWLceOoJ0QBZwKlubcWLOI0AHpsZahkgRMt5PxTSk+MEoHd0NlSgIeq78nEhJoPQx80xkQ6OtZbyT+57Vi6J61Ey6jGJikk4+6scAQ4lFAuMMVoyCGhhCquNkV0z5RhIKJMWdCcGZPnif14/J52b45KVQup2lk0R7aR0XkoFNUQdeoiuqIogf0hF7Qq/VoPVtv1vukNWNNZ3bRH1gf35QPnYo=</latexit><latexit sha1_base64="GX7UlLcYiDGDf9Yf4B4XSg2asq0=">AAACEnicbVDLSgMxFM3UV62vqks3wSJUoWVGBHUhFN24rNDaQqcOmTRtQzOZIbkjlGH+wY2/4saFiltX7vwb04egrQcunJxzL7n3+JHgGmz7y8osLC4tr2RXc2vrG5tb+e2dWx3GirI6DUWomj7RTHDJ6sBBsGakGAl8wRr+4GrkN+6Z0jyUNRhGrB2QnuRdTgkYycsf1bzEVQH2Fe/1Ib34efpp0Smxu6TkAok9V8bpoZcv2GV7DDxPnCkpoCmqXv7T7YQ0DpgEKojWLceOoJ0QBZwKlubcWLOI0AHpsZahkgRMt5PxTSk+MEoHd0NlSgIeq78nEhJoPQx80xkQ6OtZbyT+57Vi6J61Ey6jGJikk4+6scAQ4lFAuMMVoyCGhhCquNkV0z5RhIKJMWdCcGZPnif14/J52b45KVQup2lk0R7aR0XkoFNUQdeoiuqIogf0hF7Qq/VoPVtv1vukNWNNZ3bRH1gf35QPnYo=</latexit><latexit sha1_base64="GX7UlLcYiDGDf9Yf4B4XSg2asq0=">AAACEnicbVDLSgMxFM3UV62vqks3wSJUoWVGBHUhFN24rNDaQqcOmTRtQzOZIbkjlGH+wY2/4saFiltX7vwb04egrQcunJxzL7n3+JHgGmz7y8osLC4tr2RXc2vrG5tb+e2dWx3GirI6DUWomj7RTHDJ6sBBsGakGAl8wRr+4GrkN+6Z0jyUNRhGrB2QnuRdTgkYycsf1bzEVQH2Fe/1Ib34efpp0Smxu6TkAok9V8bpoZcv2GV7DDxPnCkpoCmqXv7T7YQ0DpgEKojWLceOoJ0QBZwKlubcWLOI0AHpsZahkgRMt5PxTSk+MEoHd0NlSgIeq78nEhJoPQx80xkQ6OtZbyT+57Vi6J61Ey6jGJikk4+6scAQ4lFAuMMVoyCGhhCquNkV0z5RhIKJMWdCcGZPnif14/J52b45KVQup2lk0R7aR0XkoFNUQdeoiuqIogf0hF7Qq/VoPVtv1vukNWNNZ3bRH1gf35QPnYo=</latexit><latexit sha1_base64="GX7UlLcYiDGDf9Yf4B4XSg2asq0=">AAACEnicbVDLSgMxFM3UV62vqks3wSJUoWVGBHUhFN24rNDaQqcOmTRtQzOZIbkjlGH+wY2/4saFiltX7vwb04egrQcunJxzL7n3+JHgGmz7y8osLC4tr2RXc2vrG5tb+e2dWx3GirI6DUWomj7RTHDJ6sBBsGakGAl8wRr+4GrkN+6Z0jyUNRhGrB2QnuRdTgkYycsf1bzEVQH2Fe/1Ib34efpp0Smxu6TkAok9V8bpoZcv2GV7DDxPnCkpoCmqXv7T7YQ0DpgEKojWLceOoJ0QBZwKlubcWLOI0AHpsZahkgRMt5PxTSk+MEoHd0NlSgIeq78nEhJoPQx80xkQ6OtZbyT+57Vi6J61Ey6jGJikk4+6scAQ4lFAuMMVoyCGhhCquNkV0z5RhIKJMWdCcGZPnif14/J52b45KVQup2lk0R7aR0XkoFNUQdeoiuqIogf0hF7Qq/VoPVtv1vukNWNNZ3bRH1gf35QPnYo=</latexit><latexit sha1_base64="GX7UlLcYiDGDf9Yf4B4XSg2asq0=">AAACEnicbVDLSgMxFM3UV62vqks3wSJUoWVGBHUhFN24rNDaQqcOmTRtQzOZIbkjlGH+wY2/4saFiltX7vwb04egrQcunJxzL7n3+JHgGmz7y8osLC4tr2RXc2vrG5tb+e2dWx3GirI6DUWomj7RTHDJ6sBBsGakGAl8wRr+4GrkN+6Z0jyUNRhGrB2QnuRdTgkYycsf1bzEVQH2Fe/1Ib34efpp0Smxu6TkAok9V8bpoZcv2GV7DDxPnCkpoCmqXv7T7YQ0DpgEKojWLceOoJ0QBZwKlubcWLOI0AHpsZahkgRMt5PxTSk+MEoHd0NlSgIeq78nEhJoPQx80xkQ6OtZbyT+57Vi6J61Ey6jGJikk4+6scAQ4lFAuMMVoyCGhhCquNkV0z5RhIKJMWdCcGZPnif14/J52b45KVQup2lk0R7aR0XkoFNUQdeoiuqIogf0hF7Qq/VoPVtv1vukNWNNZ3bRH1gf35QPnYo=</latexit>

15K ⌧⌫ ⇠ 0.6<latexit sha1_base64="pMA5EQCuzYu39tsHXTWg60rXTik=">AAAB+XicbVDLSsNAFJ34rPXV6tLNYBFchUTEx67oxmUFYwtNCJPppB06MwnzUErsp7hxoeLWP3Hn3zhts9DWAxcO59zLvfckOaNKe963s7S8srq2Xtmobm5t7+zW6nv3KjMSkwBnLJOdBCnCqCCBppqRTi4J4gkj7WR4PfHbD0Qqmok7PcpJxFFf0JRipK0U1+qhRiYOhYGhohx67llca3iuNwVcJH5JGqBEK659hb0MG06Exgwp1fW9XEcFkppiRsbV0CiSIzxEfdK1VCBOVFRMTx/DI6v0YJpJW0LDqfp7okBcqRFPbCdHeqDmvYn4n9c1Or2ICipyo4nAs0WpYVBncJID7FFJsGYjSxCW1N4K8QBJhLVNq2pD8OdfXiTBiXvperenjeZVmUYFHIBDcAx8cA6a4Aa0QAAweATP4BW8OU/Oi/PufMxal5xyZh/8gfP5A0a2kuU=</latexit><latexit sha1_base64="pMA5EQCuzYu39tsHXTWg60rXTik=">AAAB+XicbVDLSsNAFJ34rPXV6tLNYBFchUTEx67oxmUFYwtNCJPppB06MwnzUErsp7hxoeLWP3Hn3zhts9DWAxcO59zLvfckOaNKe963s7S8srq2Xtmobm5t7+zW6nv3KjMSkwBnLJOdBCnCqCCBppqRTi4J4gkj7WR4PfHbD0Qqmok7PcpJxFFf0JRipK0U1+qhRiYOhYGhohx67llca3iuNwVcJH5JGqBEK659hb0MG06Exgwp1fW9XEcFkppiRsbV0CiSIzxEfdK1VCBOVFRMTx/DI6v0YJpJW0LDqfp7okBcqRFPbCdHeqDmvYn4n9c1Or2ICipyo4nAs0WpYVBncJID7FFJsGYjSxCW1N4K8QBJhLVNq2pD8OdfXiTBiXvperenjeZVmUYFHIBDcAx8cA6a4Aa0QAAweATP4BW8OU/Oi/PufMxal5xyZh/8gfP5A0a2kuU=</latexit><latexit sha1_base64="pMA5EQCuzYu39tsHXTWg60rXTik=">AAAB+XicbVDLSsNAFJ34rPXV6tLNYBFchUTEx67oxmUFYwtNCJPppB06MwnzUErsp7hxoeLWP3Hn3zhts9DWAxcO59zLvfckOaNKe963s7S8srq2Xtmobm5t7+zW6nv3KjMSkwBnLJOdBCnCqCCBppqRTi4J4gkj7WR4PfHbD0Qqmok7PcpJxFFf0JRipK0U1+qhRiYOhYGhohx67llca3iuNwVcJH5JGqBEK659hb0MG06Exgwp1fW9XEcFkppiRsbV0CiSIzxEfdK1VCBOVFRMTx/DI6v0YJpJW0LDqfp7okBcqRFPbCdHeqDmvYn4n9c1Or2ICipyo4nAs0WpYVBncJID7FFJsGYjSxCW1N4K8QBJhLVNq2pD8OdfXiTBiXvperenjeZVmUYFHIBDcAx8cA6a4Aa0QAAweATP4BW8OU/Oi/PufMxal5xyZh/8gfP5A0a2kuU=</latexit>

⌧⌫ = ⌃dustk⌫<latexit sha1_base64="zbXDtg5R4rkYO/0x4uxaRjrMTXQ=">AAACCHicbVA9SwNBEN2LXzF+nVraLAbBKlxEUAshaGMZ0ZhALhx7m02yZHfv2J0VwpHWxr9iY6Fi60+w89+4Sa7Q6IOBx3szzMyLU8ENBMGXV1hYXFpeKa6W1tY3Nrf87Z07k1hNWYMmItGtmBgmuGIN4CBYK9WMyFiwZjy8nPjNe6YNT9QtjFLWkaSveI9TAk6KfBwCsVGo7Hl4w/uSRFmoJe5aA2M8nOiRXw4qwRT4L6nmpIxy1CP/M+wm1EqmgApiTLsapNDJiAZOBRuXQmtYSuiQ9FnbUUUkM51s+skYHzili3uJdqUAT9WfExmRxoxk7DolgYGZ9ybif17bQu+0k3GVWmCKzhb1rMCQ4EksuMs1oyBGjhCqubsV0wHRhIILr+RCqM6//Jc0jipnleD6uFy7yNMooj20jw5RFZ2gGrpCddRAFD2gJ/SCXr1H79l7895nrQUvn9lFv+B9fAMYQ5on</latexit><latexit sha1_base64="zbXDtg5R4rkYO/0x4uxaRjrMTXQ=">AAACCHicbVA9SwNBEN2LXzF+nVraLAbBKlxEUAshaGMZ0ZhALhx7m02yZHfv2J0VwpHWxr9iY6Fi60+w89+4Sa7Q6IOBx3szzMyLU8ENBMGXV1hYXFpeKa6W1tY3Nrf87Z07k1hNWYMmItGtmBgmuGIN4CBYK9WMyFiwZjy8nPjNe6YNT9QtjFLWkaSveI9TAk6KfBwCsVGo7Hl4w/uSRFmoJe5aA2M8nOiRXw4qwRT4L6nmpIxy1CP/M+wm1EqmgApiTLsapNDJiAZOBRuXQmtYSuiQ9FnbUUUkM51s+skYHzili3uJdqUAT9WfExmRxoxk7DolgYGZ9ybif17bQu+0k3GVWmCKzhb1rMCQ4EksuMs1oyBGjhCqubsV0wHRhIILr+RCqM6//Jc0jipnleD6uFy7yNMooj20jw5RFZ2gGrpCddRAFD2gJ/SCXr1H79l7895nrQUvn9lFv+B9fAMYQ5on</latexit><latexit sha1_base64="zbXDtg5R4rkYO/0x4uxaRjrMTXQ=">AAACCHicbVA9SwNBEN2LXzF+nVraLAbBKlxEUAshaGMZ0ZhALhx7m02yZHfv2J0VwpHWxr9iY6Fi60+w89+4Sa7Q6IOBx3szzMyLU8ENBMGXV1hYXFpeKa6W1tY3Nrf87Z07k1hNWYMmItGtmBgmuGIN4CBYK9WMyFiwZjy8nPjNe6YNT9QtjFLWkaSveI9TAk6KfBwCsVGo7Hl4w/uSRFmoJe5aA2M8nOiRXw4qwRT4L6nmpIxy1CP/M+wm1EqmgApiTLsapNDJiAZOBRuXQmtYSuiQ9FnbUUUkM51s+skYHzili3uJdqUAT9WfExmRxoxk7DolgYGZ9ybif17bQu+0k3GVWmCKzhb1rMCQ4EksuMs1oyBGjhCqubsV0wHRhIILr+RCqM6//Jc0jipnleD6uFy7yNMooj20jw5RFZ2gGrpCddRAFD2gJ/SCXr1H79l7895nrQUvn9lFv+B9fAMYQ5on</latexit>

⌃dust 0.1� 1 g cm�2<latexit sha1_base64="5rfhqIQ998JYOOUtU9OJpoq2axU=">AAACEHicbVBNS8NAEN3Ur1q/qh69LBahh7YkRVBvRS8eKxpbaGLYbLbt0t0k7G6EEupP8OJf8eJBxatHb/4bN20O2vpg4PHeDDPz/JhRqUzz2ygsLa+srhXXSxubW9s75d29WxklAhMbRywSXR9JwmhIbEUVI91YEMR9Rjr+6CLzO/dESBqFN2ocE5ejQUj7FCOlJa9cda7pgCMvdQSHQSLV5MFsWHXLqWXCwKlBzO/SenPilStmw5wCLhIrJxWQo+2Vv5wgwgknocIMSdmzzFi5KRKKYkYmJSeRJEZ4hAakp2mIOJFuOv1oAo+0EsB+JHSFCk7V3xMp4lKOua87OVJDOe9l4n9eL1H9UzelYZwoEuLZon7CoIpgFg8MqCBYsbEmCAuqb4V4iATCSodY0iFY8y8vErvZOGuYV8eV1nmeRhEcgENQBRY4AS1wCdrABhg8gmfwCt6MJ+PFeDc+Zq0FI5/ZB39gfP4AcNObrw==</latexit><latexit sha1_base64="5rfhqIQ998JYOOUtU9OJpoq2axU=">AAACEHicbVBNS8NAEN3Ur1q/qh69LBahh7YkRVBvRS8eKxpbaGLYbLbt0t0k7G6EEupP8OJf8eJBxatHb/4bN20O2vpg4PHeDDPz/JhRqUzz2ygsLa+srhXXSxubW9s75d29WxklAhMbRywSXR9JwmhIbEUVI91YEMR9Rjr+6CLzO/dESBqFN2ocE5ejQUj7FCOlJa9cda7pgCMvdQSHQSLV5MFsWHXLqWXCwKlBzO/SenPilStmw5wCLhIrJxWQo+2Vv5wgwgknocIMSdmzzFi5KRKKYkYmJSeRJEZ4hAakp2mIOJFuOv1oAo+0EsB+JHSFCk7V3xMp4lKOua87OVJDOe9l4n9eL1H9UzelYZwoEuLZon7CoIpgFg8MqCBYsbEmCAuqb4V4iATCSodY0iFY8y8vErvZOGuYV8eV1nmeRhEcgENQBRY4AS1wCdrABhg8gmfwCt6MJ+PFeDc+Zq0FI5/ZB39gfP4AcNObrw==</latexit><latexit sha1_base64="5rfhqIQ998JYOOUtU9OJpoq2axU=">AAACEHicbVBNS8NAEN3Ur1q/qh69LBahh7YkRVBvRS8eKxpbaGLYbLbt0t0k7G6EEupP8OJf8eJBxatHb/4bN20O2vpg4PHeDDPz/JhRqUzz2ygsLa+srhXXSxubW9s75d29WxklAhMbRywSXR9JwmhIbEUVI91YEMR9Rjr+6CLzO/dESBqFN2ocE5ejQUj7FCOlJa9cda7pgCMvdQSHQSLV5MFsWHXLqWXCwKlBzO/SenPilStmw5wCLhIrJxWQo+2Vv5wgwgknocIMSdmzzFi5KRKKYkYmJSeRJEZ4hAakp2mIOJFuOv1oAo+0EsB+JHSFCk7V3xMp4lKOua87OVJDOe9l4n9eL1H9UzelYZwoEuLZon7CoIpgFg8MqCBYsbEmCAuqb4V4iATCSodY0iFY8y8vErvZOGuYV8eV1nmeRhEcgENQBRY4AS1wCdrABhg8gmfwCt6MJ+PFeDc+Zq0FI5/ZB39gfP4AcNObrw==</latexit>

SPF2 14 MARCH 2017 P. CAZZOLETTI

@2mm

Page 14: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Questions to answer

1. IS THE VORTEX MASSIVE ENOUGH?

2. IS DUST BEING TRAPPED?

3. IS DUST GROWING?

14

SPF2 14 MARCH 2017 P. CAZZOLETTI

Page 15: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Is dust being trapped?

15

Rephrased:isthereanenhancementofdustwithrespecttogas?Modelsshowgas/dust~1(e.g.Pinilla+2012)

Baruteau

&Zh

u201

6 ⌃gas ⇠ 1 g cm�2<latexit sha1_base64="Glk2w7jKj0U6vUYbO5vtV/paT0U=">AAACD3icbVC7TsMwFHXKq5RXgJHFokIwlCqpkICtgoWxCEIrNaFyXCe1aieR7SBVUT6BhV9hYQDEysrG3+CmHaDlSFc6Pude+d7jJ4xKZVnfRmlhcWl5pbxaWVvf2Nwyt3fuZJwKTBwcs1h0fCQJoxFxFFWMdBJBEPcZafvDy7HffiBC0ji6VaOEeByFEQ0oRkpLPfPQvaEhR73MFRyGSOaupBzabq14uzWI+X123Mh7ZtWqWwXgPLGnpAqmaPXML7cf45STSGGGpOzaVqK8DAlFMSN5xU0lSRAeopB0NY0QJ9LLioNyeKCVPgxioStSsFB/T2SISznivu7kSA3krDcW//O6qQrOvIxGSapIhCcfBSmDKobjdGCfCoIVG2mCsKB6V4gHSCCsdIYVHYI9e/I8cRr187p1fVJtXkzTKIM9sA+OgA1OQRNcgRZwAAaP4Bm8gjfjyXgx3o2PSWvJmM7sgj8wPn8ATPybqw==</latexit><latexit sha1_base64="Glk2w7jKj0U6vUYbO5vtV/paT0U=">AAACD3icbVC7TsMwFHXKq5RXgJHFokIwlCqpkICtgoWxCEIrNaFyXCe1aieR7SBVUT6BhV9hYQDEysrG3+CmHaDlSFc6Pude+d7jJ4xKZVnfRmlhcWl5pbxaWVvf2Nwyt3fuZJwKTBwcs1h0fCQJoxFxFFWMdBJBEPcZafvDy7HffiBC0ji6VaOEeByFEQ0oRkpLPfPQvaEhR73MFRyGSOaupBzabq14uzWI+X123Mh7ZtWqWwXgPLGnpAqmaPXML7cf45STSGGGpOzaVqK8DAlFMSN5xU0lSRAeopB0NY0QJ9LLioNyeKCVPgxioStSsFB/T2SISznivu7kSA3krDcW//O6qQrOvIxGSapIhCcfBSmDKobjdGCfCoIVG2mCsKB6V4gHSCCsdIYVHYI9e/I8cRr187p1fVJtXkzTKIM9sA+OgA1OQRNcgRZwAAaP4Bm8gjfjyXgx3o2PSWvJmM7sgj8wPn8ATPybqw==</latexit><latexit sha1_base64="Glk2w7jKj0U6vUYbO5vtV/paT0U=">AAACD3icbVC7TsMwFHXKq5RXgJHFokIwlCqpkICtgoWxCEIrNaFyXCe1aieR7SBVUT6BhV9hYQDEysrG3+CmHaDlSFc6Pude+d7jJ4xKZVnfRmlhcWl5pbxaWVvf2Nwyt3fuZJwKTBwcs1h0fCQJoxFxFFWMdBJBEPcZafvDy7HffiBC0ji6VaOEeByFEQ0oRkpLPfPQvaEhR73MFRyGSOaupBzabq14uzWI+X123Mh7ZtWqWwXgPLGnpAqmaPXML7cf45STSGGGpOzaVqK8DAlFMSN5xU0lSRAeopB0NY0QJ9LLioNyeKCVPgxioStSsFB/T2SISznivu7kSA3krDcW//O6qQrOvIxGSapIhCcfBSmDKobjdGCfCoIVG2mCsKB6V4gHSCCsdIYVHYI9e/I8cRr187p1fVJtXkzTKIM9sA+OgA1OQRNcgRZwAAaP4Bm8gjfjyXgx3o2PSWvJmM7sgj8wPn8ATPybqw==</latexit>

SPF2 14 MARCH 2017 P. CAZZOLETTI

WecalculateGas/dust~1

St / ⌃�1gas

<latexit sha1_base64="r10cwt/8z3lwRYSA9fxi/4z4PsI=">AAACBnicbVA9SwNBEN2LXzF+RS0FWQyCjeFOBLUL2lhG4plA7gx7m02yZPf22J0TwpHOxr9iY6Fi62+w89+4+Sg08cHA470ZZuZFieAGXPfbyS0sLi2v5FcLa+sbm1vF7Z07o1JNmU+VULoREcMEj5kPHARrJJoRGQlWj/pXI7/+wLThKr6FQcJCSbox73BKwEqt4n4NgkSrBFRQ411JWlmgJe4SM7zPjr1hq1hyy+4YeJ54U1JCU1Rbxa+grWgqWQxUEGOanptAmBENnAo2LASpYQmhfdJlTUtjIpkJs/EfQ3xolTbuKG0rBjxWf09kRBozkJHtlAR6ZtYbif95zRQ652HG4yQFFtPJok4qMCg8CgW3uWYUxMASQjW3t2LaI5pQsNEVbAje7MvzxD8pX5S9m9NS5XKaRh7toQN0hDx0hiroGlWRjyh6RM/oFb05T86L8+58TFpzznRmF/2B8/kDq9KZYA==</latexit><latexit sha1_base64="r10cwt/8z3lwRYSA9fxi/4z4PsI=">AAACBnicbVA9SwNBEN2LXzF+RS0FWQyCjeFOBLUL2lhG4plA7gx7m02yZPf22J0TwpHOxr9iY6Fi62+w89+4+Sg08cHA470ZZuZFieAGXPfbyS0sLi2v5FcLa+sbm1vF7Z07o1JNmU+VULoREcMEj5kPHARrJJoRGQlWj/pXI7/+wLThKr6FQcJCSbox73BKwEqt4n4NgkSrBFRQ411JWlmgJe4SM7zPjr1hq1hyy+4YeJ54U1JCU1Rbxa+grWgqWQxUEGOanptAmBENnAo2LASpYQmhfdJlTUtjIpkJs/EfQ3xolTbuKG0rBjxWf09kRBozkJHtlAR6ZtYbif95zRQ652HG4yQFFtPJok4qMCg8CgW3uWYUxMASQjW3t2LaI5pQsNEVbAje7MvzxD8pX5S9m9NS5XKaRh7toQN0hDx0hiroGlWRjyh6RM/oFb05T86L8+58TFpzznRmF/2B8/kDq9KZYA==</latexit><latexit sha1_base64="r10cwt/8z3lwRYSA9fxi/4z4PsI=">AAACBnicbVA9SwNBEN2LXzF+RS0FWQyCjeFOBLUL2lhG4plA7gx7m02yZPf22J0TwpHOxr9iY6Fi62+w89+4+Sg08cHA470ZZuZFieAGXPfbyS0sLi2v5FcLa+sbm1vF7Z07o1JNmU+VULoREcMEj5kPHARrJJoRGQlWj/pXI7/+wLThKr6FQcJCSbox73BKwEqt4n4NgkSrBFRQ411JWlmgJe4SM7zPjr1hq1hyy+4YeJ54U1JCU1Rbxa+grWgqWQxUEGOanptAmBENnAo2LASpYQmhfdJlTUtjIpkJs/EfQ3xolTbuKG0rBjxWf09kRBozkJHtlAR6ZtYbif95zRQ652HG4yQFFtPJok4qMCg8CgW3uWYUxMASQjW3t2LaI5pQsNEVbAje7MvzxD8pX5S9m9NS5XKaRh7toQN0hDx0hiroGlWRjyh6RM/oFb05T86L8+58TFpzznRmF/2B8/kDq9KZYA==</latexit><latexit sha1_base64="r10cwt/8z3lwRYSA9fxi/4z4PsI=">AAACBnicbVA9SwNBEN2LXzF+RS0FWQyCjeFOBLUL2lhG4plA7gx7m02yZPf22J0TwpHOxr9iY6Fi62+w89+4+Sg08cHA470ZZuZFieAGXPfbyS0sLi2v5FcLa+sbm1vF7Z07o1JNmU+VULoREcMEj5kPHARrJJoRGQlWj/pXI7/+wLThKr6FQcJCSbox73BKwEqt4n4NgkSrBFRQ411JWlmgJe4SM7zPjr1hq1hyy+4YeJ54U1JCU1Rbxa+grWgqWQxUEGOanptAmBENnAo2LASpYQmhfdJlTUtjIpkJs/EfQ3xolTbuKG0rBjxWf09kRBozkJHtlAR6ZtYbif95zRQ652HG4yQFFtPJok4qMCg8CgW3uWYUxMASQjW3t2LaI5pQsNEVbAje7MvzxD8pX5S9m9NS5XKaRh7toQN0hDx0hiroGlWRjyh6RM/oFb05T86L8+58TFpzznRmF/2B8/kDq9KZYA==</latexit>

Page 16: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Vortex width

16

Theazimuthalwidthofthevortexdecreaseswithwavelengthaspredictedby(Birnstiel+2013)

SPF2 14 MARCH 2017 P. CAZZOLETTI

Page 17: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Questions to answer

1. IS THE VORTEX MASSIVE ENOUGH?

2. IS DUST BEING TRAPPED?

3. IS DUST GROWING?

17

SPF2 14 MARCH 2017 P. CAZZOLETTI

Page 18: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Is dust growing?

18

Band4andBand7

•  αatthelocationofthevortexisconsistentwithlargergrains•  Thelaunchingpointofthespiralisclosetowherethelargergrainsare

SPF2 14 MARCH 2017 P. CAZZOLETTI

VLT/SPHERE

Page 19: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

TAKE HOME MESSAGES & CONCLUSIONS •  Thereisobservationalevidenceofaconnectionbetweenvorticesandspiral

arms

•  VortexinHD135344Bobservedandresolvedatdifferentwavelengths:•  Azimuthalshiftdetected

•  Dustefficientlytrappedinthevortex

•  Spectralindexhintstodustgrowth

•  Consistentwithplanetesimalformationoccurringinsidethevortex.

•  Shouldwelookfortheoriginofspiralarmsinvortices?

•  Howmuchmasscanbehiddeninunobservabledustgrains?

19

SPF2 14 MARCH 2017 P. CAZZOLETTI

THANK YOU!

Page 20: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Band 9

20

SPF2 14 MARCH 2017 P. CAZZOLETTI

Page 21: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

Differences between the 4 bands

21

SPF2 14 MARCH 2017 P. CAZZOLETTI

Page 22: WHERE DO THE SPIRALS COME FROM? · SPIRALS COME FROM? A multi-wavelength, high-resolution study of HD135344B ... • Higher resolution: 0.06” • Band 3 and Band 4 data: expected

22

IRS48

vanderMarel+13

St = 0.015⇥� s

1mm

�� ⇢pc1 g cm�3

��10 g cm�2

⌃gas

<latexit sha1_base64="TIVI7kduMhki94DJ+fKZYqrvsrw=">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</latexit><latexit sha1_base64="TIVI7kduMhki94DJ+fKZYqrvsrw=">AAACenicbVHdatswFJa9dcuybku7y8EQC6MJa4Odpmy9GITtZpcZWZZAlAZZkR1RyTbS8SAYv8QerXd9k94MJicmZMkOCD6+H+mcoyCVwoDn3Tvuo8dHT57WntWfH794+apxcvrTJJlmfMQSmehJQA2XIuYjECD5JNWcqkDycXD7tdTHv7g2Iol/wCrlM0WjWISCUbDUvPF7CJ+9judfERCKGxKIqEVCTVluitwn50QrrFRR8u0dkehlMs9LMWXF1hiRc6Zu8ovL4iDge1sLXnu6NkaGIlJ0c09ETZWaN5q2o3XhQ+BXoImqGswbd2SRsEzxGJikxkx9L4VZTjUIJnlRJ5nhKWW3NOJTC2NqB53l690V+L1lFjhMtD0x4DW7m8ipMmalAutUFJZmXyvJ/2nTDMJPs1zEaQY8ZpuHwkxiSHD5EXghNGcgVxZQpoXtFbMltbsC+111uwR/f+RDMOp2rjve916z/6XaRg29Qe9QC/noI+qjb2iARoihB+etc+a0nD9u0227HzZW16kyr9E/5fb+Asoyv9Q=</latexit><latexit sha1_base64="TIVI7kduMhki94DJ+fKZYqrvsrw=">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</latexit><latexit sha1_base64="C39OhB+IczRcjLNINXH29e9lt8M=">AAAB2HicbZDNSgMxFIXv1L86Vq1rN8EiuCpTN+pOcOOygmML7VAymTttaCYzJHeEMvQFXLhRfDB3vo3pz0KtBwIf5yTk3hMXSloKgi+vtrW9s7tX3/cPGv7h0XGz8WTz0ggMRa5y04+5RSU1hiRJYb8wyLNYYS+e3i3y3jMaK3P9SLMCo4yPtUyl4OSs7qjZCtrBUmwTOmtowVqj5ucwyUWZoSahuLWDTlBQVHFDUiic+8PSYsHFlI9x4FDzDG1ULcecs3PnJCzNjTua2NL9+aLimbWzLHY3M04T+zdbmP9lg5LS66iSuigJtVh9lJaKUc4WO7NEGhSkZg64MNLNysSEGy7INeO7Djp/N96E8LJ90w4eAqjDKZzBBXTgCm7hHroQgoAEXuDNm3iv3vuqqpq37uwEfsn7+Aap5IoM</latexit><latexit sha1_base64="vn5cvVMUyiAoB+Aa5Gi/8k+QcwE=">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</latexit><latexit sha1_base64="vn5cvVMUyiAoB+Aa5Gi/8k+QcwE=">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</latexit><latexit sha1_base64="2HbayikO/Ds/65pdlMrmS3GP8SE=">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</latexit><latexit sha1_base64="TIVI7kduMhki94DJ+fKZYqrvsrw=">AAACenicbVHdatswFJa9dcuybku7y8EQC6MJa4Odpmy9GITtZpcZWZZAlAZZkR1RyTbS8SAYv8QerXd9k94MJicmZMkOCD6+H+mcoyCVwoDn3Tvuo8dHT57WntWfH794+apxcvrTJJlmfMQSmehJQA2XIuYjECD5JNWcqkDycXD7tdTHv7g2Iol/wCrlM0WjWISCUbDUvPF7CJ+9judfERCKGxKIqEVCTVluitwn50QrrFRR8u0dkehlMs9LMWXF1hiRc6Zu8ovL4iDge1sLXnu6NkaGIlJ0c09ETZWaN5q2o3XhQ+BXoImqGswbd2SRsEzxGJikxkx9L4VZTjUIJnlRJ5nhKWW3NOJTC2NqB53l690V+L1lFjhMtD0x4DW7m8ipMmalAutUFJZmXyvJ/2nTDMJPs1zEaQY8ZpuHwkxiSHD5EXghNGcgVxZQpoXtFbMltbsC+111uwR/f+RDMOp2rjve916z/6XaRg29Qe9QC/noI+qjb2iARoihB+etc+a0nD9u0227HzZW16kyr9E/5fb+Asoyv9Q=</latexit><latexit sha1_base64="TIVI7kduMhki94DJ+fKZYqrvsrw=">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</latexit><latexit sha1_base64="TIVI7kduMhki94DJ+fKZYqrvsrw=">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</latexit><latexit sha1_base64="TIVI7kduMhki94DJ+fKZYqrvsrw=">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</latexit><latexit sha1_base64="TIVI7kduMhki94DJ+fKZYqrvsrw=">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</latexit>

SPF2 14 MARCH 2017 P. CAZZOLETTI