# Presentation: 561632

## Limits on iron-dominated, non-LTE fallback disk in SN 1987A

**K. Werner**
**T. Nagel**
**T. Rauch**
**Institute for Astronomy and Astrophysics**
**University of Tübingen, Germany**

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## SN 1987A, HST ACS/F555W image (Graves et al. 2005)

**SN 1987A, HST ACS/F555W image (Graves et al. 2005)**

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## Graves et al. (2005): 

- Upper flux limit on a point source in SN 1987A Fopt<1.6∙10-14ergs s-1 cm-2, corresponds to
- 	Lopt<   8∙1033 ergs s-1
- 	(assuming 35% dust absorption in the SNR)
- Should fallback disk be present: Flux limit allows to put constraints on disk
- E.g., thin-disk accretion:
- 	Rmax<1010cm  with  M-dot< 3∙10-9 M/yr

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## Upper limits for M-dot and Rmax, e.g., Rmax=1010 cm and M-dot= 3∙10-9 M/yr

**Upper limits for M-dot and R****max****, e.g., ****R****max****=10****10**** cm**** and ****M-dot= ****3****∙****10****-9**** M********/yr**

**Graves et al. 2005:**

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## Limits on accretion rate and maximum disk size were derived with an α-disk model, divided into concentric rings emitting blackbody spectra

- Question: How do these limits change if we drop the blackbody assumption?
- Performed detailed NLTE radiation transfer calculations to achieve more realistic disk-flux spectra

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## NLTE disk modeling

- Radial structure: α-disk   (Shakura & Sunyaev 1973)
- Divide disk into concentric rings

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## NLTE disk modeling

- Radial structure: α-disk   (Shakura & Sunyaev 1973)
- Divide disk into concentric rings
- Each ring: plane-parallel radiating slab, detailed vertical structure, computed by AcDc (Accretion Disk code):
**hydrostatic equilibrium**    (gas and radiation pressure)
**radiative equilibrium**         (full line blanketing, Unsöld-Lucy scheme)
**NLTE rate equations**         (pre-conditioned  linear)
**radiation transfer eqs.**      (short characteristics, allowing for irradiation)
- Computational method: **A**ccelerated **L**ambda **I**teration (ALI) for simultaneous solution of all equations
- Kinematic viscosity parameterized by Reynolds number
- 	(Re=15 000  α0.01)

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## Non-LTE model atom for iron

- Ionisation stages Fe I – XI
- Number of line transitions: 3 001 235 (from Kurucz)
- Combined into „superlines“ between „superlevels“
- Opacity sampling with 30 700 frequency points

**photon cross-section Fe IV superline 1 ****→**** 7**

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## Input parameters for disk model presented here

MNS=1.4 M     (RNS=9.7 km) 
Inner and outer disk radii: 2000 km, 200 000 km (9 rings)
Accretion rate: 3∙10-9 M /yr
Chemical composition:                                              
     a) pure iron
     b) silicon-burning ash:  Si=0.1, S=0.1, Fe=0.8  (mass fractions)

      X-ray irradiation by central source is currently neglected

**M****NS****=1.4 M********     (R****NS****=9.7 km) **
**Inner and outer disk radii: 2000 km, 200**** ****000 km (9 rings)**
**Accretion rate: 3****∙****10****-9**** M******** /yr**
**Chemical composition:                                              **
**     ****a) pure iron**
**     ****b) silicon-burning ash:  Si=0.1, S=0.1, Fe=0.8  (mass fractions)**
**      ****X-ray irradiation by central source is currently neglected**

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## Radial disk structure:  effective temperature  Teff (R) 

**R = 40 000 km**

**T****eff ****= 33 000 K**

**Radial disk structure:  effective temperature  ****T****eff ****(R)**** **

- .
-                                           .

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## Radial disk structure:  Kepler rotation velocity  vrot(R) 

**R = 40 000 km**

**v****rot ****= 2200 km/sec   ****→  P****rot**** ******** 2 min**

**Radial disk structure:  Kepler rotation velocity  ****v****rot****(R)**** **

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- 20.11.2002

## Temperature structure, cut through disk vertical to midplane

**Temperature structure, cut through disk vertical to midplane**

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- 20.11.2002

## Teff = 300 000 K

**T****eff ****= 300 000 K**

**T****eff ****= 72 000 K**

**T****eff ****= 33 000 K**

**T****eff ****= 9800 K**

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## Vertical stratification of disk

**Vertical stratification of disk**
**at R = 40 000 km  **
**(ring 8, T****eff ****= 33 000 K)**
******Ross**=1
**z = 400 km  above midplane**
**T = 39 000 K**
**log g = 5.1 **
**log ρ = - 7.1,  n****e ****= 2.9∙10****15**** (cgs)**

**surface                                midplane**

******Ross**=1

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## Temperature structure, cut through disk vertical to midplane

**Temperature structure, cut through disk vertical to midplane**

**x**

******Ross**=1

**R = 40 000 km**

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## Effect of disk composition: pure Fe vs. Si-burning ash  (ring 8)

**Effect of disk composition: pure Fe vs. Si-burning ash  ****(ring 8)**

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## surface                                                                                         midplane

******Ross**=1

**surface                                                                                         midplane**

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- 20.11.2002

## LTE vs. non-LTE (ring 8, specific intensity at i = 87o) 

**LTE**** ****vs.**** non-LTE ****(ring 8, specific intensity at i = 87****o****) **

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## Limb darkening (ring 8, specific intensity at i = 87o and i = 18o)

**Limb darkening ****(ring 8, specific intensity at ****i = 87****o**** and ****i = 18****o****)**

**“****face-on“**

**“****edge-on“**

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

##       Limb darkening (ring 8, specific intensity at i = 87o and i = 18o)       

**      ****Limb darkening ****(ring 8, specific intensity at ****i = 87****o**** and ****i = 18****o****)       **

**blackbody**

**“****face-on“**

**“****edge-on“**

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## Complete disk spectrum, Kepler rotation included, different inclinations

**Complete disk spectrum, Kepler rotation included, different inclinations**

**i=18****o**

**i=77****o**

**i=87****o**

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## Summary

- Overall disk spectrum independent of detailed chemical composition as long as iron is the main constituent: no difference between pure-Fe and Si-burning ash compositions.
- Strong iron line blanketing causes broad (>100 Å) spectral features that could be detectable even from edge-on disks.
- Overall disk spectrum not influenced by non-LTE effects. However, equivalent widths of individual line blends can change by a factor of 2.
- Limb darkening affects the overall disk spectrum. UV/optical flux can be reduced by about a factor of 3 when disk is seen almost edge-on (in addition to foreshortening factor).

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## Depending on inclination and wavelength band, the UV/optical flux deviates from a blackbody radiating disk by up to factor +/-3

**Much** larger differences in soft X-rays: blackbody disk overestimates flux by orders of magnitude
**And what about Graves et al.’s limits on disk size and accretion rate?**

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

##       Limb darkening (ring 8, specific intensity at i = 87o and i = 18o)       

**      ****Limb darkening ****(ring 8, specific intensity at ****i = 87****o**** and ****i = 18****o****)       **

**blackbody**

**“****face-on“**

**“****edge-on“**

**They used flux limit measured in wide-band UV filter F330W that is centered at 3300 Å with half-width  500 Å.**

**Disk flux 20% larger than bb**

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002

## Conclusion: At a fixed M-dot (3∙10-9 M/yr), the disk must be significantly smaller than derived from blackbody models; much smaller than 25% because 3300Å-flux hardly depends on disk size (outer disk regions are cool, only weak contribution to UV flux) 

**Conclusion: At a fixed M-dot (3∙10****-9**** M********/yr), the ****disk must be significantly smaller**** than derived from blackbody models; much smaller than 25% because 3300****Å****-flux hardly depends on disk size (outer disk regions are cool, only weak contribution to UV flux) **
**Further modeling needed for whole parameter range to make quantitative statement**

- Lehrerfortbildung Planetarium Stuttgart

- 20.11.2002