# Presentation: 596932

## High Energy Density Laboratory Astrophysics  -> Laboratory AstrophysicsExperiments and Simulations

- Davidson Symposium, 12 June 2007
- R. Lovelace, Cornell University

##    Numerical Simulations  of Accretion to                  Magnetized Stars

**   ****Numerical Simulations  of Accretion to****                  Magnetized Stars**

**Richard Lovelace****Davidson Symposium, 12 June 2007**

- Collaborators

- Marina Romanova

- Sasha Koldoba

- Galia Ustyugova

##  Young stars:  stars at the stage of the gravitational contraction - classical T Tauri stars (CTTSs)  B=103 G

-  **Young stars**:  stars at the stage of the gravitational contraction - classical T Tauri stars (CTTSs)  B=103 G

-  **White dwarfs**: cataclysmic variables –
- Intermediate polars, Dwarf Novae,
- B=106-108 G

-  **Neutron stars:** X-ray pulsars, accreting millisecond pulsars, B=108-1015 G

- Stars with Magnetic Fields

## Pringle & Rees (1972); Ghosh & Lamb (1978-79)

- Disk-magnetosphere interaction

## 3D and 2D Simulations

- Quasi-equilibrium initial conditions were developed
- MHD equations are written in the system of coordinates rotating with the star
- Viscosity (both 2D and 3D)
- Diffusivity only in 2D code
-      vis=0.01-0.2      dif=0.01-0.2
- Godunov-type numerical method and code
-     (Koldoba, Romanova, Ustyugova, Lovelace 2002)

##            Main results of 2D simulations:

-            Main results of 2D simulations:
-                         Funnel Flows

- Romanova, Ustyugova, Koldoba & Lovelace (2002)

-  Confirmed: Accretion through the funnel flow
-                     Slow rotation (in equilibrium)
-      New:   Structure of the Disk/Funnel

## Survival of Protoplanets

## Distribution of giant planets 

- Distribution of giant planets

- From catalogue supported by Jean Schneider ( Paris Observatory)

**Romanova and Lovelace, 2006, ApJ Letter**

## 3D MHD Simulations

- * || disk
- 

- Cubed Sphere grid

- 1 block: 80x31x31 – spherical: 80x62x124
- 1 block: 100x51x51 – spherical: 100x102x204

## =15o

- =15o

## Inner region

- - Matter is stopped by the magnetosphere
-  It accretes in funnel streams
-  Accretion is not stationary

## Picture is different at different density levels

- Low density

- High density

## One of density levels

- Long 3D runs: 20-40 rotations. In the past – 3-5 rotations

## Magnetic field lines

## Large misalignment angle, =60o

- Large misalignment angle, =60o

## Typical picture of matter flow for =60o

- Typical picture of matter flow for =60o

## Magnetic field lines at =75o

- Magnetic field lines at =75o

## 

- 

- - Funnel streams are NOT homogeneous
-  Hot spot is a slice of the funnel stream
-  Hot spots are NOT homogeneous as well

- Romanova, Ustyugova, Koldoba, Lovelace 2004

## Magnetospheric Flow and Hot Spots at the Surface of the Star  for Different Misalignment Angles 

- Bow-shape

- Elongated

- Bar-shape

-   Spots are NOT homogeneous: density, velocity, temperature are higher at the center
-   Harder X-ray – smaller spot, softer X-ray – larger spot

## 

- 

- Fourier spectrum

- Wavelet

- Real light curve

- “Real” Light Curve

## Quadrupole :

- Long, Romanova & Lovelace 2006, MNRAS, submitted

- Dipole + Quadrupole : Magnetic flux is larger in North hemisphere

- Accretion to a Star with Non-dipole Field

## Comparison of Accretion to a Star with a        Dipole and Quadrupole Fields

- Long, Romanova & Lovelace 2006, MNRAS, submitted

## Matter Flow to an Inclined Quadrupole

## Accretion to a Star with a  Dipole PLUS     Quadrupole Fields

##         Slow rotation             Fast rotation

-         Slow rotation             Fast rotation

- rcr > rm

- rcr < rm

- rcr

- rm

- rm

- rcr

- Most probable state is the rotational equilibrium state
-  (Ghosh & Lamb 1978)

##  rcr < RA

- Illarionov & Sunyaev 1975;
- Lovelace, Romanova and Bisnovatyi-Kogan (1999)

-  rcr < RA

-  Fc > FG

- Disk

**Trial User:**

**FAST**** ROTATING STARS: PROPELLER STAGE**

- “Weak” propeller:

- “Strong” propeller:

-   Accretion disk is weak
-  Diffusivity is small
-  Star rotates not very fast
-  Accretion, spin-down
-  No outflows

-  Accretion disk is strong
-   Matter penetrates to the region of fast  rotating magnetosphere
-  Diffusivity is larger
- Outflows

## Slide 29

## Slide 30

##  QPO=(0.01 – 0.2) *

- Propeller-driven QPOs

****** ****QPO****=(0.01 – 0.2) ***********

**         ****Example for LMXBs: **
**         ********* ****= 400 Hz    **
******QPO ****= 4 - 80 Hz**

- Fourier spectrum

## 3D Accretion Through Rayleigh-Taylor Instability

## T=5

- Different, **Unstable**  flow has been discovered !

**       ****Low accretion rate**

**      ****High accretion rate**

- Kulkarni, Romanova, & Lovelace 2007, submitted

## T=5

- Matter “sneaks” between the field lines

## In the rotational equilibrium state matter accretes through the “settled” funnel streams and forms hot spots which only slightly vary their position

In case of slowly  rotating star, funnel streams and spots may rotate faster than the star. Matter may accrete to the star due to 3D instabilities.

In case of fast rotating star, a star is in the propeller regime. A star spins-down, the disk oscillates, and powerful conical outflows may form quasi-periodically

Congratulations Ron!

- In case of slowly  rotating star, funnel streams and spots may rotate faster than the star. Matter may accrete to the star due to 3D instabilities.
- In case of fast rotating star, a star is in the propeller regime. A star spins-down, the disk oscillates, and powerful conical outflows may form quasi-periodically
- Congratulations Ron!

- Conclusions