1. ANGULAR EXPANSION IN PLANETARY NEBULAE FROM RADIO INTERFEROMETRIC DATA Yolanda Gómez Centro de Radioastronomía y Astrofísica, UNAM México

2. Asymmetrical Planetary Nebulae IV, La Palma, España Colaborators  Lizette Guzmán (CRyA, UNAM, México)  Luis F. Rodríguez (CRyA, UNAM, México)

3. Asymmetrical Planetary Nebulae IV, La Palma, España Angular expansion technique  A geometrical method in which we substract two images, taken over a period of a few years, to estimate the angular expansion rate of the nebula,  First applied by Masson (1986) to radio interferometric data to estimate distances to PNe. v D=v/ D

4. Asymmetrical Planetary Nebulae IV, La Palma, España Some examples  This technique has been applied with success to several PNe: e.g. NGC6302 (Gómez et al. 1993), NGC6572 (Hajian et al. 1995), Vy 2-2 (Christianto & Seaquist 1998).  For PNe with distances > 1 kpc the expected angular expansion rate is < 2 mas/yr. NGC 7027 (Masson 1986; 1989)

5. Asymmetrical Planetary Nebulae IV, La Palma, España Planetary Nebula M 2-43 This is the largest distance for a PN measured, up to now, with the angular expansion technique. (Guzmán, Gómez & Rodríguez 2006) See poster by Guzmán et al. VLA 3.6 cm 1999.72–1995.651999.72+1995.65

6. Asymmetrical Planetary Nebulae IV, La Palma, España Other application for the angular expansion technique

7. Asymmetrical Planetary Nebulae IV, La Palma, España The “Saturn Nebula” NGC 7009  The ansae (handles) are present in PNe with bipolar, rotating, episodic jets ( BRETS; e.g. López et al. 1995 ) and fast, low ionization emission regions (FLIERS; Balick et al. 1993 ).  In NGC 7009 the ansae are moving at about 100 km/s in the plane of the sky, relative to the nucleus (Reay & Atheton 1985; Balick et al. 1987).  The ansae are possibly the termination points of the jets (Balick et al. 1987; López et al. 2000; Steffen et al. 2001). ansae HST Red [NII]; green [OIII]; blue [He II]

8. Asymmetrical Planetary Nebulae IV, La Palma, España Proper motions of ansae NGC 7009  Few measurements of proper motions of ansae: KjPn 8 ( Meaburn 1997), Hen 2-90 ( Sahai et al. 2002), NGC7009 ( Fernández et al. 2004).  NGC 7009: From photographic plates a PM of 16 3 mas/yr (Liller 1965) From HST images a PM for the eastern ansa of 28 8 mas/yr (Fernández et al. 2004) is derived. HST images of the east ansa (Fernández, Monteiro & Schwarz 2004)

9. Asymmetrical Planetary Nebulae IV, La Palma, España Archive VLA data for NGC 7009 at 3.6 cm in two epochs: 1989.24 and 1997.33 Observations NGC 7009 VLA Applying the angular expansion technique to NGC 7009 to measure proper motions of the ansae at radio. VLA 3.6 cm

10. Asymmetrical Planetary Nebulae IV, La Palma, España Western Eastern 23 +/- 6 mas/yr 34 +/- 10 mas/yr Ansae proper motions (Rodríguez & Gómez 2007, RevMexAA, 43, 173)

11. Asymmetrical Planetary Nebulae IV, La Palma, España Derived parameters for the ansae NGC 7009 Assuming D= 860 +/- 340 pc, the v elocities of the ansae in the plane of the sky are: EAST ansa 100 +/- 50 km/s WEST ansa 140 +/- 70 km/s If the ansae are moving ballistically the estimated age is: ~300 years if they originated from the main body ~850 years if they originated from the central star.

12. Asymmetrical Planetary Nebulae IV, La Palma, España Upper limit to the expansion Difference image D 700 pc Lower limit consistent with the average of 14 available values (Acker et al. 1992; Fernández et al. 2004), 860 +/- 340 pc.  The flux density of the main body remains constant.  The flux density of the jets decreased in 30%. With an electron density 1000 – 4000 cm -3 (Bohigas et al. 1994; Goncalves et al. 2003) the recombination timescales are between 30 to 120 yrs.

13. Asymmetrical Planetary Nebulae IV, La Palma, España Conclusions  Interferometric data taken with a few years of separation can reveal the angular expansion of the nebula and it is possible to estimate its distance (e.g. M 2-43; Guzmán et al. 2006 ).  This is the first time that proper motions of ansae in PNe are determined with radio observations (NGC 7009; Rodríguez & Gómez 2007 ).

14. Asymmetrical Planetary Nebulae IV, La Palma, España Thank you