Weighing stars with a coronagraph

Transcription

1 Weighing stars with a coronagraph J. Surdej, B. Pradhan, L. Delchambre & Vortex team (jsurdej@ulg.ac.be) And with the unwanted leftovers, maybe we could make a very good meal

2 No GL Θ S =0 Θ E GL Θ E = 4GM / c 2 D od

3 No GL = 0.9 GL 28/ ARIES - Nainital - Uttarakhand

4 If Θ S < Θ E Θ E µ T = µ A + µ B > 1.34 Lensed images A and B Strong lensing! Θ S

5 θ E σ SL = πθ E2, τ ~ 10-6

6 If Θ S > Θ E Θ E Θ A Weak lensing! Θ S

7 For θ S < 10 θ E Weak lensing 10 θ E σ WL = π(10 θ E ) 2 = 100 πθ E 2 = 100 σ SL τ ~ 10-4

8 If Θ S >> Θ E Θ A = Θ S ( 1 + (Θ E / Θ S ) 2 ) µ A = 1 + (Θ E / Θ S ) 4 The first coronagraph ever used to weigh a star (Sun) could have been the moon during the total Solar eclipse in 1919: Θ E = Θ S (Θ A / Θ S ) - 1 Θ E = 4GM / c 2 D od

9 Indeed, from the measurement of Θ A and Θ S (Dyson et al. 1920), one could derive the value of M=D od c 2 Θ S2 ((Θ A / Θ S ) -1)/4G

10 In order to further increase the probability for weak lensing measurements: use nearby and massive foreground (lensing) stars, also characterized by high proper motion and trigonometric parallax, and located in front of a very high stellar bakground We have followed two approaches: 1) search for background objects in existing stellar coronagraphic surveys (Chauvin et al all references therein, Galicher et al. 2016) 2) consider all the nearest stars as potential targets to carry out such a survey

11 1) search for background objects in existing stellar coronagraphic surveys (Chauvin et al. 2014, Galicher et al all references therein) More than 27 background companions with θ S < 2 GJ 684b: K3V, M = 0.81 M, D = pc, Heinze et al. 2010a Θ E = 22 mas, Θ S = 3.01 è Θ A = Θ S mas è Θ E / Θ S = HIP96313: A3, M = 2 M, D = 61 pc, Galicher et al Θ E = 16 mas, Θ S = è Θ A = Θ S mas è Θ E / Θ S = HR 4796: A0, M = 2 M, D = 73 pc, Galicher et al Θ E = 15 mas, Θ S = è Θ A = Θ S mas è Θ E / Θ S = 0.041

12 2) consider all nearest stars as potential targets to carry out such a survey More than 24 nearby stars with θ E > 25 mas projected on a high density stellar background Alpha Centauri A: G2V, M = 1.1 M, D = 1.35 pc, Θ E = mas, l = 315.7, b = -0.7, (L<18) = 41598, (K<16) = 41518, (V<30) = , Par = mas, PM = , mas/yr 36 Ophiuchi A: K0V, M = 0.85 M, D = 5.98 pc, Θ E = mas, l = 358.3, b = 6.9, (L<18) = , (K<19) = , (V<30) = , Par = mas, PM = , mas/yr 41 G. Arae: G8V, M = 0.81 M, D = 8.80 pc, Θ E = mas, l = 342.3, b = -5.3, (L<18) = 75706, (K<18) = 76239, (V<30) = , Par = mas, PM = mas/yr

13 Alpha Centauri A: G2V

14 Alpha Centauri A: G2V 20 Θ E

15 Alpha Centauri A: G2V

16 Alpha Centauri A: G2V

17 36 Ophiuchi A: K0V

18 41 G. Arae: G8V

19 For the case of Alpha Centauri A, the number of expected weak lensing events over a period of 5 years is (in the visible): 5 * Pi * (20 * Θ E / 3600)^2 * (V<30) 5 * PI * (20 * / 3600)^2 * ^6 = 28.2!!!

20 And Proxima Centauri?: Θ E = 26 mas

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22 How many independent coronagraphic observations are needed in order to constrain the mass of the lensing star which is animated by a proper motion and/or a parallax? Θ A = (( Θ S + ΔΘ ) / 2 ) Θ S / Θ S Θ sy with ΔΘ = Θ S Θ E 2 m Θ Sy,0 t 0 Θ A - Θ S Θ S In principle, 5 parameters: (m, Θ Sy,0, Θ, t 0, Θ E ) è Need for 3 independent observations Θ sx

23 Conclusions: Very sensitive coronagraphic observations of the nearest stars projected over a very high density stellar background ought to unravel weak lensing effects capable to lead to a very precise mass determination of the foreground lensing star. No doubt that with the advent of extremely large telecopes, it will become possible to weigh the mass of a very large number of nearby stars, providing a totally independent way of estimating stellar masses with a high precision. We should probably aim at carrying out such an exploratory survey with 10m class telescopes around a small sample (10?) of the nearest stars, just using two epoch observations.

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