SPECIFIC ANGULAR MOMENTUM DISTRIBUTION FOR SOLAR ANALOGS AND TWINS: WHERE IS THE SUN MISSING HIS ANGULAR MOMENTUM?

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1 5th International Workshop on Astronomy and Relativistic Astrophysics (IWARA2011) International Journal of Modern Physics: Conference Series Vol. 18 (2012) c World Scientific Publishing Company DOI: /S SPECIFIC ANGULAR MOMENTUM DISTRIBUTION FOR SOLAR ANALOGS AND TWINS: WHERE IS THE SUN MISSING HIS ANGULAR MOMENTUM? J. S. DA COSTA, J. D. DO NASCIMENTO JR. Universidade Federal do Rio Grande do Norte, Departamento de Física Teórica Experimental CEP: Natal, RN, Brazil jefferson@dfte.ufrn.br dias@dfte.ufrn.br It is well established that there is a breakdown in the curve of specific angular momentum as a function of mass for stars on the main sequence Ref. 5. Stars earlier than F5 and more massive than the sun, rotate rapidly over a large mass range. For spectral type F5 and later, including the Sun, much smaller rotational velocities are found. We revisit this question from a new sample to shed a light on the basis of a sample solar twins and analogs recently observed by interferometric measurements of stellar radius. Our results clearly show that, as the Sun, the solar twins present similar global behavior from their specific angular momentum. 18 Sco and HIP have a specific angular momentum one order higher than the solar value, and HIP and HIP have a specific angular momentum one order lower than the solar value. Keywords: stellar rotation; stellar angular momentum. 1. Introduction It is notorious that conservation laws are founded in many branches of physics. In stellar astrophysics is not different. The conservation law associated with the stellar rotation is the angular momentum conservation. In the 1960 s several work were developed to understand the stellar rotation, stellar angular momentum, and their consequences Ref. 1. In 1970 Kraft obtained a relationship between rotational angular momentum and stellar mass for MS stars assuming stars like a solid body and assuming a simple mass-luminosity relation. The Kraft s results showed that angular momentum is proportional to stellar mass for stars early than F0. However, for stars later than F0 this relation is not completely true. The stellar angular momentum for these stars present a sudden drop off called. In our study we are interested in the analysis of the angular momentum behavior for solar analogs and twins angular momentum. We show that breaking down provided by Ref. 5 is observed in solar analogs and twins. Consequently, we are interested in explain what 58

2 Specific Angular Momentum Distribution for Solar Analogs and Twins 59 kind of mechanism could leads this peculiar behavior in the sun, and solar analogs and twins angular momentum. 2. Observational Datas For this study we composed a bona fide sample of 118 solar analogs and twins from Refs. 6,and 2, this sample were selected through of V magnitude, and B-V color index from Hipparcos satelite. For this sample the atmospherical parameters: effective temperature (T eff ), microturbulence velocity (v mic ), surface gravity (log g), the metallicity [Fe/H], and chemical abundances were computed through of spectral synthesis from Ref. 6.Projected rotational velocity (vsini), and the stellar mass were collected respectively from Refs. 3,and Methods For estimate the specific angular momentum was acquired from a procedure composed by several steps. First, we should to compute the rotational angular momentum. From this we have to consider the stars like a solid body with this, the rotational angular momentum can be computed by the equation (1). <J(M) >= I(M) <V(M) > <R(M) > Where <V(M) > is the rotational velocity and can be defined as a function of projected rotational velocity v sini. The momentum of inertia for a massive sphere is defined by I = (2/5)MR 2. The stellar radii were computed through the Stefan - Boltzmann law equation (2). (1) L =4πR 2 T 2 eff (2) We can use this procedure because the effective temperature and stellar luminosity are parameters well determined. Consequently, to obtain the specific angular momentum per mass unit we just need to over the specific angular momentum by stellar mass. However in, our study we also analyzed the angular momentum of planet host stars. We try to simulate what is the effect on the angular momentum if each stars of our sample has a Jupiter with the same orbital velocity, mass, and position of Jupiter in the solar system. For the computation of Jupiter in the some solar system orbital angular momentum for this planet we consider the consider a elliptic orbit with a orbital semi-major axis (a), and the orbital eccentricity (e). The orbital angular momentum can be calculated by the equation (3). <J> orb = µ Ga(M + M pla )(1 e 2 ) (3)

3 60 J. S. da Costa and J. D. do Nascimento Jr. Where the M,M pla, G, a, ande are respectively the stellar mass, planetary mass, universal gravitational constant, semi-major axis, and orbital eccentricity. µ is the reduced mass, and is defined by equation (4) µ = M M pla (4) M + M pla The specific total angular momentum per mass unit will be the total sum between orbital angular momentum, and rotational angular momentum over the stellar mass. 4. Results From the Figure 1 we can see that solar analogs and twins present the same breaking down as predicted by Ref. 5. To explain this breaking we can propose two different hypothesis. First, we can assume that all G stars could be planets host stars, however Fig. 1. Distribution of specific angular momentum as a function of mass. The dashed lines represents the Kraft s curve Ref. 5, and Kawaler s curve Ref. 4. The open circles represents the solar analogs from our sample. The solid circles represents the solar twins (HIP 55459, HIP 56948, HIP 79672, and HIP ).

4 Specific Angular Momentum Distribution for Solar Analogs and Twins 61 Fig. 2. The open circles and the solid circles represents respectivelly solar analogs and twins when a Jupiter like planets is included in their specific angular momentum. when we consider the total solar angular momentum (rotational angular momentum and a Jupiter like planet angular momentum) showed in Figure 2, we recognize that total angular momentum is higher than angular momentum predicted by Kraft s theoretical low. The second hypothesis is that the radial differential rotation consume part of the angular momentum. Based on result from Figure 2, we concluded that our first hypothesis alone is not sufficient for to explain this behavior, however based on our results is not possible to explain what type of mechanism explain this angular momentum super estimation. Our future perspectives are to obtain a explanation for this phenomenon taking into account the differential rotation effects. Acknowledgments Research activities of the Stellar Board at the Federal University of Rio Grande do Norte are supported by continuous grants from CNPq and FAPERN Brazilian Agencies.

5 62 J. S. da Costa and J. D. do Nascimento Jr. References 1. Abt, H. A., Hunter, ApJ, 136, 381 (1962). 2. do Nascimento, J. D., da Costa, J. S., De Medeiros, J. R, A&A, 519, 101 (2010). 3. Holmberg, J., Nordström, B., Andersen, J, A&A, 501, 941 (2009). 4. Kawaler S. D., PASP, 99, 1322 (1987). 5. Kraft R. P., ApJ, 150, 551 (1967). 6. Takeda, Y, Kawanomoto, S., Honda, S., Ando, H., Sakurai, A&A, 468, 663 (2007).