mutlu yıldız ege university, dept. of astronomy and space sciences, turkey
DESCRIPTION
A new concept in stellar astrophysics based on internal rotation :. Effective mass and its place in the A- and B-star puzzle. Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey. The basic effect of rotation:. One dimensional hydrostatic equilibrium:. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/1.jpg)
A new concept in stellar astrophysics A new concept in stellar astrophysics based on internal rotationbased on internal rotation::
Effective mass and its place Effective mass and its place in the A- and B-star puzzlein the A- and B-star puzzle
Mutlu Yıldız
Ege University, Dept. of Astronomy and Space Sciences, Turkey
![Page 2: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/2.jpg)
The basic effect of rotation:
One dimensional hydrostatic equilibrium:
![Page 3: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/3.jpg)
For the case of solid-body rotation:
Correction in log k2 : -0.7Λs (Stothers, 1974)-0.9Λs (Claret & Gimenez,1993)-0.7Λs (Yıldız 2004)
From model properties
![Page 4: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/4.jpg)
For the case of differential rotation:
Similar equations for L and R as a function of ’rotation parameter’?
![Page 5: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/5.jpg)
Profile of the rotation rate: = (r)
Steep rotation rate gradient near the surface of PV Cas’ components :
![Page 6: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/6.jpg)
Is such a DR reasonable?
Motivations• If angular momentum transportation is not a sudden
process, such a DR can be anticipated, at least for some time.
• Time-scale of decay of differential rotation in radiative envelopes of Cp stars ~ life-time of A-type stars
(Arlt et al. 2003)
• Aerts et al. (2003) ruled out rigid rotation of β Cep type star
HD 129929 as a result of its seismic analysis.
• The temperature difference between the blue sides of magnetic Ap stars and normal stars (Hubrig et al. 2000).
![Page 7: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/7.jpg)
Hubrig et al. (2000)
The temperature difference between the blue sides of magnetic Ap stars and normal stars
dlog Teff = 0.025
For T=10000 K, dT=590 K
For T= 9000 K, dT=530 K
Compare NR models with DR models with steep rotation rate gradient near the surface!
![Page 8: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/8.jpg)
Hubrig et al. (2000)
The temperature difference between the blue sides of magnetic Ap stars and normal stars
dlog Teff = 0.025
For T=10000 K, dT=590 K
For T= 9000 K, dT=530 K
Compare NR models with DR models with steep rotation rate gradient near the surface!
![Page 9: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/9.jpg)
NR and DR models
Temperature difference between the ZAMS lines = 550 K
![Page 10: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/10.jpg)
Luminosity level as a function of rotation parameter
Consider the simplest case:Homogeneous mass distribution
Integrate the equation of Hydrostatic equilibrium :
= constant
![Page 11: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/11.jpg)
The effective mass and rotation parameter
Ideal gas pressure
Average rotation parameter
Effective mass for homogeneous mass distribution:
Luminosity primarily depends on it rather than the real mass
![Page 12: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/12.jpg)
Luminosity vs. average rotation parameter
NR, SBR and DR models (t is constant).
![Page 13: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/13.jpg)
For more realistic mass distribution
From the models of 2.55 and 2.82 Msun:
From the rotating and NR models:
Combination of these equations
![Page 14: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/14.jpg)
The effective mass of PV Cas A
For the metal rich chemical composition: Meff = 2.58 Msun
For the solar composition: Meff = 2.60 Msun
![Page 15: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/15.jpg)
The MS life-time and the effective mass
NR models
M=2.82 Msun, t(MS) =280 My
M=2.57 Msun t(MS) =370 My
DR model of PV Cas A
M=2.82 Msun t(MS) = 370 My (Meff = 2.58 Msun )
![Page 16: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/16.jpg)
The mass-luminosity relation
Observational M- L: dlogL / dlogM= 2.3
The minimum value obtained from the models (ZAMS):
dlogL / dlogM= 3.9 - 4.0
For DR models, but, Meff in place of M:
dlogL / dlogMetkin = 3.6
![Page 17: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/17.jpg)
Results
• Rapid rotation of the inner regions of stars can solve some fundamental problems in the stellar astrophysics.
• Therefore, we introduce effective mass as a novel approach. It may have also cosmological implications!
• If we find the mass of an early type star from its brightness, the mass we find is primarily its effective mass
• The effective mass of PV Cas A is about 10% less than its real mass
• Internal rotation can be the dominant discriminator for the chemically peculiar stars
• Irregular mass-luminosity relations may be due to internal rotation
![Page 18: Mutlu Yıldız Ege University, Dept. of Astronomy and Space Sciences, Turkey](https://reader036.vdocuments.pub/reader036/viewer/2022062502/56814b12550346895db82a6d/html5/thumbnails/18.jpg)
Conclusion
• The nature is always much more complicated than we anticipate, but, the effective mass may help us to find some more pieces of the puzzle.