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Dark Matter Capture in the first stars

Dark Matter Capture in the first stars. A new power source and a limit on the mass of the first stars Douglas Spolyar (UCSC). arXiv:0802.1724 K. Freese, D. Spolyar, A. Aguirre. Basic Idea. Dark star phase has ended Next, fusion powered star forms: on main sequence

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Dark Matter Capture in the first stars

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  1. Dark Matter Capturein the first stars A new power source and a limit on the mass of the first stars Douglas Spolyar (UCSC) arXiv:0802.1724 K. Freese, D. Spolyar, A. Aguirre

  2. Basic Idea • Dark star phase has ended • Next, fusion powered star forms: on main sequence • New star captures DM • Capture rate extremely high, which leads to a very large luminosity from the DM. • How big? All first stars 1 M Fixes mass of the first stars or limits DM scattering cross section.

  3. Comparison of Luminosity If LDM exceeds Ledd, stellar mass is fixed!  70M  250M   100M 50M  10M Black line- LEdd Green line-LDM Blue line-L(fitted) Red () zero metallicity stars on MS (Heger &Woosley)

  4. Outline • Determine DM luminosity • Compare DM luminosity to: • Normal stellar luminosity of the first stars L* • Eddington Luminosity Ledd • Uniquely determine mass of first stars • Drastically limit DM scattering cross section

  5. Capture Rate (Particle Physics) • Scattering • Consider only SD scattering for first stars, which are made only of H and He. SI scattering is generally subdominant. • and • DM luminosity LDM generally independent of DM mass and annihilation rate! Limits from Super-K m= 100 GeV <v>ann=3x10-26 cm3/s

  6. Capture Rate (Astrophysics) • Typical Mass of first stars • Up to 103 M (Jeans Mass) • First stars DM host halo • DM Velocity • Much slower than Milky Way since typical host halo is much smaller • DM density M~ (10 to 250) M MDM~106 M Simulations: 108 GeV/cm3 (Abel, Bryan, Norman 2002) (Blumenthal, Faber, Flores, Primack 1987) Adiabatic Contraction: 1018 Gev/cm3

  7. Capture Rate per Unit Volume Press, Spergel 85 & Gould 88 • n (number density of DM) cm-3 • n (number density of H) cm-3 We can neglect the term in the brackets because the DM velocity is much less than the escape velocity for the first stars, which makes B big. • V(r) escape velocity at a point r • velocity of the DM • c scattering cross section If the star moves relative to the DM halo, the term in the brackets changes. Luckily, we can still neglect the term.

  8. Capture Rate in the First Stars Capture Rate s-1 1 Assume constant DM density 2 Conservatively fix v(r) to the escape from surface of star (vesc). 3 Integrate nH giving the number of H in the star, which produces the second term in parentheses on the RHS below. H fraction (fH) DM density () Proton mass (Mp ) DM mass (m)

  9. DM Luminosity (LDM) • Equilibrium between the annihilation and Capture is very short • Fraction of Energy deposited (f)- we assume a third goes into neutrinos so we take f = (2/3). Independent of the mass of particle!

  10. LDM versus L • We compare the DM luminosity against fusion luminosity of zero metallicity stars half way through H burning (on the main sequence) for various masses. (Heger,Woosley, in prep) • H burning represents the largest fraction of a star’s life. • DM luminosity wins for a sufficiently high DM density.

  11. Similar and Simultaneous Work • Within a few days of each other, we and Fabio Iocco posted the same basic idea: • Both groups found that the DM luminosity can be larger than fusion for the first stars. • We went one step further: • We found that when the DM luminosity exceeds the Eddington luminosity, we can uniquely fix the mass of the first stars.

  12. Eddington Luminosity • Luminosity of a star at which the radiation pressure • overwhelms the gravitational force. C speed of light p opacity G Newton's Constant • Assume opacity (mean free path) • is dominated by Thompson scattering • since the surface of first stars is hot. M Stellar Mass

  13. Max Stellar Mass • Once LDM exceeds LEdd, star cannot accrete any more matter and mass is determined. • We can solve for the max stellar mass by setting LEdd=LDM. • We derived the above by fixing v=10 km/s • And also noting that (Vesc)2  (M)0.55, which follows since R (M)0.45 We find that the M and c are inversely related for a fixed DM density. _

  14. Max Mass 10-38 cm2 10-40 cm2 10-43 cm2 Lines correspond to fixed scattering cross section. We show the relationship between the DM density and mass of the first stars.

  15. Max Mass Example 10-38 cm2 10-40 cm2 10-43 cm2 M=10M =1014 Gev/cm3 Lines correspond to fixed cross section. We show the relationship between the DM density and mass of the first stars.

  16. First Stars: Limits on SD Scattering Limits with Stellar Mass Larger than 1M 5x1012 (GeV/cm3) Super K  5x1015 (GeV/cm3) Zeplin SI  1018 (GeV/cm3)  Xenon SI (SD limits examined in Savage, Freese, Gondolo 2005)

  17. First Stars also limit SI Scattering Limits with Stellar Mass Larger than 1M 5x1012 (GeV/cm3) Super K 5x1015 (GeV/cm3) Zeplin SI   CDMSII SI 1018 (GeV/cm3)  Xenon SI Present bounds from DMTools

  18. Conclusions • The first stars live in a DM rich environment • DM Capture can alter the first stars. • DM luminosity larger than fusion Luminosity • May uniquely determine Mass of first stars • Conversely- the first stars may offer the best bounds or opportunity to measure the the scattering cross section of DM.

  19. Prospects • We believe we can get a good handle upon the “actual” DM densities. • With better simulations and more detailed semi-analytic studies we can make a closer connection between the many various properties of the first stars and the nature of DM.

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