*Contact Email: jordan.mirocha@colorado.edu

Simulating the 21-cm Signatures of the First Stars and Black Holes: Predictions for Observations with a Lunar Farside Telescope

Jordan Mirocha1,5*, Jack Burns1,5, Stephen Skory1, Eric Hallman2,5, John Wise3, Steven Furlanetto4,51University of Colorado, 2Harvard-Smithsonian Center for Astrophysics, 3Princeton University, 4University of California at Los Angeles, 5NASA Lunar Science Institute

IntroductionDue to its tenuous ionosphere and shielding from terrestrial radio interference, the lunar farside is a unique platform for astrophysical research of the very early Universe. In particular, future measurements of the highly redshifted 21-cm line of neutral hydrogen (HI) will contain a wealth of information about the Universe’s first stars, galaxies, and black holes. While the first sources of ultraviolet radiation will send the HI signal into absorption via the Wouthuysen-Field effect, X-ray photons, once present, will heat intergalactic gas on large scales and drive the HI signal into emission. With the cosmological radiation hydrodynamics code ENZO, we study the imprint left in the 21- cm signal by the Universe’s first stars and accreting black holes. Complementary 1D radiative transfer calculations have shown that the use of monochromatic radiation fields can lead to inaccurate ionization and heating profiles around stars and X-ray sources. To address this issue, we have developed a new technique for optimally constructing discrete spectra of stars and black holes to ensure precision determination of the ionization state and temperature of the surrounding gas, and thus 21-cm signature. Our simulations will be the first to utilize this method.

Abel, T. & Wandelt, B. D. 2002, MNRAS, 330, L53O’Shea, B., Bryan, G., Bordner, J., Norman, M. L., Abel, T., Harkness, R., Kritsuk, A., 2004, arXiv:astro-ph/0403044v1Furlanetto, S., & Stoever, S., 2009, arXiv:0910.4410

Kuhlen, M., & Madau, P., 2005, MNRAS, 363, 1069Shull, J. M. & van Steenberg, M. E. 1985, ApJ, 298, 268Turk M.J., Smith B.D., Oishi J.S., Skory S., Skillman S.W., Abel T., Norman M.L., 2011, ApJS, 192, 9 Wise, J. H. & Abel, T. 2011, MNRAS, 414, 3458Acknowledgements

References

This work is supported by the NASA Lunar Science Institute, in addition to allocation AST090040 on the NSF teragrid network and early access to the Janus supercomputer at the University of Colorado. The Lunar University Network for Astrophysics Research (LUNAR) consortium, headquartered at the University of Colorado, is funded by the NLSI to investigate concepts for astrophysical observatories on the Moon.

1D Radiative Transfer•The primary 21-cm observable, the differential brightness temperature (Equation 1),

depends on the ionization state and temperature of the gas through the hydrogen neutral fraction and spin temperature (Equation 2).

•Many radiative transfer techniques that have been applied to the problem of cosmological reionization require radiation sources to have discrete spectral energy distributions (SEDs), or at least benefit from it computationally.

• In 1D, it is inexpensive to study the effects of using discrete SEDs, and determine if they adequately sample their continuous counterparts.

•See Figures 1 & 2 for a comparison of ionization and heating around sources with continuous and discrete SEDs in a static, hydrogen-only medium (nH = 10-3). Calculations done using the 1D radiative transfer code rt1d (Mirocha et al. 2011, in prep).

Figure 1: Ionization (top) and heating (bottom) profiles around a 105 K blackbody stellar spectrum 10 Myr (left) and 100 Myr (right) after the star turns on. Monochromatic spectra optimized for optically thin media (red) overestimate ionization and underestimate

heating relative to the continuous SED (black). Optimal 4-bin SED solution shown in blue.

Figure 2: Ionization (top) and heating (bottom) profiles around a 106 Msun accreting black hole (power-law X-ray spectrum) 1 Myr (left) and 10 Myr (right) after the black hole turns on. A monochromatic spectrum emitting at 0.5 keV is shown in red, while the

optimal 4-bin solution is shown in blue.

Cosmological Simulations

•Goal: Study the impact of early X-ray sources on the hydrogen content of the early universe. Use results of previous sections to ensure accurate determination of gas temperature and ionization state.

•Tools: The ENZO code (O’Shea et al. 2004): N-body + hydrodynamics cosmological code.

•Now in version 2.0, the adaptive ray-tracing radiative transfer method of Abel & Wandelt (2002). Implementation described in Wise & Abel (2011).

•Details:

•50 Mpc3 simulation volume.

•2563 dark matter particles.

•2563 root grid resolution (gas).

•Up to 4 levels of adaptive mesh refinement (AMR) allowed.

•Super-massive black hole (SMBH) particles inserted in halos above 1010 Msun between z = 8-10.

•MSMBH = 106 Msun with radiative efficiency of 10%.

•Simulation A: Optimal 3-bin X-ray spectrum for a power law with spectral index 1.5.

•Simulation B: Monochromatic X-ray emission at 0.5 keV.

Ongoing Work•Determining how accurately one can simultaneously reproduce heating and the ionization

of multiple chemical species with discrete UV and X-ray radiation fields.

•Optimization of more complex spectra, such as the multi-color disk + power law black hole spectra of Kuhlen et al. 2005.

•High resolution studies of ionization and heating around individual objects (see Figure 7). Follow formation of PopIII stars and their remnant black holes, and study their signatures in the high redshift 21-cm line.

•Starting to incorporate sources of UV photons in the large volume simulations, giving more complete picture of reionization process.

•Use on-the-fly halo finding to create X-ray sources continuously.

• Investigate the differences in the 21-cm global signal brought about by different super-massive black hole growth histories. Can future 21-cm observations tell us about the black hole accretion history in the early universe?

1D Results•To combat the issue of poor SED sampling (see Figures 1 & 2), we construct discrete spectra that optimally reproduce the ionization

and heating rates of continuous spectral energy distributions using a Monte-Carlo method called Simulated Annealing.

•We minimize the errors of the photoionization and heating rate integrals in log-space (see Equation 3), between discrete and continuous spectra. Given N energy bins, this method provides the optimal placement and normalization (fraction of total energy output) for a given radiation source, and column density regime of interest.

•The blue curves in Figures 1 & 2 were calculated using the optimal discrete spectra found with this method. Figure 3 shows the components of the 105 K blackbody solution for photo-ionization. For more details, see Mirocha et al. 2011, in prep.

T−1S ≈

T−1γ + xcT

−1K + xαT−1

C

1 + xc + xα(1) (2)δTb ≈ 9χHI(1 + δ)(1 + z)1/2

�1− Tγ(z)

TS

�mK

Figure 3: Photo-ionization rate* as a function of column density for a continuous 105 K blackbody SED (black), and the optimal 4 energy bin discrete SED (blue). Blue circles show the composite solution, while dashed blue lines show the contribution from each individual

energy bin. The solutions for the photo-ionization and heating rates were averaged for use in the calculation shown in Figure 1.

ΓHI =Lbol

4πr2

�

EHI

σHII(E)dE

E

*Right: Actual photo-ionization rate (properly normalized). I(E) is the spectral intensity, which depends on absorbing column.

(3)

Simulation Results•X-rays from accreting black holes weakly ionize hydrogen and helium, and heat gas above

1000 K, both on ~Mpc scales (Figures 4, 5 & 6).

•As expected, helium is ionized to a greater extent than hydrogen, though secondary photo-electrons do contribute to ionization of hydrogen and heating of the gas (Shull & vanSteenberg 1985, Furlanetto & Stoever 2010).

•The difference in discrete SEDs makes a significant difference in the amount of ionization and heating occurring on large scales (Figure 4).

•The environment of each X-ray source plays a significant role in how much radiation escapes to large radii (Figure 6).

Figure 7: Density weighted projections of gas density (left) and temperature (right) at z = 15 surrounding a Population III star. Peak resolution in these nested grid simulations is ~0.1 pc.

Figure 4: (Top) Density weighted projections of temperature (left), ionized hydrogen density (middle), and singly ionized helium density (right) at z = 6.3 for Simulation A.(Bottom) Same projections as top panel but for Simulation B.

50M

pc50

Mpc

90kp

c

Figure 5: Phase sphere 10 Mpc in radius surrounding the oldest X-ray source in Simulation A at z = 6.3.

Figure 6: Spherically averaged temperature profiles for 8 of the 13 X-ray sources in Simulation B at z = 6.3.