Searching for the reionization sources

Using a reionization model simultaneously accounting for a number of experimental data sets, we investigate the nature and properties of reionization sources. Such model predicts that hydrogen reionization starts at z \approx 15, is initially driven by metal-free (PopIII) stars, and is 90% complete by z \approx 8. We find that a fraction f_\gamma >80% of the ionizing power at z > 7 comes from haloes of mass M<10^9 M_sun predominantly harbouring PopIII stars; a turnover to a PopII-dominated phase occurs shortly after, with this population, residing in M>10^9 M_sun haloes, yielding f_\gamma \approx 60% at z=6. Using Lyman-break broadband dropout techniques, J-band detection of sources contributing to 50% (90%) of the ionizing power at z \sim 7.5 requires to reach a magnitude J_{110,AB} = 31.2 (31.7), where about 15 (30) (PopIII) sources/arcmin^2 are predicted. We conclude that z>7 sources tentatively identified in broadband surveys are relatively massive (M \approx 10^9 M_sun) and rare objects which are only marginally (\approx 1%) adding to the reionization photon budget.Comment: Extended discussions. Accepted to MNRAS Letter

Reionization constraints using Principal Component Analysis

Using a semi-analytical model developed by Choudhury & Ferrara (2005) we study the observational constraints on reionization via a principal component analysis (PCA). Assuming that reionization at z>6 is primarily driven by stellar sources, we decompose the unknown function N_{ion}(z), representing the number of photons in the IGM per baryon in collapsed objects, into its principal components and constrain the latter using the photoionization rate obtained from Ly-alpha forest Gunn-Peterson optical depth, the WMAP7 electron scattering optical depth and the redshift distribution of Lyman-limit systems at z \sim 3.5. The main findings of our analysis are: (i) It is sufficient to model N_{ion}(z) over the redshift range 2<z<14 using 5 parameters to extract the maximum information contained within the data. (ii) All quantities related to reionization can be severely constrained for z<6 because of a large number of data points whereas constraints at z>6 are relatively loose. (iii) The weak constraints on N_{ion}(z) at z>6 do not allow to disentangle different feedback models with present data. There is a clear indication that N_{ion}(z) must increase at z>6, thus ruling out reionization by a single stellar population with non-evolving IMF, and/or star-forming efficiency, and/or photon escape fraction. The data allows for non-monotonic N_{ion}(z) which may contain sharp features around z \sim 7. (iv) The PCA implies that reionization must be 99% completed between 5.8<z<10.3 (95% confidence level) and is expected to be 50% complete at z \approx 9.5-12. With future data sets, like those obtained by Planck, the z>6 constraints will be significantly improved.Comment: Accepted in MNRAS. Revised to match the accepted versio

The albedo of snow for partially cloudy skies

The input parameters of the model are atmospheric precipitable water, ozone content, turbidity, cloud optical thickness, size and shape of ice crystal of snow and surface pressure. The model outputs spectral and integrated solar flux snow reflectance as a function of solar elevation and fractional cloudcover. The model is illustrated using representative parameters for the Antarctic coastal regions. The albedo for a clear sky depends inversely on the solar elevation. At high elevation the albedo depends primarily upon the grain size; at low elevation this dependence is on grain size and shape. The gradient of the albedo-elevation curve increases as the grains get larger and faceted. The albedo for a dense overcast is a few percent higher than the clear sky albedo at high elevations. A simple relation between the grain size and the overcast albedo is obtained. For a set of grain size and shape, the albedo matrices (the albedo as a function of solar elevation and fractional cloudcover) are tabulated

On the Angular Variation of Solar Reflectance of Snow

Spectral and integrated solar reflectance of nonhomogeneous snowpacks were derived assuming surface reflection of direct radiation and subsurface multiple scattering. For surface reflection, a bidirectional reflectance distribution function derived for an isotropic Gaussian faceted surface was considered and for subsurface multiple scattering, an approximate solution of the radiative transfer equation was studied. Solar radiation incident on the snowpack was decomposed into direct and atmospherically scattered radiation. Spectral attenuation coefficients of ozone, carbon dioxide, water vapor, aerosol and molecular scattering were included in the calculation of incident solar radiation. Illustrative numerical results were given for a case of North American winter atmospheric conditions. The calculated dependence of spectrally integrated directional reflectance (or albedo) on solar elevation was in qualitative agreement with available observations

Two-stream theory of spectral reflectance of snow

Spectral reflectance of snow under diffuse illumination is studied using the two-stream approximation of the radiative transfer equation. The scattering and absorption within the snowcover due to the randomly distributed ice grains are characterized by the single scattering albedo and anisotropic phase function. Geometric optics calculations are used to relate the scattering and absorption parameters to grain size and density of snow. Analytical expressions for the intensity within the snowpack and the asymptotic flux extinction coefficient are also obtained. Good agreement is shown between the theory and available experimental data on visible and near-infrared reflectance and asymptotic flux extinction coefficient. The theory also may be used to explain the observed effect of aging on the snow reflectance

Microwave emission from polar firn

The microwave emission from a half-space medium, characterized by coordinate dependent scattering and absorbing centers, was calculated by numerically solving the radiative transfer equation by the method of invariant imbedding. Rayleigh scattering phase functions and scattering induced polarization of the radiation were included in the calculation. Using the scattering and extinction data of polar firn the brightness temperature was calculated for the 1.55 cm wavelength. This study was the first quantitative comparison of the results of numerical calculation using the actual measured information of crystal size with the observed data

The solar reflectance of a snow field

The radiative transfer equation was solved using a modified Schuster-Schwartzschild approximation to obtain an expression for the solar reflectance of a snow field. The parameters in the reflectance formula are the single scattering albedo and the fraction of energy scattered in the backward direction. The single scattering albedo is calculated from the crystal size using a geometrical optics formula and the fraction of energy scattered in the backward direction is calculated from the Mie scattering theory. Numerical results for reflectance are obtained for visible and near infrared radiation for different snow conditions. Good agreement was found with the whole spectral range. The calculation also shows the observed effect of aging on the snow reflectance

Testing Reionization with Gamma Ray Burst Absorption Spectra

We propose to study cosmic reionization using absorption line spectra of high-redshift Gamma Ray Burst (GRB) afterglows. We show that the statistics of the dark portions (gaps) in GRB absorption spectra represent exquisite tools to discriminate among different reionization models. We then compute the probability to find the largest gap in a given width range [Wmax, Wmax + dW] at a flux threshold Fth for burst afterglows at redshifts 6.3 < z < 6.7. We show that different reionization scenarios populate the (Wmax, Fth) plane in a very different way, allowing to distinguish among different reionization histories. We provide here useful plots that allow a very simple and direct comparison between observations and model results. Finally, we apply our methods to GRB 050904 detected at z = 6.29. We show that the observation of this burst strongly favors reionization models which predict a highly ionized intergalactic medium at z~6, with an estimated mean neutral hydrogen fraction xHI = 6.4 \pm 0.3 \times 10^-5 along the line of sight towards GRB 050904.Comment: 5 pages, 3 figures, revised to match the accepted version; major change: gap statistics is now studied in terms of the flux threshold Fth, instead of the observed J-band flux FJ; MNRAS in pres

Effect of surface roughness on the microwave brightness temperature of soils

The effect of surface roughness on the brightness temperature of a moist terrain was studied through the modification of Fresnel reflection coefficient and using the radiative transfer equation. Model calculations are in good qualitative agreement with the observed dependence of the brightness temperature on the moisture content in the surface layer