Probing the Era of Galaxy Formation Via TeV Gamma Ray Absorption by the Near Infrared Extragalactic Background [chapter]

D. Macminn, J. R. Primack
1996 TeV Gamma-Ray Astrophysics  
We h a v e developed an indirect test of the era of galaxy formation by modeling the extragalactic background light (EBL) in the near infrared portion of the spectrum|a domain dicult to observe directly due to galactic and zodiacal contamination 1;2 . A new method for probing this spectrum has been suggested 3 which i n v olves the absorption of TeV gamma rays by the EBL. TeV gamma rays have recently been detected from Markarian 421 4 , an active galactic nucleus (AGN) at a redshift of z = 0 :
more » ... 31. If several more distant T eV sources exist, it should be possible to observe for the rst time the EBL, and thus constrain the timescale over which galaxies form. The potential of this technique is illustrated by the constraints it places upon an earlier claim for a detection of the EBL 5 . It has been known for many y ears that high energy gamma rays from sources at cosmological distances will be absorbed by a diuse background of long wavelength photons 6 through electron-positron pair production. This point had been of little interest, however, until the discovery of a class of high energy -ray emitters by the EGRET detector aboard the Compton Gamma Ray Observatory 7 . These sources, all AGNs of various subclasses, were found to emit a substantial amount of energy in the GeV energy domain with a roughly E 2 spectrum. While the physical description of the emission process is uncertain, it is possible that this spectrum could continue into the TeV range for some of these sources, a hypothesis given support by the detection of Mrk 421 at TeV energies. Mrk 421 is the nearest of the EGRET sources and should not suer from appreciable EBL absorption of its gamma rays as we will show, but sources at greater distances should show evidence of absorption in the TeV domain. Models of the EBL require several inputs: a library of stellar spectra and a function describing the number distribution by mass of a stellar population (the initial mass function, IMF); a { 2 { c haracterization of galactic classes (elliptical, spiral) and the evolution of their respective stellar populations (the star formation rate, SFR) and dust content; a function describing the formation of galaxies as a function of redshift; and assumptions about the geometry of the Universe|the density parameter ( 0 ), the cosmological constant () and the Hubble constant ( H 0 ). Such models have been created before 8;9;10 with a variety of dierent assumptions, but each has a perhaps oversimplied model of galaxy formation. The conclusion reached by these earlier modelers is that the EBL proves to be a poor test of cosmology, meaning geometry, as the uncertainties in the IMF and SFR overshadow dierences due to 0 and H 0 . W e concur that the EBL proves a poor test of geometry. But this by no means limits its usefulness as a probe of cosmology, for the dominant factor inuencing the EBL is the era of galaxy formation, which in modern theories depends strongly on the nature of dark matter. For simplicity, w e h a v e c hosen to consider here only those models with a at (k = 1) geometry and = 0, i.e. = 1; the arguments that the age of the Universe t 0 > 13 Gyr then require H 0 50 km/s/Mpc. Considering also 0 < 1, especially with > 0, would tend to increase dierences due to the galaxy formation epoch. Observational work has suggested several in values for the IMF; we h a v e considered this to be a free parameter and considered the full range predicted by v arious authors 11;12 . The SFR has been given the functional form of a decaying exponential in time 13 . Galaxy formation has been treated with the Press-Schecter approximation, which expresses the number density of galaxy halos of a given mass as a function of redshift based on the results of N-body simulations 14;15 . T w o dierent cosmological models for structure formation have been considered: the cold dark matter (CDM) model, representing a moderate era of galaxy formation, and cold plus hot dark matter (CHDM), representing a late era of galaxy formation. Both are normalized to COBE and are based on the simulations of Klypin et al. 15 . There is a dicultly in describing a galactic population in this manner in that the Press-Schecter function merely predicts the abundance of dark matter halos and makes no distinction between a cluster of galaxies and a singular galaxy. One must therefore also assume a maximum galactic mass; we set the upper limit at M max = 5 10 12 M based on a comparison between the galactic luminosities obtained for a power law mass to light ratio and the normalization process described below, and we h a v e c hecked that the results do not depend sensitively on M max . The nal parameter to be set is the normalization of the SFR, or the eciency of star formation for a given galactic type. This can be directly tied to the properties of local galaxy population through a comparison of model galactic luminosities with those of the the nearby population. A number of studies have been made of the galaxy local luminosity function (LLF). Most recent is the work of Loveday et al. 16 based on the Stromlo-APM southern sky survey (LEPM LLF), the LLF of Efstathiou et al. 17 based on an average of several surveys (EEP LLF), and the LLF of DeLapparent e t a l . 18 based on the rst CfA survey (LGH LLF). Each has characterized the luminosity distributions of the galaxies in the blue magnitude band as a Schecter function, (y) dy = ? y e y dy where y = L=L ?B : (1) If one makes the assumption that the most massive galaxies are also the most luminous, one can compare the number densities of the LLF and the Press-Schecter function (at z = 0) and require { 3 { that the average age model galaxies, at the present epoch, have the expected luminosities by deriving a function which expresses the SFR normalization as a function of galactic mass. The luminosity e v olution of the galaxies is thus set by forcing the model galaxies to duplicate the local population. The model results are shown in Fig. 1 . Note the large separation between the galaxy formation model predictions; this will be seen for any combination of model parameters given that we include both early and late galaxy formation models and that we require the present d a y model galaxies match the local population. The larger magnitude predicted by the CDM model arises for several reasons: (1) stars have been contributing their light to the EBL for 2 Gyr longer in the CHDM case, (2) the initial burst of star formation in early-type galaxies has redshifted from the optical to the near IR, and (3) the galaxies are older at a given redshift and hence are composed of more evolved stars, producing a brighter ux in the red and near IR. In addition to the parameter choices discussed above, we h a v e also varied the other quantities not xed by observational data to ensure that no large deviations were found. The cross section for the absorption of -rays through e + e pair production is given by Gould & S c hr eder 6 . This cross section is maximized when where is the EBL photon energy and E is the -ray energy. The photon number density for the EBL models drops o above 1 eV ( 1 m) and below 0.1 eV; the absorption eect due to the stellar component of the EBL will be most pronounced for -ray energies of 300 GeV to 3 TeV (Fig. 2) . Above 1 0 T eV, it is likely that the dust-emitted component of the EBL makes the Universe mostly opaque, and above 100 TeV the cosmic microwave background completely absorbs any -rays from sources at cosmological distances. There is also an eect due to the redshift of the source. The absorption at some redshift along the path from the source will occur between a background photon of energy 0 (1 + z) and a -ray of energy E 0 (1 + z), hence the lower cuto in a source's spectrum will scale with (1 + z) 2 . F or sources at z 0:5 there is an additional eect from the galaxy formation models in that the magnitude of the EBL at large z is quite small for
doi:10.1007/978-94-009-0171-1_30 fatcat:ervgcuhpzbc35kjhfg4ztdth3y