A New Analysis of the Hubble Counts of Galaxies--I: The Galactic Absorption Function

The contradiction between the values of the average optical half-thickness τ of the galactic absorbing layer derived from the Lick galaxy counts ( 0.5 mag.) by Shane and from the Mt Wilson counts (0.25 mag.) by Hubble and others vanishes when various sources of bias not considered in previous discussions are taken into account. The four main causes of systematic error are (1), the zero-count fields in low galactic latitudes, (2), the longitude dependence of galactic absorption, (3) the departures of the absorption equator from the conventional galactic equator, and (4), the uncertain values of the limiting magnitude m_l and gradient x of the apparent luminosity function at m_l . When proper allowance is made for these effects and for x = 0.44, the Hubble counts lead to τB = 0.47 ± 0.02 (m.e.) in agreement with Shane's final value ( τB = 0.51 mag.) from the Lick counts. Further, the ‘ dip ’ of the absorption equator (–0 ^° .25) and the North–South asymmetry in the counts (∆log N = + 0.024) agree with other evidence indicating that the Sun is north of the galactic plane $$({z}_{0}\,\simeq\,+\,11\,\text{pc})$$ . The counts are, otherwise, consistent with the assumption that large scale isotropy obtains at the estimated magnitude limit $${m}_{l}\simeq\,19.4$$ of the Mt Wilson counts. The final expression for the dependence of the smoothed galaxy density on galactic longitude and latitude is $$\text{log}\,{N}_{C}\,=\,2.140\,+\,B\mid C\mid,$$ where $$C\,=\,\text{cosec}\,(b+{0}^{^{\circ}}.25-{1}^{^{\circ}}.7\,\text{sin}\,l-\,{1}^{^{\circ}}.0\,\text{cos}\,3l)$$ , with for the northern galactic hemisphere $$-{B}_{N}\,=\,0.193\,+\,0.031\,\text{cos} {l}+0.019\,\text{cos} {3l}$$ and for the southern galactic hemisphere $$-{B}_{S}\,=\,0.217\,+\,0.037\,\text{cos} {l}-0.003\,\text{cos} {3l}$$ . (To simplify the notation, we use l, b for l^II , b^II and l ′, b ′ for l^I , b^I .) The corresponding values of the total extinction in photographic magnitudes are listed and the normalized extinction function $$f(l,\,b)\,=\,\Delta m/\tau$$ is plotted as contours of constant absorption. For applications to the brighter galaxies, selected by apparent magnitude, an effective value $${\tau}^{\ast}\,\simeq 0.4\tau\,=\,0.20\,\text{mag}$$ . should be used if the ‘ normal ’ value of the total to differential absorption ratio $$R\,=\,{A}_{B}/{E}_{(B-V)}\,\simeq\,4$$ applies. If not, the total extinction derived from counts of faint galaxies and the differential extinction derived from colour excesses of bright galaxies lead to the improbably high value R ≃ 10 for regions outside the galactic plane.