High carbon chromium steel (JIS G4805: SUJ2) has been widely used as such bearing steel as described above.  Bearing steel is generally required to exhibit excellent rolling contact fatigue life characteristics as one of the important characteristics thereof.  In this connection, rolling contact fatigue life of a bearing is presumably shortened by presence of nonmetal inclusion or eutectic carbide in bearing steel. 
Recent studies have revealed that presence of nonmetal inclusion in bearing steel is presumably the largest factor of causing deterioration of rolling contact fatigue life characteristics of the bearing steel.  Content and size of nonmetal inclusion have been therefore controlled by decreasing oxygen content in steel to prolong product life of a bearing. 
For example, Patent Literature 1 and Patent Literature 2 each propose a technique of controlling composition, configuration or a distribution state of oxide-based nonmetal inclusion in steel.  However, there arises a problem in Patent Literature 1 and Patent Literature 2 that the techniques thereof necessitate either expensive new smelting facilities or significant modification of existing smelting facilities in order to manufacture bearing steel having relatively little nonmetal inclusion. 
Patent Literature 3 is a technique of improving rolling contact fatigue life characteristics of bearing steel by controlling degree of central segregation of carbon and contents of oxygen and sulfur in the bearing steel.  However, further reducing oxygen content in steel to manufacture bearing steel containing further less nonmetal inclusion necessitates either expensive new smelting facilities or significant modification of existing smelting facilities, which increases a burden on a manufacturer in economical terms, as described above. 
In view of the situation described above, attention is now being paid to reducing eutectic carbide in steel, as well as reducing nonmetal inclusion in the steel.  High carbon chromium steel described above, containing carbon by at least 0.95 mass % to be very hard and have good wear resistance, exhibits high segregation occurring at the cross-sectional center portion of a casting steel (which segregation will be referred to as “central segregation” hereinafter) and formation of massive eutectic carbide in the casting steel, thereby causing a problem of relatively short rolling contact fatigue life.  Due to this problem, the cross-sectional center portion of high carbon chromium steel is punched out (and the center portion thus punched out has to be disposed) or, alternatively, high carbon chromium steel is subjected to a long-hour diffusion treatment (which diffusion treatment will be referred to as “soaking” hereinafter) to sufficiently diffuse segregated element and eutectic carbide from the cross-sectional center portion of the steel. 
Patent Literature 4 discloses in order to address the aforementioned segregation problem a method comprising preparing a linear or bar-shaped rolled material having specific chemical composition, e.g. C: 0.6-1.2 mass %, such that the total area of carbide with thickness of at least 2 μm, observed in the center region including the center axis and spreading from the center axis by D/8 on respective sides in a vertical cross section passing through the center axis of the rolled material (D: width of the vertical cross section), is suppressed to 0.3% or less with respect to the area of the vertical cross section.  Further, Patent Literature 4 reveals how content of massive carbide quantitatively affects rolling contact fatigue life characteristics, thereby proving that massive eutectic carbide remaining in steel deteriorates rolling contact fatigue life characteristics of the steel. 
Patent Literature 5 discloses bearing steel having a specific chemical composition including 0.50-1.50 mass % C, 0.0010-0.0150 mass % Sb and the like and being excellent in heat treatability and productivity with minimal formation of decarburized layer.  The technique of Patent Literature 5 aims at, by adding Sb to bearing steel to achieve minimal formation of decarburized layer therein, eliminating cutting or grinding process after thermal treatment of the bearing steel to improve heat treatability and productivity of the steel.  However, antimony is suspected to be quite harmful to human body and application of antimony to steel must be discreet.  Further, addition of Sb to steel results in concentration of Sb in the central segregation zone of the steel, thereby deteriorating central segregation therein.  A portion where Sb has been concentrated of steel exhibits localized hardening, thereby generating difference in hardness between the portion and the base material and thus serving as the origin of rolling contact fatigue fracture to deteriorate rolling contact fatigue life characteristics of the steel. 
Patent Literature 6 discloses, in order to diffuse and eliminate central segregation and massive eutectic carbide in the central segregation zone generated during casting of high carbon chromium bearing steel, a method for rolling the cast steel to a billet and subjecting the billet to soaking. 
However, there is a problem in the method of Patent Literature 6 in that temperature distribution in steel is uneven during soaking and soaking temperature may locally exceed the temperature corresponding to the solidus curve, which triggers localized re-melting to cause an eutectic reaction to form massive eutectic carbide in the steel. 
In view of this, not the aforementioned high carbon chromium steel but low carbon alloy steel is sometimes employed depending on the type of bearing application.  For example, case hardening steel is generally utilized as the second option next to high carbon chromium steel.  However, it should be noted that case hardening steel, containing carbon by 0.23 mass % or less, necessitates: addition of appropriate amounts of Mn, Cr, Mo, Ni and the like thereto to obtain required hardenability and mechanical strength; and surface hardening by carburizing and carbonitriding to improve fatigue strength of the steel. 
For example, Patent Literature 7 discloses case hardening steel obtainable through carburizing treatment in a shortened time by specifying chemical composition thereof (C: 0.10-0.35% and so on) and setting the value of activation energy Q for carbon diffusion in steel defined by formula: Q=34140−605[% Si]+183[% Mn]+136 [% Cr]+122[% Mo] to be 34000 kcal or less. 
Similarly, Patent Literature 8 discloses a technique regarding a carburized material excellent in rolling contact fatigue characteristics, the material having: a specific chemical composition such as C: 0.1-0.45%; austenite grain size of carburized layer of No.  7 or above; carbon content in a surface of 0.9 to 1.5%; and an amount of retained austenite in the surface of 25 to 40%. 
However, there are problems in the techniques of Patent Literature 7 and Patent Literature 8 in that implementation of the aforementioned carburizing and carbonitriding, although it improves rolling contact fatigue life characteristics of steel, significantly increases manufacturing cost and amplifies strains and dimensional changes to decrease production yield, to eventually increase the price of the final product.  Further, the aforementioned conventional techniques necessitate significant modification of carburizing/carbonitriding facilities when bearing steel having a large cross section is to be manufactured due to specific bearing application, which increases a burden on the manufacturer in economical terms.