Pre-heating of the intergalactic medium by gravitational collapse and ultraviolet background

The preheating of intergalactic medium(IGM) by structure collapsing and ultraviolet background(UVB) are investigated in cosmological hydrodynamical simulations. When gravitational collapsing is the sole heating mechanism, we find that (1) $60\%, 45\%$ of the IGM are heated up to $S>8, 17$ kev cm$^2$ respectively at $z=0$, but the fractions drop rapidly to a few percents at $z=2$, (2) the entropy of the circum-halo gas $S_{\rm{cir}}$ is higher than the virial entropy for more than $75 \%$ of the halos with masses $M<10^{11.5}$ $M_{\odot}$ since $z=2$, but the fraction higher than the entropy, $S_{\rm{pr}}$, required in preventive model of galaxies formation is only $15-20 \%$ for halos with $M<10^{10.5} M_{\odot}$ at $z=0$, and decreases as redshift increases, (3)assuming a metallicity of $Z \leq 0.03 Z_{\odot}$, the fraction of halos whose circum-halo gas having a cooling time longer than the Hubble time $t_{cool,cir}>t_{\rm{H}}$ is merely $5-10 \%$ at $z \lesssim 0.5$, and even less at $z \geq 1$ for halos with $M<10^{10.5} M_{\odot}$. (4) gas in the filaments undergoes the strongest preheating. Furthermore, we show that the UVB can not enhance the fraction of IGM with $S>17$ kev cm$^2$, but can increase the fraction of low mass halos($<10^{10.5} M_{\odot}$) that having $S_{\rm{cir}}>S_{\rm{pr}}$ to $\sim 70 \%$ at $z=0$, and that having $t_{\rm{cool, cir}}>t_{\rm{H}}$ to $15-30 \%$ at $z \lesssim 0.5$. Our results indicate that preheating due to gravitational collapsing and UVB are inadequate to fulfil the needs of preventative model, especially for halos with $10^{10.5}<M<10^{11.5} M_{\odot}$. Nevertheless, these two mechanisms might cause large scale galactic conformity.Comment: 18 pages, 11 figures, To appear in Ap

Additive Property of Drazin Invertibility of Elements

In this article, we investigate additive properties of the Drazin inverse of elements in rings and algebras over an arbitrary field. Under the weakly commutative condition of $ab = \lambda ba$, we show that $a-b$ is Drazin invertible if and only if $aa^{D}(a-b)bb^{D}$ is Drazin invertible. Next, we give explicit representations of $(a+b)^{D}$, as a function of $a, b, a^{D}$ and $b^{D}$, under the conditions $a^{3}b = ba$ and $b^{3}a = ab$.Comment: 17 page

Uniqueness of the Ricci Flow on Complete Noncompact Manifolds

The Ricci flow is an evolution system on metrics. For a given metric as initial data, its local existence and uniqueness on compact manifolds was first established by Hamilton \cite{Ha1}. Later on, De Turck \cite{De} gave a simplified proof. In the later of 80's, Shi \cite{Sh1} generalized the local existence result to complete noncompact manifolds. However, the uniqueness of the solutions to the Ricci flow on complete noncompact manifolds is still an open question. Recently it was found that the uniqueness of the Ricci flow on complete noncompact manifolds is important in the theory of the Ricci flow with surgery. In this paper, we give an affirmative answer for the uniqueness question. More precisely, we prove that the solution of the Ricci flow with bounded curvature on a complete noncompact manifold is unique.Comment: 33 pages (Previous version has some typing errors, the present one is correct.