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We present the nearest neighbor distance (NND) analysis of SDSS DR5 galaxies. We give NND results for observed, mock and random sample, and discuss the differences. We find the observed sample gives us a significantly stronger aggregation characteristic than the random samples. Moreover, we investigate the direction of NND and find the direction has close relation with the size of the NND for the observed sample.

By the end of the 30s of last century, from the analysis of the position of galaxies on photographic film, Reference [

Compared to previous research, a significant difference of this paper is to develop the application of the Nearest Neighbor Vector (NNV) direction. Reference [

Our article is organized as follows: In Section 2 we present the nearest neighbor statistical scheme. In Section 3 we study the data from the SDSS DR5. We summarize the results in Section 4 and have conclusions in Section 5.

Reference [_{j}, y_{j}, z_{j}. For each galaxy the distance to its nearest neighboring object r_{i} is computed as [

In this paper we simply use

to calculate the average NND (nearest neighbor distance) in each sample. r_{i} is the NND for each point and n is the total number of particles. According to [

We also consider the direction of each NND in the distance field; we call it NNV (nearest neighbor vectors). We first construct a sphere to include all samples and then split the whole sphere into 180 triangles and investigate the distribution of NNV passing through each triangle. By analyzing the anisotropy of the NNV, we can find the footprint of the filaments and compare different samples in this way. The detailed description is in Section 4.

The Sloan Digital Sky Survey (SDSS) is one of the most ambitious and influential surveys in the history of astronomy. It is a major multi-filter imaging and spectroscopic redshift survey using a dedicated 2.5-m wideangle optical telescope at Apache Point Observatory in New Mexico, United States. We use the SDSS Data Release 5 as our galaxy sample, the detailed information (include the Redshift-distance formula, and a mock sample from Millennium Run Semianalytic Galaxy Catalogue [

For the observed sample we get 1.95 Mpc for average nearest neighbor distance, for the mock sample, we get 2.3 Mpc, and for the random sample we get r_{E} = 3.5 ± 0.005 Mpc (11 random samples with different seeds). Then we have

Clearly we can see observed sample has pronounced clustering on small scales compared with the random sample. Considering the extreme aggregation condition will have R = 0 and random sample has an R = 1, this observed sample is almost midway toward extreme aggregation. The clustering property of SDSS galaxies has been verified from various methods, such as two point correlation function [20-22]. The correlation length is about 5 - 7 Mpc [

this clustering property on small scale from a new way. The mock sample has a R = 0.66 in this measure value and is thus close to the observed sample.

Interestingly our analysis of the direction of the NND for each galaxy shows that the observed sample has an anisotropy property. To investigate the directional property of the NNV, we assumed all directions begin from a single point at origin, we split the whole surface of a sphere around the origin into 180 triangles (we could use the healpix method [

In

We collect the NNV for all galaxies first, and then as we know the 3-D coordinates of the three vertexes of the each triangle and the direction of NNV, we could precisely calculate which nearest neighbor vector crosses and plot them with the sequence of 180 triangles and get the distribution in

We also compute 11 random samples with different seeds to estimate the deviation. For all angles, mean value is 210 and we find that the average standard deviation (σ) is around 14 (maximum is 20) for all angles, in the following places all σ are taken from here.

Here some peaks are separated only because the arrangement of 180 triangles is arbitrary, so even two adjacent triangles may have dozens of serial number difference. Observed sample and mock sample looks very different at some specific triangles, but this is normal as the N-body simulation only simulate universe statistically, not exactly same with all details, such as the orientation of filaments. So we only focus on the global statistical properties from

From

In

larger NND than average. We plot them in

We can see for smaller NND less than average, it displays a stronger anisotropy than galaxies have larger NND than average from Figures 4(a) and (b).

We have calculated the average NND of the SDSS galaxy sample and mock samples. We find the observed sample has a lightly smaller NND than mock sample, but much smaller than random sample. This result indicates observed sample is more clustered in a special way. Moreover, we use a new method to investigate the direction distribution of NNV and find the NNV of observed sample has a global anisotropy and is similar with mock sample, but clearly different from random sample on some angles.

observed sample is more like a Poisson distribution and this leads us think about the Gaussian fluctuations of cosmic microwave background (CMB). Both of them show the anisotropy resulting from the evolution of the universe, but with somewhat different statistical property. Maybe it is because our sample size is limited and needs further observations.

As both NNV and NND display significant difference between observed and random sample, this makes us think whether the NNV and NND are correlated. Figures 4(a) and (b) show that galaxies with smaller NND have stronger antistrophic NNV.

To better understand the physical sense of the results above, we shall check on the hypothesis about a global isotropic universe. There is a distinct hierarchy on a larger scale from a few hundred kpc to a few hundred Mpc [

The project is supported by key laboratory opening funding of the Harbin Institute of Technology (HIT.KLOF. 2012.077).