兩微米近紅外巡天計劃的點源目錄(2MASS PSC) 提供了一個很好的機會以數星(star counts) 的方式來研究銀河系的結構及其成員星的光度函數(luminosity function)。我們建立了空間解析度約為1度的全天Ks波段的差異數星(differential star counts, DSC), 其對數型式呈現了一個漂亮的線性範圍可以被一個單4次函數(single power law) 的光度函數及一個三單元的銀河系模型(薄盤、厚盤及銀暈) 所擬合。我們發現銀河的模型並不會影響該線性區域的形狀, 因此我們搭配了一個常用的銀河系模型來量測Ks波段的差異數星以獲得全天的光度函數, 全天光度函數的4次函數指數(power law index) 約略均G分布, 跟銀河系座標沒有明顯關聯性, 期平均值為γ = 1.85 ± 0.035, 另外光度函數的上下限分別為Mb = −7.86 ± 0.60 Ks星等及Mf = 6.88 ± 0.66 Ks星等, 我們的結果強烈支持銀河系單一光度函數的假設。我們也發現大麥哲倫星雲(LMC) 與小麥哲倫星雲(SMC) 的光度函數跟銀河系相類似。
藉由上面得到的光度函數, 我們接著重新測量銀河系三單元的結構參數, 為了避免盤面區域複雜的小結構(fine structure) 及消光(extinction), 我們只利用銀緯大於30度的天區, 擬合結果為: 太陽附近薄盤的星數密度為(local stellar density) n0 = 0.030 ± 0.002 stars/pc3, 其結構高度(scale-height)及結構長度(scale-length)分別為Hz1 = 360±10 pc及Hr1 = 3.7±1.0 kpc; 而厚盤對薄盤的比例(local thick-to-thin disk density ratio) 及其結構高度及結構長度分別為Hz2 = 1020±30 pc,Hr2 = 5.0±1.0 kpc 及f2 = 7±1%; 另外,銀暈的軸比(axis ratio), 半徑遞減指數(power law index) 及對薄盤的比例(local thickto-thin disk density ratio) 分別為κ = 0.55±0.15,p = 2.6±0.6 及fh = 0.20±0.10%。此外, 我們發現主要結構參數(n0,Hz1, f2 and Hz2) 間存在著簡併的現象(degeneracy), 這些參數中的任兩個都呈現反相關趨勢(anti-correlated), 因此2MASS 的資料可以同時被好幾組不同的參數組合所擬合, 這也可能是為何文獻上的結構參數會有許多不同值的原因。因為只分析了中高銀緯的天區, 所以我們的擬合對盤的結構長度並不靈敏。

The point source catalog of the Two Micro All Sky Survey (2MASS PSC) provides a good opportunity to employ star counts on the investigation of the the Milky Way structure and its stellar luminosity function in a global aspect. We carry out the whole sky Ks differential star counts (DSC) with one degree spatial resolution. The logarithmic Ks DSC shows a nice linear part which can be well explained by a single power law luminosity function with a three components Galactic structure model (i.e., thin disk, thick disk and halo). It turns out that the Galactic structure does not affect the shape of the linear part of the logarithmic Ks DSC as much as the luminosity
function. Hence we measure the luminosity functions of the entire Milky Way from the Ks DSC with a fiducial Galactic model. The power law indices of the whole sky Ks luminosity function are roughly isotropic (i.e., no obvious trend with the Galactic latitude and longitude). The mean values for the power law index, the bright and the faint ends of the luminosity function are γ = 1.85 ± 0.035, Mb = −7.86 ± 0.60 Ks mag and Mf = 6.88 ± 0.66 Ks mag, respectively. Our result strongly support the notion of a universal luminosity function in our Galaxy. We also find that the
luminosity functions of the Large Magellanic Cloud and the Small Magellanic Cloud are similar to that of our Galaxy. With this luminosity function, we refine the Galactic structure parameters of three components. To avoid complication introduced by other fine structures and significant extinction near the Galactic plane, we only consider Galactic latitude |b| > 30◦ Ks DSC. Our best-fit local density of the thin disk is n0 = 0.030 ± 0.002 stars/pc3. The best-fit scale-height and length of the thin disk are Hz1 = 360 ± 10 pc and Hr1 = 3.7 ± 1.0 kpc, and those of the thick disk are Hz2 = 1020±30 pc and Hr2 = 5.0±1.0 kpc, the local thick-to-thin disk density ratio is f2 = 7±1%. The best-fit axis ratio, power law index and local density ratio of the oblate halo are κ = 0.55 ± 0.15, p = 2.6 ± 0.6 and fh = 0.20 ± 0.10%, respectively. Moreover, we find some degeneracy among the key parameters (e.g., n0,Hz1, f2 and Hz2). Any pair of these parameters are anti-correlated to each other. The 2MASS data can be well-fitted by several possible combinations of these parameters. This is probably the reason that there is a wide range of values for the structure parameters in literature similar to this study. Since only medium and high Galactic latitude data are analyzed, the fitting is insensitive to the scale-lengths of the disks.

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