Magnetic Field Orientations in Star Formation
Posted on (Update: )
\[\def\MCF{\mathrm{MCF}} \def\pixel{\mathrm{pixel}} \def\cm{\mathrm{cm}} \def\mag{\mathrm{mag}} \def\trs{\mathrm{trs}} \def\small{\mathrm{small}} \def\large{\mathrm{large}}\]Link between magnetic field orientations and star formation rates
This part is based on Li, H., Jiang, H., Fan, X., Gu, Q., & Zhang, Y. (2017). The link between magnetic field orientations and star formation rates. Nature Astronomy, 1(8), 0158.
Understanding star formation rates (SFRs) is a central goal of modern star formation models, which mainly involve gravity, turbulence and, in some cases, magnetic fields (B-fields).
However, a connection between B-fields and SFRs has never been observed.
A comparison between the surveys of SFRs and a study of cloud-field alignment shows consistently lower SFRs per solar mass for clouds almost perpendicular regulator of SFRs.
The perpendicular alignment possesses a significantly higher magnetic flux than the parallel alignment and thus a stronger support of the gas against self-gravity. This results in overall lower masses of the fragmented components, which are in agreement with lower SFRs.
Clouds with a similar mass and age can have different SFRs, as shown in the following figure.
Figure 2 correlates the SFRmass$^{-1}$ with the cloud-field angles and shows that large-angle clouds hava consistently lower values of SFRmass$^{-1}$. Perform the permutation tests and Spearman rank correlation tests to determine the significance of this trend.
Links between magnetic fields and filamentary clouds
The dynamical importance of magnetic fields in molecular clouds has been increasingly recognized, as observational evidence has accumulated. However, how a magnetic field affect star formation is still unclear.
Typical star formation models still treat a magnetic fields as an isotropic pressure, ignoring the fundamental property of dynamically important magnetic fields: their directions.
Their previous work: demonstrate how the mean magnetic field orientation relative to the global cloud elongation can affect cloud fragmentation.
The paper shows that the mass cumulative function (MCF) of a cloud is also regulated by the field orientation.
- A cloud elongated closer to the field direction tends to have a shallower MCF
The authors have conducted a series of studies on the connections between molecular cloud fragmentation and cloud-field offset (i.e., the misalignment between the ambient magnetic field direction and the cloud elongation).
- Li et al. (2013): The discovery of bimodal cloud-field offsets
- study 13 nearby Gould Belt molecular clouds and revealed that the long axes of a cloud tend to align either perpendicularly (large cloud-field offset) or in parallel (small cloud-field offset) to the mean directions of the ambient magnetic field
- a possible effect of the cloud-field offset on cloud fragmentation is due to the magnetic flux
Gould Belt: 古尔德带是横跨3,000光年直径，由恒星组成的星环的一部分，包含许多O型和B型的OB星恒星，从银河盘面翘起16至20°。古尔德带被怀疑是包含太阳在内的螺旋臂，太阳距离旋臂中心约325光年。估计存在的时间约3,000至5,000万年，但来源还未知，名称则得自1879年发现它的美国天文学家本杰明·阿普索普·古尔德。 古尔德带包含了许多星系中的亮星包括仙王座，蝎虎座，英仙座，猎户座，大犬座，船尾座，船帆座，船底座，南十字座，半人马座，豺狼座，天蝎座。在天空中可见的银河系也经过这些星座中的大部分，但在豺狼座的东南部。
The present study considers the effect of the cloud-field offset on the mass portion of gas in high density.
Data
- same catalogue of Gould belt molecular clouds as in Li et al. (2017)
- use the dust extinction maps to construct the MCFs
- a resolution of 1’
- select clouds within 500pc, which limits the distance variation between 150 and 450 pc to restrict the effect from different spatial resolutions.
ChatGPT: 天文学中的 extinction maps 是用于研究星空中星云、恒星等天体的消光（extinction）分布的地图。消光通常是由于星云等物质的吸收和散射引起的。通过制作消光分布的地图，可以帮助天文学家更好地研究星系中星云和恒星的分布、结构和性质。消光地图通常是通过测量光的颜色和亮度来获得的。
云南大学中国西南天文研究所: 星际尘埃主要产生于恒星演化晚期，它们是银河系的重要组成部分，在星系演化、恒星与行星系统的形成，乃至生命的起源中都起着重要作用。此外，星际尘埃会吸收和散射可见光与近红外波段的光线，产生消光与红化效应，所以依赖这些观测的科学研究必须考虑去除星际尘埃的影响。天文学家通过制定精确的银河系三维尘埃消光分布图，以准确地改正观测天体的消光与红化效应；并进一步测量银河系的尘埃结构参数，以研究银河系的结构、形成与演化历史。
only use pixels with extinction higher than $A_{V_{trs}}$, the “transition density” of the column density probability density functions (N-PDFs), to construct the MCFs
MCF is the amount of cloud mass that is above a given dust extinction, $\tilde A_V$,
\[\MCF(\hat A_V) = \mu m_HC\sum_{\pixel (A_V>\tilde A_V)} A_V \times A_{\pixel}\]where
- $\mu=1.37$ is the mean molecular weight
- $m_H$ is the mass of hydrogen
- $A_\pixel = [D(cm)\times R(rad)]^2$ is the area of one pixel
- $C=1.37\times 10^{21}\cm^{-2}\mag^{-1}$
星等（英语：magnitude）：是指星体在天空中的相对亮度。一般而言，这也指“视星等”，即为从地球上所见星体的亮度。在地球上看起来越明亮的星体，其视星等数值就越低。常见情况下人们使用可见光来衡量视星等，但在科学探测中，红外线等其它波段也有用到。不同波段探测到的星等数据会有所不同。一颗星星的星等，取决于它离地球的距离、它本身的光度（即为绝对星等）、星际尘埃遮蔽等多重因素。一般人的肉眼能够分辨的极限大约是6.5等。
The MCF slope is defined by
\[\text{MCF slope} = \left\vert \frac{\log(M_{trs})-\log (0.1M_\trs)}{A_{V\trs}-A_{V0.1}}\right\vert = \frac{1}{\vert A_{V\trs} - A_{V0.1}\vert}\]
Results
- molecular clouds with larger cloud-field offsets show steeper slopes
study the degree of significance of the correction between MCF slopes and cloud-field offsets
\[H_0: \mu_{\small} = \mu_{\large}\qquad H_1:\mu_\small > \mu_\large\]where $\mu_\small$ is the average MCF slope of the molecular clouds with cloud-field offsets < 45 degrees.
By the non-parametric permutation test, the resulting $p$-value is 0.01.
MCF slope uncertainties
The potential uncertainties in the MCF slopes arising from
- extinction measurement uncertainty
- line of sight (LOS) contamination
- MCF bin width
- spatial resolution
- $A_{V\trs}$ uncertainty
- $A_V$ range adopted for the MCF slope measurements