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Magnetic Field Orientations in Star Formation

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Tags: Star Formation, Magnetic Field \[\def\MCF{\mathrm{MCF}} \def\pixel{\mathrm{pixel}} \def\cm{\mathrm{cm}} \def\mag{\mathrm{mag}} \def\trs{\mathrm{trs}} \def\small{\mathrm{small}} \def\large{\mathrm{large}}\]

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.

image

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.

image

This part is based on Law, C.-Y., Li, H.-B., Cao, Z., & Ng, C.-Y. (2020). The links between magnetic fields and filamentary clouds – III. Field-regulated mass cumulative functions. Monthly Notices of the Royal Astronomical Society, 498(1), 850–858.

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: which 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

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.

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

image

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),为天文学术语,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。 source: https://zh.wikipedia.org/wiki/%E6%98%9F%E7%AD%89

The MCF slope is defined by

\[\text{MCF slope} = \left\vert \frac{\log(M_{trs})-\log (0.1M_\trs)}{A_{V\trs}-A_{V0.1}}\right\vert = \frac{1}{\vert A_{V\trs} - A_{V0.1}}\]

image

Results

image

  • 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

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