Harvard Astronomy 201b

Minimum Mass Scales for Formation of Massive Star-Forming Galaxies

In Journal Club, Journal Club 2011 on April 20, 2011 at 9:23 pm


This article describes a result from the recent paper by (Amblard et at 2011). This paper studied the Cosmic Infrared Background (CIB), emission from background sub-resolution submillimeter galaxies, using the Herschel Space Observatory. By taking a power spectrum of the CIB and comparing to models of dark matter distribution, they were able to find a lower bound on the mass scale required for a cluster to form a large, star-forming galaxy.


The observatory used for this study was the Herschel Space Observatory. Herschel is a 3.5-meter ESA telescope sensitive to the far IR and sub-mm wavelength ranges. Its Earth-trailing orbit at L2 allows it to avoid the thermal cycling and changing fields of view that challenge telescopes in Earth orbit. The specific instrument used was SPIRE, a sensitive photometer with passbands at 250, 350 and 500 microns. All three channels were used in this study.

Figure 1: Herschel Space Observatory. Figure from http://en.wikipedia.org/wiki/Herschel_Space_Observatory

Cosmic Infrared Background & Observations

Faint, sub-mm galaxies are responsible for more than 85% of extragalactic light emission. This background emission is termed the Cosmic Infrared Background. Low-resolution observations (such as Herschel SPIRES) cannot resolve these large, star-forming galaxies individually, but their clustering should still be visible in variations in the CIB intensity (Amblard et al 2011).

This paper uses these variations to study large-scale structure in the universe. To this end, the authors conduct a 13.5-hour survey of a 218’ by 218’ field in the “Lockman Hole”. This region has very little dust, meaning that the extragalactic CIB emission is more readily detected. The authors implement a number of sophisticated techniques to remove foreground objects and remove instrumental effects, creating a map of the CIB – the first to date.

Power Spectrum and Galaxy Clustering Model

So what does this map tell us? Nothing – yet. To get useful data out of this model, a few more steps are needed. First, the authors take a power spectrum of the data. This gives information on the intensity at different angular separations. If sources are tightly clustered, emission should be high at small separations, which corresponds to high k, where k=1/separation.

To proceed further, we must make some key assumptions. First, the paper assumes the dark matter distribution is traced by these galaxies; therefore, clustering of galaxies traces clustering of dark matter. Second, we must assume we know something about how this dark matter is distributed. The authors assume the Navarro-Frenk-White profile for the dark matter halo density function. The authors assume the concordance cosmology model. This allows, for example, conversion of redshift into distance.

Finally, the authors construct a model for the population of galaxies within a given dark matter halo, the Halo Occupation Distribution (HOD). This model divides galaxies into two types: central, high mass star-forming galaxies occupying the halo center, and small “satellite” galaxies. The model assumes a threshold mass M_{min} required for forming a central galaxy, so the number of central galaxies is N_{cen}=H(M-M_{min}), where H is the Heaviside step function. Note this model assumes any one halo will form at most one large star-forming galaxy. The number of satellite galaxies is taken to be N_{sat}=(\frac{M}{M_1})^{\alpha}, where M_1 and \alpha are parameters to be determined. M_1 corresponds to the mass scale required to form one satellite galaxy in addition to the central galaxy, and is constrained to be 10-25 times M_{min} based on numerical simulations.

Using these assumptions, the authors are able to derive a model power spectrum for the CIB, which they then fit to data. Figure 2 below presents the clustering power spectrum and the fits to the data. In modeling the power spectrum, the authors divide it into P(k,z)=P_{1h}(k,z)+P_{2h}(k,z), where P_{1h} represents 1-halo clustering (clustering at short scales) and P_{2h} represents 2-halo clustering (clustering at long scales).

Figure 2: Clustering power spectrum and fits at 500 microns, taken from (Amblard et al 2011: Supplemental Information). The blue line represents shot noise (subtracted off). The green lines represent power spectrum fits. The dashed green line represents the 1-halo term, the dash-dotted green line represents the 2-halo term, and the solid green line represents the total clustering power spectrum.

Key Result: Minimum Mass Scale

In executing these fits, the authors find that for every waveband, M_{min} \sim 10^{11} M_{sun}. Averaged over all wavebands, the authors find M_{min} \approx 3 \times 10^{11} M_{sun}, with uncertainty of \log10 [M_{min}/M_{sun} = \pm 0.4. This result empirically sets a minimum mass scale for the dark matter halo required to form a central, massive star-forming galaxy.

This is huge. Since these galaxies are thought to be the most active sites of star formation in the known universe, this gives “the preferred mass scale of active star formation in the universe”. Higher mass halos are of course allowed, but tend to be much rarer. The authors speculate that this minimum constraint is set by photoionization feedback: any smaller, and the gravity well of the dark matter halo would be insufficient to keep the galaxy together against radiation pressure, and it would fragment into smaller galaxies. However, this interpretation should be treated with caution. This result runs far ahead of theory; existing semi-analytic galaxy formation models predict a mass scale of order 10 times larger or more. This result provides a key empirical (though heavily model-dependent) input for theorists to consider and work towards in developing their models, and improving our understanding of galaxy formation processes in the Universe.



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