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Intrinsic alignment of galaxies

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Intrinsic alignment of galaxies










Intrinsic alignment - a systematic of cosmic shear


The cosmic shear signal is obtained by correlating the measured ellipticities of distant galaxies. Gravitational lensing causes a distortion of the galaxy shapes and adds a shear to the ellipticity. However, galaxies are not circular in shape in absence of lensing; they have an intrinsic ellipticity which is about two orders of magnitude larger than the gravitational shear. Thus, one makes use of statistics and measures the ellipticity correlations for many pairs of galaxies. In the regime of weak shears, as is the case in cosmic shear, the measured ellipticity Formula can simply be written as the sum of intrinsic ellipticity Formulaand gravitational shear Formula, so that the correlator of ellipticities for two galaxies i and j reads




Usually one assumes that the intrinsic ellipticities of galaxies are randomly distributed on the sky, so that they are correlated neither with the intrinsic ellipticities nor with the shears of other galaxies. As a consequence, only the first term on the right-hand side in Eq. (1) remains, which is the desired shear signal.


When aiming at high-precision cosmic shear measurements, the assumption of random intrinsic ellipticities becomes inaccurate since galaxies can intrinsically align and therefore have correlated intrinsic ellipticities. For instance, two physically close pairs of galaxies could be aligned by the tidal forces of the same dark matter structure surrounding them. This causes the second term on the right-hand side in Eq. (1) to be non-zero, thereby contaminating the cosmic shear measurement. This systematic runs under the name of intrinsic ellipticity correlations or II signal. Assume now that galaxy i is located at siginificantly lower redshift, i.e. closer to the observer, than galaxy j. Then the third term in Eq. (1) should vanish because the shear signal of galaxy i, which is caused by the matter between this galaxy and the observer, should not be correlated with the intrinsic shape of a background object unless one encounters rather improbable situations such as an extended matter structure along the line of sight. Figure IA1 illustrates that the fourth term in Eq. (1) can yield a contribution to the ellipticity correlator. If a matter structure (grey) causes the alignment of a nearby (blue) galaxy and contributes to the lensing signal of a background (red) galaxy, it produces shear-ellipticity correlations. The so-called GI term, first mentioned by Hirata & Seljak (2004), produces a net anti-correlation since the shear of the background galaxy is preferentially tangential with respect to the deflecting matter concentration, whereas the foreground galaxy 'points' on average to the matter structure exerting the tidal forces and is thus radially aligned. 




Figure IA1:  Sketch of a situation that can produce shear-ellipticity correlations. Left: As seen in the plane of the sky; right: view along the line of sight. The matter structure DM aligns the blue galaxy and contributes to the lensing signal of the red background galaxy.



As detailed below, both the II and GI term can contribute to the lensing signal by roughly 10% each, thus being a serious systematic of cosmic shear measurements if untreated. While here we focus on measurements at the two-point level, i.e. based on correlations of pairs of galaxies, intrinsic alignment also plays a role in higher-order cosmic shear statistics. Third-order measures for instance can be contaminated by III, GII, and GGI signals, which might constitute an even stronger systematic than at the two-point level (Semboloni et al. 2008). Although intrinsic alignment is primarily seen as a systematic to gravitational lensing today, one should bear in mind that it contains valuable information itself: Apart from potential constraints on cosmological parameters, e.g. via geometry, the intrinsic aligment of galaxies reflects the formation and evolution of galaxies in their respective dark matter environments. To date it is unclear whether it will be possible to separate the intrinsic alignment and cosmic shear signals such that both can deliver a maximum of cosmological information.



Intrinsic ellipticity correlations (II)


The II signal has been dealt with by various publications with both analytical and numerical approaches, e.g. via N-body simulations (e.g. Croft & Metzler 2000; Catelan et al. 2001; Crittenden et al. 2001; Jing 2002). They agree insofar as they predict intrinsic ellipticity correlations of 1 to 10% of the lensing signal for surveys with median redshift around unity, whereas the effect even dominates the cosmic shear signal for shallow surveys. This behavior is expected because a high median redshift corresponds to a broad redshift distribution of galaxies, which decreases the probability of finding two galaxies at the same redshift. Considering a tomography cosmic shear survey where photometric redshifts of the galaxies are used to sort them into redshift bins, the II term is a severe systematic for auto-correlations since then the redshift distribution for the corresponding bin is narrow, yielding a high probability to find close-by pairs of galaxies.


Brown et al. (2002) detected intrinsic ellipticity correlations in the SuperCosmos Survey, which is so shallow that all measured ellipticity correlations have to be purely intrinsic. Although Mandelbaum et al. (2006) did not find an II signal in the Sloan Digital Sky Survey (SDSS), their results are statistically in agreement with the SuperCosmos data.


Accurate modelling of intrinsic galaxy alignments involves the intricacies of galaxy formation and evolution within their dark matter haloes, including baryonic physics up to scales much larger than an individual galaxy. Consequently, analytic progress is cumbersome, and simulations still lack the computational power to address the problem to full extent (see e.g. Schaefer 2008). Hence, our understanding of intrinsic alignment is still at the level of toy models; see for instance Hirata & Seljak (2004).


A secure way to deal with the contamination by intrisic alignments should therefore not rely on the (still) uncertain models, but for instance make use of geometric properties of the intrinsic alignment signals. In case of the II, galaxies need to be physically close to mutually align, i.e. they have both small angular separations on the sky and similar redshifts. Thus, intrinsic ellipticity correlations are relatively easy to remove from the cosmic shear signal if redshift information is available. King & Schneider (2002) remove pairs of galaxies with small differences in redshift, depending on the accuracy of photometric redshift information. Heymans & Heavens (2003) have determined optimal weights for potentially contaminated galaxy pairs, while King & Schneider (2003) use templates to separate lensing and II signal by their different redshift behaviour. Besides, intrinsic ellipticity correlations can generate B-modes (Hirata & Seljak 2004; Heymans et al. 2006), which could be used for its identification if one were able to exclude alternative sources of a curl-component.



Shear-ellipticity correlations (GI)


In contrast to the foregoing case, shear-ellipticity correlations are not restricted to physically close pairs of galaxies, which makes their removal a more complicated issue. While the II signal prevails in shallow surveys, the GI contribution increases for larger separations in redshift of the galaxies, becoming the dominant contamination for deep surveys (Hirata & Seljak 2004). Correspondingly, shear-ellipticity correlations constitute a serious systematic of the cosmic shear signal when cross-correlating bins with largely different redshifts in tomographic surveys. N-body simulations yield an upper limit of about 10% contribution for shear-ellipticity correlations (Heymans et al. 2006), in agreement with an analytic estimate using intrinsic alignment toy models (Hirata & Seljak 2004). Such a contamination of the cosmic shear signal implies an underestimation (due to the anti-correlation of shear and intrinsic ellipticity) of the normalization of the matter power spectrum of about 5%, as well as a bias on the parameters of the dark energy equation of state by up to 50% if acting together with intrinsic ellipticity correlations (Bridle & King 2007).


Shear-ellipticity correlations were first observed in the Sloan Digital Sky Survey (SDSS), yielding an upper limit of 20% contamination of the lensing signal (Mandelbaum et al. 2006). Hirata et al. (2007) have found a best-fit intrinsic alignment model, using data from SDSS and the 2SLAQ survey, which predicts 6.5% contamination to a cosmic survey of a similar set of galaxies.


In spite of the fairly recent description (2004) and observational verification (2006) of shear-ellipticity correlations, a number of ways to deal with the GI term in the context of cosmic shear surveys have been proposed. First ideas were already discussed in Hirata & Seljak (2004). King (2005) extends the approach of template fitting (King & Schneider 2003) to include a treatment of the GI signal. Bridle & King (2007) investigate the effects on parameter constraints by assuming a GI model binned in redshift and angular frequency with free parameters, which are then marginalised over. In a purely geometrical approach Joachimi & Schneider (2008) null the GI contribution by exploiting the characteristic dependence on redshift of shear-ellipticity correlations. Moreover, Zhang (2008) has suggested to self-calibrate the GI signal via intrinsic ellipticity - galaxy density correlations, which requires that in addition to the ellipticity - ellipticity correlations (the lensing data), one also extracts ellipticity - density and density - density correlations from the cosmic shear survey.





Bridle & King 2007, NJPh, 9, 444

Brown et al. 2002, MNRAS, 333, 501

Catelan et al. 2001, MNRAS, 320, 7

Crittenden et al. 2001, ApJ, 559, 552

Croft & Metzler 2000, ApJ, 545, 561

Heymans & Heavens 2003, MNRAS, 339, 711

Heymans et al. 2006, MNRAS, 371, 750

Hirata et al. 2007, MNRAS, 381, 1197

Hirata & Seljak 2004, Phys. Rev. D,  70, 063526

Jing 2002, MNRAS, 335, 89

Joachimi & Schneider 2008, A&A, 488, 829

King 2005, A&A, 441, 47

King & Schneider 2002, A&A, 396, 411

King & Schneider 2003, A&A, 398, 23

Mandelbaum et al. 2006, MNRAS, 367, 611

Schaefer 2008, astro-ph/0808.0203

Semboloni et al. 2008, MNRAS, 388, 991

Zhang 2008, astro-ph/0811.0613



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