Clustering of high-redshift quasars with DESI DR2

M. Charles, P. Martini, A. J. Ross, D. H. Weinberg, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, F. J. Castander, T. Claybaugh, A. Cuceu, A. de la Macorra, P. Doel, S. Ferraro, A. Font-Ribera, J. E. Forero-Romero, S. Gontcho A Gontcho, G. Gutierrez, J. Guy, C. Hahn, H. K. Herrera-Alcantar, K. Honscheid, C. Howlett, M. Ishak, R. Joyce, D. Kirkby, A. Kremin, M. Landriau, L. Le Guillou, M. E. Levi, M. Manera, A. Meisner, R. Miquel, J. Moustakas, A. D. Myers, S. Nadathur, N. Palanque-Delabrouille, W. J. Percival, F. Prada, I. Pérez-Ràfols, G. Rossi, L. Samushia, E. Sanchez, D. Schlegel, M. Schubnell, D. Sprayberry, G. Tarlé, B. A. Weaver, R. Zhou

First listed 2026-06-26 | Last updated 2026-06-25

Abstract

We present clustering measurements for high-redshift quasars using data from the Dark Energy Spectroscopic Instrument Data Release 2. Our sample consists of quasars with $2.0 < z < 3.5$ in the luminosity range $M_{1450} \leq -19.94$\,mag. We measure the mean quasar bias $b_Q(\bar{z} = 2.48) = 3.61 \pm 0.01$ for the full sample of $\sim 715,000$ quasars and quantify the redshift evolution of quasar bias by dividing the sample into four equal redshift bins. There is strong evolution of the quasar bias with redshift that is well fit by the function $b_Q(z) = a [(1 + z)^2 - 6.565] + b$ with $a=0.230 \pm 0.007$ and $b=2.394 \pm 0.035$, and this fit is also a good match to lower redshift measurements in the literature. This bias evolution is consistent with a characteristic halo mass of $\bar{M}_{\mathrm{h}} \sim 10^{12}\,\mathrm{M_\odot}$ that does not vary significantly with redshift. The inferred duty cycles for quasars in our sample are $f_{\mathrm{duty}} \sim 10^{-2}$, staying mostly constant over redshifts. We investigate the luminosity dependence of quasar clustering by dividing each of our four redshift bins into three luminosity bins. The size of our quasar sample permits the first statistically significant measurement of the luminosity dependence of quasar bias at these redshifts. We measure weak dependence of quasar bias on luminosity at fixed redshift, inconsistent with no dependence, but weaker than predicted by a model in which quasar luminosity is tightly correlated with halo mass. These clustering measurements provide a stringent test for models of active black hole light curves and the black hole-halo connection at high redshift.

Short digest

Using DESI DR2, this paper measures the clustering of a huge high-redshift quasar sample of about 715,000 objects at 2.0 < z < 3.5 and M1450 <= -19.94 mag. The headline result is a precise mean bias of b_Q(zbar = 2.48) = 3.61 +/- 0.01 plus strong redshift evolution, well described by b_Q(z) = a[(1 + z)^2 - 6.565] + b, while remaining consistent with quasars living in characteristic halos of roughly 10^12 Msun. The inferred duty cycle stays near 10^-2 across the sample, implying that only a small fraction of suitable halos host an active quasar at any given time. With the sample split by luminosity as well as redshift, the authors also report the first statistically significant luminosity dependence of quasar bias at these redshifts, but the trend is weak and notably softer than expected if quasar luminosity tracked halo mass tightly, making the measurement a sharp test of black hole light-curve and halo-occupation models.

Key figures to inspect

• Figure 5. This is the cleanest summary of the paper's main clustering result: the redshift evolution of quasar bias across the four DESI DR2 bins, together with the best-fit b_Q(z) relation and comparison to earlier SDSS and DESI measurements. It is the most important figure for seeing both the precision of the new dataset and how the DESI result extends and regularizes the literature trend.
• Figure 10. This figure most directly shows why the paper claims a statistically significant luminosity dependence at fixed redshift. By plotting pulls relative to the redshift-only model and fitting a nonzero slope with luminosity, it makes the significance of the deviation easy to see and ties the abstract's claim to a concrete diagnostic.
• Figure 11. This is the key interpretation figure for the halo connection, translating the bias measurements into characteristic and minimum halo masses as a function of redshift and luminosity. It matters because the paper's conclusion that quasars inhabit halos of order 10^12 Msun with only modest evolution is one of the main physical takeaways.
• Figure 12. This figure captures the duty-cycle inference, showing that the quasar duty cycle stays near 10^-2 across the redshift and luminosity bins. It is central for understanding the occupancy implication of the clustering analysis: most halos of the relevant mass are not hosting an active quasar at a given time.
• Figure 13. This later comparison figure is especially valuable because it confronts the measured luminosity-binned bias with simple models having no scatter or large scatter between luminosity and halo mass. It helps explain why the observed luminosity dependence is described as weaker than a tight luminosity-halo mapping would predict, which is the paper's main model-level conclusion.