The Formation of Direct Collapse Black Holes at Cosmic Dawn and 21 cm Global Spectrum

Abstract JWST reveals numerous high- z galaxies and supermassive black holes (SMBHs), suggesting that stars and SMBH seeds formation at z ≳ 10 may be more efficient than previously derived. One popular SMBH seed scenario is the direct collapse black holes (DCBHs) formed in pristine atomic-cooling halos irradiated by nearby galaxies. Therefore, the efficient star formation likely facilitates the formation of DCBH. We calculate the first critical <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>k</mml:mi> <mml:msub> <mml:mi mathvariant="normal">H</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:msub> <mml:mo>‒</mml:mo> <mml:msub> <mml:mi>k</mml:mi> <mml:msup> <mml:mi mathvariant="normal">H</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:msub> </mml:math> curves for DCBH formation under the influence of X-ray radiation using the one-zone model. We then build the UV luminosity function consistent with JWST observations and incorporate it into the model that calculates the DCBH-triggering probability. We confirm that enhanced star formation promotes the DCBH formation. However, the DCBH abundance n DCBH is significantly influenced by the X-ray radiation that is also related to star formation. Since the 21 cm global spectrum is also X-ray dependent, the 21 cm absorption depth <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>δ</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">trough</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> at Cosmic Dawn encodes the DCBH abundance information. We provide a tentative trend in the n DCBH – <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>δ</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">b</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">trough</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> relation, which could be a useful guide. In our fiducial model, if <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>δ</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">trough</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>≳</mml:mo> <mml:mo>−</mml:mo> <mml:mn>100</mml:mn> </mml:math> mK, then the DCBH is rather rare; if <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>−</mml:mo> <mml:mn>150</mml:mn> <mml:mspace width="0.25em"/> <mml:mi>mK</mml:mi> <mml:mo>≲</mml:mo> <mml:mi>δ</mml:mi> <mml:msubsup> <mml:mi>T</mml:mi> <mml:mi>b</mml:mi> <mml:mi>trough</mml:mi> </mml:msubsup> <mml:mo>≲</mml:mo> <mml:mo>−</mml:mo> <mml:mn>100</mml:mn> </mml:math> mK, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">DCBH</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> cMpc −3 (comoving Mpc −3 ), consistent with the HST/JWST observed SMBHs abundance at z ≳ 6; if <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>δ</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">trough</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>≲</mml:mo> <mml:mo>−</mml:mo> <mml:mn>150</mml:mn> </mml:math> mK, n DCBH can largely exceed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">O</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> cMpc −3 . The 21 cm global spectrum observations will help to constrain the DCBH abundance.